CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to U.S. Provisional Application No. 62/483,612, filed on April 10, 2017, which has the same title and the same inventors, and which is incorporated herein by reference in its entirety.

FIELD OF THE DISCLOSURE

[0002] The present disclosure relates generally to electromagnetic wave

spectroscopy, and more particularly to a method and apparatus for the control and dynamic manipulation of electromagnetic wave spectra via external modulation of refractive index.

BACKGROUND OF THE DISCLOSURE

[0003] At present, various methods are utilized in the art for manipulation of the spectral output of high power or high pulse energy lasers. Such methods include frequency doubling in nonlinear crystals, self-phase modulation and the use of optical parametric oscillators.

[0004] Optical parametric oscillators utilize an optical resonator and a non-linear optical crystal, and oscillate at optical frequencies. These oscillators convert an input laser wave or "pump" with frequency ω _ρ into two output waves (called the "signal" and "idler") of lower frequency (<¾, a> _£ ) by means of second-order nonlinear optical interaction. The sum of the frequencies of the output waves is equal to the input wave frequency (that is, ω ₅ + iOj ~ ω„). [0005] Frequency doubling (which is also called second-harmonic generation) refers to the phenomenon where an input (pump) wave generates another wave with twice the optical frequency (and half the vacuum wavelength) in the medium. Frequency doubling may be achieved with nonlinear crystals (that is, crystalline materials which lack inversion symmetry). Such crystals may be formed, for example, from lithium niobate (LiNbCb), potassium titanyl phosphate (KTP = KT1OPO4), and lithium triborate (LBO = L1B3O5). Typically, the pump wave is delivered in the form of a laser beam, and the frequency-doubled (second-harmonic) wave is generated in the form of a beam propagating in a similar direction.

[0006] Self-phase modulation is a non-linear optical effect resulting from the interaction of light with matter. In particular, when an ultrashort pulse of light travels in a medium, it will induce a varying refractive index in the medium as a result of the Kerr effect (the Kerr effect, which is also called the quadratic electro-optical effect, refers to a change in the refractive index of a material in response to an applied electric field). This variation in refractive index produces a phase shift in the pulse, thus leading to a change in the frequency spectrum of the pulse.

SUMMARY OF THE DISCLOSURE

[0007] In one aspect, a method is provided for modifying a wavelength of electromagnetic radiation that propagates through a medium. The method comprises (a) providing a medium that exhibits a change in refractive index in response to a change in electric field; (b) impinging electromagnetic radiation from an electromagnetic radiation source onto the medium such that the electromagnetic radiation propagates through the medium; and (c) modifying at least one wavelength of the electromagnetic radiation propagating through the medium by externally inducing a temporal change in the refractive index of the medium. [0008] In another aspect, a device is provided for producing electromagnetic radiation of variable frequency. The device comprises (a) a medium that exhibits a change in refractive index in response to a change in electric field; (b) a source of electromagnetic radiation which is in optical communication with said medium such that electromagnetic radiation from the source propagates through the medium; and (c) a means for externally inducing a temporal change in the refractive index of the medium such that the frequency of electromagnetic radiation propagating through the medium is modified.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] FIG. 1 is a graph of the angle of inclination of the amplitude vector A relative to the beam axis which was generated by solving EQUATIONS 3-5 to describe the dynamic characteristics of supercontinuum formation in air produced by a 100 fs laser pulse.

[0010] FIG. 2 is a graph of laser frequency shift which was generated by solving EQUATIONS 3-5 to describe the dynamic characteristics of supercontinuum formation in air produced by a 100 fs laser pulse.

[0011] FIG. 3 is a diagram of a device which may be utilized in some of the embodiments disclosed herein.

[0012] FIG. 4 depicts the relative time durations and the frequency change induced by the system of FIG. 3, and in particular, shows the laser pulse, voltage pulse ramp up, and time propagation through the crystal, with the expected change in laser frequency and pulse shape.

DETAILED DESCRIPTION

[0013] While the aforementioned methodologies for manipulating the spectral output of high power or high pulse energy lasers may have some desirable attributes, there is still a need in the art for further advances in the control and manipulation of the spectrum of electro-magnetic waves (EMW). In particular, in many cases, the only method available for generating EMWs with the required properties produces waves with spectral outputs that are not optimal for some applications.

[0014] For example, in a laser generator, the available wavelengths of the laser radiation are limited to a number of specific, relatively narrow spectral bands, due to the physical nature of the laser emission. This limitation becomes even more restrictive if a high power or high pulse energy output is required.

[0015] For example, typical high power or high pulse energy lasers operate at wavelengths within the 9-11 μπι, 0.8-1.6 μπι, 532nm, 355nm, and 199-308nm spectral regions. The width of the spectral output of a typical laser is relatively narrow, ranging from tens of kHz to hundreds of GHz. Indeed, the narrow bandwidth of laser output is one of distinctive properties of a laser that allows near diffraction limited focusing (i.e., the spot diameter of a laser beam is almost as small as the limit dictated by the associated physics). Hence, many applications would greatly benefit if the laser output was at a different and variable central wavelength, and if the bandwidth of the laser spectral output was variable (and preferably, significantly wider).

[0016] Unfortunately, optical parametric oscillation produces a narrow spectral output with the center wavelength shifted by approximately factor of 2 towards the shorter wavelength. Similarly, frequency doubling in nonlinear crystals produces a narrow spectral output in which the center wavelength is shifted towards the longer wavelength by a factor that depends on the properties of the nonlinear crystal.

[0017] Self-phase modulation allows for a continuous shift of the laser output. In this method, the wavelength shift is induced by the laser pulse itself due to nonlinear interaction with the material of the crystal. The range of wavelength spread depends on the crystal properties and on the laser beam intensity. In order to achieve noticeable wavelength shifts using self-phase modulation, laser intensities exceeding ~10 ¹³ W/cm ² are typically required. Thus, this method is applicable for lasers producing 0.1 - 1 mJ pulse energies with pulse durations in the range of picoseconds and less.

[0018] In theoretical works considering self-induced nonlinear optical effects, a relationship is deduced that describes changes in the EMW frequency as a result of changes in refractive index. The change of the EMW frequency while propagating a distance dz in the medium is described by EQUATION 1 below:

^{2π άη ζ)} άζ , (EQUATION 1)

A dt where n(z) is the index of refraction, t is time, and λο is the EMW wavelength in a vacuum. This equation is used in nonlinear optics to compute the laser frequency shift due to changes of the refractive index as a function of laser beam intensity.

[0019] To date, it has always been assumed that the change in refractive index in self- induced nonlinear optical effects are themselves self-induced (i.e., that "self-induced phase modulation" occurs). However, in the theoretical considerations giving rise to EQUATION 1, the cause of the change in refractive index is not actually specified.

[0020] The present investigators have found that the change in refractive index may not only be self-induced, but may be externally induced as well. In particular, the present investigators have found that any process that induces a temporal variation in the index of refraction may result in the EMW frequency shift, and hence may be utilized to modify the shape of EMW spectrum. Such processes include, for example, electro-magnetic effects, thermal effects, mechanical effects, or various combinations of the foregoing. It will thus be appreciated that externally induced phase modulation may be utilized to produce modifications in the spectrum of electro-magnetic waves.

[0021] Accordingly, methods are disclosed herein for shifting or sweeping the wavelength of a laser within a large spectral range from UV to IR while maintaining coherency of the laser beam and its energy/power. Simulations of the laser frequency shift during laser beam propagation in a medium with externally induced change of refractive index may be utilized to derive optimal parameters of the nonlinear crystal and high voltage pulses. Devices may be produced in accordance with the teachings herein that shift the wavelength of any pulsed laser in the range of +/- 200nm or more.

[0022] Currently, change of laser wavelength is achieved by using either Optical Parametric Oscillation/ Amplification (OPO/OPA), semiconductor or liquid dye tunable lasers, or by cutting the desired part of the spectrum from the "white light" generated by an ultrashort pulse laser. However, these approaches, which are utilized primarily in laboratory environments, have serious shortcomings. In particular, they yield very small output energy/power and relatively low conversion efficiency, and are costly to implement.

[0023] Systems and methodologies are disclosed herein in which the wavelength shift of the laser is achieved by external modulation of the refractive index of a nonlinear crystal in which the laser beam propagates. This approach may be applied to any pulsed laser with any beam quality and any pulse energy. Unlike a self-induced nonlinear process, this approach does not require phase matching and high laser beam intensity. Moreover, in a preferred embodiment, this approach is equivalent to the use of many different laser systems operating at various wavelengths. Some of the technical underpinnings of this approach are described below.

[0024] The electromagnetic wave (EMW) propagation equation can be rewritten as follows:

ΔΕ = -^ - V(V * E) = 0 (EQUATION 2)

It is usually assumed that the third term in EQUATION 2 is negligibly small. However, the present investigators have found that retaining this term is more accurate and leads to a different equation of EMW propagation in media with an inhomogeneous refractive index, which is given as EQUATION 3 :

dk _x dA _m dk _y dA _m dk _z dA _m

+ 2i x

dx dx + d ^a y" d a ^a —y" + dz d a—z ,

- ^■ (Ae^ _x x+k,yy+k, _z < _e -i{k _x x+k _y y+k _z z) _ Q

\ n

(EQUATION 3)

Solving EQUATION 3 and adding the phase term provides the complete solution:

E = A cos( ) = A cos (ω ₀ ΐ ^~ ^ ?) (EQUATION 4) where A is the electric field amplitude, Φ is the phase, ω ₀ is the frequency of the wave in a vacuum, λ ₀ is the wavelength in a vacuum, t is the time, z is the coordinate, and n is the refractive index of the medium. The frequency of the EMW, defined as the time derivative of the phase, is changing if the refractive index is changing in time, n(t) :

2π dn(t)

ω = ω _η + άω = ω _Γ (EQUATION 5)

λ ₀ dt ^■ dz

where λ ₀ is the EMW wavelength in a vacuum.

[0025] Suitable software may be written which solves the system described by EQUATIONS 3-5. By way of example, FIGs. 1-2 were generated by solving these equations to describe the dynamic characteristics of supercontinuum formation in air produced by a 100 fs laser pulse. FIG. 1 depicts the angle of inclination of the amplitude vector A relative to the beam axis. FIG. 2 depicts the laser frequency shift. [0026] The theoretical foundation of the methods proposed herein for frequency shift due to external modulation of refractive index stems from EQUATION 5. It follows from this equation that the change of the EMW frequency while propagating a distance dz in the media with refractive index that varies with time is:

άω _{κ el} = - -— dz (EQUATION 6)

Usually, the change of laser frequency is assumed to be due to the self-induced change of the refractive index. The externally induced change of the refractive index is considered mainly in the description of phase modulators and change of polarization. The idea that externally induced changes of refractive index can produce large changes in the EMW frequency was neither considered nor practically implemented.

[0027] The External temporal variation of the refractive index resulting in the shift and change of EMW spectrum may be appreciated by suitable modification to EQUATION 6 as shown in EQUATION 7 below:

2n dn , 2π dz , 2n c , dn

d(jd _Kp i = — dz =— dn =— -— dn = ω _η —

^{K eL} λ ₀ dt λ ₀ dt λ ₀ η ^u n

(EQUATION 7)

It is known that the index of refraction can be changed due to various external effects. Here, it is proposed to apply a high voltage pulse, E _ext t), to a crystal that exhibits Pockels effect described by EQUATION 8:

n = n ₀ + rnlE _ext {t) (EQUATION 8) where n ₀ is the index of refraction of a material in the absence of the electric field and r is the constant for nonlinear response of the crystal to the electric field. Substituting EQUATION 8 into EQUATION 7 yields: ά ^ω «« = ^"ω ° nn ₀ ^r †+Z rn ₀ da ^e tt _ext t) (EQUATION 9)

If it is assumed that the externally applied electric field grows linearly as a function of time, then

Eext = ^ ² - (t + τ) = -^- (t + τ) (EQUATION 10)

' ovar ^a ' 0var where E ₀ and U ₀ are the electric field and voltage amplitude, a is the distance between the electrodes, the delay time τ describes the moment when the EMW (or laser) pulse enters the refracting medium and T _Qvar is the electric pulse length. The electric pulse length should be equal to or larger than the sum of the propagation time, T _p = and the laser pulse duration, τ _ρ .

Tovar T _0var ≥ Τ _ρ + τ _ρ = ^ + τ _ρ (EQUATION 11)

Substituting EQUATION 10 into EQUATION 9 and rearranging yields:

(EQUATION 12)

It will be appreciated from the foregoing that the center wavelength of the laser line will be shifted toward lower frequencies (red shift) for an increasing electric field and shifted toward higher frequencies (blue shift) for decreasing electric field. Integration of

EQUATION 12 from t = 0 to exit time t = T = gives the fre uency shift Δω _Κβ1 :

^Δω ΚεΙ _ da> _K ei _

(EQUATION 13)

EQUATION 13 can be approximated as follows:

(EQUATION 14) where τ is within the segment [θ, τ _ρ ] . If the time of propagation of EMW through the length of the refractive medium is much longer than the pulse duration τ _ρ , the frequency shift is the largest: _{¾ rn} 2 I (EQUATION 15)

Lug

Otherwise, the shift of the frequency is smaller by a factor of approximately -^- « 1. The latter conditions are typical for the phase modulation that is dramatically different from the method of frequency shift proposed herein. Thus, from EQUATION 14, it follows that the shift of laser frequency will have maximum value:

Δω _β γ « -ω ₀ τη ² ₀ Ε _0βχί = ω ₀ τη ² ₀ ^ (EQUATION 16)

Then, the corresponding increase of the wavelength will be given by formula

Δλ = A ₀ rn§ ^ (EQUATION 17) where λ ₀ is the laser wavelength in a vacuum.

[0028] Using EQUATION 17, an estimate may be obtained for the shift of the laser wavelength expected from a device that will utilize commonly available technology. For lithium niobate (LiNb0 ₃ ), the electro-optical coefficient at the wavelength of λ ₀ = 632nm is r = 31 x l0 ^"12 m/V, and the refractive index is n ₀ = 2.28. For a high voltage pulse producing amplitude U ₀ = 1 MV and for the thickness of the LiNb0 ₃ crystal a = 5mm, the shift of the laser wavelength will be

Δλ = A ₀ rn§ ^ = (632 nm)(31xl0- ¹² m/V)(2.28) ² (10 ⁶ V/5- ³ m) ~ ±20nm

(EQUATION 18)

For taking into account dispersion and assuming similar Pockels coefficient, the shift of the laser wavelength will be

Δλ = _Q rnl ^ = (1064 nm)(31xl0- ¹² m/V)(2.24) ² (10 ⁶ V/5- ³ m) ~ ±33nm

(EQUATION 19)

[0029] The systems disclosed herein may utilize multiple crystals. After propagation through n crystals, the output laser wavelength will be

λ _η = λ ₀ (l + m (EQUATION 20) Then, for the same laser wavelength of 632nm, the maximum change of the laser wavelength ΔΛ = 203nm. Hence, the wavelength may be selected continuously in the range from 632 nm to 835 nm.

[0030] Various considerations may govern the crystal design in the devices and methodologies disclosed herein. For example, for a laser pulse duration t = lOps, the required optical path inside of the crystal is preferaby larger than approximately

Z «— τ = ^3*1Q8m/s 10 = 1.31mm (EQUATION 21) n ₀ 2.28 ^ '

An optical path length of 13.1cm corresponds to a propagation time that is 100 times larger than the lOps pulse duration and matches a Ins pulser raise time. For a zig zag beam path in a crystal of length L=3cm, this will require N = Z/L = 5 passes. The width of the crystal, W, accommodating 5 passes should be W>N><2s. For laser beam radius s ~ 1mm, the required width W > 10mm. It is well within the current technological capabilities to grow LiNbCb crystals of required orientation and size LxW ^x D = 30mmx l0mmx5mm.

[0031] For a laser pulse duration τ = 10ns, the required optical path inside of the crystal should be larger than approximately

Z «— τ = ^3*1Q8m/s 10 ^"8 s = 1.31m (EQUATION 22) n ₀ 2.28 ^ '

If the optical propagation length in the crystal is 5.65m, the propagation time is 5 times larger than the laser pulse duration.

[0032] For an unoptimized zig zag shape of the laser beam path in a crystal of length L = 6cm, N = Z/L passes are required (that is, N~ 22). In that case, the width of the crystal, W, should be approximately W=Nx2o, where σ is the laser beam radius. For laser beam radius σ ~ 1mm, the required width of the nonlinear crystal should be larger than 4.4cm. It is well within the current technological capabilities to grow LiNb0 ₃ crystals of required orientation and size LxWxD = 6cmx5cmx0.5cm.

[0033] For LiNb0 ₃ , ε ~ 5, then for S=2 cm ² electrode area and crystal thickness a=0.5 cm, the capacitance will be C=8.85 10 ^_12 x5x2 10 ^"4 /5 10 ^"3 = 1.77 10 ^"12 F and the current I _a = CUmax/tau ~ 210 A. The peak power on the load will then be Ppeak « Uala « 25 MW. For an RFP = 1 kHz repetition rate, the average power consumption will be Pav « PmaxxtauxRPF = 2510 ⁶ χ 10 ^"9 χ 1000 =25W.

[0034] A first particular, non-limiting embodiment of the methodology disclosed herein involves the external modulation of refractive index with an electric field. In this embodiment, a laser beam is transmitted through a (typically crystalline) material that exhibits changes in refractive index in response to changes in an applied electric field (that is, the material exhibits the Pockels or Kerr electro-optic effect). Application of a controlled variable voltage to the lateral sides of the material will produce a variable electric field inside of the material, thus resulting in controlled manipulation of the spectrum of the laser radiation on output from the material. Since, at any given moment, the wave front of the laser beam on the output from the material has a high degree of spatial and temporal coherence that is similar to these properties in the original laser beam, the ability to focus the spectrally modified beam into a small spot will be retained.

[0035] For example, in such an embodiment, if the electric field applied is linearly time dependent, the output spectrum will have the same shape as the input spectrum (that is, the spectrum of the laser beam at the input of the device). However, compared to the input spectrum, the output spectrum will be shifted towards lower frequencies (that is, the output spectrum will undergo a red shift) for a linearly increasing electric field, and towards higher frequencies (that is, the output spectrum will undergo a blue shift) for a linearly decreasing electric field. In this case, during the time (T) of light propagation through the optical path (Z) inside of the crystal, the light frequency will change in accordance with EQUATION 2:

Δω = -6> ₀ rn§£, (EQUATION 23) where ω ₀ is the original frequency, r is the constant for the nonlinear response of the crystal to the electric field, and n ₀ is the refractive index of the crystal without electric field. This equation is deduced for the crystal in which the refractive index change depends on the applied electric field according to EQUATION 24: An = rnlE. (EQUATION 24)

[0036] If the applied electric field both increases and decreases during laser propagation in the material, the central frequency of the output laser beam will scan first toward the red portion of the spectrum, and then toward the blue portion of the spectrum. When the laser frequency shift covers the optical range and the variation in the electric field occurs faster that the response time of the detector (for example, the human eye), the observer will perceive the illumination as white light. However, the ability to focus such quasi-white light will be same as for focusing a coherent laser beam.

[0037] A second particular, non-limiting embodiment of the methodology disclosed herein involves the external mechanical modulation of the refractive index of a material. In such an embodiment, a laser beam may be transmitted through a medium that exhibits photoelasticity (that is, a change of refractive index as a function of mechanical strain). In such an embodiment, an acoustic or shock wave will transversely propagate through the laser beam, thereby producing a variation of refractive index and inducing a change in the spectrum of the output laser beam.

[0038] A third particular, non-limiting embodiment of the methodology disclosed herein involves the external electric modulation of refractive index of a medium placed in front of a LIDAR (Light Detection and Ranging) system. A controlled change in the electric field applied to the medium may be utilized to produce a shift (at LIDAR frequencies) in the emission spectrum. This arrangement may be utilized to provide hyperspectral detection (that is, detection at multiple frequencies). Such detection may be useful to thwart certain stealth technologies, or to provide detection in various atmospheric conditions (for example, during rain or sand storms).

[0039] FIG. 3 depicts a diagram of a particular, non-limiting embodiment of a prototypical device in accordance with the teachings herein. The device 101 depicted therein comprises a laser diode 103, a beam splitter 105, a first stable resonator mirror 107, a first polarization rotator 109, a first mirror 111, a crystal medium 113 (comprising a nonlinear crystal 119 with first 115 and second 117 electrodes attached thereto and having an HV electric field region 121), a second mirror 123, a second polarization rotator 125, a second stable resonator mirror 127, a spectrophotometer 129, a data acquisition device 131, an oscilloscope 133, an HV (high voltage) pulser 135 equipped with a pulse multiplier, a pulse generator 137, and a diode laser driver 139.

[0040] The diode laser 103 may be any suitable laser. The beam splitter 105 splits the beam from the diode laser 103 into two beams. The first 107 and second 127 stable resonator mirrors operate in conjunction with the first 109 polarization rotator to cause the pulse to experience multiple passes through the crystal 119 following a zig-zag path. In particular, the first 109 polarization rotator rotates the polarization of the pulse (for example, by 90°) so it is trapped within the crystal medium 113. The second 125 polarization rotator rotates the polarization of the pulse so it escapes the crystal medium 113

[0041] In operation, a pulse is created by the diode laser 103 and is injected into the system by opening the first polarization rotator 109. The pulse may then be removed from the system by opening the second polarization rotator 125. An electric field is applied as the pulse propagates through the system by way of the first 115 and second 117 electrodes. These electrodes are under the control of the HV pulser 135.

[0042] The pulse generator 137 provides synchronous pulses with appropriate delay by opening and closing the first 109 and second 125 polarization rotators and by controlling the pulse coming out of the diode laser 103. The pulse generator 137 also controls the HV pulser 135. The HV pulser 135 is triggered by an incoming pulse and multiplies the pulse into a train of high voltage pulses. The oscilloscope 133 cooperates with the data acquisition system 131 to characterize the performance of the system.

[0043] The particular prototypical device 101 depicted in FIG. 3 consists of two consecutive cells of externally driven nonlinear medium. Each cell may be expected to shift laser wavelength by approximately +/-20nm. Thus, this device may be expected to provide a continuously variable shift in the range +/- 40nm. The device of FIG. 3 may be used in conjunction with a theoretical model of laser frequency shift due to externally induced time variation of the refractive index of nonlinear medium.

[0044] The heart of the device 101 of FIG. 3 is the crystal medium 113. In one embodiment, the crystal medium 113 consists of a nonlinear crystal 119 with first 115 and second 117 metallic electrodes deposited on the top and bottom plane surfaces of the crystal 119. The electrodes 115, 117 are connected to the HV pulse generator 137 by way of the pulser 135. In this embodiment, the HV pulse generator 137 produces l ^"10 ns pulses with a voltage amplitude of about lOOkV. The device 101 shifts the wavelength of the diode laser 103, thus generating pulses with variable duration in picosecond - nanosecond range as shown in FIG. 4. Both the diode laser 103 and HV pulser 135 operate with a repetition rate in the range from 100 Hz to 1 kHz.

[0045] After passing through the nonlinear crystal 119, the output beam of the probe diode laser is analyzed with the spectrophotometer 129. Of course, one skilled in the art will appreciate that various devices may be fabricated in accordance with the teachings herein in which the output pulse is used for any desired purpose or use.

[0046] FIG. 4 depicts the relative time durations and the frequency change induced by the system of FIG. 3, and shows the laser pulse, voltage pulse ramp up, and time propagation through the crystal, with expected change in laser frequency and pulse shape. As seen therein, as the laser pulse propagates through the nonlinear crystal, a change in wavelength or frequency occurs.

[0047] It will be appreciated that the systems and methodologies described herein may be applied to laser systems having any pulse energy (e.g., low, medium, high, extra high) or power. By contrast, existing methodologies produce small pulse energies and cannot exceed certain energy levels (these systems thus produce limited power outputs).

[0048] It will also be appreciated that the systems and methodologies described herein may be applied to any mode composition. By contrast, current methods known to the art are typically applied to a single mode composition. [0049] Any desired beam quality may be obtained using the systems disclosed herein. These include, for example, single mode, multimode, or supermultimode beam qualities. By contrast, typical existing systems may be applied only to very small pulse energies and to very high quality single mode beams.

[0050] The above description of the present invention is illustrative, and is not intended to be limiting. It will thus be appreciated that various additions, substitutions and modifications may be made to the above described embodiments without departing from the scope of the present invention. Accordingly, the scope of the present invention should be construed in reference to the appended claims.