System and method for multi-transverse mode multiply-and-accumulate (MTM-mac) operation

Abstract

An optical computing system comprises light sources configured to emit input optical signals having optical modes associated therewith, optical modulators configured to receive the input optical signals and to modulate an intensity thereof for generating modulated optical signals, beam splitters configured to split the modulated optical signals onto optical paths each having a given optical mode associated therewith, weight banks configured to generate weighted optical signals based on the modulated optical signals, each weight bank optically coupled to a respective optical path and configured to excite the given optical mode for generating a weighted optical signal, a superposition unit configured to noncoherently superpose the weighted optical signals onto an output optical waveguide, and an accumulation unit optically coupled to the output optical waveguide for receiving the weighted optical signals thereat, the accumulation unit configured to noncoherently accumulate the weighted optical signals for completing at least one multiply-and-accumulate (MAC) operation.

Description

[0001] SYSTEM AND METHOD FOR MULTI-TRANSVERSE MODE MULTIPLY-AND-ACCUMULATE (MTM-MAC) OPERATION

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] The present application claims the benefit of Unites States Provisional Application No. 63 / 569,326 filed on March 25, 2024, the contents of which are hereby incorporated by reference.

[0004] FIELD

[0005] The improvements generally relate to the field of photonic computation and modulation, and more particularly to multi-transverse mode multiply-and-accumulate (MTM-MAC) operations.

[0006] BACKGROUND

[0007] Photonic accelerators potentially provide promising solutions to the ever-increasing compute-resource intensive processing demands. Multiply-and-accumulate (MAC) operation, as a cornerstone of these processing tasks, was demonstrated in the optical domain using microring resonator (MRR) weight banks. The weighting operation is attained by tuning the MRRs in and out of resonance and hence intensity modulating the signal at a certain wavelength accordingly, while an intensity modulated array of Wavelength Division Multiplexing (WDM) signals (A1 :An) prepares the input vector for the multiplication (dot product) operation. A photodetector incoherently accumulates the weighted optical signal completing the MAC operation.

[0008] Due to the susceptibility of MRRs to thermal fluctuations and presence of inter-channel crosstalk in such WDM systems, attaining a reasonable weight resolution remains challenging. Although photonic accelerators are desired to achieve a comparable computational resolution with their electronic counterparts, improving the weight resolution deals with two major challenges. First, higher weight accuracy is only achievable at the cost of increased power consumption of the control circuitry, which deteriorates the system’s overall energy efficiency. Second, the resonance extinction ratio is inherently finite and MRRs with higher resonance quality factor not only demand for more complex and power-hungry control circuitry but also slow down the system due to a larger photon lifetime within the resonator. Therefore, there is a need for improvement.

[0009] SUMMARY

[0010] In accordance with one aspect, there is provided an optical computing system, the system comprising a plurality of light sources configured to emit a plurality of input optical signals having at least two optical modes associated therewith, a plurality of optical modulators configured to receive the plurality of input optical signals and to modulate an intensity thereof for generating a plurality of modulated optical signals, a plurality of beam splitters configured to split the plurality of modulated optical signals onto a plurality of optical paths, each optical path having a given one of the at least two optical modes associated therewith, a plurality of weight banks configured to generate a plurality of weighted optical signals based on the plurality of modulated optical signals, each weight bank optically coupled to a respective one of the plurality of optical paths and configured to excite the given optical mode for generating a weighted optical signal, a superposition unit configured to noncoherently superpose the plurality of weighted optical signals onto an output optical waveguide, and an accumulation unit optically coupled to the output optical waveguide for receiving the plurality of weighted optical signals thereat, the accumulation unit configured to noncoherently accumulate the plurality of weighted optical signals for completing at least one multiply-and-accumulate (MAC) operation.

[0011] In at least one embodiment in accordance with any previous / other embodiment described herein, the accumulation unit is configured to noncoherently accumulate the plurality of weighted optical signals for completing the at least one MAC operation comprising a multiplication of a weight matrix and one of an input vector and an input matrix.

[0012] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of optical modulators is configured to modulate the intensity of the plurality of input optical signals for generating the plurality of modulated optical signals representative of the one of the input vector and the input matrix.

[0013] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of weight banks is configured to generate the plurality of weighted optical signals representative of the weight matrix. In at least one embodiment in accordance with any previous / other embodiment described herein, the optical computing system further comprises a Wavelength Division Multiplexing (WDM) unit for combining the plurality of input optical signals into a multiplexed signal.

[0014] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of beam splitters is a first plurality of beam splitters and the plurality of optical paths is a first plurality of optical paths, and the optical computing system further comprises a second plurality of beam splitters coupled to the WDM unit and configured to split the multiplexed signal along a second plurality of optical paths for output to the plurality of optical modulators.

[0015] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of optical modulators are arranged in at least two branches, each branch comprising an array of the plurality of optical modulators and having a given one of the at least two optical modes associated therewith.

[0016] In at least one embodiment in accordance with any previous / other embodiment described herein, the first and the second plurality of beam splitters comprise one of multimode interferometers (MMIs), multimode directional couplers, and multimode splitters.

[0017] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of optical modulators comprise one of microring modulators (MRMs), microring resonators (MRRs), Mach-Zehnder modulators (MZMs), and Mach-Zehnder interferometers (MZIs).

[0018] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of weight banks comprise one of microring resonators (MRRs), phase change materials (PCMs), and Mach-Zehnder interferometers (MZIs).

[0019] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of weight banks comprise a plurality of multi-transverse mode microring resonators (MRRs) configured to implement a most significant bit of each weight of the weight matrix, and a plurality of fundamental mode MRRs configured to implement a least significant bit of each weight. In at least one embodiment in accordance with any previous / other embodiment described herein, wherein the superposition unit comprises one of a plurality of multimode interferometers (MMIs) and a plurality of multimode combiners.

[0020] In at least one embodiment in accordance with any previous / other embodiment described herein, the accumulation unit comprises one of a plurality of mode-insensitive photodetectors a plurality of multiport photodetectors.

[0021] In at least one embodiment in accordance with any previous / other embodiment described herein, the at least two optical modes comprise one of at least two transverse electric (TE) modes, at least two quasi-TE modes, at least two transverse magnetic (TM) modes, and at least two quasi-TM modes.

[0022] In accordance with another aspect, there is provided an optical computing method, the method comprising emitting a plurality of input optical signals having at least two optical modes associated therewith, modulating an intensity of the plurality of input optical signals for generating a plurality of modulated optical signals, splitting the plurality of modulated optical signals onto a plurality of optical paths, each optical path having a given one of the at least two optical modes associated therewith, generating a plurality of weighted optical signals based on the plurality of modulated optical signals by exciting the given optical mode in each optical path, and noncoherently superposing and accumulating the plurality of weighted optical signals for completing at least one multiply- and-accumulate (MAC) operation.

[0023] In at least one embodiment in accordance with any previous / other embodiment described herein, the at least one MAC operation comprises a multiplication of a weight matrix and one of an input vector and an input matrix.

[0024] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of modulated optical signals are representative of the one of the input vector and the input matrix.

[0025] In at least one embodiment in accordance with any previous / other embodiment described herein, the plurality of weighted optical signals are representative of the weight matrix. In at least one embodiment in accordance with any previous / other embodiment described herein, the optical computing method further comprises combining the plurality of input optical signals into a multiplexed signal, and splitting the multiplexed signal along a plurality of additional optical paths for output to the plurality of optical modulators.

[0026] In at least one embodiment in accordance with any previous / other embodiment described herein, the at least two optical modes comprise one of at least two transverse electric (TE) modes, at least two quasi-TE modes, at least two transverse magnetic (TM) modes, and at least two quasi-TM modes.

[0027] Many further features and combinations thereof concerning embodiments described herein will appear to those skilled in the art following a reading of the instant disclosure.

[0028] DESCRIPTION OF THE FIGURES

[0029] In the figures,

[0030] FIG. 1 is a schematic diagram of an example of a MTM-MAC system, in accordance with one embodiment;

[0031] FIG. 2A is a schematic diagram of a first example implementation of the MTM-MAC system of FIG. 1 , in accordance with one embodiment;

[0032] FIG. 2B is a micrograph of a MRR-TEO device for the MTM-MAC system of FIG. 2A, in accordance with one embodiment;

[0033] FIG. 2C is a micrograph of a MRR-TE1 device for the MTM-MAC system of FIG. 2A, in accordance with one embodiment;

[0034] FIG. 3 is a schematic diagram of an experimental testbed for testing the MTM-MAC system of FIG. 2A, in accordance with one embodiment;

[0035] FIG. 4A is a plot of the TEO output power transmission spectra for the experimental testbed of FIG. 3, in accordance with one embodiment;

[0036] FIG. 4B is a plot of the TE1 output power transmission spectra for the experimental testbed of FIG. 3, in accordance with one embodiment; FIG. 4C is a plot of the tunability characterization for the experimental testbed of FIG. 3, in accordance with one embodiment;

[0037] FIG. 4D is a plot of the theoretical optical output power levels for the experimental testbed of FIG. 3, in accordance with one embodiment;

[0038] FIG. 5A is a schematic diagram of a second example implementation of the MTM-MAC system of FIG. 1 , in accordance with another embodiment;

[0039] FIG. 5B is a schematic diagram of a vector-matrix multiplication implemented using the MTM-MAC system of FIG. 5A, in accordance with one embodiment; and

[0040] FIG. 6 illustrates the flowchart of an optical computing method, in accordance with one embodiment.

[0041] Many further features and combinations thereof concerning embodiments described herein will appear to those skilled in the art following a reading of the instant disclosure.

[0042] DETAILED DESCRIPTION

[0043] Described herein are systems and methods for multi-transverse mode (MTM) computation (or modulation), which are WDM compatible. In particular, there is described systems and methods for deploying optical modes in separate optical paths to be weighted using modulators and incoherently accumulated by photodetectors. The systems and methods described herein may be used to perform MTM-MAC operations in a plurality of applications including, but not limited to, photonic accelerators and photonic processors. As used herein, the term “MAC operation” refers to the calculation of the product of two numbers and the addition of the result to an accumulator. It will be appreciated that a variety of linear mathematical operations, including, but not limited to, vector or matrix multiplications, convolutions, and dot products, may be represented by a series of MAC operations. While reference is made herein to the systems and methods described herein being used for analog applications (e.g., vector-matrix or matrix-matrix multiplication), it will also be appreciated that digital applications may also apply. Such digital applications may include transceivers where the systems and methods described herein may be used to generate N-level pulse amplitude modulation (PAM-N), where N = 4 with two optical modes, N = 8 with three optical modes, and N = 16 with four optical modes. The systems and methods described herein may be used for Optical Logic Gate applications. Other embodiments may apply.

[0044] FIG. 1 shows an example of an MTM-MAC system 100, in accordance with one embodiment. As will be described further below, the system 100 may be used to perform MAC operations by computing the product of an input vector (or matrix) B and a weight matrix A, to produce a result C. As used herein, the term “weight” refers to an element (aij) of the weight matrix by which the input vector (or matrix) is multiplied, the weight being indicative of the strength of the connection from one node i of the system 100 to another node j of the system 100.

[0045] The system 100 comprises a plurality of interconnected components, namely one or more light sources (e.g., laser sources) 102, a WDM unit 104, a plurality of first beam splitters 106a, a plurality of second beam splitters 106b, a plurality of first optical modulators 108a (or a plurality of second optical modulators 108b, depending on the application, as will be described further below), a plurality of weight banks 110, a superposition block (or unit) 112, and an accumulation block (or unit) 114. The system 100 (and / or elements thereof) may be implemented as one or more integrated circuits (e.g., on one or more photonic integrated circuit platforms). The system 100 may include one or more elements implemented in a silicon photonics platform. The system 100 may additionally or alternatively be implemented in any other suitable device structure(s).

[0046] The light sources 102 are configured to emit light which is coupled to a plurality (n) of optical channels 103i, 1032, ... , 103n. Each channel 103i, 1032, ... , 103nthus provides an input optical signal having a given optical characteristic, i.e. a given wavelength Ai, A2, ... , An, associated therewith. In one embodiment, the light sources 102 comprise one or more laser devices. It should however be understood that the light sources 102 may additionally or alternatively comprise any suitable light emitter including, but not limited to, one or more light-emitting diodes (LEDs).

[0047] The WDM unit 104 is configured to receive the input optical signals from the light sources 102 (e.g., via channels 103i, 1032, ... , 103n) and to combine (i.e. multiplex) the received input optical signals onto at least one output path (e.g., a waveguide, not shown). Multiple optical carriers can therefore coexist and travel in the same output path without interfering with one another, thus creating multiple independent information channels within the same physical channel. In one embodiment, the WDM unit 104 comprises an optical multiplexer, such as an arrayed waveguide grating (AWG). It should however be understood that the WDM unit 104 may comprise any suitable device configured to combine multiple optical signals (e.g., channels) onto at least one output path. The output of the WDM unit 104 is a multiplexed signal having a number of optical modes associated therewith. In one embodiment, the optical modes are transverse electric (TE) orthogonal optical modes (e.g., the fundamental TE mode, or TEO, and the first order TE mode, or TE1). It should however be understood that other embodiments may apply. For example, the optical modes may comprise the TE2 and TE3 modes. In addition, the optical modes may comprise transverse magnetic (TM, or quasi-TM) modes (e.g., a fundamental TM mode, or TM0, and a first order TM mode, or TM1) instead of (or in addition to) TE (or quasi-TE) modes.

[0048] The multiplexed signal may be provided by the WDM unit 104 to the first splitters 106a. The first splitters 106a may be configured to split the multiplexed signal along a plurality of paths (e.g., waveguides) for output to the first modulators 108a (or the second modulators 108b, depending on the application). In one embodiment, the number of paths onto which the multiplexed signal is split is based on the number of optical modes associated with the multiplexed signal. The first splitters 106a and the second splitters 106b described herein may comprise any suitable device configured to split a received signal equally (or substantially equally) or unequally between all paths. In one embodiment, the splitters 106a, 106b comprise multimode interferometers (MMIs). In another embodiment, the splitters 106a, 106b comprise multimode directional couplers. The splitters 106a, 106b may also comprise multimode splitters. Other embodiments may apply.

[0049] The modulators 108a, 108b are configured to alter signal(s) received directly from the WDM unit 104 or received from the splitters 106a. As will be described further below, either the plurality of first modulators 108a or the plurality of second modulators 108b may be used, depending on the application. Each modulator from the first modulators 108a or the second modulators 108b is configured to modulate the intensity of the received signal at a given wavelength to generate a modulated signal. In one embodiment, each modulator 108a, 108b alters a single signal (e.g., wavelength) while the other signals (e.g., wavelengths) pass through the modulator 108a, 108b unaltered. In other embodiments, alternatively or additionally, some or all of the modulators 108a, 108b may affect more than one signal. The modulators 108a, 108b may be configured based on target analog computation tasks (e.g., vector-matrix or matrix-matrix multiplication) for realizing the input vector (or matrix). Depending on the application (e.g., on the target computation tasks), the input modulators 108a, 108b may be singlemode or multimode modulators. Examples of devices suitable for use as the modulators 108a, 108b include, but are not limited to, microring modulators (MRMs) and Mach- Zehnder modulators (MZMs). The modulators 108a, 108b may be controlled through high-resolution continuous (analog), multi-level, or dual-level modulation schemes.

[0050] Still referring to FIG. 1 , the second splitters 106b are configured to receive the modulated signal (from the first modulators 108a or the second modulators 108b) and to split the modulated signal along a plurality paths (e.g., waveguides) for output to the weight banks 110. In one embodiment, the number of paths onto which the modulated signal is split is based on the number of optical modes. In order to achieve a modular and scalable design, multiple second splitters 106b may be cascaded according to the number of weight banks 110. In one embodiment, 50 / 50 (3-dB) second splitters 106b are arranged in a cascade configuration. In another embodiment, 75 / 25 second splitters 106b are arranged in a cascade configuration. Other embodiments may apply.

[0051] The weight banks 110 serve as a photonic tensor core and are configured to perform, based on the modulated signals received from the modulators 108a or 108b via the second splitters 106b, photonic computations (e.g., vector-matrix multiplication or matrixmatrix multiplication) in order to implement one or more MAC operations. The weight banks 110 are configured to operate in parallel, with each weight bank 110 having a given optical mode (e.g., TEO, TE1 , ...) associated therewith. In operation, a given weight bank 110 applies a coefficient of transmission to the received modulated signal by continuously tuning its drop state to drop a portion of the signal. Using the weight banks 110, it thus becomes possible to have full transmission or no transmission for a given optical mode, and at a given wavelength. By controlling the amount of energy that is transferred, precise weighting (i.e. multiplication) of the input optical (e.g., WDM) signal can in turn be achieved. The weight banks 110 thus implement the weight matrix, which comprises a number of elements that is preferably equal to the number of wavelengths in the optical signal input received at the weight banks 110. The weight banks 110 may comprise any suitable device including, but not limited to, MRRs, phase change materials (PCMs), and Mach-Zehnder interferometers (MZIs). As understood by those skilled in the art, the working principle of a MRR is based on the resonance phenomenon. An MRR is a ring waveguide having a ring circumference (also referred to as the “optical path length”) that determines the MRR’s resonant wavelength. The MRR resonance occurs when the optical length through the MRR is a multiple integer of the input wavelength. By varying the MRR radius, various resonances can be achieved. It is however desirable for the resonance of the MRRs to match the optical carrier wavelengths in order to access each channel independently. Successive passes of the input signal through the MRR interfere constructively so as to result in a resonant power build-up at the resonance wavelength. As previously noted, the weighting operation described herein may be achieved by tuning (e.g., using heaters) the MRRs provided in the weight banks 110 in and out of resonance and thus modulating the signal intensity at a certain wavelength. Using the weight banks 110, a weighted signal is thus generated for each optical mode.

[0052] The output of the weight banks 110 (i.e. the weighted signals) is then provided to the superposition block 112, via inputs 116. The superposition block 112 comprises a plurality of devices configured to non-coherently superpose the weighted signals on a single optical waveguide 118. Examples of devices suitable for use in the superposition block 112 include, but are not limited to, MMIs and multimode combiners. The superposed signals which are output by the superposition block 112 are then fed, via the waveguide 118, to the accumulation block 114.

[0053] The accumulation block 114 comprises a plurality of devices configured to noncoherently accumulate the signals received from the superposition block 112 over the optical waveguide 118, thereby causing a desired calculation to be performed (i.e., multiplying the input vector or input matrix by the weight matrix) and completing the MAC operation. In one embodiment, a nonlinear activation function is integrated into the accumulation block 114 for implementing neural network applications. The nonlinear activation function may be photonic, electronic, or optoelectronic. Examples of devices suitable for use in the accumulation block 114 include, but are not limited to, photodetectors (e.g., photodiodes). In one embodiment, the accumulation block 114 comprises a plurality of mode-insensitive photodetectors. In another embodiment, the accumulation block 114 comprises a plurality of multiport photodetectors. The multiport photodetectors may be coupled to the superposition block 112 or directly connected to the weight banks 110 (without a superposition block 112). Other embodiments may apply. Referring now to FIG. 2A, a first example implementation of the MTM-MAC system 100 of FIG. 1 will now be described. In FIG. 2A, there is illustrated an architecture 200 of a MRR-based photonic accelerator enabled with both WDM and MDM technologies for realizing MAC operations based on two optical modes, namely the fundamental (TEO) and first-order transverse-electric (TE1) modes. Rather than multi-bit resolution weight control of an MRR as done in conventional weight banks, it is proposed to split the signal into multiple multimode branches and to weight the signal with single-bit resolution for yielding the same number of resolved output power levels. In one embodiment, a four- level resolved output power may be realized by single-bit weight control of two MRRs (i.e., MRR-TE0 and MRR-TE1). In this embodiment, the plurality of first modulators 108a may be used to implement an input vector. In this case, the first modulators 108a may be implemented using MRRs, MZIs, MRMs, or MZMs. The first modulators 108a may alternatively be used to implement an input matrix rather than an input vector. For this purpose, the plurality of first splitters (reference 106a in FIG. 1) may be used to split the multiplexed signal output by the WDM unit 104 and the split signal may be fed to an array of single modulators as in 108a. The modulated signal may then be sent to the weight banks 110.

[0054] In one embodiment, both multi-transverse and fundamental mode MRRs are deployed in the weight banks 110 to implement the most significant bit or MSB (using an array of MRRs labelled “MRR-TE1 array” in FIG. 2A) and the least significant bit or LSB (using an array of MRRs labelled “MRR-TE0 array” in FIG. 2A) of each weight, respectively. In the illustrated embodiment, each weight matrix element (aij) is realized with a set of two (2) MRRs 202i, 2022, which are part of the weight bank 110. The MRRs 202i, 2022 are respectively coupled to the TEO and TE1 signal paths bearing an input optical power with a given splitting ratio (e.g., of 0.33:0.66) implemented by the splitters 106b. The weighted TEO and TE1 signals are then fed to a 2x1 MMI 204, which is part of the superposition block 112. Due to the orthogonality of the TEO and TE1 optical signals, the TEO and TE1 signals are superposed incoherently to the MMI output path without any prior phase matching requirements. The optical signal path (i.e. the output of the MMI 204) ends up directly at a photodetector 206, which is part of the accumulation block 114. The photodetector 206 is inherently mode insensitive and accumulates the weighted TEO and TE1 signals to complete the MAC operation. For a specific wavelength and a single-bit resolution weighting control for TEO and TE1 as the least and most significant bits (LSB, MSB), respectively, four (4) different optical power levels are achieved at the system’s output. The proposed architecture 200 can therefore relax the requirements of the weight control circuitry and potentially increase the optical output resolved power levels.

[0055] It will be appreciated that expanding the architecture 200 by further deployment of higher-order modes (TE2, TE3) may scale up the number of distinct output power levels leading to a higher resolution MAC operation. In this case, the power splitting scheme (i.e. the splitting ratio implemented by the splitters 106b) would be modified. In the embodiment where the TEO, TE1 , TE2, and TE3 modes are considered, the splitting ratio may be set to 0.50:0.25:0.125:0.0625 instead of the ratio of 0.33:0.66 illustrated in FIG. 2A for TEO and TE1 signals. Other embodiments may apply.

[0056] As a proof-of-concept design, the weight matrix architecture (i.e. the weight banks 110) with a single pair of the MRR-TE0 and MRR-TE1 devices (also referred to herein as “rings”) was fabricated in the silicon-on-insulation (SOI) technology platform. FIG. 2B illustrates a micrograph of the MRR-TE0 device 210 and FIG. 2C illustrates a micrograph of the MRR-TE1 device 220 in the fabricated SOI chip. The MRR-TE0 device 210 and the MRR-TE1 device 220 may have any suitable dimensions. In one embodiment, the MRR-TE0 device 210 has a radius of 6.5 pm and a coupling length 10 pm, and the MRR-TE1 device 220 has a radius of 20 pm and a coupling length of 95 pm. The resonance tunability is realized through titanium tungsten metal heaters deposited on top of the oxide cladding. The measured free spectral range (FSR) of the MRR-TE0 device is 9.27 nm. The MRR-TE1 device 220 is designed with an expected FSR of 1 .69 nm, which is in agreement with the measured FSR of 1 .71 nm.

[0057] FIG. 3 illustrates a schematic diagram of an experimental testbed 300 used to validate the proof-of-concept design described above as a device under test (DUT) 301 , and to characterize the TEO and TE1 ring waveguides. An external 50:50 optical splitter 302 and variable optical attenuator (VOA) 304 adjust the power levels to the 0.33:0.66 ratio with respect to the insertion loss of each optical path through the output. In the illustrated embodiment, the TE1 mode is excited on-chip using a mode converter 305. The output optical signal is then converted to the fundamental TEO mode (i.e. demultiplexed) with an adiabatic coupler 306 (also referred to as an adiabatic mode demultiplexer ADC) and measured off-chip. It should however be understood that integrated photodetectors may be used, alleviating the need for the adiabatic coupler 306. The normalized optical power transmission spectrum of the TEO and TE1 signals are respectively monitored with the first optical power meter (or PM1) 308i of FIG. 3 and with the second optical power meter (or PM2) 3082 of FIG. 3.

[0058] FIG. 4A shows a plot 400 of the TEO output power transmission spectra measured by PM1 , and FIG. 4B shows a plot 410 of the TE1 output power transmission spectra measured by PM2. As can be seen from FIGs. 4A and 4B, a maximum extinction ratio of more than 20 dB is achieved in the wavelength range of [1530:1550] nm for both TEO and TE1 rings (references 210, 220 in FIG. 3). The insets 402 and 412 of FIGs. 4A and 4B demonstrate the power transmission in the case of single mode excitation (i.e., disconnecting the other signal path from the external splitter output) enabling modal crosstalk evaluation. In the insets 402, 412, the primary crosstalk signals are indicated by the solid curves 404, 414 and the modal crosstalk signals are indicated by the dashed curves 406, 416. A worst-case modal crosstalk of approximately -12 dB is measured in the wavelength range of [1530:1550] nm for the TEO signal.

[0059] FIG. 4C shows a plot 420 of the tunability characterization of the DUT 301 of FIG. 3 with sweeping of the applied current to the ring heaters for MRR-TE0 (LSB, solid curve 422) and MRR-TE1 (MSB, dashed curve 424) at 1538 nm incident wavelength when the other ring is biased at its ‘0’ state. In particular, the resonance wavelength tunability of both TEO and TE1 rings at 1538 nm is characterized using a current source to find the resonance (also referred to as the ‘0’ state) and the off-resonance (also referred to as the T state) bias conditions for each ring. For the TEO (LSB) ring, a bias condition of 8 mA is selected for the ‘0’ state and a bias condition of 12.2 mA is selected for the ‘1 ’ state. For the TE1 (MSB) ring, a bias condition of 11 mA is selected for the ‘0’ state and a bias condition of 16.4 mA is selected for the ‘1 ’ state. In some embodiments, it may be desirable to deploy a weight control scheme to precisely align the resonance of both TEO and TE1 rings in order to realize the high extinction ratio observed in the transmission spectra of FIGs. 4A and 4B.

[0060] TE modes are orthogonal, allowing a photodetector to combine the optical power of two TE modes without requiring coherent summation, much like the photodetector combines different wavelengths. In some embodiments, an on-chip photodetector may be used. Alternatively, the light may be coupled, using a multimode grating coupler, to a few- mode fiber or to an off-chip photodetector. In the illustrated embodiment, the TE1 signal is converted to the TEO mode using an adiabatic mode demultiplexer (reference 306 in FIG. 3) before coupling out this mode. Two off-chip photodetectors were used to independently monitor the TEO and TE1 modes and sum the power levels of the two photodetectors. FIG. 4D shows a plot 430 of the theoretical optical output power levels to be received at the photodetector based on the experimental power levels. A random Gaussian noise is considered to model the MRRs’ output power fluctuations observed in FIGs. 4A and 4B, near the 1538 nm wavelength.

[0061] Referring now to FIG. 5A, a second example implementation of the MTM-MAC unit system 100 of FIG. 1 will now be described. In FIG. 5A, there is illustrated an architecture 500 of a MRR-based photonic accelerated enabled with both WDM and MDM technologies. The proposed architecture 500 may be used to directly increase the scalability of matrix multiplication operation of the MRR weight banks (photonic tensor cores) described herein by simultaneously using WDM and MDM technologies. In particular, larger weight matrices may be realized beyond limitations of conventional MRR weight banks based on WDM. In this embodiment, the plurality of second modulators 108b may be used to implement an input vector. The plurality of second modulators 108b may alternatively be used to implement an input matrix rather than an input vector. For this purpose, the plurality of first splitters 106a may be used to split the multiplexed signal output by the WDM unit 104 and the split signal may be fed to multiple branches as in 302 (having a number equal to the number of target optical modes to be deployed) going through multiple arrays of single and multimode modulators 108b. Considering the two first modes (TEO, TE1), as illustrated in FIG. 5A, the modulators 108b realize half of the input vector with an MRR-TE0 array 304i and the other half with an MRR-TE1 array 3042 (i.e., using single-mode and multimode MRMs). In other words, the modulators 108b are therefore arranged in multiple branches 302 each comprising an array 304i, 3042 of modulators 108b and having a given optical mode (TEO or TE1) associated therewith. The modulated signal is then sent to the weight banks 110. Each modulated signal (output by the modulators 108b) is indeed split and distributed to the respective MRR weight banks 110, where each weight bank 110 represents half of the weight matrix (A). The weighted MTM signal is finally superposed on a single waveguide (reference 118 in FIG. 1) by the superposition block 112 (i.e. to an MMI 306) to be noncoherently accumulated at the accumulation block 114, by a photodetector 308. Although reference is made herein to the architecture 500 being applicable for deploying the TEO and TE1 modes, it should be understood that the architecture 500 may scale to higher order modes.

[0062] FIG. 5B illustrates the vector-matrix multiplication that may be implemented using the architecture 500 of FIG. 5A, in accordance with one embodiment. In this example, a WDM-MDM configuration consisting of three (i.e., n = 3) wavelengths and two (2) multitransverse modes, namely TEO and TE1 , are considered. The multiplication of a 6x6 weight matrix (A) by a 6x1 input vector (B) is illustrated in FIG. 5B. From FIG. 5B, it can be seen that, in order to support both the fundamental (TEO) mode and the first order (TE1) mode, the 6x6 weight matrix A is split in two 6x3 half matrices, namely matrix A’ for the TEO mode and matrix A” for the TE1 mode, and the 6x1 input vector B is split in two 3x1 vectors, namely vector B’ for the TEO mode and vector B” for the TE1 mode. As previously noted, it should be understood that the architecture 500 may scale to higher order modes such that any suitable number (n) of wavelengths other than three may apply.

[0063] FIG. 6 illustrates a flowchart of an optical computing method 600, in accordance with one embodiment. The method 600 may be performed using the MTM-MAC system 100 of FIG. 1. Step 602 comprises emitting a plurality of input optical signals. This may be achieved using the light sources 102 of FIG. 1. The input optical signals have at least two optical modes (e.g., TEO and TE1) associated therewith, as described herein above. Step 604 comprises modulating an intensity of the plurality of input optical signals for generating a plurality of modulated optical signals. This may be achieved in the manner described herein above, using the optical modulators 108a, 108b of FIG. 1. Step 606 comprises splitting the plurality of modulated optical signals onto a plurality of optical paths. This may be achieved in the manner described herein above, using the beam splitters 106b of FIG. 1. Each optical path has a given optical mode associated therewith. Step 608 comprises generating a plurality of weighted optical signals based on the plurality of modulated optical signals by exciting the given optical mode in each optical path. This may be achieved in the manner described herein above, using the weight banks 110. Step 610 comprises noncoherently superposing and accumulating the plurality of weighted optical signals for performing at least one multiply-and-accumulate (MAC) operation. Step 610 may be performed using the superposition block 112 and the accumulation block 114, as described herein above. In one embodiment, the systems and methods proposed herein, in which MDM technology is integrated with MRR-based photonic processors, may be used to increase the number of output power levels while relaxing the weight control circuitry requirement (i.e. mitigating the complexity of the weight control circuitry) to a single-bit resolution. For example, the systems and methods described herein may be used to increase the computational resolution of MRR-based photonic accelerators by realizing MTM-MAC operations using two rings (i.e. MRR-TEO and MRR-TE1) with single-bit resolution control to attain four (4) distinct output power levels. Furthermore, the proposed architecture may be scaled to higher-order modes for increasing the number of resolved output power levels toward realizing more accurate MAC operations.

[0064] The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without departing from the scope of the invention disclosed. Still other modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure.

[0065] Various aspects of the systems and methods described herein may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments. Although particular embodiments have been shown and described, it will be apparent to those skilled in the art that changes and modifications may be made without departing from this invention in its broader aspects. The scope of the following claims should not be limited by the embodiments set forth in the examples, but should be given the broadest reasonable interpretation consistent with the description as a whole.

Claims

WHAT IS CLAIMED IS:1 . An optical computing system, the system comprising: a plurality of light sources configured to emit a plurality of input optical signals having at least two optical modes associated therewith; a plurality of optical modulators configured to receive the plurality of input optical signals and to modulate an intensity thereof for generating a plurality of modulated optical signals; a plurality of beam splitters configured to split the plurality of modulated optical signals onto a plurality of optical paths, each optical path having a given one of the at least two optical modes associated therewith; a plurality of weight banks configured to generate a plurality of weighted optical signals based on the plurality of modulated optical signals, each weight bank optically coupled to a respective one of the plurality of optical paths and configured to excite the given optical mode for generating a weighted optical signal; a superposition unit configured to noncoherently superpose the plurality of weighted optical signals onto an output optical waveguide; and an accumulation unit optically coupled to the output optical waveguide for receiving the plurality of weighted optical signals thereat, the accumulation unit configured to noncoherently accumulate the plurality of weighted optical signals for completing at least one multiply-and-accumulate (MAC) operation.

2. The optical computing system of claim 1 , wherein the accumulation unit is configured to noncoherently accumulate the plurality of weighted optical signals for completing the at least one MAC operation comprising a multiplication of a weight matrix and one of an input vector and an input matrix.

3. The optical computing system of claim 2, wherein the plurality of optical modulators is configured to modulate the intensity of the plurality of input optical signals for generating the plurality of modulated optical signals representative of the one of the input vector and the input matrix.

4. The optical computing system of claim 3, wherein the plurality of weight banks is configured to generate the plurality of weighted optical signals representative of the weight matrix.

5. The optical computing system of any one of claims 1 to 4, further comprising a Wavelength Division Multiplexing (WDM) unit for combining the plurality of input optical signals into a multiplexed signal.

6. The optical computing system of claim 5, wherein the plurality of beam splitters is a first plurality of beam splitters and the plurality of optical paths is a first plurality of optical paths, further comprising a second plurality of beam splitters coupled to the WDM unit and configured to split the multiplexed signal along a second plurality of optical paths for output to the plurality of optical modulators.

7. The optical computing system of claim 6, wherein the plurality of optical modulators are arranged in at least two branches, each branch comprising an array of the plurality of optical modulators and having a given one of the at least two optical modes associated therewith.

8. The optical computing system of claim 6, wherein the first and the second plurality of beam splitters comprise one of multimode interferometers (MMIs), multimode directional couplers, and multimode splitters.

9. The optical computing system of any one of claims 1 to 8, wherein the plurality of optical modulators comprise one of microring modulators (MRMs), microring resonators (MRRs), Mach-Zehnder modulators (MZMs), and Mach-Zehnder interferometers (MZIs).

10. The optical computing system of any one of claims 1 to 9, wherein the plurality of weight banks comprise one of microring resonators (MRRs), phase change materials (PCMs), and Mach-Zehnder interferometers (MZIs).

11. The optical computing system of claim 10, wherein the plurality of weight banks comprise a plurality of multi-transverse mode microring resonators (MRRs) configured to implement a most significant bit of each weight of the weight matrix, and a plurality of fundamental mode MRRs configured to implement a least significant bit of each weight.

12. The optical computing system of any one of claims 1 to 11 , wherein the superposition unit comprises one of a plurality of multimode interferometers (MMIs) and a plurality of multimode combiners.

13. The optical computing system of any one claims 1 to 12, wherein the accumulation unit comprises one of a plurality of mode-insensitive photodetectors and a plurality of multiport photodetectors.

14. The optical computing system of any one of claims 1 to 13, wherein the at least two optical modes comprise one of at least two transverse electric (TE) modes, at least two quasi-TE modes, at least two transverse magnetic (TM) modes, and at least two quasi-TM modes.

15. An optical computing method, the method comprising: emitting a plurality of input optical signals having at least two optical modes associated therewith; modulating an intensity of the plurality of input optical signals for generating a plurality of modulated optical signals; splitting the plurality of modulated optical signals onto a plurality of optical paths, each optical path having a given one of the at least two optical modes associated therewith; generating a plurality of weighted optical signals based on the plurality of modulated optical signals by exciting the given optical mode in each optical path; and noncoherently superposing and accumulating the plurality of weighted optical signals for completing at least one multiply-and-accumulate (MAC) operation.

16. The optical computing method of claim 15, wherein the at least one MAC operation comprises a multiplication of a weight matrix and one of an input vector and an input matrix.

17. The optical computing method of claim 16, wherein the plurality of modulated optical signals are representative of the one of the input vector and the input matrix.

18. The optical computing method of claim 17, wherein the plurality of weighted optical signals are representative of the weight matrix.

19. The optical computing method of any one of claims 15 to 18, further comprising combining the plurality of input optical signals into a multiplexed signal, and splitting the multiplexed signal along a plurality of additional optical paths for output to the plurality of optical modulators.

20. The optical computing method of any one of claims 15 to 19, wherein the at least two optical modes comprise one of at least two transverse electric (TE) modes, at least two quasi-TE modes, at least two transverse magnetic (TM) modes, and at least two quasi-TM modes.

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