More particularly, the invention relates to electro- optical apparats that are useful in a variety of optical measuring devices that perform extremely accurate measurement of changes in either length or optical length.

2. Background and Prior Art The use of optical interferometry to measure changes in either length, distance, or optical length has grown significantly due not only to technological avances in lasers, photosensors, and microelectronics but also to an ever increasing demand for high precision, high accuracy measurements [cf. N. Bobroff,"Recent avances in displacement measuring interferometry,"Meas. Sci.

Technol., 4 (9), 907-926 (1993)]. The prior art interferometers can be generally categorized into two types based on the signal processing technique used, i. e., either homodyne or heterodyne. The interferometers based on the heterodyne technique are generally preferred because (1) they are insensitive to low frequency drift and noise and (2) they can more readily have their resolution extended. Within the heterodyne type of

interferometers, of particular interest are the ones based on the use of two optical frequencies.

In the prior art two-optical frequency heterodyne interferometers, the two optical frequencies are produced by one of the following techniques: (1) use of a Zeeman split laser, see for example, Bagley et al., U. S. Patent No. 3,458,259, issued Jul. 29,1969; G. Bouwhuis, "Interferometrie Mit Gaslasers,"Ned. T. Natuurk, 34,225- 232 (Aug. 1968); Bagley et al., U. S. Patent No. 3,656,853, issued Apr. 18,1972; and H. Matsumoto,"Recent interferometric measurements using stabilized lasers," Precision Engineering, 6 (2), 87-94 (1984); (2) use of a pair of acousto-optical Bragg cells, see for example, Y.

Ohtsuka and K. Itoh,"Two-frequency Laser Interferometer for Small Displacement Measurements in a Low Frequency Range,"Applied Optics, 18 (2), 219-224 (1979); N. Massie et al., "Measuring Laser Flow Fields With a 64-Channel Heterodyne Interferometer,"Applied Optics, 22 (14), 2141- 2151 (1983); Y. Ohtsuka and M. Tsubokawa,"Dynamic Two- frequency Interferometry for Small Displacement Measurements,"Optics and Laser Technology, 16,25-29 (1984); H. Matsumoto, ibid; P. Dirksen, et al., U. S.

Patent No. 5,485,272, issued Jan. 16,1996; N. A. Riza and M. M. K. Howlader,"Acousto-optic system for the generation and control of tunable low-frequency signals," Opt. Eng., 35 (4), 920-925 (1996); (1) use of a single acousto-optic Bragg cell, see for exaraple, G. E.

Sommargren, commonly owned U. S. Patent No. 4,684,828, issued Aug. 4,1987; G. E. Sommargren, commonly owned U. S.

Patent No. 4,687,958, issued Aug. 18,1987; P. Dirksen, et al., ibid; or (4) use of two longitudinal modes of a

randomly polarized HeNe laser, see for example, J. B.

Ferguson and R. H. Morris,"Single Mode Collapse in 6328 Å HeNe Lasers,"Applied Optics, 17 (18), 2924-2929 (1978).

As for the prior art use of a Zeeman split laser to produce the two optical frequencies, this approach is only applicable to certain lasers (e. g., HeNe) and limits the frequency difference between the two optical frequencies to about 2 MHz. This imposes a limit on the maximum rate at which the length or optical length being measured can be change. In addition, the available power from a Zeeman split laser is less than 500 microwatts, which can be a serious limitation when one laser source must be used for the measurement of multiple axes, such as three to six axes.

As for the prior art use of a single Bragg cell in the commonly owned U. S. Patent No. 4,687,958 by Sommargren, the diffraction efficiency may be low because the optic axis of the uniaxial crystal of the Bragg cell, the direction of the input optical beam, and the direction of the acoustic beam are approximately collinear, and under these conditions, a small change in the direction of the input beam, such as caused by diffraction, will result in an unacceptable momentum mismatch. Also in commonly owned U. S. Patent No. 4,687,958 by Sommargren, the diffraction efficiency may be low for a number of different types of uniaxial crystals because the efficiency of the dominant Bragg diffraction mode in this group of uniaxial crystals is proportional to the sine of the angle between the optic axis of the uniaxial crystal and either one or the other of the directions of the optical beam components or the direction of the acoustic

beam. These two potential low diffraction efficiency problems are not encountered in the present invention because the optic axis of the uniaxial crystal and the direction of the acoustic beam are approximately orthogonal, i. e. small angle Bragg diffraction.

To compensate for the possibility of low diffraction efficiency resulting from the latter of these two reasons in U. S. Patent No. 4,687,958, the path length in the uniaxial crystal of the Bragg cell may be increased.

However, this procedure may lead to a uniaxial crystal that is inordinately long which, in turn, can result in an expensive apparats. Also, an extended length may lead to a diffracte beam with width elongated in the plane of diffraction and an increased lateral separation, also in the diffraction plane between orthogonally polarized beam components. In addition, if the uniaxial crystal in the Bragg cell of commonly owned U. S. Patent No. 4,687,958 is optically active (e. g., quartz), there may be an accompanying reduction in the diffraction efficiency which subsequently requires a further increase in the required path length in the uniaxial crystal for what is already an expensive apparats.

The angle between the optic axis and acoustic beam can also be increased in commonly owned U. S. Patent No.

4,687,958 by Sommargren in order to achieve a reduction of the momentum mismatch problem and of the required path length. However, the amount that this angle can be increased is restricted, up to approximately 27 degrees in Lino, for example, because the orthogonally polarized beam components generally will suffer total internal

reflection at the exit face of the uniaxial crystal for larger angles, and the device would cease to function.

As for the prior art use of a single Bragg cell in commonly owned U. S. Patent No. 4,684,828 by Sommargren, the apparats has many parts which are separated and require more space, is sensitive to misalignment of the various parts, is more sensitive to thermal gradients in the apparats as a result of multiple parts and the required separation of multiple parts, and is not as efficient as the present invention, i. e., approximately 50% of the input beam intensity is transformed into the output beam with the commonly owned U. S. Patent No.

4,684,828 by Sommargren as compare to nominally 100% with the apparats described herein.

As for the prior art use of a single Bragg cell in Dirksen, et al., ibid., the frequency difference between the two orthogonally polarized components of the exit beam is twice the frequency of the acoustic beam. Starting with a higher frequency difference, the task of resolution extension becomes more difficult and expensive. Also with the single Bragg cell apparats in Dirksen, et al., ibid., the efficiency is limited to approximately 80%, and there are significant non uniform intensity distributions across the two orthogonally polarized exit beam components in contrast to the present invention described herein. These non-uniform intensity distributions across the width of the two orthogonally polarized exit beam components have a negative cross-correlation coefficient which further exacerbates the effect of non-uniform beam component intensities for interferometry.

There is generally polarization mixing in both of the two exit beam components from the single Bragg cell apparats of Dirksen et al., ibid., since this apparats uses the normal Bragg diffraction mode which limits its utility in precision interferometric measurements.

The single Bragg cell apparats of Dirksen et al., ibid., is also relatively more complex, requiring a minimum of two optical elements in addition to the Bragg cell, and generates two desired and two undesired beam components which must be separated by external masks to occult the undesired beam components. There is more sensitivity to changes in temperature and temperature gradients because of multiple elements comprise of different materials and because of larger angles between the beam components inside the single Bragg cell aparatus of Dirksen et al., ibid., in contrast to that found in the apparats of the present invention described herein. The angles between the beam components inside the single Bragg cell apparats of Dirksen et al., ibid., are generally larger by design because, in part, Dirksen et al., ibid., must spatially separate the desired and undesired beam components as a result of using normal Bragg diffraction in contrast to the present invention described herein which uses anisotropic Bragg diffraction.

The Dirksen et al., ibid., single Bragg cell apparats, which requires separation of parts, is sensitive to misalignment with additional sensitivity to thermal gradients. In addition, since the acoustic frequency for a single Bragg cell apparats as in Dirksen et al., ibid., is one half of the frequency difference between the two orthogonally polarized components of the

exit beam, the apparats in Dirksen et al., ibid., must operate at a lower acoustical frequency by a factor of two in relation to that for the apparats of the present invention described herein to obtain a given frequency difference between the two orthogonally polarized components of the exit beam, which leads to an additional reduction in efficiency.

As for the prior art use of two Bragg cells in the apparats of Dirksen et al., ibid., such apparats has more parts than the single Bragg cell apparats of Dirksen et al., ibid., which are well separated and require more space, there is generally polarization mixing in each of two exit beam components since the two Bragg cell apparats of Dirksen et al., ibid., uses normal Bragg diffraction mode, is sensitive to misalignment of the various parts, is more sensitive to thermal gradients in the apparats as a result of multiple parts and the required separation of multiple parts, is not as efficient as the apparats of the present invention described herein, i. e., approximately 60% to 80% of the input beam intensity is transformed into the output beam with the two Bragg cell apparats of Dirksen et al., ibid., as compare to nominally 100% with the apparats described herein, generates two desired and either two or six undesired exit beam components depending on apparats configuration selected, has increased non uniform intensity distributions across two orthogonally polarized exit beam components, the non uniform intensity distributions across widths of two orthogonally polarized exit beam components have negative cross-correlation coefficient which further exacerbates the effect of non uniform beam component

intensities, and external masks are required to occult undesired beam components.

Finally, although the prior art use of two longitudinal modes of a randomly polarized HeNe laser provides a laser beam with two orthogonally polarized frequencies in a rather convenient, cost-effective form, the frequency difference is approximately 500-600 MHz which requires complicated, expensive detection and processing electronics. Furthermore, by starting out with such a high frequency difference, the task of resolution extension becomes difficult and expensive.

It is thus an object of this invention to provide apparats for generating orthogonally polarized beams of different frequency with a predetermined angle of divergence between them and a predetermined lateral separation between their energy flux profiles.

It is yet another object of the present invention to provide apparats for generating orthogonally polarized, parallel beams of different frequency that have energy flux profiles that are either partially coextensive or substantially coextensive.

Other avantages and objects of the invention will, in part, be obvious and will, in part, appear hereinafter when the detailed description is read in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS The structure, operation, and methodology of the invention, together with other objects and avantages thereof, may best be understood by reading the detailed

description in connection with the drawings in which each similar part has an assigne numeral that identifies it wherever it appears in the various drawings and wherein: FIGS. la-lc taken together illustrate, in diagrammatic form, the presently preferred first embodiment of the instant invention with FIG. la showing a source in dashed box 15 and the optical path between source 15 and acousto-optical apparats 40; FIG. lb diagrammatically illustrates acousto-optical apparats 40 and the paths of the optical beams through apparats 40 for the first embodiment; FIG. lc diagrammatically illustrates various angular relationships between the facets of acousto-optical crystal 47 of the first embodiment; FIGS. ld-lf taken together illustrate, in diagrammatic form, the presently preferred first variant of the first embodiment of the instant invention with FIG. ld showing source 15 and the optical path between source 15 and acousto-optical apparats 40; FIG. le diagrammatically illustrates acousto-optical apparats 40 and the paths of the optical beams through apparats 40 for the first variant of the first embodiment; FIG. lf diagrammatically illustrates various angular relationships between the facets of acousto-optical crystal 47 for the first variant of the first embodiment; FIG. lg illustrates, in diagrammatic form, the presently preferred second variant of the first embodiment of the instant invention with FIG. lg showing source 15 and the optical path between source 15 and acousto-optical apparats 40;

FIGS. 2a-2b taken together illustrate, in diagrammatic form, the presently preferred second embodiment of the instant invention with FIG. 2a showing source 15 and the optical paths between source 15 and acousto-optical apparats 240 FIG. 2b diagrammatically illustrates acousto-optical apparats 240 and the paths of the optical beams through apparats 240 for the second embodiment along with various angular relationships within this embodiment; FIG. 2c illustrates, in diagrammatic form, acousto- optical apparats 240 and the paths of the optical beams through apparats 240 for the presently preferred first variant of the second embodiment of the instant invention; FIGS. 2d-2e taken together illustrate, in diagrammatic form, the presently preferred second variant of the second embodiment of the instant invention with FIG. 2d showing source 15 and the optical paths between source 15 and acousto-optical apparats 240; FIG. 2e diagrammatically illustrates acousto-optical apparats 240 and the paths of the optical beams through apparats 40 for the second variant of the second embodiment along with various angular relationships within this embodiment; FIG. 2f illustrates, in diagrammatic form, the presently preferred third variant of the second embodiment of the instant invention with FIG. 2f showing source 15 and the optical paths between source 15 and acousto- optical apparats 240; FIG. 3 illustrates, in diagrammatic form, the presently preferred third embodiment of the instant invention showing source 15 and the optical paths between

source 15, acousto-optical apparats 340, and opaque stops 80 and 81; FIGS. 4a-4c illustrate, in diagrammatic form, the presently preferred fourth embodiment of the instant invention with FIG. 4a showing source 15 and the optical paths between source 15 and acousto-optical apparats 440; FIG. 4b diagrammatically illustrates acousto-optical apparats 440 and the paths of optical beams associated with input beam 18 through apparats 440 of the fourth embodiment along with various angular relationships among the facets thereof; FIG. 4c diagrammatically illustrates acousto-optical apparats 440 and the paths of optical beams associated with input beam 19 through apparats 440 of the fourth embodiment; FIGS. 4d-4f illustrate, in diagrammatic form, the presently preferred first variant of the fourth embodiment of the instant invention with FIG. 4d showing source 15 and the optical paths between source 15 and acousto- optical apparats 440; FIG. 4e diagrammatically illustrates acousto-optical apparats 440 and the paths of optical beams associated with input beam 18 through apparats 440 of the first variant of the fourth embodiment along with various angular relatonships among the facets thereof; FIG. 4f diagrammatically illustrates acousto-optical apparats 440 and the paths of optical beams associated with input beam 19 through apparats 440 of the first variant of the fourth embodiment along with various angular relationships among the facets thereof;

FIGS. 4g-4h illustrate, in diagrammatic form, the presently preferred second variant of the fourth embodiment of the instant invention with FIG. 4g showing source 15 and the optical paths between source 15 and acousto-optical apparats 540; FIG. 4h diagrammatically illustrates acousto-optical apparats 540 and the optical paths through apparats 540 for the second variant of the fourth embodiment along with various angular relationships among its facets; FIG. 4i illustrates, in diagrammatic form, the presently preferred third variant of the fourth embodiment of the instant invention showing source 15 and the optical paths between source 15 and acousto-optical apparats 640; and FIG. 5 depicts the relative orientations of the optical axis of acousto-optical crystals employed in the various embodiments and variants of the invention and wavevector construction describing Bragg diffraction at a frequency vd=vi-fo in a negative uniaxial crystal for use in the present invention when the incident wave is ordinarily polarized.

SUMMARY OF THE INVENTION The present invention relates to apparats for providing linearly-orthogonally polarized light beams of different frequency for use in precision metrology applications such as in the measurement of length or length changes using interferometric techniques. The linearly-orthogonally polarized light beams are preferably parallel but may beneficially have a predetermined angle

of divergence or convergence between them. A number of different embodiments of the invention are disclosed in the form of electro-optical devices for transforming a single-frequency input beam comprising individual, linearly-orthogonally polarized beams from a light source, preferably a laser of frequency, fL, into an output beam having two principal, linearly-orthogonally polarized, preferably parallel output beams differing in frequency from each other and from the light source frequency, fL.

The energy flux profiles of the output beams may be spatially separated, partially coextensive, or substantially coextensive in accordance with the details of particular device embodiments. The input beam is introduced to a multifaceted anisotropic acousto-optical crystal for travel through an interactive region where it experiences an acoustic beam that diffracts it via small angle Bragg diffraction to form two sets of orthogonally polarized internal beam components that are separated by a small angle of divergence and subsequently become four external beams two of which, the principal ones, are available outside of the acousto-optical crystal for use in anticipated downstream applications. The remaining two of the four output beams are preferably reduced to nominally zero intensities compare to the intensity of the input laser beam so as to achieve a high efficiency conversion of the input laser beam into the principal output beams thus rendering the two output beams with reduced intensities spurious. The spurious beams do not to present deleterious feedback to the laser cavity or deleterious effects in downstream application in part because of the reduced'intensities. Also, beams that

travel back through the apparats to the laser cavity generally will have been changed in frequency and so essentially do not contribute to deleterious feedback to the laser cavity. Spatial filtering may be used to further control any negative impact of the spurious beams.

In all of the embodiments, the multifaceted or multifaced anisotropic acousto-optical crystal has an optic axis,: :, and a first facet that is nominally parallel to the optic axis. The acousto-optical crystal preferably is a uniaxial crystal comprising lithium niobate.

Transducer means, preferably in the form of a piezoelectric transducer, are affixed to the first acousto-optical crystal facet for generating an acoustic beam so that it propagates generally perpendicular to the optic axis to provide an interaction region within the optical crystal, where the width of the interaction region is generally coextensive with the width of the acoustic beam. The acoustic beam preferably is a shear wave.

The transducer is driven with an electrical signal at a frequency, fo, from a frequency stabilized electronic oscillator and an electronic amplifier. The electrical signal is transformed to the acoustic shear wave via the transducer and propagates inside of the acousto-optical crystal to form the interactive region. The principal output beams have frequencies fL fo. The angle of incidence of the input laser beam at an entrance facet of the acousto-optical crystal is chosen along with orientations of internal crystal facets so as to effect a high efficiency conversion of the input laser beam into the principal output beams. Power is used as a means of

reducing the intensity of the spurious beams to nominally zero.

The input laser beam is introduced into the acousto- optical crystal so that it propagates through the interaction region at least once with a predetermined portion of each of its components converted by small angle Bragg diffraction to diffracte beams. The diffracte beams, which are derived from the initial individual linearly-orthogonally polarized input beams, are orthogonally polarized with respect to their respective individual linearly-orthogonally polarized input beams and altered in frequency by the frequency, fo, of the oscillator. The remainder of the individual linearly- orthogonally polarized input beams and their respective associated diffracte beams continue to propagate through the anisotropic acousto-optical crystal along respective paths as slightly diverging orthogonally polarized emergent beams. Depending on the specific embodiment, selected ones of the emergent beams are either intercepted within the acousto-optical crystal or outside of it to be rendered preferably parallel by collimating means. The collimating means can be in the form of interna reflecting and/or integral refracting surfaces and/or external elements. However, if desired, the selected ones of the external beams can be non-parallel such that they have a predetermined angle of divergence or convergence between them.

The degree of overlap or spatial separation between the energy flux profiles of the principal, linearly- orthogonally polarized, external beams is controlled by various interna reflecting and refracting properties of

the acousto-optical crystal, its bi efringence, the acoustical and optical properties of the acousto-optical crystal, the length of the physical path of travel experienced by the emergent beams, and/or the use of external control elements. Thermal compensation may be provided via the use of symmetry in the design of the crystal or the arrangement of external components with respect to the crystal or some combination of both. High diffraction efficiency may be achieved via the use of multiple pass arrangements through the interaction zone to reduce input power requirements. In multiple pass arrangements, phase control is implemented via external components or the use of selective transits through the crystal.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention relates to apparats for providing linearly-orthogonally polarized light beams for use in precision metrology applications such as in the measurement of length or length changes using interferometric techniques. A number of different embodiments of the invention are disclosed in the form of electro-optical devices for transforming a single- frequency beam comprise of two linearly-orthogonally polarized, preferably parallel input beams from a light source, preferably a laser of frequency fL, into a beam comprise substantially of two linearly-orthogonally polarized, preferably parallel principal output beams differing in frequency'from each other and from the

frequency fL of the input beams. While the directions of propagation of the input beams are preferably parallel and the directions of propagation of the principal output beams are preferably parallel, they need not be and instead the individual beams of the input beam and the principal output beams may beneficially have their own predetermined angle of divergence or convergence, respectively. The energy flux profiles of the individual input beams may be spatially separated, partially coextensive, or substantially coextensive, and the energy flux profiles of the principal output beams may be spatially separated, partially coextensive, or substantially coextensive in accordance with the details of particular device embodiments and the requirements of the metrology or other contemplated application. In addition, thermal compensation may be made available through the exploitation of the principales of symmetry while power requirements may be reduced through the use of multiple pass arrangements for optical beams through the interaction region of an anisotropic acousto-optical crystal. In the embodiments to be described, the input beams preferably are coextensive, and the principal output beams preferably are coextensive.

Referring to the drawings in detail, and initially to FIGS. la-lc, FIG. la depicts, in diagrammatic form, the presently first preferred embodiment of the apparats for the present invention. While the apparats of the present invention has application for a wide range of radiation sources, the following description is taken, by way of example, with respect to an optical measuring system. The term"optical energy"as used herein inclues, but is not

limited to, electromagnetic energy of all frequency ranges.

In accordance with the first embodiment of the present invention, an acousto-optical apparats is provided that is capable of transforming a single frequency beam comprise of two linearly-orthogonally polarized input beams into a beam comprise of two principal and two spurious secondary output beams. The principal output beams are linearly-orthogonally polarized, preferably have the same directions of propagation, and preferably have coextensive energy flux profiles. The frequencies of the principal output beams are different one from the other and different from the frequency of the input beams. The intensities of the two principal output beams are substantially equal, and the combine intensities of the principal output beams is substantially equal to the combine intensities of the input beams. In addition, thermal compensation is incorporated through the exploitation of principles of symmetry and a series of internal reflections in the acousto-optical apparats wherein the thermal compensation is with respect to the relative phase of the principal output beams.

FIG. lb depicts in diagrammatic form the detailed propagation of input beams 18 and 19 through an anisotropic acousto-optical crystal 47 such that the nominal angle between the input beams 18 and 19 and output beams 30A, 30B, 31A, and 31B is an angle specified by the design of the acousto-optical crystal 47 to be equal to approximately 0 degrees and substantially independent of

small changes in the orientation of the acousto-optical crystal 47.

A light source 10, most preferably a laser, provides a beam 12 of optical energy which has a single, stabilized frequency and is linearly polarized. Light source 10 can be any of a variety of lasers. For example, it can be a gas laser, e. g. a HeNe, stabilized in any of a variety of conventional techniques known to those skilled in the art to produce beam 12, see for example, T. Baer et al., "Frequency Stabilization of a 0.633 Am He-Ne-longitudinal Zeeman Laser,"Applied Optics, 19,3173-3177 (1980); Burgwald et al., U. S. Pat. No. 3,889,207, issued June 10, 1975; and Sandstrom et al., U. S. Pat. No. 3,662,279, issued May 9,1972. Alternatively, light source 10 can be a diode laser frequency stabilized-.'-n one of a variety of conventional techniques known to those skilled in the art to produce beam 12, see for example, T. Okoshi and K.

Kikuchi,"Frequency Stabilization of Semiconductor Lasers for Heterodyne-type Optical Communication Systems," Electronic Letters, 16,179-181 (1980) and S. Yamaqguchi and M. Suzuki,"Simultaneous Stabilization of the Frequency and Power of an AlGaAs Semiconductor Laser by Use of the Optogalvanic Effect of Krypton,"IEEE J.

Quantum Electronics, QE-19,1514-1519 (1983).

The specific device used for source 10 will determine the diameter and divergence of beam 12. For some sources, e. g. a diode laser, it likely will be necessary to use conventional beam shaping optics 14, e. g. a conventional microscope objective, to provide beam 16 with a suitable diameter and divergence for the elements that follow.

When source 10 is a HeNe laser, for example, beam shaping

optics 14 may not be required. The elements 10 and 14 are shown in dashed box 15 which represents the source of beam 16. Beam 16 has one stabilized frequency fL and is linearly polarized.

The plane of polarization of beam 16 is rotated about the axis of beam 16 using techniques known to those skilled in the art, e. g. phase retardation plates, to form a beam comprise of input beams 18 and 19. The two input beams 18 and 19 are linearly polarized perpendicular to the plane of FIG. la and linearly polarized in the plane of FIG. la, respectively. Beams 18 and 19 further have the same frequency fL. The relative intensities of beams 18 and 19 are adjusted by control of the degree of rotation applied to the plane of polarization of beam 16.

Beams 18 and 19 are incident on acousto-optical apparats 40 as illustrated in FIG. la. The paths of beams in acousto-optical apparats 40 originating from beams 18 and 19 are shown in FIG. lb.

Electrical oscillator 41 (Fig. lb) preferably provides a frequency stabilized electrical signal 42 of frequency gO to a conventional power amplifier 43. An electrical output 44 of power amplifier 43 is preferably used to drive a conventional piezoelectric transducer 46, preferably of multielement array configuration, affixed to the acousto-optical crystal 47. Piezoelectric transducer 46 is used to generate an acoustic beam, preferably of the shear wave type. Known to those skilled in the art of acousto-optical modulation, the shear wave may be generated with the piezoelectric transducer 46 affixed to acousto-optical crystal 47 as shown in FIG. lb or by reflecting an appropriately directe longitudinal acoustic

wave from an appropriately oriente surface of acousto- optical crystal 47. Conventional techniques known to those skilled in the art of acousto-optical modulation are used to absorb in a preferred distribution the acoustic beam that passes through to the walls of acousto-optical crystal 47 for the purpose of substantially reducing temperature gradients in acousto-optical crystal 47. The absorption of the acoustic beam at the walls of acousto- optical crystal 47 is by absorber 48. The distribution of absorber 48 on the surface or surfaces of acousto-optical crystal 47 is a design which permits absorber 48 to make the distribution of energy dissipation of the acoustic beam at the walls of acousto-optical crystal 47 correspond to the preferred distribution of absorption of the acoustic beam.

The presently preferred acousto-optical crystal 47 of the first embodiment is made of a uniaxial crystal [e. g., LiNb03 or potassium dihydrogen phosphate (KDP)] having an optical axis 50 in the plane of FIG. lb which makes an angle + (cf. FIG. 5) with the direction of propagation of the acoustic wave 52 generated by the piezoelectric transducer 46. The diagrammatic illustrated in FIG. lb is for an acousto-optical crystal 47 comprise of a negative uniaxial crystal.

Input beam 18, such as illustrated in FIGS. lb and lc, preferably enters the acousto-optical crystal 47 at surface 54 with an angle of incidence l (See Fig. lac), becoming an ordinarily polarized beam 20. Beam 20 is reflected by surface 55 becoming an ordinarily polarized beam 22. Beam 22 is reflected by surface 56 becoming ordinarily polarized incident beam 24A. Due to the

photoelastic interaction of incident beam 24A with the acoustic wave 52 [see for example, R. W. Dixon,"Acoustic Diffraction of Light in Anisotropic Media,"IEEE Journal of Quantum Electronics, QE-3,85-93 (1967); A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York), Chap.

9, (1984)], an extraordinarily polarized beam, diffracte beam 24B, is generated by small angle Bragg diffraction when the following relationships are satisfied; where n ; and nd are the indices of refraction for the incident and diffracte beams, respectively, R0 is the optical wavelength in vacuum, and v is the acoustic speed. The angles Oj and od are the angles between incident beam 24A and the normal to the acoustic K-vector and the angle between diffracte beam 24B and the normal to the acoustic K-vector, respectively. The definitions of positive Oj and od are illustrated in FIG. 5.

The index of refraction ii for an extraordinarily polarized beam in a birefringent crystal is given by the expression:

where the angle 0 is the angle between the extraordinarily polarized beam and the optical axis of the acousto-optical crystal and zlo and ne are the ordinary and extraordinary principal indices of refraction of the acousto-optical crystal, respectively.

Diffracte beam 24B propagates at a small angle to that of the non diffracte incident beam 24A, the polarization of diffracte beam 24B being orthogonal to that of incident beam 24A. In addition, the frequency of beam 24B is fL-fo while the frequency of beam 24A is fL.

Beams 24A and 24B are reflected by crystal face 57 as beams 26A and 26B, respectively, beams 26A and 26B are reflected by crystal face 58 as beams 28A and 28B, respectively, and beams 28A and 28B exit acousto-optical crystal 47 at face 59 as beams 30A and 30B, respectively.

Input beam 19, such as illustrated in FIGS. lb and lc, preferably enters the acousto-optical crystal 47 at surface 54 with an angle of incidence +1, becoming an extraordinarily polarized beam 21. Beam 21 is reflected by surface 55 becoming an extraordinarily polarized beam 23. Beam 23 is reflected by surface 56 becoming extraordinarily polarized incident beam 25A. Due to the photoelastic interaction of incident beam 25A with the acoustic wave 52, an ordinarily polarized, diffracte beam 25B is generated by small angle Bragg diffraction when the relationships given by Eqs. (1) and (2) are satisfied.

Diffracte beam 25B propagates at a small angle to that of non diffracte incident beam 25A, the polarization of diffracte beam 25B being orthogonal to that of incident beam 25A. In addition, the frequency of beam 25B is fL +fo while the frequency of beam 25A is fL. Beams

25A and 25B are reflected by crystal face 57 as beams 27A and 27B, respectively, beams 27A and 27B are reflected by crystal face 58 as beams 29A and 29B, respectively, and beams 29A and 29B exit acousto-optical crystal 47 at face 59 as beams 31A and 31B, respectively.

The respective angles of incidence and refraction for beams 18,19,20, and 21 at surface 54, the respective angles of incidence and reflection for beams 20,21,22, and 23 at surface 55, and the respective angles of incidence and reflection for beams 22,23,24A, and 25A at surface 56 are chosen such that the angle of deviation between beams 24B and 25B is c-6 where £ iS a small angle, preferably OSs S8, the angle of deviation between beams 24A and 24B is 8, the angle of deviation between beams 25A and 25B is -#, and the angle of deviation between beams 24A and 25A is 5+E where 6 is specified by the equation #0 #0 sinsin# = cos#d = cos#i (4) ni# nd# and A is the wavelength of the acoustic beam in acousto- optical crystal 47. These conditions with respect to relative directions of propagation of beams 24A, 24B, 25A, and 25B are obtained by choosing the apex angles a1 and a2 defined in FIG. lc to satisfy the equation

where nie = n2e are the indices of refraction for beam 21 at surfaces 54 and 55, respectively, n2e = i73e are the indices of refraction for beam 23 at surfaces 55 and 56, respectively, and n3e is the index of refraction for beam 25A at surface 56.

The respective angles of incidence and reflection for beams 24A, 24B, 25A, 25B, 26A, 26B, 27A, and 27B at surface 57, the respective angles of incidence and reflection for beams 26A, 26B, 27A, 27B, 28A, 28B, 29A, and 29B at surface 58, and the respective angles of incidence and refraction for beams 28A, 28B, 29A, 29B, 30A, 30B, 31A, and 31B at surface 59 are chosen such that beams 30B and 31B preferably are parallel. Beams 30B and 31B preferably are spatially displaced by a minute amount, i. e. a small fraction of the beam diameters, therein being substantially coextensive. The conditions with respect to the relative directions of propagation of beams 31B and 30B are obtained by choosing the apex angles such that

where a3 and a4 are defined in FIG. lc, n4e-n5e are the indices of refraction for beam 28B at surfaces 59 and 58, respectively, are the indices of refraction for beam 26B at surfaces 58 and 57, respectively, and n6e is the index of refraction for beam 24B at surface 57.

Clearly, when it is desired to have the beams 30B and 31B <BR> <BR> <BR> <BR> be not parallel, i. e. 2 for beam 30B not the same as ¢2 for beam 31B, then the values of the parameters of Eqs.

(5) and (6) may be chosen so that beams 30B and 31B have a predetermined angle of divergence or convergence between them. In addition, it is clear that when it is desired to have beams 18 and 19 be not parallel, i. e. l for beam 18 not the same as l for beam 19, then the values of the parameters of Eqs. (5) and (6) may also be chosen so that beams 18 and 19 have a predetermined angle of divergence or convergence between them.

Beams 30A and 31A are spurious secondary output beams and beams 30B and 31B comprise principal output beams.

The spatial displacements between beams 30A, 30B, 31A, and 31B preferably are only small fractions of the beam diameters. If desired, however, it is clear that principal output beams 30B and 31B may be separated or partially separated, for example, through the separation or partial separation, respectively, of input beams 18 and 19. For purposes of illustration, these displacements are shown greatly exaggerated in FIG. lb.

Preferably, the electrical output 44 of the power amplifier 43 is adjusted so that intensity of principal output beam 30B relative to the intensity of the input beam 18 is some preselected nominal value between 0% and

100%, preferably 100%. The ratio of the intensity of principal output beam 31B to the intensity of beam 19 is substantially the same as the ratio of the intensity of beam 30B to the intensity of beam 18. Further, beams 30B and 31B are orthogonally polarized and substantially coextensive. The frequencies of principal output beams 30B and 31B are different by 2fo and different from the frequency of beam 16 by +, fi, respectively.

The ratio of the intensity of principal output beam 30B to the sum of the intensities of principal output beams 30B and 31B is adjusted to some preselected nominal value between 0% and 100%, preferably 50%, through the rotation of the polarization of beam 16.

Spurious secondary output beams 30A and 31A are orthogonally polarized beams with frequencies the same as the frequency of beam 16. The directions of propagation of secondary output beams 30A and 31A deviate from the direction of propagation of principal output beams 30B and 31B by approximately-nO£ and respectively. The intensities of the secondary output beams 30A and 31A preferably have nominal values of 0% of the intensities of principal output beams 30B and 31B, respectively, a consequence of the adjustment of electrical output 44 of the power amplifier 43 so that intensity of either principal output beam 30B relative to the intensity of the input beam 18 or principal output beam 31B relative to the intensity of the input beam 19 preferably is the nominal value of 100%.

An important feature of the first embodiment is an intrinsically low level of contamination of the output beams with non frequency shifted components having

directions of propagation substantially parallel with the direction of propagation of the principal output beams 30B and 31B. The low level of contamination in the inventive apparats is a consequence of using non normal Bragg diffraction, Bragg diffraction in an uniaxial crystal, instead of normal Bragg diffraction and the absence of additional optical elements such as those comprise of birefringent crystals that would otherwise be required in the path of the output beams to make a pair of output beams parallel. The orientation of the polarization states of the principal output beams when using non normal Bragg diffraction are determined by a plane and a normal to the plane, the plane being defined by the optical axis of the acousto-optical crystal 47 and the direction of propagation of the incident beams 24A and 25A in the acousto-optical crystal 47. In a normal Bragg diffraction process, however, the orientation of the polarization state of the diffracte component of an output beam is the same as the polarization state of the progenitor incident beam. This feature of a normal Bragg diffraction process generally leads to a requirement for an additional birefringent optical element to follow the acousto-optical apparats and render, if desired, the components of an output beam parallel. An additional birefringent optical element is a potential generator of output beam contamination, the output beam contamination arising from a misalignment of the additional birefringent optical element with respect to the acousto-optical apparats.

Three objectives in the design of the acousto-optical crystal 47 are to select the orientations for faces 54, 55,56,57,58, and 59 so that Eqs. (5) and (6) are

satisfied; to produce an acousto-optical apparats which is temperature compensated with respect to temperature induced phase shifts between principal output beams 30B and 31B relative to the phase of the acoustic beam; and to effectively isolate laser beam source 15 with respect to coupling between the laser beam source 15 and return beams, the return beams being backscattered and/or reflected portions of beams 30A, 30B, 31A, and 31B passing back through the inventive apparats and entering laser beam source 15. For the configuration of acousto-optical crystal 47 shown in FIG. lb, the design parameters and their concomitant effects relevant to the three cited objectives are highly decoupled: the conditions expressed by Eqs. (5) and (6) are satisfied primarily through the adjustment of one parameter such as the orientation of face 55; the conditions required for the temperature compensation are satisfied primarily through the exploitation of the principles of symmetry and additionally through the adjustment of a second independent parameter such as the orientation of face 54; and the condition required for isolation of the laser source 15 is met through adjustment of the acoustic power generated by the piezoelectric transducer 46. This feature with respect to a decoupling of the adjustments used to obtain the three cited objectives makes for a robust design of an acousto-optical apparats amenable to production and to use in non laboratory environments.

Temperature induced phase shifts between principal output beams 30B and 31B relative to the phase of the acoustic beam arise primarily from two effects, the change with temperature in the difference between the ordinary

and extraordinary principal indices of refraction of acousto-optical crystal 47 and the change with temperature in the speed of the acoustic beam in the acousto-optical crystal 47. The temperature coefficient for the difference in effective indices of refraction of the beams 30B and 31B arising from a change with temperature in the ordinary and extraordinary principal indices of refraction in acousto-optical crystal 47 is very low in the inventive apparats, of the order of or less than 10 8/ (deg C).

The low effective temperature coefficient is the result of a combination of two factors, the first factor being a sin20 that appears in the expression (no-ne)sin2# for the difference in indices of refraction for ordinarily and extraordinarily polarized beams where 0 is the angle between the direction of propagation of the extraordinarily polarized beam and the optical axis of the acousto-optical crystal. The second factor follows from the high level of symmetry in the design of the acousto- optical apparats. The sin20 factor for the first embodiment is typically less than or of the order of 0.015. For beams 24B and 25B in particular, the sin2# factor is of the order of 3 x 10-4.

In regard to the second factor, progenitors of beam 30B are ordinarily polarized beams 20 and 22 and extraordinarily polarized beams 26B and 28B while the progenitors of beam 31B are extraordinarily polarized beams 21 and 23 and ordinarily polarized beams 27B and 29B. Thus for beams 30B and 31B, they are each individually compensated to a high level for temperature induced changes in ii, and ne as a result of substantially

equal paths of respective progenitor beams as ordinarily and as extraordinarily polarized beams. The combination of the individual compensations, the six 20 factor, and a [d(ne-no)/dT]=34x10-6 per deg C in Lino3 yield the effective temperature coefficient of the order of or less than 10 8/ (deg C).

The change with temperature in the speed of the acoustic beam in the acousto-optical crystal 47 if not compensated will give rise to a temperature induced change in the phase between beams 30B and 31B relative to the phase of the acoustic beam of the order of 0.02 rad/ (de C). This effect in the inventive apparats may be compensated for example by changing a3 by an angle of the order of 10 min. of arc consistent with satisfying Eqs.

(5) and (6) so as to use the temperature induced change in (ne-nO) to compensate for the phase shift caused by a temperature induced change in the speed of the acoustic beam.

The preferred mode of operation of the first embodiment with respect to conversion of nominally 100% of beams 18 and 19 into beams 30B and 31B is also a mode wherein the first embodiment is an effective isolator of laser beam source 15 with respect to coupling between the laser beam source 15 and the return beams. The acousto- optical apparats 40 transforms components of the return beam in a manner analogous to the transformations experienced by beams 18 and 19 except for a reversa in the direction of frequency shifts (cf. R. W. Dixon, ibid.). Consequently, the primary components of the return beam that emerge from the acousto-optical apparats

40 in a direction opposite to and substantially parallel to input beams 18 and 19 will be frequency shifted with respect to the frequency of source 10 by either fo or 2fo depending on the progenitors of the return beam components and on the direction of propagation of the return beam components on entering the acousto-optical apparats 40. Also, any component of the return beam that emerges from the acousto-optical apparats 40 in a direction opposite to and substantially parallel to input beams 18 and 19 and frequency shifted by fo with respect to the frequency of source 10 will have a nominal intensity of 0% of the intensities of input beams 18 and 19.

The components of a return beam that couple into a laser mode of laser source 15 will be those components that have the same frequency as beams 18 and 19 and therefore the same frequency of the laser mode. The intensity IRe Of a component of a return beam component having the same frequency as the laser mode can be expressed as (7)IRe=#2RII where II is the intensity of the progenitor input beam, either input beam 18 or 19, R is the reflection coefficient giving the fraction of the progenitor spurious secondary output beam, either beam 30A or 31A or both, that became the non frequency shifted return beam component, and Ç is the fraction of beams 18 and 19 that become non frequency shifted beams 30A and 31A,

respectively. In the preferred mode of operation of the first embodiment, the intensities of secondary output beams 30A and 31A preferably have nominal values of 0% of the intensities of principal output beams 30B and 31B, a consequence of the adjustment of the electrical output 44 of the power amplifier 43 so that intensities of beams 30B and 31B relative to the intensities of the input beams 18 and 19, respectively, are preferably nominal values of 100%. Thus in the preferred of operation, a typical value for ruz may be n 910-2 (8) Therefore, the first embodiment of the present invention improves the isolation of laser source 15 with respect to non frequency shifted return beam components typically by a factor of over prior art two frequency generators, the effect of the factor R being omitted as a consequence of the effect of the factor R being common to both the first embodiment of the present invention and prior art two frequency generators.

The angle c may be made either larger than or smaller than the value of 6 in order to either increase or decrease the deviation between the respective directions of propagation of secondary output beams 30A and 31A and the directions of propagation of principal output beams 30B and 31B. A change in the size of c relative to the size of 6 may be effectively achieved for example by altering the design of the acousto-optical

crystal 47 shown in FIG. lb so that reflecting surface 58 is not orthogonal to acoustic wave vector 52.

However, there is a restriction on the range of values of c that can be used. The restriction arises from consideration of the diffraction efficiency of the acousto-optical apparats which is discussed further in a subsequent description of the seventh preferred embodiment and variants thereof depicted in FIGS. 7a-7i.

The deviation of the energy flux vector from the wave front vector for an optical beam propagating in a birefringent crystal, a well known property of birefringent crystals, causes a relative displacement of a beam from the path of the optical wave vector. The net relative displacements for beams 30B and 31B are compensated to a high level in the first embodiment. The net relative displacement for beam 30B is substantially equal only to the sum of the relative displacements experienced by beams 26B and 28B, the relative displacements of ordinarily polarized beams 20 and 22 being zero. The net relative displacement for beam 31B is substantially equal only to the sum of the relative displacements experienced by beams 21 and 23, the relative displacements of ordinarily polarized beams 27B and 29B being zero. Because of the high level of symmetry in the design of the acousto-optical apparats with respect to the propagation of beams 21 and 23 and of beams 26B and 28B in acousto-optical crystal 47, the sum of the relative displacements of beams 21 and 23 and the sum of the relative displacements of beams 26B and 28B are substantially equal both in sign and magnitude. The symmetry referenced in this paragraph is in regard to both

the angle of propagation of a beam relative to the optical axis 50 as well as the sign of the direction of propagation.

The relative displacements of beams 24A, 24B, 25A, and 25B further contribute to an improvement in the performance of the apparats of the first embodiment. For the acousto-optical apparats shown in FIG. lb, the angle r between the energy flux vector of a beam and the optical axis is where 0 is the angle between the normal to the wave front and the optical axis [cf. Section 7 of Chapter 10 by J.

Bennett and H. Bennett,"Double Refraction in Calcite," Handbook of Optics (McGraw-Hill, New York) 1978]. By mathematical manipulation of Eq. (9) and using Eqs. (1) and (2), the difference (r-0) can be expressed as Comparison of sin8 given by Eq. (4) and sin (r-0) given by Eq. (10) shows that to a good approximation for a wide range of applications in which # #1, r-0=26. (11)

The angle of deviation between beams 24A and 25A given by Eq. (5) is b+£ where # # # + # # 2# for the preferred mode of 0 # # # # and is of the opposite sign as that of the displacement (1--0). Therefore the deviation by 6 +E : between the normals to the wavefronts of beams 25A and 24A is partially offset by the displacement r-0=26 leading to improved properties in the present invention of the first embodiment.

In summary, the relative displacements in the first embodiment produced by the deviation of the energy flux vector from the wave front vector of an optical beam propagating in a birefringent crystal are both substantially compensated in and used to improve the performance of the present invention of the first embodiment.

The direction of the optical axis 50 or z axis of acousto-optical crystal 47 is chosen so as to improve the effective length of the photoelastic interaction path for a given geometry of acousto-optical crystal 47. It is generally known that the energy flux vector deviates from the wave normal for an acoustic beam propagating in a anisotropic crystal. This property is sometimes referred to as"walkoff" (cf. I. C. Chang,"Tunable Acousto-Optical Filter Utilizing Acoustic Beam Walkoff In Crystal Quartz," Appl. Phy. Lett. 25 (6), 323-324,1974). In Lino3 for example, the deviation is approximately 7 degrees in the (y,z) plane for an acoustic shear wave propagating in the y direction with a shear displacement in the x direction (S. H. Harris and R. W. Wallace, "Acousto-Optic Tunable Filter,"JOSA 59 (6), 744-747,1969). The effective length

of the photoelastic interaction path is optimized by choosing the direction of the optical axis 50 so that the deviation of the energy flux vector of acoustic beam 52 is away from instead of towards surface 54.

The acousto-optical apparats of the first embodiment also has the feature that the directions of propagation of the principal output beams 30B and 31B are substantially unaffected by tilts of the inventive apparats. This property is a consequence of an even number of reflections executed by a beam in passing through the acousto-optical apparats. The sensitivity to tilts that is present arises primarily from a difference between the angle of incidence at surface 54 and the angle of refraction at surface 59 of acousto-optical crystal 47 for beams 18 and 30B, respectively, and a corresponding difference for beams 19 and 31B. It will be apparent to those skilled in the art that the differences between angles of incidence at surface 54 and respective angles of refraction at surface 59 can be substantially eliminated for example by adjusting the orientation of surface 59. This option can also be used to introduce an additional parameter that can be of value in achieving an improved compensation for temperature induced changes in the phase between beams 30B and 31B relative to the phase of the acoustic beam.

Referring now to FIGS. ld-lf, FIGS. ld-lf depict a first variant of the first preferred embodiment wherein the length of the piezoelectric transducer 46 has been increased relative to the length of acousto-optical crystal 47. The apparats of the first variant in FIGS. ld-lf comprises substantially the same elements as the first embodiment in FIGS. la-lc, elements of the first

variant of the first embodiment performing like operations as like denoted elements in the first embodiment, wherein the dimension of acousto-optical crystal 47 in direction 52, the direction of propagation of acoustic beam, has been increased and reflection surface 58 of the first embodiment is not used.

With respect to the fraction of the intensity of input beams 18 and 19 which are transformed into principal output beams 30B and 31B, respectively, for a given input acoustic power, the first variant of the first embodiment has improved efficiency in relation to the first embodiment. However, the first variant of the first embodiment is relatively more sensitive in first order to tilts of the acousto-optical apparats as a consequence of an odd number of reflections executed by a beam in passing through the acousto-optical apparats.

Referring to FIG. le, the respective angles of incidence and refraction for beams 18, 19,20, and 21 at surface 54, the respective angles of incidence and reflection for beams 20,21,22, and 23 at surface 55, and the respective angles of incidence and reflection for beams 22,23,24A, and 25A at surface 56 are chosen such that the angle of deviation between beams 24B and 25B is s-8 where £ iS a small angle, preferably F,-=5 for the first variant of the first embodiment, and 6 is specified by the Eq. (4). The angle of deviation between beams 24A and 24B ils 6, the angle of deviation between beams 25A and 25B ils-6 and the angle of deviation between beams 24A and 25A is 8+E. These conditions respect to relative directions of propagation of beams 24A, 24B, 25A, and 25B

are obtained by choosing the apex angles al and a2 defined in FIG. lf to satisfy Eq. (5).

The respective angles of incidence and reflection for beams 24A, 24B, 25A, 25B, 26A, 26B, 27A, and 27B at surface 57 and the respective angles of incidence and refraction for beams 26A, 26B, 27A, 27B, 30A, 30B, 31A, and 31B at surface 59 are chosen such that beams 30B and 31B preferably are parallel. Beams 30B and 31B are spatially displaced by a minute amount, i. e., a small fraction of the beam diameters. The conditions with respect to the relative directions of propagation of beams 31B and 30B are obtained by choosing the apex angles such that

where a3 and are defined in FIG. lof, 4 indices of refraction for beam 26B at surfaces 59 and 57, respectively, and n5, is the index of refraction for beam 24B at surface 57. Again, when it is desired to have the beams 30B and 31B be not parallel, i. e. 2 for beam 30B not the same as 2 for beam 31B, then the values of the parameters of Eqs. (5) and (12) may be chosen so that beams 30B and 31B have a predetermined angle of divergence or convergence between them. In addition, it is clear that when it is desired to have the beams 18 and 19 be not parallel, i. e. f1 for beam 18 not the same as fl for beam

19, then the values of the parameters of Eqs. (5) and (12) may also be chosen so that beams 18 and 19 have a predetermined angle of divergence or convergence between them.

Beams 30A and 31A are spurious secondary output beams, and beams 30B and 31B comprise principal output beams. The spatial displacements between beams 30A, 30B, 31A, and 31B preferably are only small fractions of the beam diameters. If desired, however, it is clear that principal output beams 30B and 31B may be separated or partially separated, for example, through the separation or partial separation, respectively, of input beams 18 and 19. For purposes of illustration, these displacements are shown greatly exaggerated in FIG. le.

It will be apparent to those skilled in the art that differences in the angle of incidence at surface 54 and the angle of refraction at surface 59 for beams 18 and 30B, respectively, and for beams 19 and 31B, respectively, may be substantially eliminated by adjusting, for example, the orientation of surface 59. This option can alternatively be used to introduce an additional parameter that can be of value in achieving an improved compensation for temperature induced changes in the phase between principal output beams 30B and 31B relative to the phase of the acoustic beam.

The remainder of the description for the first variant of the first embodiment is preferably the same as the corresponding portions of the description presented for the first preferred embodiment illustrated in FIGS. la-lc.

FIG. lg depicts a second variant of the first preferred embodiment depicted in FIGS. la-lac wherein the length of the piezoelectric transducer 46 has been increased relative to the length of acousto-optical crystal 47 in comparison to that of the first embodiment, and there is an even number of reflections experienced by a beam passing through the acousto-optical apparats. The apparats of the second variant depicted in FIG. lg comprises substantially the same elements as the first variant of the first embodiment, elements of the second variant in FIG. lg performing like operations as like denoted elements in the first variant in FIGS. ld-lf, with an additional an optical means, preferably a non- birefringent prism 70 as shown in FIG. lg, to reflect the beams transmitted through surface 59 of acousto-optical crystal 47. Prism 70 may be affixed to acousto-optical crystal 47 as shown in FIG. lg.

With respect to the fraction of the intensities of input beams 18 and 19 which are transformed into principal output beams 30B and 31B, respectively, for a given input acoustic power, the second variant of the first embodiment has the improved efficiency of the first variant of the first embodiment in relation to the first embodiment.

However, the acousto-optical apparats of the second variant of the first embodiment has the following feature in common with the first embodiment, i. e., the direction of the principal output beams 30B and 31B are substantially unaffected by tilts of the inventive apparats. This property is a consequence of an even number of reflections executed by a beam in passing through the acousto-optical apparats.

It will be apparent to those skilled in the art that the optical element 70 in FIG. lg may be orientated to reflect beams 30A, 30B, 31A, and 31B in a clockwise direction in the plane of FIG. lg instead of in the counter clockwise direction as shown in FIG. lg without departing from the spirit and the scope of the second variant of the first embodiment.

The remainder of the description for the second variant of the first embodiment is substantially the same as the corresponding portions of the description for the first variant of the first embodiment illustrated in FIGS. ld-lf.

An unusual and inventive characteristic of acousto- optical apparats 40 of the first preferred embodiment and variants thereof is the compensation for changes in temperature of the acousto-optical apparats. In the inventive apparats, temperature induced changes between optical path lengths of ordinarily and extraordinarily polarized beams, beams which are progenitors of the principal output beams in a birefringent acousto-optical apparats, are compensated by exploiting the principles of symmetry in the layout of the optical path configurations in the birefringent acousto-optical apparats. Also in the inventive apparats, temperature induced changes between the optical path lengths of ordinarily and extraordinarily polarized beams in a birefringent acousto- optical apparats are combine with the temperature induced change in the speed of the acoustic beam in the acousto-optical apparats to produce orthogonally polarized output beams for which the relative phase shift between two principal output beams relative to the phase

of the acoustic beam is compensated for changes in temperature of the acousto-optical apparats. The utilization of the principals of symmetry and of the respective temperature sensitivities to produce orthogonally polarized principal output beams wherein the relative phase shift between the two principal output beams relative to the phase of the acoustic beam is compensated for changes in temperature of the acousto- optical apparats is believed to be taught herein for the first time.

Another unusual and inventive characteristic of acousto-optical apparats 40 of the first preferred embodiment and variants thereof is the utilization of the difference between an energy flux vector and an optical wavefront vector of an optical beam produced when propagating in a birefringent crystal, at angles either not orthogonal to or not parallel to the optical axis of the birefringent crystal, to compensate for the effects of different directions of wavefront propagation of non diffracte and diffracte beams in a acousto-optical apparats. The difference between the energy flux vector and the optical wavefront vector produced by propagating in a birefringent crystal is known in the art as double refraction in birefringent crystals and is used for example as a means to spatially separate orthogonally polarized beams. A difference between optical wavefront vectors due to different directions of propagation of non- diffracte and diffracte beams in a acousto-optical apparats is known in the art as a mechanism which separates the energy flux profiles and distorts the energy flux profiles across the wavefront of a beam generated by

Bragg diffraction. However, the inventive combination of the difference between the energy flux vector and the optical wavefront vector produced by propagating in a birefringent crystal and of a difference between wavefront vectors due to different directions of propagation of non- diffracte and Bragg diffracte beams in the acousto- optical apparats to effectively compensate one with the other is believed to be taught herein for the first time in the art.

Another unusual and inventive characteristic of acousto-optical apparats 40 of the first preferred embodiment and variants thereof is the isolation of the laser source from a return beam comprise in part of non- frequency-shifted components of portions of the output beams of the inventive apparats which are scattered and/or reflected back through the acousto-optical apparats 40. The properties of an acousto-optical apparats which incorporates non-normal Bragg diffraction are known in the art. However, the inventive combination of these properties for the transformation of an input beam into an output beam and subsequently the transformation of the return beam so as to effectively not couple to the modes of the laser source is believed to be taught herein for the first time in the art.

In accordance with a second preferred embodiment of the present invention, an acousto-optical apparats is provided that is capable of transforming a single frequency beam comprise of two linearly-orthogonally polarized input beams into an output beam comprise of two principal and two spurious secondary output beams. The principal output beams are linearly-orthogonally

polarized, preferably have the same directions of propagation, and preferably have coextensive energy flux profiles. The frequencies of the principal output beams are different one from the other and different from the frequency of the input beams. The intensities of the two principal output beams are substantially equal and the combine intensities of the principal output beams are substantially equal to the combine intensities of the input beams. In addition, thermal compensation is incorporated through the exploitation of the principles of symmetry and a pair of external birefringent prisms wherein the thermal compensation is with respect to the relative phase of the principal output beams.

FIGS. 2a-2b depict in diagrammatic form the second embodiment of the present invention with similar elements of the second embodiment performing like operations as like denoted elements in the FIGS. la-lob of the first preferred embodiment. The source of beams 18 and 19 as shown in FIG. 2a are the elements in dashed box 15.

Beams 18 and 19 are incident on acousto-optical apparats 240. The paths of beams in acousto-optical apparats 240 originating from beams 18 and 19 are shown in FIG. 2b. The description of elements 41,42,43,44, 46, and 48 of the second embodiment is the same as the description presented for like numbered elements of the first preferred embodiment.

The presently preferred acousto-optical crystal 247 of the second embodiment is made of a uniaxial crystal (e. g., LiNb03) having an optical axis 50 in the plane of FIG. 2b which makes an angle Q (c. f. FIG. 5) with the direction of propagation of the acoustic wave 52 generated

by the piezoelectric transducer 46. The schematic illustrated in FIG. 2b is for a acousto-optical crystal 247 comprise of a negative uniaxiai crystal.

Input beam 18, such as illustrated in FIG. 2b, preferably enters birefringent prism 62 at surface 54 with an angle of incidence ¢1, becoming an extraordinarily polarized beam 20. The optical axis 63 of birefringent prism 62, preferably made of the same birefringent material as acousto-optical crystal 247, is parallel to the edge of prism 62 associated with apex angle al defined in FIG. 2b and perpendicular to the plane of FIGS.

2a and 2b. The function of birefringent prism 62 is to change the relative directions of propagation of orthogonally polarized beams such as used in commonly owned U. S. Patent No. 4,684,828 in the name of G.

Sommargren issued Aug. 1987 for"Apparatus To Transform A Single Frequency, Linearly Polarized Laser Beam Into A Beam With Two, Orthogonally Polarized Frequencies,"and incorporated herein by reference.

Beam 20 exits birefringent prism 62 at surface 55 becoming beam 22. Beam 22 enters birefringent truncated prism 64 at surface 56 becoming an ordinarily polarized beam 24. The angle a2 is the angle between the surfaces 55 and 56. The optical axis 65 of birefringent truncated prism 64, preferably made of the same birefringent material as acousto-optical crystal 247, is nominally perpendicular to the direction of propagation of beam 24 and parallel to the planes of FIGS. 2a and 2b. The edges corresponding to angles a3 and a4 of truncated prism 64 are orthogonal to the planes of FIGS. 2a and 2b. Beam 24 exits truncated prism 64 at surface 57 becoming beam 26.

Beam 26 enters acousto-optical crystal 247 at surface 58 (cf. Fig. 2b) becoming incident beam 28A, incident beam 28A being ordinarily polarized. Due to the photoelastic interaction of incident beam 28A with the acoustic wave 52, an extraordinarily polarized beam, diffracte beam 28B, is generated by small angle Bragg diffraction when Eqs. (1) and (2) are satisfied. The optical axis in acousto-optical crystal 247 is shown in FIG. 2b at 50.

Diffracte beam 28B propagates at a small angle to that of the non-diffracted incident beam 28A, the polarization of the diffracte beam 28B being orthogonal to that of incident beam 28A. In addition, the frequency of beam 28B is fol-po while the frequency of beam 28A is fL. Beams 28A and 28B exit acousto-optical crystal 247 at surface 59 as beams 30A and 30B, respectively.

Input beam 19, such as illustrated in FIG. 2b, preferably enters the birefringent prism 62 at surface 54 with an angle of incidence l, becor. ing an ordinarily polarized beam 21. Beam 21 exits birefringent prism 62 at surface 55 as beam 23. Beam 23 enters truncated prism 64 at surface 56 becoming an extraordinarily polarized beam 25. Beam 25 exits truncated prism 64 at surface 57 becoming beam 27. Beam 27 enters acousto-optical crystal 247 at surface 58 becoming incident beam 29A, incident beam 29A being extraordinarily polarized.

Due to the photoelastic interaction of incident beam 29A with the acoustic beam 52, an ordinarily polarized beam, diffracte beam 29B, is generated by small angle Bragg diffraction when the relationships given by Eqs. (1) and (2) are satisfied.

Diffracte beam 29B propagates at a small angle to that of non-diffracted incident beam 29A, the polarization of diffracte beam 29B being orthogonal to that of incident beam 29A. In addition, the frequency of beam 29B is fL +fo while the frequency of beam 29A is fL. Beams 29A and 29B exit acousto-optical crystal 247 at surface 59 as beams 31A and 31B, respectively.

The respective angles of incidence and refraction for beams 18,19,20, and 21 at surface 54; the respective angles of incidence and refraction for beams 20,21,22, and 23 at surface 55; the respective angles of incidence and refraction for beams 22,23,24, and 25 at surface 56; the respective angles of incidence and refraction for beams 24,25,26, and 27 at surface 57; and the respective angles of incidence and refraction for beams 26,27,28A, 28B, 29A, and 29B at surface 58 are chosen such that the angle of deviation between beams 28B and 29B is c-8 where c is some small angle, preferably s-8 for the second embodiment, the angle of deviation between beams 28A and 28B is #, the angle of deviation between beams 29A and 29B ils-6 and the angle of deviation between beams 28A and 29A is # + # where # is specified by Eq. (4). The conditions with respect to relative directions of propagation of beams 28A, 28B, 29A, and 29B are obtained by choosing the angles al, a2, a3, a4, and α5 defined in FIG. 2b to satisfy the equation

where n'5e in the index of refraction for beam 29A at surface 58.

The treatment of the propagation of the beams after the photoelastic interaction region in the second embodiment is such that the respective angles of incidence and refraction for beams 28A, 28B, 29A, 29B, 30A, 30B, 31A, and 31B at surface 59 are chosen such that beams 30B and 31B preferably are parallel. Beams 30B and 31B are spatially displaced by a minute amount, preferably a small fraction of the beam diameters. The conditions with respect to the relative directions of propagation of beams 30B and 31B are obtained by choosing the orientation of surface 59 such that

where slíe is the index of refraction for beam 28B at surface 59. When it is desired to have beams 30B and 31B <BR> <BR> <BR> <BR> be not parallel, i. e. 2 for beam 30B not the same as ¢2 for beam 31B, then the values of the parameters of Eqs.

(13), (14), (15), and (16) may be chosen so that beams 30B and 31B have a predetermined angle of divergence or convergence between them. Also, it is clear that when it is desired to have the beams 18 and 19 be not parallel, i. e. l for beam 18 not be the same as l for beam 19, then the values of the parameters of Eqs. (13), (14), (15), and (16) may also be chosen so that beams 18 and 19 have a predetermined angle of divergence or convergence between them.

Beams 30A and 31A are spurious secondary output beams, and beams 30B and 31B comprise principal output beams. The spatial displacements between the energy flux profiles of beams 30A, 30B, 31A, and 31B preferably are only small fractions of the beam diameters. If desired, however, it is clear that principal output beams 30B and 31B may be separated or partially separated, for example, through the separation or partial separation, respectively, of input beams 18 and 19. For purposes of illustration, these displacements are shown greatly exaggerated in FIG. 2b.

Three objectives in the design of the acousto-optical crystal 247 are to select the orientations for faces 54, 55,56,57,58, and 59 so that Eqs. (13), (14), (15), and (16) are satisfied; to produce an acousto-optical

apparats which is temperature compensated with respect to temperature induced phase shifts between principal output beams 30B and 31B relative to the phase of the acoustic beam; and to effectively isolate laser beam source 15 with respect to coupling between the laser beam source 15 and return beams, the return beams being backscattered and/or reflected portions of beams 30A, 30B, 31A, and 31B passing back through the inventive apparats and entering laser beam source 15. For the configuration of acousto-optical crystal 247 shown in FIG. 2b, the design parameters relevant to the three cited objectives are highly decoupled: the conditions expressed by Eqs. (13), (14), (15), and (16) are satisfied primarily through the adjustment of one set of parameters, the angles (xi, i = 1,..., 5; the conditions required for the temperature compensation are satisfied primarily through the adjustment of a second set of independent parameters, the thickness of prism 62 relative to the thickness of truncated prism 64, and the application of principals of symmetry; and the condition required for isolation of the laser source 15 met through adjustment of the acoustic power generated by the piezoelectric transducer 46. This feature with respect to decoupling the adjustments used to obtain the three cited primary objectives makes for a robust design of an acousto-optical apparats amenable to production and to use in nonlaboratory environments.

Temperature induced changes between optical path lengths of ordinarily and extraordinarily polarized beams, beams which are progenitors of the principal output beams 30B and 31B in birefringent acousto-optical apparats 40, are compensated wherein optical path configurations in the

birefringent acousto-optical apparats 40 are designed by way of application of principals of symmetry. The principals of symmetry as applied in the second embodiment are accommodated by arranging the optical axes of prisms 62 and 64 to be orthogonal and by'prisms 62 and 64 having substantially the same thickness at the optical beam path locations, the two progenitors of principal output beam 30B in prisms 62 and 64 being extraordinarily and ordinarily polarized, respectively, and the two progenitors of principal output beam 31B in prisms 62 and 64 being ordinarily and extraordinarily polarized, respectively.

Also in the second embodiment, the change with temperature in the speed of the acoustic beam in the acousto-optical crystal 247, if not compensated, will give rise to a temperature induced change in the phase between principal output beams 30B and 31B relative to the phase of the acoustic beam of the order of 0.02 rad/ (de C).

This is compensated in the second embodiment by adjusting the thickness of prism 62 relative to the thickness of truncated prism 64, consistent with the temperature compensation of prism 62 by prism 64 as seen by principal output beams 30B and 31B, so as to use the temperature induced change in (ne-olo) to compensate for the phase shift between principal output beams 30B and 31B relative to the phase of the acoustic beam caused by a temperature induced change in the speed of the acoustic beam.

The remainder of the description for the second embodiment depicted in FIGS. 2a-2b is substantially the same as corresponding portions of the description for the first preferred embodiment illustrated in FIGS. la-lc.

It will be appreciated by those skilled in the art that prism 62 may be affixed to truncated prism 64 and/or truncated prism 64 may be affixed to acousto-optical crystal 247 without departing from the spirit and the scope of the second embodiment. A first variant of the second preferred embodiment is depicted in FIG. 2c wherein prism 62 is affixed to truncated prism 64 and truncated prism 64 is affixed to acousto-optical crystal 247. The temperature compensation in the second embodiment and in the first variant of the second embodiment for temperature induced phase shifts between principal output beams 30B and 31B relative to the phase of the acoustic beam requires that the acousto-optical crystal 247, prism 62, and truncated prism 64 be maintained at substantially the same temperature. This requirement is more easily met in the first variant of the second embodiment where elements 62,64, and 247 are thermally coupled by way of element 62 being affixed to element 64 and element 64 being affixed to element 247.

The remainder of the description for the first variant of the second embodiment is substantially the same as corresponding portions of the description for the second preferred embodiment illustrated in FIGS. 2a-2b.

FIGS. 2d-2e show in diagrammatic form a second variant of the second preferred embodiment. As shown in FIGS. 2d-2e, the second variant of the second embodiment comprises the same elements as the second embodiment except for the omission of truncated prism 64 of the second embodiment and the addition CL prism 66, similar elements of the second variant of the second embodiment

performing like operations as like denoted elements in the second embodiment depicted in FIGS. 2a-2b.

Input beam 18, such as illustrated in FIG. 2e, preferably enters birefringent prism 62 at surface 54 with an angle of incidence ¢1, becoming an extraordinarily polarized beam 20. Beam 20 exits birefringent prism 62 at surface 55 becoming beam 22. Beam 22 enters acousto- optical crystal 247 at surface 56 becoming incident beam 24A, incident beam 24A being ordinarily polarized.

Due to the photoelastic interaction of incident beam 24A with the acoustic wave 52, an extraordinarily polarized beam, diffracte beam 24B, is generated by small angle Bragg diffraction when Eqs. (1) and (2) are satisfied.

Diffracte beam 24B propagates at a small angle to that of the non-diffracted incident beam 24A, the polarization of the diffracte beam 24B being orthogonal to that of incident beam 24A. In addition, the frequency of beam 24B is fol-po while the frequency of beam 24A is .fL Beams 24A and 24B exit acousto-optical crystal 247 at surface 57 as beams 26A and 26B, respectively. Beams 26A and 26B enter prism 66 at surface 58 becoming an extraordinarily and ordinarily polarized beams 28A and 28B, respectively. The optical axis of prism 67 of birefringent prism 66, preferably made of the same birefringent material as acousto-optical crystal 247, is parallel to the edge of prism 66 with apex angle a4 and perpendicular to the planes of FIGS. 2d and 2e. Beams 28A and 28B exit prism 66 at surface 59 becoming beams 30A and 30B, respectively.

Input beam 19, such as illustrated in FIG. 2e, preferably enters the birefringent prism 62 at surface 54 with an angle of incidence +1, becoming an ordinarily polarized beam 21. Beam 21 exits birefringent prism 62 at surface 55 as beam 23. Beam 23 enters acousto-optical crystal 247 at surface 56 becoming incident beam 25A, incident beam 25A being extraordinarily polarized. Due to the photoelastic interaction of incident beam 25A with the acoustic beam 52, an ordinarily polarized beam, diffracte beam 25B, is generated by small angle Bragg diffraction when the relationships given by Eqs. (1) and (2) are satisfied.

Diffracte beam 25B propagates at a small angle to that of non-diffracted incident beam 25A, the polarization of diffracte beam 25B being orthogonal to that of incident beam 25A. In addition, the frequency of beam 25B i s fL + fo whi le the f requency of beam 2 5A i s fL.

Beams 25A and 25B exit acousto-optical crystal 247 at surface 57 as beams 27A and 27B, respectively. Beams 27A and 27B enter prism 66 at surface 58 becoming an ordinarily and extraordinarily polarized beams 29A and 29B, respectively. Beams 29A and 29B exit prism 66 at surface 59 becoming beams 31A and 31B, respectively.

The respective angles of incidence and refraction for beams 18,19,20, and 21 at surface 54; the respective angles of incidence and refraction for beams 20,21,22, and 23 at surface 55; and the respective angles of incidence and refraction for beams 22,23,24A, 24B, 25A, and 25B at surface 56 are chosen such that the angle of deviation between beams 24B and 25B is c-5 where £ iS some small angle, preferably 0 s-8, for the second

variant of the second embodiment, the angle of deviation between beams 24A and 24B is 5, the angle of deviation between beams 25A and 25B ils-6, and the angle of deviation between beams 24A and 25A is 6 +6 where 6 is specified by Eq. (4). The conditions with respect to relative directions of propagation of beams 24A, 24B, 25A, and 25B are obtained by choosing the angles a1 and a2, defined in FIG. 2e to satisfy the equation

where iz,', is the index of refraction for beam 24B at surface 56.

The treatment of the propagation of the beams after the photoelastic interaction region in the second embodiment is such that the respective angles of incidence and refraction for beams 24A, 24B, 25A, 25B, 26A, 26B, 27A, and 27B at surface 57; the respective angles of incidence and refraction for beams 26A, 26B, 27A, 27B, 28A, 28B, 29A, and 29B at surface 58; and the respective angles of incidence and refraction for beams 28A, 28B, 29A, 29B, 30A, 30B, 31A, and 31B at surface 59 are chosen such that beams 30B and 31B preferably are parallel. The energy flux profiles of beams 30B and 31B are spatially displaced by a minute amount, preferably a fraction of the beam diameters. The conditions with respect to the relative directions of propagation of beams 31B and 30B are obtained by choosing the apex angles a4 and (x, such that

where n6e=l3e is the index of refraction for beam 24B at surface 57. Also, when it is desired to have beams 30B and 31B be not parallel, i. e. 2 for beam 30B not the same as 2 for beam 31B, then the values of the parameters of Eqs. (17) and (18) may be chosen so that beams 30B and 31B have a predetermined angle of divergence or convergence between them. It is further clear that if when is desired to have beams 18 and 19 be not parallel, i. e. l for beam 18 not be the same as fl for beam 19, then the values of the parameters of Eqs. (17) and (18) may also be chosen so that beams 18 and 19 have a predetermined angle of divergence or convergence between them.

Beams 30A and 31A are spurious secondary output beams, and beams 30B and 31B comprise principal output beams. The spatial displacements between the energy flux profiles of beams 30A, 30B, 31A, and 31B preferably are only small fractions of the beam diameters. If desired, however, it is clear that principal output beams 30B and 31B may be separated or partially separated, for example, through the separation or partial separation,

respectively, of input beams 18 and 19. For purposes of illustration, these displacements are shown greatly exaggerated in FIG. 2e.

Temperature induced changes between optical path lengths of ordinarily and extraordinarily polarized beams, beams which are progenitors of the principal output beams 30B and 31B in birefringent acousto-optical apparats 240, are compensated in the second variant of the second embodiment wherein optical path configurations in the birefringent acousto-optical apparats 240 are designed by way of application of principals of symmetry. The principals of symmetry as applied in the second variant of the second embodiment are accommodated by optical axes of prisms 62 and 66 having parallel orientations, prisms 62 and 66 having substantially the same thickness at the optical beam path locations, the two progenitors of principal output beam 30B being extraordinarily and ordinarily polarized in prisms 62 and 66, respectively, and the two progenitors of principal output beam 31B being ordinarily and extraordinarily polarized in prisms 62 and 66, respectively.

Also in the second variant of the second embodiment, the change with temperature in the speed of the acoustic beam in the acousto-optical crystal 247, if not compensated, will give rise to a temperature induced change in the phase between principal output beams 30B and 31B relative to the phase of the acoustic beam of the order of 0.02 rad/ (de C). This is compensated in the second variant of the second embodiment by adjusting the thickness of prism 62 relative to the thickness of prism 66, consistent with the temperature compensation of prism

62 by prism 66 as seen by principal output beams 30B and 31B, so as to use the temperature induced change in (l1e-no to compensate for the phase shift between principal output beams 30B and 31B relative to the phase of the acoustic beam caused by a temperature induced change in the speed of the acoustic beam.

The remainder of the description for the second variant of the second embodiment depicted in FIGS. 2d-2e is substantially the same as the corresponding portion of the description for the second preferred embodiment illustrated in FIGS. 2a-2b.

The temperature compensation in the second variant of the second embodiment for temperature induced phase shifts between principal output beams 30B and 31B relative to the phase of the acoustic beam requires that the acousto- optical crystal 247, prism 62, and prism 66 be maintained at substantially the same temperature. This requirement is more easily met in a third variant of the second embodiment wherein the elements 62,66, and 247 are thermally coupled by way of elements 62 and 66 being affixed to element 247.

A third variant of the second preferred embodiment is depicted in FIG. 2f where prism 62 and prism 66 are affixed to acousto-optical crystal 247, similar elements of the third variant of the second embodiment performing like operations as like denoted elements in the second variant of the second embodiment depicted in FIGS. 2d-2e.

The remainder of the description for the third variant of the second embodiment is substantially the same as corresponding portions of the description for the second

variant of the second embodiment illustrated in FIGS. 2d- 2e.

FIG. 3 shows in diagrammatic form a third preferred embodiment of the present invention. As shown in FIG. 3, the third embodiment comprises the same elements as the first preferred embodiment except for the addition of spatial filters 80 and 81. Like reference numerals are used in FIG. 3 for like elements previously described with reference to FIGS. la-lc. The third embodiment employs an acousto-optical apparats 340, similar to 40 of the first embodiment, in a mode of operation which supports the use of spatial filtering to discriminate against secondary beams so that they are not deleterious to downstream applications or to the laser source.

By way of example, beams 30A and 31A are spurious secondary output beams which are orthogonally polarized with frequencies the same as the frequency of beam 16.

The directions of propagation of beams 30A and 31A deviate from the direction of propagation of the principal output beams 30B and 31B by approximately nos and-nos, respectively. The intensities of beams 30A and 31A preferably have nominal values of 0% of the intensities of beams 30B and 31B, respectively, a consequence of the adjustment of the electrical output 44 of the power amplifier 43 so that intensity of either principal output beam 30B relative to the intensity of the input beam 18 or principal output beam 31B relative to the intensity of the input beam 19 is some preselected nominal value between 0% and 100%, preferably 100%.

Secondary output beams 30A and 31A, having directions of propagation different from principal output beams 30B

and 31B, are eliminated in the third embodiment by opaque stop 80. The function of blocking secondary output beams 30A and 31A could, alternatively, be performed using a conventional pinhole spatial filter arrangement. In summary, the elimination of the secondary output beams 30A and 31A is achieved by two independent mechanisms operating concurrently in the third embodiment: the isolation mechanism described for the first preferred embodiment based on reduction in intensity in transmission through the acousto-optical crystal 47 and the isolation mechanism described for the third preferred embodiment based on spatial filtering.

The remainder of the description for the third embodiment depicted in FIG. 3 is substantially the same as corresponding portions of the description for the first embodiment illustrated in of FIGS. la-lc.

A spatial filter 81 may also be used in the third embodiment in a mode of operation which supports the use spatial filtering to increase the isolation of laser beam source 15 with respect to return beams, the return beams being backscattered and/or reflected portions of the principal output beams 30B and 31B and secondary output beams 30A and 31A passing back through the inventive apparats and entering laser beam source 15.

The acousto-optical apparats 340 in this mode of operation transforms the components of the return beam in a manner analogous to the transformations experienced by input beams 18 and 19 except for the direction of frequency shifts which are reverse (cf. R. W. Dixon, ibid.). Consequently, the primary components of the return beam that emerge from the acousto-optical apparats

340 in a direction opposite to and substantially parallel to input beams 18 and 19 will be frequency shifted with respect to the frequency of source 10 by either +-,/'o or 2fo depending on the progenitors of the respective components of the return beam and on the direction of propagation of the respective components of the return beam on entering the acousto-optical apparats 340. The spatial filter 81 eliminates the portion of the primary return beam components that are frequency-shifted by +Je and +2Jo and have directions of propagation different from the reverse direction of propagation of beam 16. The spatial filter 81 will also eliminate the portion of a secondary return beam component that is not frequency- shifted by #f0 and 2fo and has a direction of propagation different from the reverse direction of propagation of beam 16. The secondary return beam component has substantially reduced intensity as described in corresponding portion of description for the first preferred embodiment. In summary, the isolation of laser beam source 15 is achieved by two independent mechanisms operating concurrently in the fifth embodiment: the isolation mechanism described for the first embodiment based on reduction in intensity in transmission through the acousto-optical crystal 47 and the isolation mechanism described for the fifth embodiment based on spatial filtering.

The remainder of the description for the third embodiment depicted in FIG. 3 is substantially the same as the corresponding portions of the description for the first embodiment illustrated in FIGS. 1a-1c.

It will be apparent to those skilled in the art that the spatial filtering described in connection with the third embodiment may be employed simultaneously or separately at either the input or output ends of the acousto-optical apparats without departing from the spirit and the scope of the invention.

In accordance with the fourth preferred embodiment of the present invention, an acousto-optical apparats is provided that is capable of transforming a single frequency beam comprise of two linearly-orthogonally polarized input beams into an output beam comprise of two principal and two spurious secondary output beams. The transformation by the acousto-optical apparats has improved diffraction efficiency with respect to power of an acoustic beam through exploitation of multiple passes of optical beams through the acousto-optical interaction region of the acousto-optical apparats. The principal output beams are linearly-orthogonally polarized, preferably have the same directions of propagation, and preferably have coextensive energy flux profiles. The frequencies of the principal output beams are different one from the other and different from the frequency of the input beams. The intensities of the principal output beams are substantially equal and the combine intensities of the principal output beams is substantially equal to the combine intensities of the input beams. In addition, thermal compensation is incorporated through the exploitation of the principles of symmetry and a series of internal reflections in the acousto-optical apparats wherein the thermal compensation is with respect to the relative phase of the output beam components.

FIGS. 4a-4c depict in diagammatic form the fourth embodiment of the present invention. The fourth embodiment incorporates a double pass of the optical beams through the acousto-optical interaction region in a acousto-optical apparats to improve diffraction efficiency of the acousto-optical apparats with respect to the power of an acoustic beam.

The source of input beams 18 and 19 as shown in FIG.

4a comprises the elements in dashed box 15 which are the same as described for dashed box 15 in FIG. la of the first preferred embodiment. Like reference numerals are used in FIGS. 4a-4c for similar elements previously described with reference to FIGS. la-lb. Beams 18 and 19 are incident on acousto-optical apparats 440. The paths of beams in acousto-optical apparats 440 originating from beams 18 and 19 are shown in FIGS. 4b and 4c, respectively. The descriptions of elements 41,42,43, 44,46, and 48 of the fourth embodiment, shown in FIGS. 4b and 4c, are the same as the description presented for like numbered elements of the first embodiment shown in FIG. lb.

The presently preferred acousto-optical crystal 447 of the fourth embodiment is made of a uniaxial crystal (e. g., LiNb03) having an optical axis 50 in the plane of FIGS. 4b and 4c which makes an angle Q (c. f. FIG. 5) with the direction of propagation 52 of the acoustic beam generated by the piezoelectric transducer 46. The diagrammatic illustration in FIGS. 4b and 4c is for an acousto-optical crystal 447 comprise of a negative uniaxial crystal.

Input beam 18, such as illustrated in FIG. 4b, enters optical element 71, preferably a non-birefringent optical material, at surface 54 becoming beam 20. Beam 20 exits optical element 71 and enters acousto-optical crystal 447 at surface 55 becoming an ordinarily polarized beam 22.

Beam 22 is reflected by surface 56 becoming an ordinarily polarized beam 24. Beam 24 is reflected by surface 57 becoming ordinarily polarized incident beam 26A. Due to the photoelastic interaction of incident beam 26A with the acoustic beam 52 (cf. R. W. Dixon, ibid.; A. Yariv and P.

Yeh, ibid.), an extraordinarily polarized beam, diffracte beam 26B, is generated by small angle Bragg diffraction when the relationships given by Eqs. (1) and (2) are satisfied.

Diffracte beam 26B propagates at a small angle to that of the non-diffracted incident beam 26A, the polarization of diffracte beam 26B being orthogonal to that of incident beam 26A. In addition, the frequency of beam 26B is fol-po while the frequency of beam 26A is fL.

Beams 26A and 26B exit acousto-optical crystal 447 at surface 55 and enter optical element 71 as beams 28A and 28B, respectively. Beams 28A and 28B represent the results of a first pass through acousto-optical crystal 447 wherein the conditions expressed by Eqs. (1) and (2) are satisfied.

Beams 28A and 28B are reflected by surface 58 of optical element 71 as beams 30A and 30B, respectively.

Beams 30A and 30B exit optical element 71 and enter acousto-optical crystal 447 at surface 55 as beams 32A and 32B, respectively. Due to the photoelastic interaction of beams 32A and 32B with the acoustic beam 52, i. e. small

angle Bragg diffraction, the relative amplitudes of beams 32A and 32B are transformed in transit through acousto- optical crystal 447 when the relationships given by Eqs.

(1) and (2) are satisfied.

Upon reflection at surface 58, beams 28A and 28B suffer a relative phase shift, a first phase shift of A radians. The first ii phase shift occurs in beams 28A and 28B without a corresponding n phase shift being introduced in the phase of the acoustic beam after the photoelastic interaction. This type of phase shift will be referenced as a relative acousto-optical phase shift between two optical beams relative to the phase of the acoustic beam. To understand the impact of the first z phase shift, consider, for example, the simple case of the surfaces 55 and 58 being in contact. In this case, the amplitude of beam 32B would be nominally zero at surface 59: as a result of the first phase shift, the effects of the small angle Bragg diffraction resulting from the first pass through the acousto-optical crystal 447 are substantially offset by the effects of the small angle Bragg diffraction generated on the second pass through the acousto-optical crystal 447. However, a second z phase shift, a relative acousto-optical phase shift of n radians, between beams 32A and 32B relative to the phase of the acoustic beam after the photoelastic interaction of the first pass and introduced before the photoelastic interaction of the second pass will cause the amplitudes of beams 32A and 32B to evolve on transit through the acousto-optical crystal 447 substantially as though the second pass through acoustic beam 52 were simply a direct

continuation of the photoelastic interaction path of the first pass.

In the fourth embodiment, the preferred means to effect the second n phase shift is to introduce a displacement of beams 32A and 32B relative to beams 28A and 28B at surface 55 while essentially not altering the actual relative optical phase of beams 32A and 32B. For the case of surface 55 being orthogonal to optical axis 50, the second z phase shift is introduced between the relative phase of beams 32A and 32B relative to the phase of the acoustic beam in between the first and second passes modulus 2z to a high level of accuracy when where d is the distance between surfaces 55 and 58, sl'ls the index of refraction of non birefringent optical element 71, and 3 is the angle of incidence of beam 26A at surface 55 defined in FIG. 4b. It will be apparent to those skilled in the art that the surface 55 can be orientated at an angle other than at 90 degrees with respect to the optical axis 50 as other wise required without departing from the spirit and scope of the fourth embodiment.

Beams 32A and 32B are reflected by surface 59 as beams 34A and 34B, respectively, and beams 34A and 34B exit acousto-optical crystal 47 at face 60 as beams 36A and 36B, respectively.

The input beam 19, such as illustrated in FIG. 4c, preferably enters optical element 71 at surface 54 with an

angle of incidence Ql becoming beam 21. Beam 21 exits optical element 71 at surface 55 and enters acousto- optical crystal 447, becoming extraordinarily polarized beam 23. Beam 23 is reflected by surface 56 becoming an extraordinarily polarized beam 25. Beam 25 is reflected by surface 57 becoming extraordinarily polarized incident beam 27A. Due to the photoelastic interaction of incident beam 27A with the acoustic beam 52, an ordinarily polarized beam, diffracte beam 27B, is generated by small angle Bragg diffraction when the relationships given by Eqs. (1) and (2) are satisfied.

Diffracte beam 27B propagates at a small angle to that of non-diffracted incident beam 27A, the polarization of diffracte beam 27B being orthogonal to that of incident beam 27A. In addition, the frequency of beam 27B is fL +fo while the frequency of beam 27A is fL.

Beams 27A and 27B exit acousto-optical crystal 447 at surface 55 and enter optical element 71 as beams 29A and 29B, respectively. Beams 29A and 29B represent the results of a first pass through acousto-optical crystal 447 wherein the conditions expressed by Eqs. (1) and (2) are satisfied.

Beams 29A and 29B are reflected by surface 58 of optical element 71 as beams 31A and 31B, respectively.

Beams 31A and 31B exit optical element 71 and enter acousto-optical crystal 447 at surface 55 as beams 33A and 33B, respectively. Due to the photoelastic interaction of beams 33A and 33B with the acoustic beam 52, i. e. small angle Bragg diffraction, the relative amplitudes of beams 33A and 33B are transformed in transit through acousto-

optical crystal 447 when the relationships given by Eqs.

(1) and (2) are satisfied.

Upon reflection at surface 58, beams 29A and 29B suffer a relative acousto-optical phase shift, a third Z phase shift. The third z phase shift must be offset by introducing a relative acousto-optical phase shift of Z radians, a fourth Z phase shift, for the same reason the corresponding first z phase shift incurred by beams 28A and 28B had to be offset by the second z phase shift.

The fourth z phase shift for beams 33A and 33B is automatically introduced in the process of effecting the second Z phase shift for beams originating from beam 18 after completion of the first pass and before initiating the second pass.

Beams 33A and 33B are reflected by surface 59 as beams 35A and 35B, respectively, and beams 35A and 35B exit acousto-optical crystal 447 at face 60 as beams 37A and 37B, respectively.

The respective angles of incidence and refraction for beam components 18 and 19 and beams 20 and 21 at surface 54; the respective angles of incidence and refraction for beams 20,21,22, and 23 at surface 55; the respective angles of incidence and reflection for beams 22,23,24, and 25 at surface 56; and the respective angles of incidence and reflection for beams 24,25,26A, 26B, 27A, and 27B at surface 57 are chosen such that the angle of deviation between beams 26B and 27B is c-8 where s ils a small angle, preferably c=-5 and 8 is specified by the Eq.

(4). The angle of deviation between beams 26A and 26B is 6, the angle of deviation between beams 27A and 27B is -5, and the angle of deviation between beams 26A and 27A

is # + #. These conditions with respect to relative directions of propagation of beams 26A, 26B, 27A, and 27B are obtained by choosing the apex angles α1, α2, and α3 defined in FIGS. 7b and 7b to satisfy the equation where níe=n2e are the indices of refraction for beam 23 at surfaces 55 and 56, respectively, n2e=n3e are the indices of refraction for beam 25 at surfaces 56 and 57, respectively, and n3e is the index of refraction for beam 27A at surface 57.

The respective angles of incidence and reflection for beams 32A, 32B, 33A, 33B, 34A, 34B, 35A, and 35B at surface 59 and the respective angles of incidence and refraction for beams 34A, 34B, 35A, 35B, 36A, 36B, 37A, and 37B at surface 60 are chosen such that beams 36B and 37B preferably are parallel. The energy flux profiles of beams 36B and 37B preferably are coextensive. The conditions with respect to the relative directions of propagation of beams 36B and 37B are obtained by choosing the apex angles α3, α4, and α5 consistent with the condition expressed by Eq. (20) such that

where a3, a4, and a5 are defined in FIGS. 4b and 4c, are the indices of refraction for beam 34B at surfaces 60 and 59, respectively, and né is the index of refraction for beam 32B at surface 59. When it is desired to have beams 36B and 37B not parallel, i. e. 2 for beam 36B not the same as 2 for beam 37B, then the values of the parameters of Eqs. (20) and (21) may be chosen so that beams 36B and 37B have a predetermined angle of divergence or convergence between them. The output beam is comprise of principal output beams 36B and 37B and spurious output beams 36A and 37A. In addition, it is clear that when it is desired to have the beams 18 and 19 be not parallel, i. e. l for beam 18 not the same as l for beam 19, then the values of the parameters of Eqs. (20) and (21) may also be chosen so that beams 18 and 19 have a predetermined angle of divergence or convergence between them.

Beams 36A and 37A are spurious secondary output beams, and beams 36B and 37B comprise principal output beams. The spatial displacements between beams 36A, 36B, 37A, and 37B preferably are only small fractions of the beam diameters. If desired, however, it is clear that principal output beams 36B and 37B may be separated or partially separated for example through the separation or partial separation, respectively, of input beams 18 and

19. For purposes of illustration, these displacements are shown greatly exaggerated in FIG. lb.

The fraction of the intensity Iincident°f the input beam transformed into the intensity Idiffracted °f the diffracte beam is given by Idiffracted-Slri2KL(22) Incident where L is the photoelastic interaction path length and K is a coupling constant which is a function of the square root of the acoustic beam intensity and of the photoelastic interaction coefficient (cf. A. Yariv and P.

Yeh, ibid.). Thus, the fourth embodiment with its double pass feature has increased diffraction efficiency with respect to. the acoustic power in comparison to the diffraction efficiency of the first preferred embodiment.

For example, in the case of K L « 1, the diffraction efficiency of the fourth embodiment is a factor of 4 times larger than the diffraction efficiency of the first embodiment, the acoustic beam power being the same in the two embodiments. Alternatively, the acoustic beam power may be decreased by a factor of 4 in the fourth embodiment relative to the acoustic beam power in the first embodiment for the two embodiments operating at the same diffraction efficiency.

The remainder of the description of the fourth embodiment depicted in FIGS. 4a-4c is substantially the same as the corresponding portions of the description for the first embodiment illustrated in FIGS. la-lc.

An unusual and inventive characteristic of the acousto-optical apparats of the fourth embodiment is the use of multiple passes of the optical beams through the acoustic beam to increase the diffraction efficiency of the acousto-optical apparats. Multiple passes of the acoustic beam in the acousto-optical crystal referred to in the literature as"folding the acoustic beam"has been used to increase the diffraction efficiency of an acousto- optical apparats. See, for example, the article entitled "An Improved Read-In Technique for Optical Delay Line Correlators"by M. P. Wenkoff and M. Katchky, Appl. Opt., 9,135-147 (1970) and the article entitled"Opto-Acoustic Processing of Large Time-Bandwidth Signals"by M.

Gottlieb, J. I. Conroy, and T. Foster, Appl. Opt., 11, 1068-1077 (1972). However, the use of multiple passes of an optical beam in the acousto-optical apparats is believed to be taught herein for the first time.

FIGS. 4d-4f depict in diagrammatic form a first variant of the fourth preferred embodiment of the present invention. As shown in FIGS. 4e-4f, the first variant of the fourth embodiment comprises the same elements as the fourth embodiment except for the means used to introduce the second and fourth A phase shifts. Like reference numerals are used in FIGS. 4d-4f for like elements previously described with reference to FIGS. 4a-4c. As shown in FIG. 4e, the second and fourth z phase shifts are introduced with an optical element 72, preferably a quarter-wave phase retardation plate. The quarter-wave phase retardation plate is preferably made of the same birefringent material as acousto-optical crystal 447 and orientated so that beams 30A, 30B, 31A, and 31B have the

correct orientation to satisfy Eqs. (1) and (2). The optical axis of optical element 72 is orientated so as to not cause mixing of the progenitors of beams 30A, 30B, 31A, and 31B. The thickness dR of the phase retardation plate 72 required to introduce the second phase z shift modulus 2n when the optical axis of optical element 72 for example is orthogonal to the planes of FIGS. 4e and 4f is given by the equation <BR> <BR> <BR> <BR> <BR> <BR> <BR> dR=,,(l2p+l,p=0,(l2p+l,p=0, 1,2,... (23)<BR> <BR> <BR> <BR> 4110-ne) The fourth n phase shift is automatically introduced in the process of effecting the second Z phase shift for beams originating from beam 18 after completion of the first pass and before initiating the second pass. The output beam is comprise of principal output beams 34B and 35B and spurious secondary output beams 34A and 35A.

The remainder of the description for the first variant of the fourth embodiment depicted in FIGS. 4d-4f is substantially the same as corresponding portions of the description for the fourth embodiment illustrated in FIGS.

4a-4c.

FIGS. 4g-4h depict in diagrammatic form a second variant of the fourth preferred embodiment of the present invention designated at 540. As shown in FIGS. 4g-4h, the second variant of the fourth embodiment comprises the same elements as the fourth embodiment except for the means used to introduce the second and fourth Z phase shifts.

Like reference numerals are used in FIGS. 4g-4h for like elements previously described with reference to FIGS. 4a-

4c. Referring to FIG. 4h, the second z phase shift is introduced in the transit of ordinarily polarized beam 26A and extraordinarily polarized beam 26B across an acousto- optical crystal 547, the transit of beams 26A and 26B across acousto-optical crystal 547 representing an additional pass of optical beams through the acousto- optical crystal 547 with respective directions of propagation such that Eqs. (1) and (2) are not satisfied.

The two sections of paths comprising the first and second passes in acousto-optical crystal 547 for which the photoelastic interaction is effective, i. e. Eqs. (1) and (2) are satisfied, are those paths of beams 24A and 24B and beams 28A and 28B, respectively. The orientations of the paths of beams 26A and 26B which introduce the second phase # shift modulus 2n are given by the equation <BR> <BR> <BR> <BR> <BR> <BR> nisec#i'[1-(tan#i'-tan#'d)tan#i']-nd'sec#d'=<BR> <BR> <BR> <BR> <BR> (24)<BR> +°tanOj+ °p, p=1, 2,.... where 0 ! and 6d are the directions of propagation of beams 26A and 26B, respectively, ni and n'are the indices of refraction for beams 26A and 26B, respectively, and x is the width of acousto-optical crystal 547 in the direction of the optical axis 50 between the reflection points of beam 26A on surfaces 57 and 58.

The fourth # phase shift is automatically introduced in the process of effecting the second n phase shift for beams originating from beam 18 after completion of the first pass and before initiating the second pass. The

output beam is comprise of spurious secondary output beams 30A and 31A and principal output beams 30B and 31B.

The remainder of the description for the second variant of the fourth embodiment depicted in FIGS. 4g-4h is the same as corresponding portions of the description for the fourth embodiment illustrated in FIGS. 4a-4c.

It will be apparent to those skilled in the art that the technique of the fourth embodiment and variants thereof can be applied to expand the number of passes of the optical beam through an acousto-optical crystal to three, four or more times wherein Eqs. (1) and (2) are satisfied without departing from the spirit and scope of the seventh embodiment and first and second variants thereof. For an example, FIG. 4i depicts in diagrammatic form a third variant of the fourth embodiment wherein the third variant of the fourth embodiment, designated generally as 640, uses the double pass technique of the fourth embodiment twice, operating in tandem, in the acousto-optical apparats 640 to effect a quadruple pass of the optical beams through an acousto-optical crystal 647 wherein Eqs. (1) and (2) are satisfied to obtain a higher diffraction efficiency for a given acoustic beam power. The second double pass is arrange principally through the addition of the non-birefringent element 72 as illustrated in FIG. 4i.

It will be apparent to those skilled in the art that the spatial filtering techniques previously described may either be employed singly or simultaneously with the fourth preferred embodiment and variants thereof without departing from the spirit and the scope of the invention.

There is a limitation on the values of c and on the length of the acousto-optical interaction region that can be effectively used. This limitation may also impact on the number of passes of the optical beams through an acousto-optical crystal at orientations satisfying Eqs.

(1) and (2) that can be effectively used. This limitation arises from a condition imposed by the inventive apparats wherein the progenitors of the output beam components with frequencies vL fo are required to have directions of propagation in the acousto-optical crystal which differ by 6-s in those path sections where Eqs. (1) and (2) are satisfied. The photoelastic interaction coupling coefficient K will remain effective as long as the total length Ltotal satisfies the condition noA2 CS J-nou 2 Cb J 1 Ltotal <<-2 (25) 0 0, fi where Lota ! is comprise of the lengths of the first and last passes through the acousto-optical crystal for which the photoelastic interaction is operative and the length of all path sections in between.

It is evident from Eq. (25) that operation of the preferred embodiments and variants disclosed herein with a preferred value for s being as large as s=8 can lead to a significant reduction in the value of Ltot,,, whether operating a single pass or multiple pass embodiment or variant thereof. This reduction in Ltotal may be partially ameliorated by operating at lower acoustic frequencies as

demonstrated by Eq. (25) where L,, t, l is proportional to (11fo) An unusual and inventive characteristic of the acousto-optical apparats of the fourth embodiment and variants thereof is the ability to significantly increase the value for Lt, t, l beyond that given by Eq. (25) for a given value of c by having the effective average values of dOi/dO and dOd/dO, the average of respective quantities over a set of multiple passes, be different from the values of dOildO and dOd/dO specific to the optical path sections for which the conditions for Bragg diffraction are satisfied. It is generally desirable in optical path sections for which the conditions for Bragg diffraction are satisfied to have <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> d#id#d<BR> <BR> <BR> <BR> 1(26)## <BR> d# d# in order to maintain high diffraction efficiency as the angle of an input beam and/or of an acoustic beam is changed by a small amount.

The efficiency of Bragg diffraction is reduced when a momentum matching condition is not maintained for a change in the angle Oj of an incident beam, e. g. beam 24A of the first preferred embodiment, and/or a change in the direction of propagation of the acoustic beam (52) according to subsequently set fourth Eq. (28). For an acousto-optical modulator, it is also preferable that the variation in od within the diffracte beam, e. g. beam 24B of the first preferred embodiment, not be substantially

different from the variation in Oj within the incident beam 24A. From the derivative with respect to Oj of sinb given by Eq. (4) and noting that #=#i+#d, cf. FIG. 8, an equation for the ratio of the differential change in Od required to match a differential change in Oj can be obtained with the result <BR> <BR> <BR> <BR> <BR> <BR> ae 1<BR> <BR> <BR> d8;1+tanbtan6 It is evident from Eq. (27) that |d#d/d#i| # 1 in general for small angle Bragg diffraction where Oj is small, such as is the case for the inventive apparats disclosed herein, and #<1. With respect to the condition that #<1, consider the example of an acoustic beam shear wave propagating in an acousto-optical crystal made of Lino3, #0=0. 633 µm, and fo=20 Mhz wherein 6=1. 12x10 3 radians.

Thus, the preferred operating condition where the variation in od within the diffracte beam 24B is not substantially different from the variation in Oj within the incident beam 24A is available for the first preferred embodiment of the present invention, with the same property with respect to (dOd/dOj) existing for subsequently described embodiments and variants thereof which are all based on small angle Bragg diffraction.

Another unusual and inventive characteristic of the acousto-optical apparats of the fourth embodiment is the improved maximum diffraction efficiency that can be achieved for a given photoelastic interaction length. A

momentum mismatch between the momentum of the incident and diffracte optical beams and the acoustic beam limits the maximum diffraction efficiency for a single pass to where KAO is the momentum mismatch in the direction of propagation of the optical beams and K is the magnitude of the coupling constant [c. f. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York), Section 9.5.1 entitled"Small-Angle Bragg Diffraction"].

When the angle between the direction of propagation of the light beam and the acoustic wavefront is small, the interaction length L is the width of the acoustic beam.

Consequently, the optical mode amplitudes A1 and A2 are functions of z only, because z mesures the depth of penetration in this interaction configuration. The development of the amplitudes A1 and A2 during transit through the photoelastic interaction region are governed by the coupled differential equations where K12 is the coupling constant (c. f. Yariv and Yeh, ibid.). The general solution to Eqs. (29) is given by

where za and zb are the bounds of the acoustic beam in the .-direction and the matrix elements Cj of matrix C(zb,za,#α) are given by the equations (36)K2=K12K12*,

Da=K08, (37) and for the pth pass, Those skilled in the art will appreciate that when the amplitude of the acoustic beam is not uniform in z over the interval Za to Zb, the resulting mathematical expression for matrix C(zb,za,#α) is more complicated than that given Eqs. (31), (32), (33), (34), and (35).

However, the important features relevant to the present discussion are retained in the case for which the amplitude of the acoustic beam is uniform in z over the interval Za to Zb- A momentum mismatch can be caused by a change in the direction of propagation of either the acoustic beam or the optical beam with respect to the optical axis of the Bragg cell. For a single pass acousto-optical apparats, the effect of either of the two causes of a momentum mismatch are the same and given by Eqs. (30), (31), (32), (33), (34), and (35). However, for the multiple pass acousto-optical apparats of the seventh embodiment, the effects of the momentum mismatch are different for the two causes. A momentum mismatch ha on the first pass produced by a change in the direction of the acoustic beam will be manifeste in the second pass as a momentum

mismatch-Da. A momentum mismatch ha on the first pass produced by a change in the direction of the optical beam is characterized by the same momentum mismatch ha on the second pass but with the relative phases of the two optical beams shifted with respect to the phase of the acoustic beam, the relative phase shift depending on the technique used to introduce the second z phase shift.

The diffraction efficiency is given by the equation Id =C21C21* (40) Ii Single Pass The effect of a change in acoustic beam direction by ## or a change in optical beam direction boy-06 is given by Eq. (34) as where it has been assumed that za = 0 and zb = L. The maximum value of C21C21 is for

(43)sL=(#/2).

The result expressed by Eq. (42) is the same as that given by Eq. (28). Thus, the maximum diffraction for a single pass is in general less than one for a finite value of ha.

The Effect of a Change in Acoustic Beam Direction for Multiple Pass Configuration Double Pass The solution for the mode amplitudes when there is a change in acoustic beam direction by AO in a double pass configuration is The second row, first column matrix element of matrix C(z2,z1,-#α)C(z1,z0,#α)is sz1sins(z2-z1)].x[sinsz2-i2(#α/2ssin

The ratio of the intensity of the diffracte beam to the intensity of the input beam is given by the magnitude squared of the matrix element [C(z2,z1,-#α)C(z1,z0,#α)]21 as expressed by Eq. (40). For the case of (z2-z1)=(z1-z0), the maximum value of for Thus, the maximum diffraction efficiency for a double pass can be 1 for a finite value of Aa.

Triple Pass The solution for the mode amplitudes when there is a change in acoustic beam direction by AO in a triple pass configuration is

where A1(z2) and A2(z2) are given by Eq. (45). The second row, first column matrix element of matrix C(z3,z2,#α)C(z2,z1,-#α)C(z1,z0,#α)is The ratio of the intensity of the diffracte beam to the intensity of the input beam is given by the magnitude squared of the matrix element [C(z3,z2,#α)C(z2,z1,-#α)C(z1,z0,#α)]21 as expressed by Eq. (40).

For the case of (z2-z1)=(z1-z0),theand maximum value of is

Thus, the maximum diffraction efficiency for a triple pass can be 1 for a finite value of hua.

Quadruple Pass The solution for the mode amplitudes when there is a change in acoustic beam direction by ## in a quadruple pass configuration is where A1(z3) and A2 (z3) are given by Eq. (49). The second row, first column matrix element of matrix C(z4,z3,-#α)C(z3,z2,#α)C(z2,z1,-#α)C(z1,z0,#α)is

The ratio of the intensity of the diffracte beam to the intensity of the input beam is given by the magnitude squared of the matrix element [C(z4,z3,-#α)C(z3,z2,#α)C(z2,z1,-#α)C(z1,z0,#α)]21 as expressed by Eq. (40). For the case of-z- and (z2-z1)=(z1-z0), the maximum value of for Thus, the maximum diffraction efficiency for a quadruple pass can be 1 for a finite value of ha.

Fifth and Higher Order Multiple Pass The results for the second, triple, and quadruple pass configurations each can have a maximum diffraction efficiency of 1 for a finite value of Da when

where the parameter q is the number of passes. The obvious extrapolation of these properties is that the maximum diffraction efficiency for a finite value of Au can be 1 for configurations with multiple passes of q : 5 when Eq. (57) is satisfied.

The Effect of a Change in Optical Beam Direction for Multiple Pass Configuration Double Pass The solution for the mode amplitudes when there is a change in optical beam direction by AO in a double pass configuration is where matrix R introduces the phase shift 2ß between the two orthogonally polarized incident and diffracte optical beams relative to the phase of the acoustic beam during period of the first and second passes through the acousto-optical crystal by the respective optical beams.

The phase shift ß is given by the expression

and the matrix R (P) is The coupling constant for the pth pass is The ratio of the intensity of the diffracte beam to the intensity of the input beam is given by the magnitude squared of the matrix element [C(z2,z1,#α)R(ß)C(z1,z0,#α)]21 as expressed by Eq. (40). For the case of (z2-z1)=(z1-z0), the maximum value of is

Thus, the maximum diffraction efficiency for a double pass can be 1 for a finite value of ha.

Triple and Ouadruple Pass Results obtained for triple and quadruple pass configurations are similar to the results obtained for the double pass configuration: the maximum diffraction efficiency for a triple and quadruple pass can be 1 for a finite value of ha when Eqs. (52) and (56), respectively, are satisfied and Eq.(64).$satisfies Fifth and Higher Order Multiple Pass The results for the second, triple, and quadruple pass configurations each can have a maximum diffraction efficiency for a finite value of ha when Eq. (57) is satisfied and ß satisfis Eq. (64). The obvious extrapolation of these properties is that the maximum diffraction efficiency for a finite value of ha can be 1 for configurations with multiple passes of q ! 5 when Eq.

(57) is satisfied and ß satisfis Eq. (64).

Having now described several embodiments of the invention, it will be clear the sum of its principal avantages are that the apparats: is comprise of a single crystal with a piezoelectric transducer bonded

directly to the crystal or comprise of a single crystal with piezoelectric transducer bonded directly to the crystal and an external element or elements in a compact size, has high diffraction efficiency, generally has no requirement for external beam stops, has efficiency of nominally 100% for conversion of input intensity into intensities of two orthogonally polarized exit beam components, and the intensity of each of two orthogonally polarized exit beam components may be adjusted to nominally 50% of the input intensity. The apparats of the present invention also exhibits reduced polarization mixing and has a compact size because of the use of anisotropic Bragg diffraction and generally through the use of internal reflections in an ani-sotropic crystal.

The apparats of the present invention can produce high diffraction efficiency with reduced acoustic power levels by the use of multiple passes of the optical beams through the acoustic beam at conditions for which the photo- elastic interaction is effective. Furthermore, the angular displacement between orthogonally polarized exit beam components has reduced sensitivity to changes in the temperature or to temperature gradients of the apparats due in part to the use of anisotropic Bragg diffraction.

Changes in the relative phase shift between the output beams and the acoustic beam may be compensated for changes in temperature of the apparats of the present invention by a symmetrical treatment of the propagation of the output beam components in the anisotropic crystal. The lateral displacement between the components of the output beam may be reduced or compensated in the apparats of the present invention also by a symmetrical treatment of the

propagation of the output beam components in the anisotropic crystal. In addition, the output beams may be parallel or not. There are also no multiple elements of the type to create misalignment of directions of the components of the output beam.

While the invention has been described with reference to particular embodiments thereof, those skilled in the art will be able to make the various modifications to the described embodiments of the invention without departing from the true spirit and scope of the present invention.

For example, it will be apparent that biaxial crystals, which are another species of anisotropic crystal, except with two optic axes, can be adapted to beneficial use according to the teachings and principles of the present invention. Moreover, either ordinarily or extraordinarily linearized light may be adopted to serve as the input with the conversion being to the opposite to that adopted for the input state. Also, antireflection coatings may be used on facets where ever appropriate to improve coupling efficiency. Therefore, it is intended that all equivalent combinations of elements and steps which perform substantially the same function in substantially the same way to achieve the same result be within the scope of the present invention.