All-optical computing using a multimode waveguide

Abstract

Apparatuses, systems and methods for all-optical computing are disclosed. An optical computing apparatus includes a multimode optical waveguide, 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 multimode optical waveguide, thereby exciting propagating modes in the multimode optical waveguide whose overall operation corresponds to a matrix multiplying the vectors. The detector is coupled to receive and sense the coherent optical radiation that has propagated through the waveguide so as to decode a result of the matrix operation. In some embodiments, the multimode optical waveguide is coupled with a gain medium so as to apply a nonlinear operation on the propagating modes.

Description

[0001]

[0002] CROSS-REFERENCE TO RELATED APPLICATION

[0003] This application claims the benefit of U.S. Provisional Patent Application 63 / 549,589, 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 a multimodal waveguide 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 light propagation in a multimode waveguide.

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

[0011] In various embodiments of the apparatus, the vectors include data and control information, and the matrix operation corresponds to processing of the data in accordance with 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 multimode optical waveguide is bent to induce coupling between the propagating modes.

[0014] In various embodiments of the apparatus, the multimode optical waveguide includes a multimode optical fiber.

[0015] In various embodiments of the apparatus, the apparatus includes a mechanical actuator configured to modify the shape of the multimode optical fiber to allow additional mechanical degrees of freedom for controlling the operation of the apparatus .

[0016] In various embodiments of the apparatus, the apparatus includes an optical fiber amplifier coupled with the multimode optical waveguide so as to apply a nonlinear gain to the propagating modes .

[0017] In accordance with aspects of the present disclosure, a reservoir computing system includes the disclosed apparatus and partial reflectors, which are configured to direct the spatially modulated coherent optical radiation to pass through the apparatus repeatedly.

[0018] In various embodiments of the apparatus, the apparatus includes one or more thermo-optic phase-modulators configured to modify the index of refraction profile of the multimode optical fiber to allow additional degrees of freedom for controlling the operation of the apparatus.

[0019] 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 layers includes a multimode optical waveguide, a spatial light modulator, and an optical fiber amplifier. The spatial light modulator is configured to spatially modulate vectors of operand values onto the coherent optical radiation and to direct the spatially modulated coherent optical radiation into the multimode optical waveguide, thereby exciting propagating modes in the multimode optical waveguide corresponding to a matrix operation over the vectors. The optical fiber amplifier is coupled with the multimode optical waveguide so as to apply a nonlinear gain to the propagating modes. The detector is coupled to receive and sense the coherent optical radiation that has propagated through the multiple concatenated computational layers so as to decode a result.

[0020] In various embodiments of the network, the vectors include data and control information, and the matrix operation corresponds to processing of the data in accordance with the control information. In various embodiments of the network, the multimode optical waveguide i s bent to induce coupling between the propagating modes .

[0021] In various embodiments of the network, the multimode optical waveguide includes a multimode opti cal fiber .

[0022] In various embodiments of the network, one or more layers of the multiple concatenated computational layers includes a mechanical actuator confi gured to modi fy the shape of the respective mul timode optical waveguide to allow additional mechanical degrees of f reedom for controlling the operation of the optical neural network .

[0023] In accordance with aspects of the pres ent di sclosure , a method for optical computing includes exciting propagating modes in a multimode optical waveguide corre sponding to a matrix operation over vectors of operand values via at least one l ight source and decoding a result of the matrix operation via a detector , wherein the detector i s coupled to receive and sense the coherent optical radiation that has propagated through the waveguide . The excitation o f the propagating modes includes spati ally modulating the vectors onto coherent optical radiation and directing the spatially modulated coherent optical radiation into the multimode optical waveguide .

[0024] In various embodiments of the method, the vectors include data and control information, and the matrix operation corresponds to proces s ing of the data in accordance with the control information .

[0025] In various embodiments of the method, the at least one light source includes a laser , which i s configured to output a laser beam, and a spatial li ght modulator , which i s controlled so as to apply the operand values in modulating the laser beam.

[0026] In various embodiments of the method, the multimode optical waveguide is bent to induce coupling between the propagating modes.

[0027] In various embodiments of the method, the multimode optical waveguide includes a multimode optical fiber.

[0028] In various embodiments of the method, the method includes modifying the shape of the multimode optical fiber.

[0029] In various embodiments of the method, the method includes applying a nonlinear gain to the propagating modes via an optical fiber amplifier coupled with the multimode optical waveguide.

[0030] 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, the multimode optical waveguide and the optical fiber amplifier repeatedly via partial reflectors.

[0031] In various embodiments of the method, the method includes modifying the index of refraction profile of the multimode optical fiber.

[0032] 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 multimode optical waveguide corresponding to a matrix operation over vectors of operand values via at least one spatial light modulator and applying a nonlinear gain to the propagating modes via an optical fiber amplifier coupled with the multimode optical waveguide. The method further includes decoding a result via a detector, wherein the detector is coupled to receive and sense the coherent optical radiation that has propagated through the concatenating 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 multimode optical waveguide.

[0033] In various embodiments of the method, the vectors include data and control information, and the matrix operation corresponds to processing of the data in accordance with the control information.

[0034] In various embodiments of the method, the multimode optical waveguide is bent to induce coupling between the propagating modes.

[0035] In various embodiments of the method, the multimode optical waveguide includes a multimode optical fiber.

[0036] In various embodiments of the method, the method further includes modifying the shape of the multimode optical waveguide of one or more layers of the concatenated multiple computational layers.

[0037] BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The above and other aspects and features of the disclosure will become more apparent in view of the following detailed description when taken in conjunction with the accompanying drawings wherein like reference numerals identify similar or identical elements.

[0039] FIG. 1 is an illustration of an exemplary apparatus or system for all-optical computation using a multimodal optical fiber, in accordance with aspects of the disclosure; FIG. 2 is a flow diagram of a method for implementing all-optical computation, in accordance with aspects of the disclosure ;

[0040] FIG. 3 is a block diagram of an exemplary all-optical artificial neural network, in accordance with aspects of the present disclosure; and

[0041] FIG. 4 is an image of an exemplary output frame of the apparatus of FIG. 1, in accordance with aspects of the disclosure .

[0042] 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.

[0043] DETAILED DESCRIPTION

[0044] 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.

[0045] Embodiments of the present invention provide methods and apparatuses or systems for implementing all-optical computation based on propagation of coherent light in a multimode waveguide, of which a multimode optical fiber (MMF) is one example. In these methods and apparatuses, both data and control fields are modulated onto a laser light beam and coupled into the waveguide. The control field processes the data field through interference and mode coupling within the waveguide, realizing functions corresponding to multiplication by a matrix.

[0046] In some embodiments, following the linear operation, a nonlinear operation in the data can be realized by using a multimode gain system, of which a multimode gain fiber is an example. Thus, a single tandem of linear and amplifier waveguides can serve as a single computational layer in an artificial neural network, which can be scaled to include more layers, or be used with feedback to realize a Reservoir Computing platform. Such systems and methods can be used as universal solvers similarly to electronic artificial neural networks .

[0047] Some embodiments use an MMF with a large number of modes (~10,000 modes) . This sets the number of degrees of freedom (DOF) of the system. The data and control fields excite a superposition of the MMF modes, and these modes propagate within the fiber. The control-excited modes interfere and couple with the data modes. According to some aspects, the coupling of the modes may be ensured to exist by using a bent fiber. For this purpose, for example, a fiber spooled over a small cylinder (e.g. , having a radius between a few millimeters to a few centimeters) may be used.

[0048] If the field at the input to the MMF is written as a vector of amplitudes of the modes of the MMF, the overall controlled action of the MMF on the data can be described up to this point as the application of a matrix to this vector. That is - the action that is being realized is linear. The control field determines the operation applied to the data field when the matrix operates on a vector whose entries represent both the data and control fields.

[0049] In some embodiments, the MMF is coupled in series with an optical fiber amplifier, based on a multimode fiber with a similar number of modes. The fiber amplifier induces nonlinear gain in the excited modes that are output from the MMF, thus realizing a nonlinear functionality upon the amplitude vector describing the state of the system.

[0050] Another embodiment uses a multimode waveguide fabricated on a photonic chip. The waveguide can be bent to induce mode coupling. Part of the waveguide can include gain media to provide gain when used with an auxiliary pump laser.

[0051] Generally speaking, the data field and control field described above represent vectors of operand values. In each such vector, some of the entries represent a data field and other entries represent a control field. The multimode optical waveguide performs a matrix operation, such as a convolution, over these vectors.

[0052] Thus, some embodiments of the present invention provide optical computing apparatus, comprising a multimode optical waveguide, at least one light source and at least one spatial light modulator, which spatially modulates the light to represent vectors of operand values and directs the spatially modulated optical radiation into the multimode optical waveguide. The modulated radiation excites propagating modes in the multimode optical waveguide corresponding to a matrix operation over the vectors. Further transmission of the radiation through a gain medium induces a nonlinear operation over the vectors. A detector receives and senses the optical radiation that has propagated through the waveguide so as to decode the results of the matrix operation. Reference is now made to FIG. 1, which is an illustration of an exemplary apparatus or system 100 for all-optical computation using a multimodal optical fiber 140. Apparatus 100 includes a light source 115, a multimodal optical fiber 140 and a detector 170. In some embodiments two or more light sources may be used. Light source 115 includes a light generator, e.g. , configured to generate coherent optical radiation, such as laser 105, and a Spatial Light Modulator (SLM) 120. Laser 105 is configured to output a laser beam 110. SLM 120 may be controlled so as to apply the operand values in modulating laser beam 110. SLM 120 spatially modulates laser beam 110 to represent vectors of operand values and directs the spatially modulated optical radiation of laser beam 110 into MMF 140. The modulated radiation excites propagating modes in MMF 140 corresponding to a matrix operation over the vectors. In some embodiments, light source 115 may further include lenses, such as lenses 125A-125D. Lenses 125A and 125B may be configured to expand laser beam portion 110A of laser beam 110 to receive laser beam portion HOB of laser beam 110, configured to fill SLM 120. Lenses 125C and 125D may be configured to couple efficiently laser beam portion HOC reflected off SLM 120 into MMF 140. Detector 170 may be, for example, a digital camera, as shown in FIG. 1. Detector 170 is configured to receive and sense optical radiation 145 which is the outcome of the propagation of laser beam 110 through MMF 140 so as to decode the results of the matrix operation.

[0053] In some embodiments, apparatus 100 may further include a gain medium (not shown) , such as an amplifier fiber, coupled with MMF 140 to receive output optical radiation 145. Further transmission of radiation 145 through a gain medium induces a nonlinear operation over the vectors. The radiation output by the gain medium may be then received and sensed by detector 170.

[0054] In some embodiments, such as embodiments employing a digital camera as a detector, apparatus 100 may further include an objective lens 160 coupled, for example, as shown in FIG. 1, with the distal end of MMF 140. An objective lens 160 magnifies the distal end of MMF 140 and detector 170 (e.g. , a digital camera) records the received speckle pattern .

[0055] In some embodiments employing an MMF, apart from the optical degrees of freedom for controlling the action of the system, additional mechanical degrees of freedom can be employed. For this purpose, a mechanical actuator can be applied to modify the shape of the fiber, for example by bending, twisting or straining the fiber. The shape can be modified so as to optimize the computational performance of the apparatus or system. One embodiment of such a technique can use a spooled fiber on a cylinder over which a second cylinder is used as a cover. An array of piezoelectric actuators may apply pressure to the fiber at different locations .

[0056] With reference to FIG. 1, apparatus 100 may further include a mechanical actuator 150. In the example of FIG. 1, mechanical actuator 150 includes four stages 150A-150D. However, mechanical actuator 150 may include a single stage or multiple stages, other than four stages, or may allow or provide one or multiple points of shape alteration along MMF 140. MMF 140 is attached to stages 150A-150D. Each stage of stages 150A-150D can move along a single axis. As shown in the example of FIG. 1, a proximal portion of MMF 140, which is not attached to mechanical actuator 150, is held stationary between fixed stages 130A and 130B. MMF 140 floats in the air between the attachment points of stages 130A, 130B and 150A- 150D along MMF 140 so that MMF 140 moves only due to the movement of stages 150A-150D. A mechanical actuator may be implemented in various manners as known to a person skilled in the art. In some embodiments, the mechanical actuator may be configured to allow changing of the shape of MMF 140 in an automatic manner.

[0057] In some embodiments, the disclosed apparatuses or systems (e.g. , apparatus 100) may include one or more thermooptic phase-modulators configured to modify the index of refraction profile of the multimode optical fiber to allow additional degrees of freedom for controlling the operation of the apparatuses or systems.

[0058] Reference is now made to FIG. 2, which shows a flow diagram of a method 200 for implementing all-optical computation. Method 200 will be described while further referring to FIG. 1. At a step 220, propagating modes in a multimode optical waveguide are excited via at least one light source, such as light source 115 of apparatus 100 of FIG. 1. The propagating modes correspond to a matrix operation over vectors of operand values. The vectors may include data and control information, and the matrix operation may correspond to processing of the data in accordance with the control information .

[0059] In some embodiments 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 multimode optical waveguide. In some embodiments, the at least one light source, e.g. , light source 115, includes a light generator, e.g. , a laser, such as laser 105, and an SLM, such as SLM 120 of apparatus 100. The laser is configured to output a laser beam, such as laser beam 110. The spatial modulating may be performed via the SLM. The method may further include controlling the SLM so as to apply the operand values in modulating the laser beam. Controlling the SLM may be performed, for example, automatically via a control unit, including, for example, at least one controller or hardware processor. In some embodiments, the multimode optical waveguide is bent to induce coupling between the propagating modes. In some embodiments, the multimode optical waveguide includes an MMF, such as MMF 140 of apparatus 100 of FIG. 1.

[0060] At a step 240, a result of the matrix operation 220 and optional subsequent nonlinear operation 230 is decoded via a detector, such as detector 170 of apparatus 100. The detector is coupled to receive and sense the coherent optical radiation that has propagated through the waveguide, e.g. , radiation 145 of FIG. 1.

[0061] At an optional step 210, the shape of the multimode optical waveguide (e.g. , MMF 140 of apparatus 100 of FIG. 1) is modified to allow additional mechanical degrees of freedom for controlling the interaction between the modes of the optical radiation propagating through the waveguide, as shown for example with respect to MMF 140 via mechanical actuator 150. In some embodiments, modifying the shape of an MMF includes bending, twisting or straining the MMF. In some embodiments, modifying the shape of a multimodal waveguide may be performed in an automatic manner, e.g. , via the controlling unit. At an optional step 230, a nonlinear gain may be applied to the propagating modes via an optical fiber amplifier coupled with the multimode optical waveguide. The optical fiber amplifier may be coupled with the waveguide at the distal end of the waveguide, to receive the optical radiation propagated through the waveguide.

[0062] In some embodiments, the method may further include modifying the index of refraction profile of the multimode optical fiber, e.g. , via one or more thermo-optic phasemodulators to allow additional degrees of freedom for controlling the operation of the method.

[0063] As noted earlier, embodiments of the present invention can be applied in optical neural network (ONN) computations. The present embodiments simplify these sorts of optical computation schemes by using standard multimode waveguides, such as multimode fibers (MMFs) , as they are relatively cheaper and simpler for manufacturing. Another option is to use a multimode waveguide fabricated on a photonic chip. A major benefit of these approaches is that many modes are naturally supported in multimode waveguides, and there is no need for special fabrication (e.g. , increasing the number of cores in a multi-core fiber) to support each and every mode in the system.

[0064] A mechanism inherent to multimode waveguides that can be harnessed to make an all-optical multimode waveguide-based NN is the strong dependence of the multimode waveguide transmission matrix (TM) on its shape. Several processes, among which are bending-induced Berry phase, refractive index profile variation, and birefringence, change the way light propagates inside the multimode waveguide under different bending conditions. This difference is evident in the changing of the TM of the multimode waveguide, which is the matrix that describes the relation between the field at the input to the waveguide and that at the output of the waveguide. Based on these principles, particularly in low-light conditions that do not give rise to nonlinear effects, a multimode waveguide can implement the linear operation between two layers of an artificial neural network, where light propagation in the multimode waveguide, which is described mathematically by the waveguide's TM, will be equivalent to the matrix multiplication typical between layers in an artificial neural network.

[0065] Additionally, since the optical intensity is a nonlinear function of the electric field, detecting the intensity at the output of the waveguide can implement the non-linear activation function of the neural network. Moreover, tweaking the entries of the waveguide's TM, which are analogous to the weights of the neural network, can be achieved by controlling the shape of the multimode waveguide.

[0066] ONNs based on the present embodiments include one or more computational layers . The overall action of a linear multimode waveguide and a gain medium can be treated as a computational layer in disclosed artificial neural networks. Such units can be concatenated to realize a deep neural network. From the theory of neural networks, it is known that it is enough to use three layers to realize a universal approximator, which is a computational system that can approximate any well-behaved function with appropriate training and sufficient degrees of freedoms. In some embodiments, a two-layer architecture can be realized with only a single pair of linear multimode waveguides and gain media by using beam splitters at the two ends of the system, allowing the light to pass twice through the system. In some embodiments, a single SLM can also be used for this purpose, for example, by dedicating two different areas of the SLM to two different modulations coupled to the fiber.

[0067] In some embodiments, partial mirrors may be used at the ends of an apparatus or system made of a single computational layer. The information will go then back and forth through the apparatus, allowing for feedback, although there is just a single layer at which the control of the apparatus is applied. Such an architecture is based on Reservoir Computing techniques, and it excels at processing time series data while using limited computational resources.

[0068] Training of the disclosed optical NNs to realize a desired functionality can be based on a variety of algorithms, such as backpropagation- f ree methods employing physical local learning or applying backpropagation to a general physical system.

[0069] Reference is now made to FIG. 3, which shows a block diagram of an exemplary all-optical artificial NN 300 (will be also referred to as ONN 300) . ONN 300 includes three concatenated computational layers 310: 370A, 370B and 370C. Layer 370A is the first layer, layer 370B is the middle layer and layer 370C is the last layer of ONN 300. Each layer of ONN 300, such as layers 370A, 370B and 3700, includes an SLM, such as respective SLMs 320A, 320B and 3200, a multimode optical waveguide, such as respective multimode optical waveguides 330A, 330B and 3300, and a fiber amplifier, such as respective fiber amplifiers 340A, 340B and 3400. ONN 300 further includes a light generator 315 (e.g. , a laser) and a detector 350. Within each layer, each SLM is coupled with its respective multimode optical waveguide and each multimode optical waveguide is further coupled with its respective fiber amplifier.

[0070] Light generator 315 is configured to generate a laser beam and direct it into SLM 320A, which is the SLM of the first layer of ONN 300, layer 370A. Each SLM, e.g. , SLM 320A, 320B and 320c is configured to modulate its received optical radiation, as determined based on the training process, and direct it into the multimode optical waveguide. The modulated laser beam may then propagate in the coupled multimode optical waveguide (e.g. , an MME) , e.g. , respective multimode optical waveguides 330A, 330B and 330C. The radiation output from the multimode optical waveguide may then go through the coupled fiber amplifier, e.g. , respective fiber amplifiers 340A, 340B and 340C. Each fiber amplifier is configured to induce nonlinear gain in the excited modes that are output from the respective multimode optical waveguide. The radiation output from fiber amplifiers 340A and 340B, except from fiber amplifier 340C, which is the last amplifier of concatenated computational layers 310, is then received by the SLM of the next layer, e.g. , SLM 320B and SLM 320C, respectively. Accordingly, the output of each of layers 370A and 370B is used in driving the SLM of each of the next layers, SLMs 320B and 320C of layers 370B and 370C, respectively The radiation output from the last fiber amplifier, fiber amplifier 340C, is then received by coupled detector 350 to decode the result. Detector 350 provides the final output of ONN 300.

[0071] In some embodiments, the light generator, such as light generator 315, or the detector of the ONN, such as detector 350, may be coupled with a control unit, such as a control unit 360. Control unit 360 may be configured to set or adjust light generator 320 and to receive and optionally process the result of ONN 300 provided by detector 350. Control unit 360 may include at least one controller or hardware processor. In some embodiments, control unit 360 may be included in ONN 300.

[0072] A method for implementing an Optical Neural Network (ONN) is further disclosed. The method may include concatenating multiple computational layers in series, as shown, for example, in FIG. 3, where each layer may be implemented according to method 200 of FIG. 2 with the required adaptations. Each computational layer of the ONN may be implemented by exciting propagating modes in a multimode optical waveguide (such as MMF 140 of apparatus 100 of FIG. 1) corresponding to a matrix operation over vectors of operand values via at least one SLM (such as SLM 120 of apparatus 100) . 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 multimode optical waveguide. A nonlinear gain may be then applied to the propagating modes via an optical fiber amplifier coupled with the multimode optical waveguide. In some embodiments, the method may further include modifying the shape of the multimode optical waveguide of one or more layers of the concatenated multiple computational layers, as shown, for example, in Fig. 1, and as described, for example, with respect to method 200 of FIG. 2.

[0073] A method for implementing a reservoir computing apparatus or system is further disclosed. The method includes method 200 of FIG. 2. The method further includes directing the spatially modulated coherent optical radiation to pass through the apparatus repeatedly via partial reflectors. EXPERIMENTS

[0074] An all-optical inference engine (will be also referred herein as "the system") in accordance with the disclosed apparatuses, systems and methods was implemented by the inventors, and several experiments were conducted to examine the performance of the engine. In these experiments, a classification of digits was demonstrated. Digits from the Modified National Institute of Standards and Technology (MNIST) data-set were input to an MMF based on light concentration at specific points at the output of the MMF by means of fiber shape optimization. The system was found to be capable of classifying a single digit from all other digits based on light intensities at two small areas at the output of an MMF, enabling an optical classification of the digits. Both the position of four points along an MMF, as well as the best positions to concentrate light at the fiber's output for different digits, were optimized using a genetic algorithm to maximize the prediction accuracy. The experiments further demonstrated that mechanical degrees of freedom can be utilized for all-optical computation in an MMF.

[0075] An illustration of the system is shown in FIG. 1 (system 100) . The purpose of the system was to enable the classification of digits input to an MMF by finding the best shape of the fiber (under some constraints) that causes a concentration of light at specific points at the output of the fiber.

[0076] For this purpose, in an experiment, a 2m long MMF (Thorlabs FG105LCA, core diameter 105 pm, 0.22NA; MMF 140) was attached to four stages 150A-150D (Standa 8MT175, 0.31 m resolution) that can move along a single axis. As shown in FIG. 1, the rest of fiber 140 was held stationary between fixed points 130A and 130B throughout the experiment. As was indicated hereinabove with respect to FIG. 1, fiber 140 moves only due to the movement of stages 150A-150D. The temperature in the lab was controlled with precision of 1°C during the experiments. Light from a 532nm-wavelength continuous wave (CW) laser 105 was first expanded by lenses 125A and 125B to fill SLM 120 (Holoeye Pluto) . The surface of SLM 120 was imaged onto the proximal end of fiber 140 using a 4h system that consists of lenses 125C and 125D so that the light input to fiber 140 was phase-modulated. The distal end of fiber 140 was magnified using an objective lens 160 (Newport M-lOx) and a digital camera 170 recorded the speckle pattern.

[0077] In order to enable classification of the digits, a small window, which is a small square area on the camera, was assigned to each possible class of the digits. In the experiment a recognition of a single digit only was demonstrated, and thus, two classes were received: "true" - the digit is the one that its recognition is desired, and "false" - the digit is a digit other than the digit which its recognition is desired. Reference is now made to FIG. 4, which is an image of an exemplary output frame 400 of system 100 of FIG. 1, where the system has to recognize the digit 7. As shown in FIG. 4, (xt,yt) and (xr,yr) are used to denote the xy coordinates of the top left corner of the "true" and "false" windows, indicated 410 and 420, respectively. The predicted class of the digit was the class that belongs to the window with the highest intensity among the two windows. As a result, the purpose of the training process was to find the fiber shape, i.e. , the position of four stages 150A-150D, that maximizes the intensity at the correct window for each digit input to fiber 140, according to the digit' s class. The ability of the system to concentrate light at specific points on camera 170 is limited both by the number of guided modes of fiber 140 and by the number of stages 150. The fiber that was used carries approximately 9000 guided modes, of which approximately 400 are excited on average. For this reason, it was considered that the number of stages 150 limited the performance of the system.

[0078] In order to allow for better classification accuracy, additional degrees of freedom were added to the system in the form of a second optimization layer that also finds the best positions of the windows for each shape of fiber 140. This means that for each configuration of stages 150 (i.e. , a shape of fiber 140) , the speckle patterns of the digits were recorded by camera 170, and another optimization algorithm was used to find the locations of the windows in the frame of camera 170 that optimize performance. The shape of fiber 140 and window positions were optimized in layers, rather than being jointly optimized, because it was much more efficient computationally .

[0079] The power in each window in the system is analogous to the outputs of a NN. The powers were first normalized by the largest one of them and then passed to a softmax function. The loss used was the cross-entropy loss used in many deep learning procedures, with one-hot encoding. The power at the window that corresponds to the I'th class when the i'th sample is input to fiber 140 is denoted by Pi1, where 1 E { t,f} denoting the set of "true" or "false". The normalized powers are thus . The normalized powers were passed to the softmax function to obtain the probability that the i'th sample belongs for the I'th class, as follows: if thetrue class of the i'th sample is denoted by li, the loss that corresponds to the i'th sample is then: . This loss awards high power at the window of the true class of the sample compared to that in the other window.

[0080] Both optimization layers (for the shape of fiber 140 and window position optimizations) were implemented using genetic algorithms .

[0081] To train the system, a training set was chosen out of the full MNIST data-set of handwritten numerals. This set was then randomly divided into multiple batches of equal sizes, and at every iteration of the shape optimization algorithm, a different batch was used to evaluate the individuals. In each iteration of the algorithm, the stages traversed through all possible individuals (shapes of fiber 140) in the population, and for each of these shapes, all the digits of the current batch were projected into fiber 140. Since it was desired to optimize the locations of the windows as well, the loss of the n' th shape of fiber 140 at the k'th batch, wasthe minimal loss among window locations based on the speckle patterns of the samples m that batch. Mathematically this can be written as follows : where Ik is the set of all indices of the samples in the k'th batch. At the end of each ition, a new population of shapes of fiber 140 was generated, and it was passed to the next iteration of the algorithm. As was stated hereinabove, the minimization over window locations was the second layer of optimization in the experiment, and it was implemented using a genetic algorithm as well.

[0082] At the end of the training phase, an additional validation stage was conducted, where the best system configuration (a shape of fiber 140, along with its corresponding window positions) was chosen based on its loss in the validation set, that included other samples from the MNIST dataset. To measure the performance of the chosen system, an additional test set was chosen from the MNIST dataset, where the system predicted the class of each sample merely by choosing the window of highest power in the speckle pattern that corresponds to it. In each of the datasets (train, validation, and test) , half the samples belong to the digit the system has to recognize, while the rest were of the other digits in equal numbers. The sizes of these sets, however, were different. It is worth mentioning that in the shape optimization of fiber 140, the optimization was done in a range of 10mm for each stage.

[0083] To demonstrate the operation of the system, an experiment was conducted aiming to distinguish the digit 7 from all other digits. In the experiment, the train, validation, and test sets included 324, 90, and 180 samples respectively. The train set was randomly split into six batches, which is also the number of iterations of the genetic algorithm. The duration of the optimization phase (which includes training and validation) was 2580 seconds. Although inference is optical in principle, the overall speed of the system depends on the time it takes to measure the intensity at the two windows . These times depend on the specific detector and can be quite fast with the use of dedicated hardware such as fast photodiodes. The overall accuracy of the system over the test set was 81%.

[0084] A few points can be noted from the results. First, for the samples that were classified correctly, the intensity in the window that corresponds to the correct class of the sample is much higher compared to that in the other window. Moreover, the speckle dot in the window that corresponds to the correct class of the sample is among the strongest speckle dots in the whole speckle pattern. An additional aspect that is evident in the results is that in the samples that were classified incorrectly, the difference in the intensities in the two windows is much smaller than that in the samples that were classified correctly.

[0085] Nine more experiments were performed, where in each of experiments the system was trained to recognize a different digit from all other digits. The sets were randomly sampled from the whole MNIST dataset for every experiment. It should be emphasized that the results of the experiments were different, and thus, for recognizing each digit, a different shape of fiber 140 and window locations were used. The median and the average of the accuracies of the results of the ten experiments were 80% and 80.83% respectively. While recognizing some digits achieved relatively lower accuracies, such as the cases of the digits 8, 2, and 3, recognizing the digits 0 and 1 resulted in accuracies of 91% and 88% respectively. It is possible that digits such as the ones that obtained a lower accuracy, are harder to recognize because they might resemble in shape other digits, which leads to more similar mode distribution. In all experiments the "true" rates were higher than the "false" rates. Improving the accuracy of the classification, enabling classification into more classes (ideally a full classification of 10 classes) , and allowing for focusing the light into predefined locations at the output of fiber 140, thus eliminating the need to optimize these locations, may improve the performance of system 100. All of these may be related (but not only) to the very limited number of mechanical degrees of freedom in system 100, which is the number of control points along fiber 140. Adding more control points along fiber 140 can aid to better tailor the TM of fiber 140 to the specific desired functionality. This may enable focusing the light into predefined locations, as well as focusing the light into more points, enabling classification into more classes. Along with adding more control points along fiber 140, the accuracy of the system could possibly be improved by harnessing non-linear processes in the fiber, e.g. , as indicated hereinabove, which will enable separation of classes that are not linearly separable.

[0086] To test the stability of such a system, it was trained, and repeating tests were conducted for an hour. During this hour the accuracy did not fall more than 5% below its initial value, and the maximal temperature variation in the lab was 0.2°C. This means that temperature control of the package can be used to keep the system reproducible.

[0087] In alternative embodiments, the fiber (e.g. , fiber 140) may be spooled to make the system more compact, and packed inside a thermally controlled package for thermal and vibrational insulation.

[0088] In these experiments an all-optical inference engine based on shape optimization of an MMF that is capable of recognizing a single digit from the MNIST data-set by light concentration at two points at the output of the fiber with an average accuracy of 80.83% was implemented. The optimization of the shape of the fiber, as well as that of the positions to concentrate light, was achieved using genetic algorithms. Alternative embodiments may include adding more control points along the fiber, as well as harnessing nonlinear propagation in the fiber for improving the accuracy, allowing for concentrating the light at desired points (rather than optimized ones) , and allowing for a full classification of the digits.

[0089] The embodiments described above are cited by way of example, and the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.

Claims

CLAIMS1 . Optical computing apparatus , comprising : a multimode optical waveguide ; 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 multimode optical waveguide , thereby exciting propagating modes in the multimode optical waveguide corresponding to a matrix operation over the vectors ; and a detector, which is coupled to receive and sense the coherent optical radiation that has propagated through the waveguide so as to decode a result of the matrix operation .2 . The apparatus according to claim 1 , wherein the vectors comprise data and control information, and wherein the matrix operation corresponds to processing of the data in accordance with 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 multimode optical waveguide is bent to induce coupling between the propagating modes .5 . The apparatus according to claim 1 , wherein the multimode optical waveguide comprises a multimode optical fiber .6 . The apparatus according to claim 5, wherein the apparatus comprises a mechanical actuator configured to modi fy the shape of the multimode optical fiber to allow additional mechanical degrees of freedom for controlling the operation of the apparatus .7 . The apparatus according to any of the preceding claims , and comprising an optical fiber ampli fier, which is coupled with the multimode optical waveguide so as to apply a nonlinear gain to the propagating modes .8 . A reservoir computing system comprising the apparatus of claim 7 and partial reflectors configured to direct the spatially modulated coherent optical radiation to pass through the apparatus repeatedly .9 . The apparatus according to claim 1 , wherein the apparatus comprises one or more thermo-optic phasemodulators configured to modi fy the index of refraction profile of the multimode optical fiber to allow additional degrees of freedom for controlling the operation of the apparatus .10 . An optical neural network comprising : at least one light generator configured to output coherent optical radiation; multiple concatenated computational layers , each layer comprising :a multimode optical waveguide ; a spatial light modulator configured to spatially modulate vectors of operand values onto the coherent optical radiation and to direct the spatially modulated coherent optical radiation into the multimode optical waveguide , thereby exciting propagating modes in the multimode optical waveguide corresponding to a matrix operation over the vectors ; and an optical fiber ampli fier, which is coupled with the multimode optical waveguide so as to apply a nonlinear gain to the propagating modes ; and a detector, which is coupled to receive and sense the coherent optical radiation that has propagated through the multiple concatenated computational layers so as to decode a result .11 . The optical neural network according to claim 10 , wherein one or more layers of the multiple concatenated computational layers comprises a mechanical actuator configured to modi fy the shape of the respective multimode optical waveguide to allow additional mechanical degrees of freedom for controlling the operation of the optical neural network .12 . A method for optical computing, the method comprising : exciting propagating modes in a multimode optical waveguide corresponding to a matrix operation over vectorsof 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 multimode optical waveguide ; and decoding a result of the matrix operation via a detector, wherein the detector is coupled to receive and sense the coherent optical radiation that has propagated through the waveguide .13 . The method according to claim 12 , wherein the vectors comprise data and control information, and wherein the matrix operation corresponds to processing of the data in accordance with the control information .14 . The method according to claim 12 , 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 .15 . The method according to claim 12 , wherein the multimode optical waveguide is bent to induce coupling between the propagating modes .16 . The method according to claim 12 , wherein the multimode optical waveguide comprises a multimode optical fiber .17 . The method according to claim 16 , wherein the method comprises modi fying the shape of the multimode optical fiber .18 . The method according to any of the preceding claims , wherein the method comprises applying a nonlinear gain to the propagating modes via an optical fiber ampli fier coupled with the multimode optical waveguide .19 . A method for implementing a reservoir computing system comprising the method of claim 18 and directing the spatially modulated coherent optical radiation to pass through a spatial light modulator of the light source , the multimode optical waveguide and the optical fiber ampli fier repeatedly via partial reflectors .20 . The method according to claim 12 , wherein the method comprises modi fying the index of refraction profile of the multimode optical fiber .21 . 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 multimode optical waveguide corresponding to a matrix operation 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; directing the spatially modulated coherent optical radiation into the multimode optical waveguide ; and applying a nonlinear gain to the propagating modes via an optical fiber ampli fier coupled with the multimode optical waveguide ; and decoding a result via a detector, wherein the detector is coupled to receive and sense the coherent optical radiation that has propagated through the concatenating multiple computational layers .22 . The method according to claim 21 , wherein the method further comprises modi fying the shape of the multimode optical waveguide of one or more layers of the concatenated multiple computational layers .

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