All-optical computing using nonlinear diffraction

Abstract

Apparatuses, systems and methods for all-optical computing are disclosed. An optical computing apparatus includes a nonlinear optical crystal, at least one light source, and a detector. The at least one light source is configured to spatially modulate vectors of operand values onto coherent optical radiation and to direct the spatially modulated coherent optical radiation into the nonlinear optical crystal, thereby exciting propagating modes in the nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over the vectors. The detector is coupled to receive and sense the coherent optical radiation that has propagated through the nonlinear optical crystal so as to decode the computational result.

Description

[0001] ALL-OPTICAL COMPUTING USING NONLINEAR DIFFRACTION

[0002] CROSS-REFERENCE TO RELATED APPLICATION

[0003] This application claims the benefit of U.S. Provisional Patent Application 63 / 549,590, filed February 5, 2024, which is incorporated herein by reference.

[0004] FIELD

[0005] The present invention relates generally to optical computing and more specifically, to methods and apparatuses or systems for all-optical computing using nonlinear diffraction in a variety of manners and configurations.

[0006] BACKGROUND

[0007] Computing with electronics, the prevailing technology for computing for many years, is nearing the end of the Moore's Law era, after which scaling up of computing capabilities will become much more difficult and costly. This raises the need for new physical platforms that can transcend the limitations associated with electronic computational platforms. In this regard, optical systems have the promise to provide such a platform for computations .

[0008] SUMMARY

[0009] The present disclosure provides methods and apparatuses or systems for an all-optical computing platform based on nonlinear diffraction.

[0010] In accordance with aspects of the present disclosure, an optical computing apparatus includes a nonlinear optical crystal , at least one light source , and a detector . The at least one light source is configured to spatially modulate vectors of operand values onto coherent optical radiation and to direct the spatially modulated coherent optical radiation into the nonlinear optical crystal , thereby exciting propagating modes in the nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over the vectors . The detector is coupled to receive and sense the coherent optical radiation that has propagated through the nonlinear optical crystal so as to decode the computational result .

[0011] In various embodiments of the apparatus , the vectors include both data and control information, and the computational result includes nonlinear processing of the data determined by the control information .

[0012] In various embodiments of the apparatus , the at least one light source includes a laser, which is configured to output a laser beam, and a spatial light modulator, which is controlled so as to apply the operand values in modulating the laser beam .

[0013] In various embodiments of the apparatus , the spatially modulated coherent optical radiation is focused into the nonlinear optical crystal so as to cause nonlinear di f fraction due to second harmonic generation .

[0014] In various embodiments of the apparatus , the temperature of the nonlinear optical crystal is adj usted to be below the collinear phase-matching condition of the apparatus .

[0015] In various embodiments of the apparatus , the apparatus includes a heat sink accommodating the nonlinear optical crystal , where the temperature of the nonlinear optical crystal is adj usted via the heat sink to tune the performance of the apparatus .

[0016] In accordance with aspects of the present disclosure , a reservoir computing system includes the disclosed apparatus and partial reflectors configured to direct the spatially modulated coherent optical radiation to pass through the apparatus repeatedly .

[0017] In accordance with aspects of the present disclosure , an optical neural network includes at least one light generator configured to output coherent optical radiation, multiple concatenated computational layers , and a detector . Each layer of the multiple computational layers includes a nonlinear optical crystal and a spatial light modulator configured to spatially modulate vectors of operand values onto coherent optical radiation and to direct the spatially modulated coherent optical radiation into the nonlinear optical crystal , thereby exciting propagating modes in the nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over the vectors . The detector is coupled to receive and sense the coherent optical radiation that has propagated through the concatenated computational layers so as to decode the computational result .

[0018] In various embodiments of the network, the vectors include both data and control information, and the computational result includes nonlinear processing of the data determined by the control information .

[0019] In various embodiments of the network, in one or more layers of the multiple concatenated computational layers , the spatially modulated coherent optical radiation is focused into the respective nonlinear optical crystal so as to cause nonlinear di f fraction due to second harmonic generation .

[0020] In various embodiments of the network, in one or more layers of the multiple concatenated computational layers , the temperature of the respective nonlinear optical crystal serves as a hyper parameter for tuning the performance of the network .

[0021] In various embodiments of the network, one or more layers of the multiple concatenated computational layers includes a heat sink configured to accommodate the nonlinear optical crystal , where the temperature of the nonlinear optical crystal is adj usted via the heat sink to tune the performance of the network .

[0022] In accordance with aspects of the present disclosure , a method for optical computing includes exciting propagating modes in a nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over vectors of operand values via at least one light source , and decoding the computational result via a detector, where the detector is coupled to receive and sense the coherent optical radiation that has propagated through the nonlinear optical crystal . The excitation of the propagating modes includes spatially modulating the vectors onto coherent optical radiation and directing the spatially modulated coherent optical radiation into the nonlinear optical crystal .

[0023] In various embodiments of the method, the vectors include both data and control information, and the computational result includes nonlinear processing of the data determined by the control information . In various embodiments of the method, the at least one light source includes a laser, which is configured to output a laser beam, and a spatial light modulator, which is controlled so as to apply the operand values in modulating the laser beam .

[0024] In various embodiments of the method, the method includes focusing the spatially modulated coherent optical radiation into the nonlinear optical crystal so as to cause nonlinear di f fraction in which spatial modes at the fundamental frequency are di f fracted to spatial modes at the second harmonic frequency .

[0025] In various embodiments of the method, the method includes adj usting the temperature of the nonlinear optical crystal to be below the respective collinear phase-matching condition .

[0026] In various embodiments of the method, the method includes adj usting the temperature of the nonlinear optical crystal .

[0027] In various embodiments of the method, the method implements a reservoir computing system by directing the spatially modulated coherent optical radiation to pass through a spatial light modulator of the light source and the nonlinear optical crystal repeatedly via partial reflectors .

[0028] In accordance with aspects of the present disclosure , a method for implementing an optical neural network includes concatenating multiple computational layers . Each layer is implemented according to a method including exciting propagating modes in a nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over vectors of operand values via at least one spatial light modulator, and decoding a computational result via a detector coupled to receive and sense the coherent optical radiation that has propagated through the concatenated multiple computational layers . The excitation of the propagating modes includes spatially modulating the vectors onto coherent optical radiation and directing the spatially modulated coherent optical radiation into the nonlinear optical crystal .

[0029] In various embodiments of the method, the vectors include both data and control information, and the computational result includes nonlinear processing of the data determined by the control information .

[0030] In various embodiments of the method, the method includes , in one or more layers of the multiple concatenated computational layers , focusing the spatially modulated coherent optical radiation into the respective nonlinear optical crystal so as to cause nonlinear di f fraction in which spatial modes at the fundamental frequency are di f fracted to spatial modes at the second harmonic frequency .

[0031] In various embodiments of the method, the method includes , in one or more layers of the multiple concatenated computational layers , using the temperature of the respective nonlinear optical crystal as a hyper parameter for tuning the performance of the network .

[0032] In various embodiments of the method, the method includes , in one or more layers of the multiple concatenated computational layers , adj usting the temperature of the respective nonlinear optical crystal .

[0033] In various embodiments of the method, the method includes , in one or more layers of the multiple concatenated computational layers , adj usting the temperature of the nonlinear optical crystal to be below the respective collinear phase-matching condition .

[0034] BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The above and other aspects and features of the disclosure will become more apparent in view of the following detailed description when taken in conj unction with the accompanying drawings wherein like reference numerals identi fy similar or identical elements .

[0036] FIG . 1 is an illustration of an exemplary apparatus or system for all-optical computation using a nonlinear optical crystal , in accordance with aspects of the disclosure ;

[0037] FIG . 2 is a flow diagram of a method for implementing all-optical computation, in accordance with aspects of the disclosure ;

[0038] FIG . 3 is diagrams illustrating phase-matching vectors for di f ferent temperatures of a nonlinear optical crystal , in accordance with aspects of the present disclosure ; and

[0039] FIG . 4 is a diagram of an exemplary all-optical arti ficial neural network, in accordance with aspects of the present disclosure .

[0040] It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale . For example , the dimensions and / or aspect ratio of some of the elements can be exaggerated relative to other elements for clarity . Further, where considered appropriate , reference numerals can be repeated among the figures to indicate corresponding or analogous elements throughout the serial views . DETAILED DESCRIPTION

[0041] The benefits of using optics for computing may include easy parallelism, which may be achieved by combining together many optical modes in the same volume ; speed, since it allows performing calculations at the speed of light ; and possibly a favorable power budgets , as linear operations ( like matrix multiplications ) can be performed with very low energy .

[0042] Embodiments of the present disclosure provide methods and apparatuses or systems for an all-optical computing based on optical nonlinear di f fraction in a Second-Harmonic- Generation ( SHG) nonlinear crystal . According to the present disclosure , both data and control fields may be modulated onto a laser light beam and then focused into the nonlinear crystal . The control field processes the data field through both interference and by participating in mode mixing in the nonlinear crystal . Training algorithms may be applied to determine the control fields required to perform a speci fic calculation . The physical outcome according to the present disclosure can be either the field image at the fundamental frequency or at the second- harmonic frequency . Layered architecture may be easily reali zed, allowing to build a deep arti ficial neural network . The disclosed apparatuses , systems and methods reali ze together both linear and nonlinear operations acting on the field, allowing reali zation of universal computational tasks .

[0043] According to the present disclosure , a Spatial Light Modulator ( SLM) is used to modulate a coherent laser beam with data upon which some required processing is to be reali zed . The laser beam is then focused into a nonlinear crystal where second-harmonic-generation takes place . In addition to the data, the SLM also modulates a control field whose purpose is to control the action that the disclosed methods , systems , or apparatuses would reali ze upon the data . The number of degrees of freedom for data representation and processing is determined by the number of pixels on the SLM . Typical numbers are between a million to ten million pixels for SLMs which are available commercially .

[0044] The data and control fields propagate and interact together within the nonlinear crystal . The interaction taking place is characteri zed by both interference of modes and nonlinear wave mixing where pairs of modes combine together to generate a mode at the second-harmonic of the laser frequency . The basis of modes that can be used is one that spans all the possible propagating electromagnetic fields in the system or apparatus , such as the set of all plane waves accommodated by the optical system .

[0045] Reference is now made to FIG . 1 , which is an illustration of an exemplary apparatus or system 100 for all-optical computation using a nonlinear optical crystal 140 . Apparatus 100 includes a light source 115 , a nonlinear optical crystal 140 and a detector 170 . Light source 115 is coupled with nonlinear optical crystal 140 and nonlinear optical crystal 140 is coupled with detector 170 . Light source 115 may include a laser 105 , and an SLM 120 . Laser 105 may be coupled with SLM 120 . Laser 105 may be configured to output a laser beam 110 . Laser 105 may be used as a pump . SLM 120 may be configured to modulate received laser beam 110 . In some embodiments , light source 115 may include multiple light sources ( e . g . , two or more light sources such as light source 115 ) . Detector 170 , such as the CCD camera speci fically shown in FIG . 1 , is configured to receive and sense coherent optical radiation 160 that has propagated through nonlinear optical crystal 140 .

[0046] In some embodiments , light source 115 may further include one or more optical elements , such as a beam expander 125A, a mirror 125B, lenses 125C, 125E and 125G, an aperture stop 125D and a waveplate 125F .

[0047] A portion 110A of laser beam 110 output by laser 105 may be passed through beam expander 125A to receive an expanded laser beam portion 110B of laser beam 110 . Laser portion 110B may be then reflected from mirror 125B to receive a reflected laser beam portion 110C directed towards SLM 120 and such that its wavefront covers SLM 120 . A modulated laser beam portion 110D of laser beam 110 output by SLM 120 may be converged by lens 125C to receive a laser beam portion 110E converged at an aperture of an aperture stop 125D to allow utili zation of a first order di f fraction . A di f fracted laser beam portion 110F of laser beam 110 may be then collimated by lens 125E and passed through waveplate 125F to ensure that laser beam 110 enters nonlinear optical crystal 140 at a suitable or desired polari zation . A collimated and polari zed laser beam portion 110H of laser beam 110 may be then converged by lens 125G at nonlinear optical crystal 140 .

[0048] Nonlinear optical crystal 140 may be located in a heat sink 130 . The temperature of heat sink 130 may be maintained by a temperature controller 135 . Heat sink 130 may be used to adj ust the temperature of nonlinear optical crystal 140 . An optical radiation 160 that has propagated through nonlinear optical crystal 140 may be then filtered by a filter 150A at the exit from nonlinear optical crystal 140, e.g., to allow only the Second Harmonic (SH) radiation generated in nonlinear optical crystal 140 to pass through. The SH-filtered beam may be then further passed through a collimating lens 150B to be received by or imaged on detector 170. The data output by detector 170 may be recorded, stored or analyzed using a computing device 180. Computing device 180 may include a controller and a storage device 180A and a display 180B. The data output by detector 170 may be analyzed by the controller, e.g., by executing instructions stored on the storage device. The data output by detector 170 or the data as analyzed by the controller may be stored via the storage device. The output data or the data as analyzed may be then displayed via display 180B.

[0049] Reference is now made to FIG. 2, which is a flow diagram of a method 200 for implementing all-optical computation. Method 200 will be described while further referring to FIG. 1. According to some aspects, method 200 may be implemented by using apparatus 100 of FIG. 1.

[0050] At a step 220, propagating modes in a nonlinear optical crystal, such as nonlinear optical crystal 140, corresponding to a computational result of linear and nonlinear operations performed over vectors of operand values, may be excited via at least one light source, such as light source 115. The excitation of the propagating modes may include spatially modulating the vectors onto coherent optical radiation and directing the spatially modulated coherent optical radiation into the nonlinear optical crystal (e.g., crystal 140) . The vectors may include both data and control information and the computational result may include nonlinear processing of the data determined by the control information.

[0051] In some embodiments, the at least one light source may include a light generator, e.g., a laser, such as laser 105, and an SLM, such as SLM 120. The laser is configured to output a laser beam, such as laser beam 110. The SLM may be controlled so as to apply the operand values in modulating the laser beam. In some embodiments, the spatially modulated coherent optical radiation (e.g., laser beam portion 110H) may be focused into the nonlinear optical crystal (e.g., nonlinear optical crystal 140) so as to cause nonlinear diffraction due to second harmonic generation .

[0052] At a step 230, the computational result may be decoded via a detector, such as detector 170 of FIG. 1. The detector is coupled to receive and sense the coherent optical radiation (e.g., radiation 160) that has propagated through the nonlinear optical crystal (e.g., nonlinear optical crystal 140) .

[0053] At an optional step 210, the temperature of the nonlinear optical crystal (e.g., nonlinear optical crystal 140) may be adjusted. The temperature of the nonlinear optical crystal may be adjusted, for example, via a heat sink such as heat sink 130 of apparatus 100. The temperature may be adjusted to tune the performance of the computation performed by method 200. When SHG is employed in the nonlinear optical crystal, as shown in FIG. 1, the temperature of the nonlinear optical crystal is preferably tuned to be below the respective colinear phase matching condition for optimized performance. Referring to FIG . 1 , as an example , the data and control fields populate pump laser beam 110 with a large number of spatial modes (plane waves ) which propagate and focus together into nonlinear crystal 140 where due to the high number of spatial modes and mixing property of SHG, numerous SH pathways exist : every two pump photons belonging to either a single mode or to a couple of di f ferent modes would emit , with some probability, an SH photon in a mode that minimi zes the phase mismatch between the triplet of these modes ' photons . The probability of emission for each such SH photon depends on the phase mismatch and on the walk-of f of each modes triplet . The vectorial phase matching condition reads : where Ak is the phase mismatch between the sum of momenta of pump laser beam 110 ( fundamental harmonic ) photons i = 1, 2 and the momentum of the SH photon KSH. The magnitude of the vectors are given with : being the "ordinary" and " extraordinary" temperature-dependent refractive indices and are the fundamental (pump ) and SH wavelengths respectively .

[0054] Reference is now made to FIG . 3 , which shows diagrams illustrating phase-matching vectors for di f ferent temperatures of a nonlinear optical crystal , such as crystal 140 of FIG . 1 . Diagram 300A illustrates collinear phase-matching for T = TPM. Diagram 300B illustrates a collinear configuration when T > TPM. As one can see clearly, the process there is not phase-matched . Further, there is no arrangement , regardless of the relative angles between the wave-vectors of the two pump photons that leads to phase matching . Diagram 300C illustrates a collinear arrangement at T < TPM. The process there is not phase- matched . Diagram 300D illustrates a non-collinear phasematching, which is possible for T < TPM.

[0055] For the collinear case in which ( diagram 300A) , phase matching i s satis fied at the phasematching temperature TPM. It is denoted for brevity When as illustrated in diagram 300B, which means that the SH wave vectors are longer than the FH wave vectors . A trivial geometric argument shows that in this case not only collinear phase-matching is not satis fied but also noncollinear phase matching is impossible . When T < TPM, then (T) and non-colinear phase-matching is possible , as illustrated in diagrams 300C and 300D . All these entail consequences on the performance of disclosed apparatuses , systems and methods as a computational engine which can be understood through a simple argument : When T = TPMmost probably any SH photon generated is created from two FH photons at the same spatial mode . In that case there is no mixing of modes and the system, apparatus or method should not perform better than a linear one . When T < TPMthe possibility for phase-matching non-collinear processes would allow mixing of spatial modes , making the system, apparatus or method richer (more complex ) in its response and should provide better performance . In some embodiments , i f T is set too far apart from TPM, the ef ficiency of SHG pathways may drop too much due to walk-of f between the pump and SH photons and the computational efficiency of the apparatus, system or method may drop as a consequence. When T > TpMr spatial mode mixing is not probable and the emission of SH photons in general is reduced and thus one should expect that the performance of the system, apparatus or method would drop. Thus, optimal performance would be achieved for a temperature which is somewhat below TPMand whose exact value depends on the spatial statistics of the data presented to the system through the SLM. Thus, adjusting the temperature of the nonlinear optical crystal, e.g., nonlinear optical crystal 140, to be below the respective collinear phase-matching condition, e.g., via heat sink 130 and temperature controller 135, would increase the performance of disclosed all-optical computing employing SHG.

[0056] At an optional step, the collinear phase-matching condition of the employed apparatus or system may be determined. In some embodiments, the collinear phasematching condition may be determined experimentally, e.g., by experimentally determining the temperature at which colinear, temperature tuned (also known as ' noncritical ' ) phase matching occurs. The SH power as a function of the nonlinear optical crystal temperature (e.g., nonlinear optical crystal 140) is measured, using only a Gaussianshaped beam applied to the crystal, with a Rayleigh range which is much longer than the crystal. This approximates the application and phase matching of a single spatial mode .

[0057] As noted earlier, embodiments of the present invention can be applied in optical neural network (ONN) computations. The combination of having both linear di f fraction (between the SLM and the nonlinear crystal but also within the nonlinear crystal ) together with nonlinear di f fraction within the nonlinear crystal (where modes in one frequency are di f fracted onto modes at another frequency) allows to treat the disclosed methods , apparatuses and systems as supplying the required mathematical elements for an arti ficial neural network (ANN) . In particular, an ANN is made of layers where each layer reali zes a linear operation acting on the data ( described with matrix multiplication) and a nonlinear operation, usually known as an activation function . In some embodiments , a layer may be reali zed by letting the data make a pass through the nonlinear crystal . For multiple passes , while between passes the beam is incident again on the SLM ( to allow application of further control fields ) , a multi-layer ANN is reali zed . When the number of layers is at least three , the ANN is a "Deep Neural Network" ( DNN) . A DNN is important as it is a universal approximator - able to approximate any well-behaved function and thus can serve as a general-purpose computational platform .

[0058] A method for implementing an optical neural network is thus further disclosed . The method may include concatenating multiple computational layers . Each layer may be implemented according to method 200 of FIG . 2 with the required adaptations .

[0059] Reference is now made to FIG . 4 , which shows a block diagram of an exemplary all-optical arti ficial NN 400 (will be also referred to as ONN 400 ) .

[0060] ONN 300 includes three concatenated computational layers 410 : layer 450A, layer 450B and layer 450C . Layer 450A is the first layer, layer 450B is the middle layer and layer 450C is the last layer of ONN 400. Each layer of ONN 400 includes an SLM, such as respective SLMs 420A, 420B and 420C, and a nonlinear optical crystal, such as respective crystals 430A, 430B and 430C. ONN 400 further includes a light generator 415 (e.g., a laser) and a detector 440. Within each layer, each SLM is coupled with its respective nonlinear optical crystal.

[0061] Light generator is configured to generate a laser beam and direct it into SLM 420A, which is the SLM of the first layer of ONN 400, layer 450A. Each SLM, e.g., SLM 420A, 420B and 4200 is configured to modulate its received optical radiation, e.g., as determined based on the training process, and direct it into the nonlinear optical crystal. The modulated laser beam may then propagate in the coupled nonlinear optical crystal, e.g., respective nonlinear optical crystal 430A, 430B and 4300. The radiation output from nonlinear optical crystals 430A and 430B, except from nonlinear optical crystal 4300, which is the last nonlinear optical crystal of concatenated computational layers 410, is then received by the SLM of the next layer, e.g., SLM 420B and SLM 4200, respectively. Accordingly, the output of each of layers 450A and 450B is used in driving the SLM of each of the next layers, SLMs 420B and 4200 of layers 450B and 4500, respectively. The radiation output from the last nonlinear optical crystal, nonlinear optical crystal 4300, is then received by coupled detector 440 to decode the result. Detector 440 provides the final output of ONN 400. In some embodiments, detector 440 may include two or more detectors.

[0062] In some embodiments, the light generator, such as light generator 415, the SLMs, such as SLMs 420A, 420B and 420C, or the detector of the ONN, such as detector 440 , may be coupled with a control unit , such as a control unit 460 . Control unit 460 may be configured to set or adj ust light generator 415 and SLMs 420A, 420B and 420C, and to receive and optionally process the result of ONN 400 provided by detector 440 . Control unit 460 may include at least one controller or hardware processor . In some embodiments , control unit 460 may be included in ONN 400 .

[0063] In some embodiments , two beams having two wavelengths , FH beam and SH beam, are generated . The FH beam may be generated by a laser and the SH beam may be generated at the nonlinear optical crystal . Once the SH is generated, it also changes the FH beam, thus both beams are being changed when propagating through the nonlinear optical crystal . Thus , in some embodiments of the ONN, the changed FH and SH radiation output from the nonlinear optical crystal , may be filtered in one or more of the layers of the ONN, such that only the changed FH radiation is received by the next layer . In some embodiments , the SH radiation is filtered from the radiation output by the nonlinear optical crystal in each layer of the ONN . Either or both of the FH and SH radiation output by the last layer of the ONN may be measured . I f both are measured two detectors might be needed . Referring to FIG . 4 , the radiation output from nonlinear optical crystal 430A or 430B may be filtered such that only changed FH radiation is received by SLM 420B or SLM 4200, respectively . The FH or the SH radiation output from nonlinear crystal 4300 in last layer 4500 of ONN 400 , may be then measured via detector 440 .

[0064] Apart from using a multi-layer architecture , the disclosed all-optical scheme can also be used in a configuration, generally known as Reservoir Computing (RC ) , in which there is only one hidden recurrent (having feedback loops ) layer, and the adj ustment of control parameters is being done only in the input / output to / from the system . Such a configuration may be reali zed using the disclosed systems , apparatuses or methods by further using mirrors to bounce the optical beam several times through the nonlinear crystal while making sure there is a signi ficant overlap between the beams passing several times through the same region of the crystal . Accordingly, a method for implementing a reservoir computing system is further disclosed . The method may include method 200 of FIG . 2 . The method may further include directing the spatially modulated coherent optical radiation to pass through the disclosed apparatuses or systems ( e . g . , apparatus 100 of FIG . 1 ) , repeatedly, mutatis mutandis , via partial reflectors .

[0065] Training of the disclosed systems , apparatuses or implemented networks to reali ze a desired functionality can be based on a variety of known algorithms , including forward- forward method employing physical local learning or applying backpropagation to a general physical system .

[0066] EXPERIMENTS

[0067] The utility of the disclosed all-optical computing was demonstrated by reali zing an image classi fication task . Furthermore , it was shown that the performance of a system according to disclosed optical computation employing SHG is dependent on the of fset of the optical nonlinear frequency conversion from its co-linear phase-matching condition . The spatial degrees of freedom of SHG were used, employing in effect nonlinear optical diffraction to realize an inference task of classifying hand-written numerical digits. The importance of the non-linearity in this system is recognized by virtue of mixing different spatial modes when the working point of the nonlinear optical process is off the co-linear phase matching condition .

[0068] The experimental setup was as shown in FIG. 1. Laser beam, such as laser beam 105, of 800 picosecond (ps) pulses at a repetition rate of 1 Kilohertz (kHz) and central wavelength of XI = 1064 nanometer (nm) was used as a pump (InnoLas Picolo-AOT MoPa Nd: YVO) while its power was set to P = 1 milliwatt (mW) . The laser beam (e.g., laser beam portion 110 and laser beam portion 110A, in particular) is passed through a beam expander, such as beam expander 125A, and after reflection from a mirror, such as mirror 125B, its wavefront covers a reflective SLM (SLM, Holoeye PLUTO- 2.1 LCOS) , such as SLM 120. This SLM has 1920X1080 pixels, each with 256 available phase levels, which determines the number of degrees of freedom available with this system. With the SLM an encoding scheme described by Bolduc et al. (E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, Opt. letters 38, 3546 (2013) ) was applied and the first order diffraction (other diffraction orders are blocked by an aperture stop) generated by this scheme to realize a background-free amplitude and phase modulated pump beam was used. After the aperture (e.g., of aperture stop 125D) , the beam (e.g., beam portion 110F) was focused into a Mg:CLN nonlinear crystal (e.g., nonlinear crystal 140) , while passing on the way through a A. / 2 plate (e.g., waveplate 125F) , to ensure the beam enters the crystal at the correct polarization to utilize the d31 component of the 2nd order nonlinear susceptibility tensor. The crystal was located inside a custom-made copper heat sink (e.g., heat sink 130) . The temperature of the latter was maintained by an external ElectroTherm / Watlow PT100 S50 controller (e.g., controller 135) with a resolution of 0.1°C. The beam was then filtered by a Thor Labs FGB37 bandpass filter (e.g., filter 150A) at the exit from the crystal, allowing only the SH generated in the crystal to pass through. The SH beam was finally imaged on a Thorlabs DCC1240M camera (1280x1024 pixels, 6.78x5.43 millimeter (mm) ) (e.g., detector 170) . The data from the camera was recorded and analyzed using MATLAB.

[0069] The principle of the computational operation of the system was as described herein below. For any desired computational task for which a given set of data elements (images) was given, a desired output was defined (an image resulting by the desired computation) . The phase of the FH pump beam was imprinted by the input images while the output SH intensity images were detected as the output of the system. It was assumed that there exists a set of control parameters in the form of an image which when superposed with any of the input data images would result in the desired output image for each such input image. An optimization procedure was used to find a control image solution to satisfy the required computation. A formal equivalence between the elements of the system to a computational layer of an Artificial Neural Network (ANN) may be also set as follows: the inputs to the system, at the fundamental frequency, are considered as a set of n plane waves (modes) , each with a specific direction and corresponding amplitudes which may be arranged in a vector: In this notation is the amplitude of the mode having wave-vector k . Prior to entering the crystal, these waves underwent a linear unitary transformation determined by diffraction. The amplitude of the ithSH mode generated within the nonlinear crystal is denoted by This amplitude can be derived under the assumption of small angles and considering all possible FH wave pairs k and kk' . This leads to the SH amplitude of mode i , , to be expressed as a nonlinear function of the vector the phase mismatch. The coefficient K is proportional to component of the nonlinear susceptibility tensor being employed for SHG in the crystal. The nonlinear function plays the role of an activation function in an ANN.

[0070] The task which was solved is partial classification of handwritten numerical digits taken from the Modified National Institute of Standards and Technology (MNIST) database. In particular, the system was optimized to detect a specific digit from all possible ten digits, and the optimization was repeated for each of the digits, resulting in ten control images. Each control image was responsible for the detection of a specific digit. The control images chosen to work with comprise of nine normalized superpixels, each sized 150x150 pixels of the SLM, and with a value ranging from zero to one assigned to every superpixel, representing amplitude modulation of the input image. The size of the handwritten digits on the SLM was selected to cover that of the nine superpixels (450x450 pixels) . For the optimization task a genetic algorithm (GA) was used.

[0071] The output of the system involved obtaining the intensity of the nonlinear field and computing its center of mass:

[0072] Where represent the intensities of each entry in the vector obtained by summing the columns (rows) of the image, xj and yj represent the physical location for each entry in the vector in pixel units. I denotes the total intensity of the image. With these one can calculate the Loss function between two different classes (different handwritten digits) using Euclidean distance:

[0073] Here, represent the mean value of the center of mass over N different images in either class 1 or class 2. F was used to sort all the individuals (candidate solutions) , which are different combinations of nine superpixels, in the population. Half of the lowest F scores were selected to be parents for the next generation and their genetic material was combined to create the offspring. The genetic algorithm generates new populations by applying genetic operators, such as mutation and crossover, to the individuals in the current population. Over time, the population is expected to evolve towards better solutions as the genetic algorithm progress. Ultimately, just a single optimal candidate was picked from the population. In the context of machine learning optimization, an epoch corresponds to a single iteration through the entire training dataset. In the particular scenario, an epoch is defined as the processing of a fixed number N = 30 of training examples belonging to each class. During a single epoch, the optimization procedure was executed once. Following the completion of the training process, the K- Nearest Neighbors (KNN) algorithm was utilized to partition the camera plane into two distinct classes, using a set of Mk = 300 test images from the dataset. Subsequently, an additional set of Mt = 300 test images was employed to identify the test digits, using the center of mass location on the camera plane as a basis. the results showed that it is possible to produce an SHG platform that carries out computations using nonlinear optical diffraction, without relying on digital electronic activation functions or output layers. A primary advantage of this training process is that the physical hardware directly executes the forward pass, which has been demonstrated to be more accurate than with simulation.

[0074] The nonlinear platform was trained to differentiate between two classes: a single handwritten digit (such as ’ O' ) and all other handwritten digits (including ’ 1' , ’ 2’ , ..., and ’ 9' ) . The training was repeated for each digit separately. Additionally, this whole sequence was repeated (for all digits) for various temperatures. In all training sessions a population of P = 16 individuals was initiated, with each superpixel randomly selected from a Uniform distribution. The random variable for each individual, represented as [Ai, A2, . .., A9], adheres to the U(0, 1) distribution. In order to converge to an optimal solution, the platform was trained, at each session, over ten epochs. As an example, the classification held an accuracy (ACC) of 89.67% and a sensitivity rating (Sn) of 94% for the digit 'O', when training was done at T = 113°C.

[0075] The accuracy and sensitivity are defined by specific metrics :

[0076] The accuracy ACC is a measure used to determine the correctness of a classification model. It is computed as the ratio of correctly predicted instances to the total instances. The sensitivity Sn is also known as the true positive rate (TPR) and indicates the proportion of actual positives that are correctly identified as such. TN denotes True Negative, that is, the accurate classification of negative instances. TP means True Positive, correctly identifying positive instances. FP represents False Positive, incorrectly classifying negative instances as positive, and FN signifies False Negative, misclassifying positive instances as negative. Mt = 300 handwritten digits were classified at T =113° for each experiment and achieved mean classification accuracy of 78.87% and mean sensitivity of 86.33% for all the handwritten digits.

[0077] To extend the SH nonlinear platform to a more general classifier capable of classifying all ten handwritten digits in one experiment, one could either increase the degrees of freedom, leading to increased training time and iterations, or incorporate additional passes through the crystal (e.g., by realizing computational layers) .

[0078] As indicated above, by adjusting the temperature of the crystal below the collinear phase-matching condition, the performance of the system may be tuned in its role as a computational engine . For this end, the temperature at which co-linear, temperature tuned ( also known as ’ noncritical ' ) phase matching occurs may be determined experimentally . For that, the SH power was measured as a function of the crystal temperature , using only a Gaussianshaped beam applied to the crystal , with a Rayleigh range which is much longer than the crystal . This approximates the application and phase matching of a single spatial mode . The collinear phase matching temperature TPM was seen in the results to be equal to 114 °C . The results also exhibited the accuracy of the classi fication task undertaken by the system ( averaged over classi fication of all digits ) as a function of temperature . As anticipated, the system indeed demonstrated optimal performance at a temperature of 113 °C (which is lower than TPM) where spatial mode mixing is taking place through non-collinear phase matching . Above TPM such mode mixing is not probable , while somewhat below this temperature the system demonstrated the most ef ficient non-linear dependence on the propagation angle .

[0079] It is also possible to explain by how much the temperature needs to drop below the collinear phase matching condition for optimal results . For this SH may be considered by only a single pair of FH modes at a given temperature . The dependency of the SH on the angle 0 between each of these modes to the generated SH, has the standard phase-mismatch dependency which can easily be calculated in the system for di f ferent temperatures . The general trend of the results is that as the temperature drops below the collinear phase matching conditions , the phase-mismatch curve is centered around a larger value of 0 . For these measurements , an amplitude mask on the SLM was utili zed to create a pump beam that is a superposition of Gaussian and Bessel beams . The di f ference between the measured and analytical curves is attributed to possible temperature di f ferences between the location of the temperature probe adj acent to the crystal and the location where the beam actually passes through the crystal . The average angular spectrum of 100 randomly chosen handwritten digits of the dataset inside the nonlinear crystal were also calculated . This calculation took into account the full path of propagation, including all optical elements , of the images in the system till the nonlinear crystal . It may be assumed that the performance of the system would peak at the temperature at which the angular spectrum of the data is congruent with the phase-matching curve , indicating a matched " acceptance window" of the system to the processed data . It was seen that the angular spectrum curve was close to the phase-matching curve for a temperature of T = 113 °C at which the performance peaked . These results showed that the temperature in the system served as a hyper-parameter for tuning the performance of the system .

[0080] A platform or system for an all-optical inference engine based on nonlinear optical di f fraction according to the disclosure was used for the experiment , as described herein above . A genetic algorithm was used to directly train the platform . The platform was demonstrated through image classi fication experiments using nonlinear SHG . The input data and parameters were encoded into the phase and amplitude ( respectively) of the near-infrared fundamental frequency field using an SLM . The nonlinear crystal produced an SH field, the intensity pattern of which was measured to determine the computation' s outcome . The platform success fully achieved handwritten single digit classi fication, with the predicted digit identi fied by the center of mass ' s location at the system' s output . The temperature of the crystal played a crucial role in the system' s operation and served as a hyper parameter for tuning the system performance . It was shown that the system exhibits optimal performance at a temperature below the colinear PM temperature , where spatial mode mixing of the input data is most ef ficient .

[0081] Although the disclosure is not limited in this regard, by using the term "or" when listing two or more items or options , it is meant that each item, and each plaus ible or feasible combination of the listed items including a combination of all listed items may be considered .

[0082] Embodiments of the present invention are further described in an Appendix entitled "Optical inference using nonlinear optical di f fraction, " which is an integral part of the present patent application .

Claims

CLAIMS1 . Optical computing apparatus , comprising : a nonlinear optical crystal ; at least one light source , which is configured to spatially modulate vectors of operand values onto coherent optical radiation and to direct the spatially modulated coherent optical radiation into the nonlinear optical crystal , thereby exciting propagating modes in the nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over the vectors ; and a detector, which is coupled to receive and sense the coherent optical radiation that has propagated through the nonlinear optical crystal so as to decode the computational result .2 . The apparatus according to claim 1 , wherein the vectors comprise both data and control information, and wherein the computational result comprises nonlinear processing of the data determined by the control information .3 . The apparatus according to claim 1 , wherein the at least one light source comprises a laser, which is configured to output a laser beam, and a spatial light modulator, which is controlled so as to apply the operand values in modulating the laser beam .4 . The apparatus according to claim 1 , wherein the spatially modulated coherent optical radiation is focused into the nonlinear optical crystal so as to cause nonlinear di f fraction due to second harmonic generation .5 . The apparatus according to claim 4 , wherein the temperature of the nonlinear optical crystal is adj usted to be below the collinear phase-matching condition of the apparatus .6 . The apparatus according to claim 1 , the apparatus comprising a heat sink accommodating the nonlinear optical crystal , wherein the temperature of the nonlinear optical crystal is adj usted via the heat sink to tune the performance of the apparatus .7 . A reservoir computing system comprising the apparatus of any of claims 1 - 6 and partial reflectors configured to direct the spatially modulated coherent optical radiation to pass through the apparatus repeatedly .8 . An optical neural network comprising : at least one light generator configured to output coherent optical radiation; multiple concatenated computational layers , each layer comprising : a nonlinear optical crystal ; and a spatial light modulator configured to spatially modulate vectors of operand values onto coherent optical radiation and to direct the spatially modulated coherent optical radiation into the nonlinear optical crystal , thereby exciting propagating modes in the nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over the vectors ; and a detector, which is coupled to receive and sense the coherent optical radiation that has propagated through theconcatenated computational layers so as to decode the computational result .9 . The optical neural network according to claim 8 , wherein in one or more layers of the multiple concatenated computational layers , the spatially modulated coherent optical radiation is focused into the respective nonlinear optical crystal so as to cause nonlinear di f fraction due to second harmonic generation .10 . The optical neural network according to claim 8 , wherein in one or more layers of the multiple concatenated computational layers , the temperature of the respective nonlinear optical crystal serves as a hyper parameter for tuning the performance of the network .11 . A method for optical computing, the method comprising : exciting propagating modes in a nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over vectors of operand values via at least one light source , wherein the excitation of the propagating modes comprises : spatially modulating the vectors onto coherent optical radiation; and directing the spatially modulated coherent optical radiation into the nonlinear optical crystal ; and decoding the computational result via a detector, wherein the detector is coupled to receive and sense the coherent optical radiation that has propagated through the nonlinear optical crystal .12 . The method according to claim 11 , wherein the vectors comprise both data and control information, and wherein the computational result comprises nonlinear processing of the data determined by the control information .13 . The method according to claim 11 , wherein the at least one light source comprises a laser, which is configured to output a laser beam, and a spatial light modulator, which is controlled so as to apply the operand values in modulating the laser beam .14 . The method according to claim 11 , wherein the method comprises focusing the spatially modulated coherent optical radiation into the nonlinear optical crystal so as to cause nonlinear di f fraction in which spatial modes at the fundamental frequency are di f fracted to spatial modes at the second harmonic frequency .15 . The method according to claim 14 , wherein the method comprises adj usting the temperature of the nonlinear optical crystal to be below the respective collinear phasematching condition .16 . The method according to claim 11 , wherein the method comprises adj usting the temperature of the nonlinear optical crystal .17 . A method for implementing a reservoir computing system comprising the method of any of claims 10- 16 and directing the spatially modulated coherent optical radiation to pass through the apparatus repeatedly via partial reflectors .18 . A method for implementing an optical neural network comprising :concatenating multiple computational layers , wherein each layer is implemented according to a method comprising : exciting propagating modes in a nonlinear optical crystal corresponding to a computational result of linear and nonlinear operations performed over vectors of operand values via at least one spatial light modulator, wherein the excitation of the propagating modes comprises : spatially modulating the vectors onto coherent optical radiation; and directing the spatially modulated coherent optical radiation into the nonlinear optical crystal ; and decoding a computational result via a detector coupled to receive and sense the coherent optical radiation that has propagated through the concatenated multiple computational layers .19 . The method according to claim 18 , wherein the method comprises , in one or more layers of the multiple concatenated computational layers , focusing the spatially modulated coherent optical radiation into the respective nonlinear optical crystal so as to cause nonlinear di f fraction in which spatial modes at the fundamental frequency are di f fracted to spatial modes at the second harmonic frequency .20 . The method according to claim 18 , wherein the method comprises , in one or more layers of the multiple concatenated computational layers , using the temperatureof the respective nonlinear optical crystal as a hyper parameter for tuning the performance of the network .

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