Provisional Application No. 60/138,942 filed on June 11,1999.

ORIGIN OF THE DISCLOSURE The systems and techniques described herein were made in the performance of work under a NASA contract, and are subject to the provisions of Public Law 96-517 (35 USC 202) in which the Contractor has elected to retain title.

BACKGROUND This application relates to modulation of optical signals, and more specifically, to methods and devices for modulating an optical signal by using electro-optical modulators.

Optical communication systems use one or more optical carrier waves to provide high-speed and wide bandwidth signal transmission. An optical carrier wave can be transmitted either through the free space or in an optical waveguiding channel such as a fiber link. The data capacity of a fiber link can be increased by using a wavelength-division

multiplexing technique which simultaneously transmits optical carriers of different wavelengths over the same fiber so that different channels of data can be sent at the same time. Many other non- optical communication systems, such as wired networks, radio wireless networks, satellite communication systems, can be combined with optical systems to meet various communication needs and requirements.

An optical communication system may include a light source such as a laser to produce the optical carrier wave, an optical modulator to modulate the optical carrier wave to carry information, and an optical receiver which may include a photodetector to convert the optical information into a desired electronic format for further processing. The optical modulator may modulate either the phase or t amplitude of the optical carrier wave. It is desirable to obtain high energy efficiency and a high modulation speed in an optical modulator for optical communication and other applications.

SUMMARY The present techniques and devices for optical modulation include an electro-optic light modulators formed from gallery-whispering-mode resonators. One

embodiment of such a modulator includes a gallery- whispering-mode resonator formed of an electro- optical material, a first optical coupler to couple an input laser beam into the resonator, a second optical coupler to couple the optical energy out of the resonator to produce an optical output, and an electrical coupler to apply a. driving electrical signal. The optical energy from the input laser beam is coupled to into the resonator in one of the whispering gallery modes. The applied electrical signal modulates the dielectric constant of the resonator and hence the mode of the whispering gallery modes. This modulates the intensity of the output from the second optical coupler.

One configuration of various forms of the gallery-whispering-mode resonator may be a disk-like resonator formed around an equator of a sphere.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows one embodiment of an optical modulator based on a whispering-gallery-mode resonator made of an electro-optic material.

FIGS. 2A and 2B show a disk resonator fabricated from a sphere with two different orientations of the optic axis of the electro- optical crystal.

FIG. 3 shows one implementation of the device shown in FIG. 1.

FIG. 3A shows optical coupling by angle- polished waveguide or fiber.

FIGS. 4,5, and 6 show examples of RF electrodes for a disk-like whispering-gallery-mode resonator.

FIG. 7 shows the mode spectrum of a whispering- gallery-mode sphere resonator obtained by tuning the input laser frequency.

FIG. 8 illustrates the effect of applied RF field on the spectrum of optical whispering-gallery modes where intensity modulation is achieved at appropriately set input laser frequencies.

DETAILED DESCRIPTION An optical resonator uses an optical feedback mechanism to store optical energy only in certain resonator modes. An optical wave in a supported resonator mode circulates in the resonator. When the recirculating optical wave has a phase delay of N2 (N=1, 2,3,...), the optical resonator operates in resonance and optical energy accumulates inside the resonator and can be transmitted through the resonator with a minimum loss. If the optical is coupled out at this resonance condition, the output of the resonator is maximized. However, when the recirculating wave in the resonator has a phase delay other then N2s, the amount of optical energy accumulated in the resonator is reduced and, accordingly, the coupled output is also reduced from its maximum value.

If the phase delay in the optical cavity can be modulated, a modulation on the output from an optical resonator can be achieved. The modulation on the phase delay of recirculating wave in the cavity is equivalent to a shift between a resonance condition and a non-resonance condition and can be between any two different values in the phase delay.

In fact, the initial value of phase delay (i. e. detuning from resonance) may be biased at a value

where a change in the phase delay produces the maximum change in the output energy.

The present disclosure includes a use of the above modulation mechanism in a whispering-gallery- mode resonator to modulate light. The phase delay of the optical feedback (i. e. positions of optical cavity resonances) is changed by changing the components of refractive index of the resonator via electro-optic modulation. An external electrical signal is used to modulate the optical phase in the resonator to shift the whispering-gallery mode condition and hence the output coupling. Such an optical modulator can operate at a low operating voltage, in the millivolt range. This can achieve a high modulation speed at tens of gigahertz or higher, and have a compact package. The optical coupling with the resonator may be implemented with waveguides or fibers for integration with other fiber optical elements or integrated electro-optical circuits formed on substrates. Hence, such optical modulators may be used in a variety of applications having optical modulation, including optical communication and optical signal processing.

A whispering-gallery-mode resonator may be formed from a transparent sphere made of a dielectric material. Other geometries based on a

sphere are also possible, including a disk cavity or a ring cavity. Optical energy can be coupled into a resonator by evanescent coupling, e. g., using an optical coupler near the sphere by less than one wavelength of the optical radiation. Such resonators have a special set of resonator modes known as"whispering gallery modes". These modes represent fields confined in an interior region close to the surface of the sphere around its equator due to the internal reflection of the radiation. Microspheres with 10 micron or larger diameter have a resonator dimension much larger than the wavelength of light. Thus the loss due to the finite curvature of the resonator may be negligible.

The resonators may be designed to have a high quality factor, Q, that are only limited with attenuation of radiation in the dielectric material and the surface imhomogeneities. Some microspheres have been shown to have very high quality factors for light waves, exceeding 109 for quartz microspheres. See, e. g., Braginsky V. B., Gorodetsky M. L., Ilchenko V. S, Phys. Lett., Vol. 137, p. 393 (1989) and Collot et al., Europhys. Lett., Vol. 23, p. 327 (1993).

Such high Q values may allow concentration of strong fields in the whispering gallery modes.

High-Q microsphere resonators have been used in a number of devices, including narrow band filters, lasers, laser stabilizers, and quantum nondemolition energy measurement devices. The use of droplet microcavities has also been recently made to demonstrate enhanced gain in such nonlinear optical processes as Raman and Rayleigh-wing scattering, as well as in four-wave parametric oscillation. Here the use of dielectric microspheres of materials with an electro-optic effect for the modulation of optical radiation is proposed.

For a given whispering-gallery-mode sphere, the resonator modes and quality factor, Q, at a particular wavelength of radiation may be found by solving the following equations for the TMn, m, q (z) modes: where n is the mode index, z = x-iy, Q = x/2y, e is the dielectric constant of the sphere, and Jn ? i/2 (z) and Hnq : i/2 (z) are respectively the Bessel and Hankel functions. See, e. g., an example description in Lin and Campillo, Phys. Rev. Lett., Vol. 73, p. 2440 (1994). Similarly, the equation for the TEn, m, q (z) modes is:

These equations may be solved numerically to find the appropriate modes for supporting the optical waves.

Under proper configurations, either the sphere resonator alone or the sphere resonator in connection with a proper electrical strip line can form an electrical resonator to support electrical energy in the same whispering gallery modes with proper phase matching conditions. Hence, electrical and optical waves can coexist and co-propagate in certain whispering gallery modes. When the sphere is formed of an electro-optic material, the electrical wave can be used to alter or modulate the dielectric constant of the sphere and hence modulate the light based on the electro-optic effects.

One consequence of Equations (1) and (2) is that for certain values of the dielectric constant s and the sphere radius R, whispering gallery modes with very high Q exist, for a given wave with wavelength B. For example, in quartz spheres of diameter on the order of 100 microns, modes with Q's in the range of 108 and higher may be excited. These whispering gallery modes may propagate very close to the surface of the resonator, typically in a thickness less than 10 microns. High Q values can also be achieved for waves in the mm and microwave regions of the electromagnetic spectrum. Fore example, a Q value about 109 has been observed with sapphire resonators at cryogenic temperatures.

FIG. 1 shows an optical modulator 100 with a whispering-gallery-mode resonator 110 according to one embodiment of the disclosure. Two optical couplers 121 and 122 are placed close to the resonator 110 as optical input coupler and output coupler, respectively. An input optical beam 104, e. g., a laser beam from a laser 102, is coupled into the resonator 110 as the internally-circulating optical wave 112 in the whispering gallery modes by the coupler 121. The coupling may be achieved through the evanescent coupling so that the couplers 121 and 122 are placed close to the resonator 110 by

a spacing less than one wavelength of the beam 104.

In evanescent coupling, the evanescent fields at the surface of the sphere decays exponentially outside the sphere. Once coupled into the resonator, the light undergoes total internal reflections at the surface of the sphere. The effective optical path length is increased by such circulation. The output coupler 122 couples a portion of the circulating optical energy in the resonator 110, also through the evanescent coupling, to produce an output beam 124.

Alternatively, the optical coupling may be implemented by using angle-polished fibers or waveguides 391 and 392 as shown in FIG. 3A. The angle-polished tip is placed near the resonator 310 to effectuate the evanescent coupling. The index of refraction of the fibers or waveguides 391 and 392 has to be greater than that of the resonator 310, and the optimal angle of the polish has to be chosen depending on the ratio of indices (V. S. Ilchenko, X. S. Yao, L. Maleki, Opt. Lett, Vol. 24,723 (1999).

An electrical coupler 130 is also disposed near the resonator 110 to couple an electrical wave which causes a change in the dielectric constant s due to the electro-optic effects. An electronic driving circuit 140 is coupled to supply the electrical wave

to the electrical coupler 130. A control signal 150 can be fed into the circuit 140 to modulate the electrical wave. This modulation is then transfered to a modulation in the optical output 124 of the resonator 110.

The resonator 110 may be formed from any electro-optic material such as lithium niobate. The whispering gallery modes essentially exist near the equator of the sphere, the resonator 110 may be not a whole sphere but a portion of the sphere near the equator that is sufficiently large to support the whispering gallery modes. Hence, rings, disks and other geometries formed from spheres may be used.

FIG. 2A shows a disk-like whispering gallery mode resonator. It is formed from a sphere by removing top and bottom portions of the sphere to leave a portion containing the sphere equator 200.

This embodiment of the resonator 110 includes a top circular surface 210 and a bottom circular surface 220, both with diameters less than the diameter of the original sphere. The side surface 230 may be a spherical surface. The spacing, d, between the top and bottom surfaces 210 and 220 is sufficiently large that the optical and electrical modes centered at the equator 200 remain essentially undisturbed by the geometry. A small spacing d can be used to

achieve a sufficient electrical field strength for the electro-optic modulation at a low voltage, e. g., on the order of millivolts.

In general, the optic axis of the electro-optic material for the resonator 110 may be in any direction. FIG. 2B shows a disk configuration where the optic axis c (202) is different from the axis z (201) perpendicular to the equatorial circular plane. In certain applications, the optic axis c (202) may be aligned with the axis z (201) as in FIG. 2A.

The optical modulator 100 in FIG. 1 may support rf (i. e. mm and microwave) signals, and light, simultaneously in a sphere of material with the electro-optic effect. Lithium niobate, for example, changes its real part of the index of refraction in response to the applied electric field. Other materials may respond to the electric field differently. Multiple quantum well structures of III-V compounds, for example, change their imaginary part of the index of refraction when the electric field is applied.

A resonator formed from a lithium niobate sphere with a diameter on the order of 3 mm, whispering gallery modes with Q's larger than 107 can be supported. Since lithium niobate has an 8 of

about 50 in the rf range, the same sphere can support waves with mode index n=5 or larger. For these waves Q would be on the order of 104. Now the applied electrical field can be arranged to change the speed of propagation of the optical field, which propagates in a thickness of only a few microns near the perimeter of the sphere around its equator. The rf mode field also occupies the same region, and owing to the relatively large Q of the mode, high electrical field values can be obtained at a small input RF power, to change the index of refraction by a significant amount.

Assume, as a first order approximation, that the relation between the radius R of the sphere, the mode index number n, and the wavelength of light is 2d ni (3) This relation suggests that the change in X is approximately linear with the change in Fe. Now the mode detuning by electro-optical effect required to transfer the energy from this mode to a different mode may be on the order of Q~1 (for X = 1300nm ; Q =107). Thus, to change the energy out of this mode,

a change in the index less than a part per million is required. This is at least two orders of magnitude smaller than the fields required in many traveling-wave electro-optic modulators.

Another approach for estimating the required half-wave voltage Vn in comparing the microsphere to the traveling wave modulator is to consider the following. The electrical length of the microspherical resonator is on the order of few meters, compared to the centimeter long length of the traveling wave modulator, which requires a Vn of a few volts. This implies that, for the microsphere, the interaction length is increased by a factor of about 102 to about 103. This reduces the needed Vit by the same factor. This increased efficiency will also be further improved with the electric field applied in the whispering gallery mode to allow a Q multiplication (by a factor of 104) of the energy density in the sphere. Even with the built-in inefficiency (on the order of 3 dB) associated with the coupling of the rf and light power, the modulator 100 shown in FIG. 1 can be orders of magnitude more efficient than those traveling wave modulators. In addition, in the case of materials with electro-absorption, where the electric field can best be applied directly, rather

than in a whispering gallery mode, again many orders of magnitude in efficiency is expected.

The resonator 110 with a high Q factor has a number of other advantages. For example, the resonator 110 can effectuate an increase in the energy storage time for either the optical energy or the electrical energy and hence reduce the spectral linewidth and the phase noise of both. Also, the mode matching conditions make the optical modulator 100 also operate as a signal filter so that only certain input optical beam 104 can be coupled through the resonator 110 to produce a modulated output by rejecting other signals that fail the mode matching conditions.

FIG. 3 shows one implementation of a light modulator 300 in a modulator housing 380 based on the system 100 in FIG. 1. Optical fibers 332 and 334 are used to guide input and output optical beams. Microlenses 331 and 222, such as gradient index lenses, are used to couple optical beams in and out of the fibers. Two prisms 321 and 322 operate as the optical couplers to provide evanescent coupling with the whispering gallery mode resonator 310. Different from the system 100 which uses the resonator 110 alone to support the electrical modes, a RF microstrip line electrode 350

is combined with the resonator 310 to form a RF resonator to support the electrical modes. An input RF coupler 330 formed from a microstrip line is implemented to input the electrical energy into the RF resonator. A circuit board 360 is used to support the microstrip lines and other RF circuit elements for the modulator.

The modulator 300 also includes a second RF coupler 370, which may be formed from a microstrip line on the board 360, to produce a RF output. This signal can be used as a monitor for the operation of the modulator or as an electrical output for further processing or driving other components.

FIGS. 4,5, and 6 show examples of the microstrip line electrode 350 when the resonator 310 is similar to the disk configuration shown in FIGS.

2A and 2B. In FIG. 4, the electrode 350 is formed on the top surface of the resonator 310 and the another electrode 410 is formed in contact with the bottom surface of the resonator 310. FIG. 5 shows a half-circuit microstrip line as the top electrode 350 on the rim of the top surface. FIG. 6 shows two pieces of circular microstrip lines 350A and 350B (solid lines) as the top electrode 350 and two pieces of circular microstrip lines 410A and 410B as bottom electrodes (dot liens with shades).

FIGS. 7 and 8 show measured data from the modulator 300 in FIG. 3 where the resonator 310 is a whole sphere. The electrodes are formed at the opposite poles of the sphere. A commercial-grade lithium niobate crystal (Casix Inc.) is used to form the disk-like resonator 310. The LiNb03 crystal has a low optical absorption at about a t 0. 02 cm~1, allowing the quality-factor Q =2wn/ (ak) ~107 for the whispering-gallery modes. The resonator is custom fabricated and polished.

High-quality spheres are in general difficult to fabricate from crystalline materials via fusion as with amorphous materials. Upon fusion of crystalline materials, spontaneously forming boundaries between misoriented crystalline grains, or blocks, may create significant optical inhomogeneities through the bulk of the sphere and on the surface, thus increasing the scattering losses beyond the acceptable level. However, self- organized spheres of cubic (non-birefringent) crystalline material were reported. Because of their sub-grain few-micron size, they can be used to support WG modes of reasonable Q~104-105. To obtain high-surface quality spheres of birefringent crystalline materials, one method is to machine and polish them using conventional optical methods. On

flat or low-curvature substrates, modern methods allow to obtain angstrom size residual inhomogeneities-compatible to the roughness of fire-polished silica and therefore allowing ultimate Q>109. These methods, however, are generally not used or adapted for making very small radii of curvature. In one of the early works, WG modes with quality-factor of about 1x108 were observed in a 3.8- cm diameter mechanically for the Gravity Probe B experiment. In the meantime, with a given size of surface inhomogeneity, limitation of Q by scattering losses is in direct proportion to the sphere diameter.

The optical prism optical couplers 321 and 322 for the evanescent wave coupling may be miniature diamond prisms of refraction index of about 2.4 higher than that of the resonator material (no = 2.220 ; ne = 2.146). A DFB laser at about 1550nm is used to produce the optical beam and is frequency- scannable via current modulation. The spectral data in FIG. 7 suggests that the employed prism coupling technique has a coupling efficiency about 50% in the loaded regime. The observed free spectral range (FSR) of about 8.3 GHz corresponds to the sequence of successive principal mode numbers 1 for TE-type WG modes excited in the plane perpendicular to the

crystal axis. The estimated loaded quality-factor of the modes is about 1.2x106.

The non-Lorentzian shape of the observed resonance dips in FIG. 7 indicates the presence of clusters of slightly non-degenerate modes. It is discovered that, the character of the observed spectrum appears to critically depend on the orientation of the crystal with respect to the normal direction of the equator plane. With the excitation off the perpendicular plane to the crystal axis, the observed spectrum became dense with a reduced linewidth. This increases the Q factor. This preliminary measurement confirms that inexpensive fabrication and polishing techniques can be used to achieve the Q factor in the spheres of crystalline lithium niobate that is close to the limits defined by the material attenuation.

FIG. 8 shows the measured optical output power (curve 820) as a function of the laser frequency detuning for the input beam to the resonator. Curve 810 represents the corresponding optical whispering modes of the resonator. The intensity modulation in the curve 820 demonstrates the low-frequency electro-optical intensity modulation by the lithium niobate sphere. During continuous monitoring of WG mode spectrum in the sphere by tuning the laser, a

100kHz RF voltage with Veff = 40V (-125V peak-to- valley) is applied to the electrodes. This produces an amplitude modulation maximal near the slopes of individual cavity resonance peaks.

The above electro-optical modulator based on whispering-gallery-mode resonators generally has limited operating bandwidth, though operable to produce high modulation speeds, due to the resonance conditions and mode-matching requirement. Such modulators may be suitable for a number of applications where optical carrier is fixed, and the cavity spectrum can be trimmed to have optical modes at the carrier frequency and the modulation sidebands. With development of appropriate fabrication techniques and reduction of the sphere size (at least 100 fold reduction is possible without compromising the optical Q), this inconvenience will be compensated by two serious advantages over many other optical modulators. For example, the controlling voltage (analog of the half-wave voltage Vn) can be reduced into milliVolt domain. In addition, tiny capacity of electro-optic microspheres can simplify application of microwave fields, compared to both plane-wave bulk electro- optical modulators and integrated Mach-Zender interferometer modulators.

Although only a few embodiments are described, various modifications and enhancements may be made without departing from the following claims.