Resonator-based programmable optical neural network

Abstract

The invention relates to a programmable optical neural network based on resonators. Systems and methods are provided for devices and methods for implementing an optical neural network (ONN) by utilizing resonator structures, such as on micro-ring resonators (MRRs). Examples include a lattice configured to perform a linear transformation on an optical signal. Each lattice includes a plurality of signal mixing components optically coupled between adjacent waveguides, where each signal mixing component corresponds to a different wavelength and is configured to mix optical signals at different wavelengths on adjacent waveguides. Each lattice also includes a plurality of phase tuning components, each phase tuning component corresponding to a different wavelength and configured to adjust a phase of the mixed optical signal at the different wavelength.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of and priority to U.S. Provisional Application No. 63 / 513,678, filed on July 14, 2023, the contents of which are incorporated herein by reference in their entirety. Background Art

[0003] Artificial neural networks ("ANNs") have become an important tool for machine learning. ANNs are used in a wide range of fields, such as, but not limited to, image recognition, natural language processing, and game playing. For more complex tasks, larger and deeper ANNs become more important. These larger and deeper ANNs require faster and more energy-efficient computing hardware. BRIEF DESCRIPTION OF THE DRAWINGS

[0004] The present disclosure is described in detail according to one or more different embodiments with reference to the following drawings. The drawings are provided for illustrative purposes only and depict only typical or example embodiments.

[0005] Figure 1 A schematic block diagram of a unit cell according to the presently disclosed technology is depicted.

[0006] Figure 2 Depicted are example implementations of lattices in accordance with the presently disclosed technology.

[0007] Figure 3A and Figure 3B Depicted are example transmission responses and phase responses of a phase tuning component according to example implementations disclosed herein.

[0008] Figure 4 Depicted are example transmission responses of a signal mixing component according to example implementations disclosed herein.

[0009] Figure 5 Another example implementation of a lattice according to the presently disclosed technology is depicted.

[0010] Figure 6 Yet another example implementation of a lattice according to the presently disclosed technology is depicted.

[0011] Figure 7 Depicted is another example transmission response of a signal mixing component according to example implementations disclosed herein.

[0012] Fig. 8A Depicted is a schematic diagram of an optical system for performing multiple matrix-vector multiplications according to example embodiments disclosed herein.

[0013] Figure 8B Describes the Fig. 8A Schematic representation of the multiple matrix-vector multiplication operations performed by the optical system.

[0014] Fig. 9A Depicted is a schematic diagram of an optical system for performing multiple matrix-vector multiplications on a set of inputs according to example implementations disclosed herein.

[0015] Fig. 9B Describes the Fig. 9A Schematic representation of multiple matrix-vector multiplication operations performed by an optical system on a set of inputs.

[0016] Fig. 10A Depicted is a schematic diagram of an optical system for performing general matrix multiplication according to example implementations disclosed herein.

[0017] Fig. 10B Describes the Fig. 10A Schematic representation of the general matrix multiplication operation performed by the optical system.

[0018] Fig.11 is an example computing component that can be used to implement an optical neural network according to embodiments disclosed herein.

[0019] Fig.12 is an example computer system that can be used to implement the optical neural network of the present disclosure.

[0020] The drawings are not exhaustive and do not limit the disclosure to the precise forms disclosed. DETAILED DESCRIPTION

[0021] Examples of the presently disclosed technology provide devices and methods for implementing optical neural networks (ONNs). Examples disclosed herein provide optical devices, systems, and methods that can be implemented for fully connected layers in microring resonators (MRRs)-based ONNs. The present disclosure provides a lattice including one or more MRRs that can be implemented to perform linear transformations based on trained weights of the ONN. Each lattice can be coupled between two adjacent waveguides. Each lattice includes a signal mixing component for mixing optical signals propagating on two adjacent waveguides and a phase tuning component for adjusting the phase of the resulting mixed optical signal. The mixing and phase tuning can be adjusted to achieve a desired linear transformation.

[0022] As mentioned above, ANN can be a tool for machine learning (ML). As ANNs become larger and deeper, they require faster and more energy-efficient computing hardware. Specially designed computing hardware platforms (such as graphics processing units (GPUs) and tensor processing units (TPUs)) have been developed to address this demand for growing computing resources. However, traditional electronic ANNs have multiple limitations, including high energy consumption, limited processing speed, and susceptibility to electromagnetic interference. Therefore, ONNs have attracted increasing attention because they rely on light rather than electronic signals to perform calculations and processing. Relying on light can overcome the above-mentioned bottlenecks of electronic ANNs. For example, the operating rate of ultra-high-speed optoelectronic devices (such as photodiodes and modulators) can be one to two orders of magnitude higher than the operating rate of electronic counterparts. Further, relying on light can provide ONNs that are resistant to electromagnetic interference, whose resistance is not affected by length, and have low energy consumption. Therefore, since ONNs provide energy-saving, compact, and high-speed ML accelerators, ONNs have been regarded as a competitive solution.

[0023] The building blocks of ANN are fully connected (FC) layers. FC layers are abstract layers of a neural network where each neuron applies a linear transformation to the input vector via a weight matrix. Therefore, all possible connections from one layer to the next exist so that every input vector to one layer can affect every output vector from the next layer.

[0024] In ONNs, the FC layer can be implemented through a programmable photonic circuit architecture. Traditionally, Mach-Zehnder Interferometers (MZIs) have been used as building blocks for these programmable photonic circuits. In this case, by changing the relative phase between the branches of the MZI, each MZI can arbitrarily control the power splitting ratio and relative phase shift between the input port and the output port of the MZI. By cascading the MZIs in a grid structure, the MZI grid can be used to perform complex ML tasks. However, the driving power of the MZI may be relatively high. For example, the dynamic power consumed by training an MZI-based ONN can be 200fJ / bit per MZI, while the static power consumption after training can be 30mW per MZI. In addition, the footprint of such photonic circuits may be relatively large, with lengths typically being hundreds of μm or longer. Therefore, footprint considerations and power consumption considerations affect the fabrication of high-density ONNs utilizing MZIs. As ONNs become larger and deeper, the density will also increase, resulting in a larger device footprint and increased power consumption.

[0025] Thus, embodiments of the present disclosure provide optical devices that can be used as building blocks for programmable photonic circuit architectures for implementing ONNs (e.g., but not limited to FC layers). As described above, the present disclosure provides optical devices that utilize MRR-based lattices. These lattices include one or more MRRs that are configured to perform linear transformations on optical signals of multiple wavelengths according to a weight matrix of a trained neural network. Relative to MZI-based methods, the lattices disclosed herein consume less power. For example, dynamic power consumption during training can be on the order of tens of fj / bit (e.g., 10 fj / bit) per MRR, while static power consumption after training can be on the order of single-digit mW (e.g., 4 mW) per MRR. Therefore, the lattices according to the present disclosure can enable a wide range of applications and different matrix operations performed by ONNs.

[0026] In an example embodiment, the lattice may include a plurality of sub-lattices optically coupled between adjacent waveguides. Each sub-lattice includes a signal mixing component and a phase tuning component, so that the lattice includes a plurality of signal mixing components and a plurality of phase tuning components. The plurality of signal mixing components may be configured to mix optical signals propagating on each adjacent waveguide of a plurality of optical wavelengths. The plurality of phase tuning components may be configured to adjust the phase of the mixed optical signal for a plurality of wavelengths. Each sub-lattice is configured to operate on a different optical wavelength. Thus, the signal mixing component and the phase tuning component of a given sub-lattice are configured to operate on corresponding different optical wavelengths. Therefore, a plurality of optical signals may be encoded onto a plurality of wavelengths included in a single input signal, so that each optical signal propagates at a different wavelength.

[0027] As used herein, "optically coupled" refers to an interconnection between devices for transmitting an optical signal or a portion of an optical signal from one device to another. In various examples, optical coupling can be achieved by an optical coupler (such as, but not limited to, a directional coupler) through a beam splitter, etc. A directional coupler can include two or more waveguides that are closely positioned together so that light can be evanescently transmitted from one waveguide to another waveguide (e.g., via evanescent coupling).

[0028] According to various examples of the currently disclosed technology, each phase tuning component can be provided as an MRR optically coupled to a waveguide in an adjacent waveguide. The MRR of the corresponding sub-lattice can be configured to resonate at a wavelength corresponding to the sub-lattice. A phase shifting mechanism can be coupled to the MRR and tuned to change the refractive index of the MRR, which can be selectively controlled to change the phase and tune the resonance of the MRR. The phase change caused by the phase shifting mechanism can be tuned so that the weights of the trained weight matrix are applied to perform a linear transformation on the optical signal of the wavelength corresponding to the sub-lattice. The phase shifting mechanism can be implemented as a mechanism or device that provides thermo-optical tuning (e.g., a coupled resistive heater that generates heat based on an applied voltage), electro-optical tuning (e.g., a PN diode), metal oxide semiconductor capacitor (MOSCAP) tuning, etc. Examples of MOSCAPs are provided, for example, in US Patent No. 9,612,503; US Patent Application Serial No. 17 / 972,927; and US Patent Application Serial No. 18 / 175,970, the disclosures of which are incorporated herein by reference in their entireties.

[0029] According to the present disclosure, a signal mixing component can receive an optical signal propagating on an adjacent waveguide, mix the optical signal, and output the mixed optical signal to an adjacent waveguide, which can be used downstream. By mixing the input optical signal to output it to an adjacent waveguide, each signal input to the lattice may affect each output of the lattice. The mixing ratio of the optical signal output from the lattice can be controlled according to the weights of the trained weight matrix to perform a linear transformation.

[0030] The signal mixing component can be implemented in a variety of ways. Several illustrative examples are provided herein, but other embodiments are possible. In one example, the signal mixing component can be provided as a dual-ring MRR coupled in series, the dual-ring MRR having a first MRR optically coupled to a first waveguide and a second MMR optically coupled to the first MRR. The second MMR can also be optically coupled to a second waveguide adjacent to the first waveguide. The first and second MRRs have resonances at a common wavelength that is different from the corresponding sub-lattice and is different between the multiple signal mixing components that constitute the lattice. In another example, the signal mixing component includes an MRR optically coupled to the first waveguide and optically coupled to the second waveguide via a reverse coupler. In yet another example, the second waveguide includes a plurality of waveguide crossings, and the sub-lattice includes an MRR optically coupled to the first waveguide and optically coupled to different waveguide crossings in the plurality of waveguide crossings.

[0031] In each embodiment of the signal mixing component, the MRRs constituting the signal mixing component may include a phase shifting mechanism that can be tuned to ensure that the resonance of the MRR matches the wavelength corresponding to the sub-lattice, thereby optically coupling the optical signal propagating on each waveguide into the signal mixing component at the corresponding wavelength, mixing the optical signals, and optically coupling the mixed optical signal to the waveguide. However, in some cases, the phase shifting mechanism may affect the energy consumption of the lattice, and in the case of a dual MRR structure, may complicate the tuning because the two MRRs may need to be tuned one by one for matching. Therefore, an embodiment of the signal mixing component including fewer MRRs can be used to reduce the number of phase shifting mechanisms, which translates into reduced energy consumption and reduced operational complexity.

[0032] In some examples according to the present disclosure, as described above, the ONN may be implemented as an MRR-based grid structure comprising a plurality of cascaded lattices. As a result of the MRR-based lattice according to the present disclosure, a grid structure may be realized that occupies at least 10 times less space than a conventional MZI-based approach, wherein the MZI-based lattice may be 100 μm×400 μm. In an MRR-based grid structure, a plurality of waveguides may be provided, and a building block or lattice including a plurality of signal mixing components and a plurality of phase tuning components may be optically coupled between adjacent waveguides. The MRR-based lattice may be combined with wavelength division multiplexing (WDM) technology that implements multiplication with different matrices by sub-lattices configured for different optical wavelengths. This approach may be used to reduce computation time by increasing the computation speed of the matrix multiplication function of the ONN, while also providing an ONN with increased density and reduced footprint. Furthermore, by using WDM and exploiting the multiple free spectral ranges (multi-FSRs) of MRR, the matrix-vector multiplication (MVM) of a single photon kernel can be extended to multiple general matrix multiplication (GEMM) operations through parallel processing within a single optical device.

[0033] Figure 1A schematic block diagram of a lattice 100 according to the currently disclosed technology is depicted. The lattice 100 can receive a first input signal 140a via a first input port 104a and a second input signal 140b via a second input port 104b. Each of the first input signal 140a and the second input signal 140b may include a plurality of optical signals propagating at a plurality of optical wavelengths. In various examples, the first input signal 140a and the second input signal 140b include the same plurality of optical wavelengths. Each optical signal of each wavelength of the first input signal 140a and the second input signal 140b may be encoded with information. For example, the optical signal of the first wavelength of the first input signal 140a may be encoded with first information (e.g., data of the first element of a vector or matrix), the optical signal of the second wavelength of the first input signal 140a may be encoded with second information (e.g., data of the second element of a vector or matrix), and so on. Similarly, the optical signal at the first optical wavelength of the second input signal 140b may be encoded with first information (e.g., data of the first element of a vector or matrix), the optical signal at the second optical wavelength of the second input signal 140b may be encoded with second information (e.g., data of the second element of a vector or matrix), and so on. The lattice 100 may be configured to apply weights to information encoded on the first input signal 140a and the second input signal 140b by mixing the input signals and tuning the phase of the mixed signal according to trained weights programmed into the lattice 100. As a result of the mixing and phase tuning, the weighted information may be encoded on the resulting output signal, which is output from the first output port 106a as the first output signal 150a and from the second output port 106b as the second output signal 150b.

[0034] The lattice 100 includes a plurality of sublattices 110a-110n (individually referred to as sublattices 110 herein as illustrative examples, or collectively referred to as sublattices 110 herein). The sublattices 110 include signal mixing components 120a-120n (individually referred to as signal mixing components 120 herein as illustrative examples, or collectively referred to as signal mixing components 120 herein) and phase tuning components 130a-130n (individually referred to as phase tuning components 130 herein as illustrative examples, or collectively referred to as phase tuning components 130 herein). For example, the sublattice 110a includes the signal mixing component 120a and the phase tuning component 130a, the sublattice 110b includes the signal mixing component 120b and the phase tuning component 130b, and so on.

[0035] The signal mixing component 120 can be configured to mix the first input signal 140a and the second input signal 140b. Each sub-lattice 110 can be associated with light of different wavelengths in a plurality of wavelengths. The signal mixing component 120 of the corresponding sub-lattice 110 can be configured to mix the optical signal of the first input signal 140a of the associated wavelength with the optical signal of the second input signal 140b of the same wavelength. For example, the sub-lattice 110a can be associated with the first optical wavelength, and the sub-lattice 110b can be associated with the second optical wavelength. The first input signal 140a and the second input signal 140b each include information encoded on the first wavelength and information encoded on the second wavelength. The signal mixing component 120a can be configured to mix the optical signal propagated at the first wavelength from the first input signal 140a and the second input signal 140b, and the signal mixing component 120b can be configured to mix the optical signal propagated at the second wavelength from the first input signal 140a and the second input signal 140b.

[0036] The phase tuning component 130 may be configured to adjust the phase of the mixed input signals 140a and 140b for each corresponding wavelength in the plurality of wavelengths. Each phase tuning component 130 may be configured to operate on a wavelength of light associated with a corresponding sub-lattice in the sub-lattice 110. Referring to the above example, the phase tuning component 130a may be configured to adjust the phase of the mixed signal at a first wavelength output from the signal mixing component 120a. The phase tuning component 130b may be configured to adjust the phase of the mixed signal at a second wavelength output from the signal mixing component 120b.

[0037] Thus, multiple input optical signals may be encoded onto multiple wavelengths included in the input signals 140a and 140b, such that each optical signal propagates at a different wavelength corresponding to a given signal mixing component 120 and a given phase tuning component 130. The phase tuning component 130 may be used to independently control the relative phase difference in different ports (e.g., the second input port 104b and the first input port 104a), and the signal mixing component 120 may be implemented to connect and mix the signals of the different ports.

[0038] Figure 2 Depicted are example implementations of lattices in accordance with the presently disclosed technology. Figure 2A lattice 200 is depicted, which is an example implementation of the lattice 100. The lattice 200 includes a plurality of sub-lattices, illustratively shown as sub-lattices 210a to 210c (individually referred to herein as sub-lattices 210 as illustrative examples, or collectively referred to herein as sub-lattices 210). The sub-lattices 210a to 210c include signal mixing components 220a to 220c (individually referred to herein as signal mixing components 220 as illustrative examples, or collectively referred to herein as signal mixing components 220) and phase tuning components 230a to 230c (individually referred to herein as phase tuning components 230 as illustrative examples, or collectively referred to herein as phase tuning components 230). The signal mixing components 220 and the phase tuning components 230 are example implementations of the signal mixing components 120 and the phase tuning components 130, respectively. Although Figure 2 Three sub-lattices 210 are shown in FIG. 2 , but this is for illustration purposes only. Any number of sub-lattices 210 may be included in the lattice 200 .

[0039] The lattice 200 is optically coupled between adjacent waveguides, which are shown as first waveguide 202a and second waveguide 202b (referred to herein as waveguide 202 or bus waveguide 202 individually as illustrative examples, or collectively referred to herein as waveguide 202 or bus waveguide 202). Waveguides 202a and 202b can be formed of semiconductor materials such as silicon or other IV materials or III-V materials. A first input signal 240a and a second input signal 240b can be injected into the first waveguide 202a and the second waveguide 202b, respectively. The first input signal 240a and the second input signal 240b can be substantially similar to the first input signal 140a and the second input signal 140b. As such, the first input signal 240a and the second input signal 240b include a plurality of optical signals propagating at a plurality of wavelengths, wherein each optical signal is encoded with information. A first output signal 250a and a second output signal 250b are output from the first waveguide 202a and the second waveguide 202b, respectively.

[0040] The sub-lattice 210 can be implemented as a resonator structure. For example, the signal mixing component 220a includes a first resonator structure 222a optically coupled to the first waveguide 202a and a second resonator structure 224a optically coupled to the second waveguide 202b. The first resonator structure 222a is optically coupled to the second resonator structure 224a. The configuration of the first resonator structure 222a and the second resonator structure 224a can be referred to as a dual resonator structure coupled in series. In the case of the signal mixing component 220b (or the signal mixing component 220c), the first resonator structure 222b (or the first resonator structure 222c) and the second resonator structure 224b (or the second resonator structure 224c) are optically coupled together and optically coupled to the first waveguide 202a and the second waveguide 202b, respectively. The first resonator structures 222a-222c are individually referred to as resonant structures 222 herein as illustrative examples, or are collectively referred to as first resonator structures 222 herein. The second resonator structures 224a-224c are individually referred to herein as resonant structures 224 as illustrative examples, or are collectively referred to herein as second resonator structures 224. Figure 2 In the example of FIG. 1 , the resonator structures 222 and 224 are provided as MRRs forming a dual-ring MRR structure coupled in series.

[0041] Like the signal mixing component 220, the phase tuning component 230 includes at least one resonator structure optically coupled to the second waveguide 202b. For example, the phase tuning components 230a-230c include a resonator structure 232a, a resonator structure 232b, and a resonator structure 232c (individually referred to herein as resonant structures 232 as illustrative examples, or collectively referred to herein as resonator structures 232) optically coupled to the second waveguide 202b, respectively. In various examples, the corresponding resonator structure 232 of a given phase tuning component 230 is optically coupled to the second waveguide 202b downstream of the corresponding signal mixing component 220. Figure 2 In the case of FIG. 2 , the phase tuning component 230a is located between the signal mixing component 220a and the signal mixing component 220b. However, according to some embodiments, the phase tuning component 230a may be located downstream of the signal mixing component 220b.

[0042] As described above, in some examples, the resonator structures 222, 224, and 232 can be implemented as MRR or other optical ring resonators. The resonator structure can be a closed loop waveguide formed of a semiconductor material such as silicon or other Group IV materials. The shape of the loop can be, for example, but not limited to, a circle, an ellipse, an oblong shape, etc., thereby forming a resonator structure. The resonator structure can have an initial resonant wavelength (λ) defined by the circumference of the resonator structure (e.g., a radius in the case of an MRR). The resonator structure also includes multiple resonant frequencies separated by an integer number of FSRs of the resonator structure (e.g., λ+(k-1)Δλ, where k is a non-zero integer).

[0043] In various examples, the resonator structures 222, 224, and 232 are evanescently coupled to another waveguide (e.g., a bus waveguide or another resonator structure) using a directional coupler. In the case of evanescent coupling, the amount of light optically coupled from one waveguide to another waveguide is based on the distance between the waveguides and the resonant frequency of the resonator structure. The amount of light optically coupled can be represented by a coupling coefficient or coupling ratio. The distance between the waveguides can be controlled so that one waveguide is as close to the other waveguide as possible. The coupling length represents the effective curve length of the resonator structure over which the coupling phenomenon with the waveguide occurs, which can be based on the radius of curvature of the resonator structure over which the evanescent coupling occurs. Figure 2 In the case of , the radius of the MRR structure can be designed to achieve a desired curve length for a desired resonant frequency. The resonant frequency also depends on the effective refractive index between the waveguide and the optical ring resonator.

[0044] An input optical signal can be optically coupled into and output from the resonator structure based on the resonant frequency of the resonator structure. For example, an input optical signal propagating at a wavelength aligned with the resonant frequency of the resonator structure can be optically coupled into the resonator structure, while other wavelengths are unknown to the resonator structure. Thus, the resonant frequencies of the resonator structures included in the sub-lattices 210 can be tuned to configure each of the sub-lattices 210 to operate on a different wavelength of light, thereby associating a different wavelength of light with each sub-lattice 210.

[0045] For example, in Figure 2In the case of, the first input signal 240a and the second input signal 240b may include optical signals propagating at the first wavelength, the second wavelength, and the third wavelength. The resonant frequencies of the resonator structures 222a, 224a, and 232a of the sub-lattice 210a may be aligned with the first wavelength. Therefore, the optical signal at the first wavelength may be optically coupled to and output from the first resonator structure 222a and the second resonator structure 224a and the resonator structure 232a. Similarly, the resonant frequencies of the resonator structures 222b, 224b, and 232b may be aligned with the second wavelength, so that the optical signal at the second wavelength may be optically coupled to and output from the resonator structures 222b, 224b, and 232b. Similarly, the resonant frequencies of the resonator structures 222c, 224c, and 232c may be aligned with the third wavelength, so that the optical signal at the third wavelength may be optically coupled to and output from the resonator structures 222c, 224c, and 232c.

[0046] For a given phase tuning component 230, the electric field transfer function (T) of the optical signal input from the second waveguide 202b into the resonator structure 232 and the optical signal output to the second waveguide 202b after passing through the resonator structure 232 is provided below. PT_Double_MRR ).

[0047]

[0048] Wherein, a is the one-way round-trip amplitude transmission in the resonator structure, which is determined based on the material of the waveguide forming the resonator structure and the bending loss in the resonator structure; t is the transmission coefficient, which is based on the coupling coefficient (k) between the resonator structure 232 and the second waveguide 202b. pt ), as t 2 +k pt 2 =1; θ is the phase of light propagating in the resonator structure; and j is an imaginary number. The phase of light (θ) in the resonator structure can be provided as θ=2πfn(L / c), where f represents the resonant frequency, n is the refractive index of the resonator structure; L is the circumference of the resonator structure; and c is the speed of light.

[0049] The resonator structure 232 can be turned on / off resonance tuned by changing the phase θ, which can be achieved by changing the refractive index of the waveguide forming the resonator structure 232. The resonator structures 232a - 232c can include phase shifters 234a - 234c (referred to herein individually as phase shifter 324 or collectively as phase shifters 234 for illustrative examples) disposed thereon, which are respectively configured to change the effective refractive index of the waveguide of the corresponding resonator structure 232. The phase shifter 234 can be implemented by thermo - optic tuning (e.g., a resistor coupled to a waveguide that generates heat based on an applied voltage), electro - optic tuning (e.g., coupling a PN diode to the waveguide), metal - oxide - semiconductor capacitor (MOSCAP) tuning, etc. As described below, the phase shifters 234 can be controlled independently or jointly to change the effective refractive index of the corresponding resonator structure, thereby tuning the resonance of the corresponding resonator structure.

[0050] The phase tuning component 230 can operate in an over - coupled state. For example, the resonator structure 232 can be over - coupled with the second waveguide 202b. As used herein, "over - coupled" refers to evanescent coupling between waveguides having a relatively high coupling coefficient (k). The coupling coefficient (k) is a value between 0 and 1, where a value of 1 represents perfect coupling or 100% coupling of light from one waveguide to another. A high coupling coefficient can be, for example, greater than the round - trip loss per pass (1 - a 2 ) of the power coupling coefficient (k 2 )(e.g., k 2 >1 - a 2 or t < a). In an example embodiment, k 2 is set to 0.2 (e.g., k is approximately 0.45), and a is 0.953 (e.g., a 2 = 0.907). Any coupling coefficient is possible as long as the above conditions are met. As discussed above, the coupling coefficient depends on the distance between the waveguides and the resonance frequency of the resonator structure 232.

[0051] Figure 3A and Figure 3B depict example transmission responses and phase responses of a phase tuning component according to example embodiments disclosed herein. Figure 3A shows the transmission response curve graph 310, and Figure 3BA phase response graph 320 at the output of an example phase tuning component 230 is shown, wherein normalized transmission and phase shift in radians are plotted as a function of phase detuning in radians. Phase detuning refers to the detuning of the resonant frequency of the phase tuning component 230 by the phase shifting mechanism, and phase shift refers to the change in the phase of light in the resonator structure after tuning relative to the untuned phase. The transmission response graph 310 depicts the transmission response 312 of an ideal all-pass filter in which the transmission response remains unity. The transmission response graph 310 also depicts the transmission response 314 of an example implementation of the phase tuning component 230, wherein the coupling coefficient (k) of the resonator structure 232 to the second waveguide 202b is approximately 0.45. The phase response graph 320 depicts the phase response 324 of an example implementation of the phase tuning component 230. From Figure 3A and Figure 3B It can be seen that a phase shift can be achieved by detuning the phase tuning component 230 with minimal impact on the transmission (eg, amplitude) of the output signal. In this example, the transmission loss is at most 5%.

[0052] While the phase tuning component 230 can be used to independently control the relative phase difference between different waveguides, the signal mixing component 220 can be implemented to connect and mix the signals from different waveguides. Figure 2 As described above, the signal mixing component 220 can be implemented as a dual resonator structure coupled in series. Fig. 8A , Fig. 9A and Fig. 10A As described, this configuration can be used to couple signals in different waveguides propagating in a common direction and at a common wavelength, and enables cascading multiple components using a grid arrangement for multi-port linear transformations while keeping the bus waveguides straight without the need for waveguide bends or crossings.

[0053] Return to reference Figure 2 In an example embodiment, the resonator structure 222 and the resonator structure 224 of a given signal mixing component 220 may be identical. For example, the resonator structure 222 and the resonator structure 224 may have the same perimeter, waveguide material, and resonant frequency. The resonator structure 222 and the resonator structure 224 may have the same separation distance between their waveguides and the first waveguide 202a and the second waveguide 202b, respectively. As such, the resonator structure 222 and the resonator structure 224 may have the same coupling coefficient (k 0 The coupling coefficient (expressed as k) between the resonator structure 222 and the resonator structure 224 1) can be configured to provide a flat optical response from input to output, which means that resonator structure 222 is coupled to resonator structure 224 with minimal or no loss between input and output. If the optical response is not flat, then response losses may occur that may be difficult to tune. Therefore, embodiments disclosed herein utilize coupling coefficients (k) that are as high as possible. 1 ), while maintaining a flat optical response. In an example embodiment, k 1 2 is set to 0.013 (e.g., k 1 is approximately 0.114), which provides a flat optical response. Figure 2 The electric field transmission matrix (T MT_Double_MRR ) (also called the transfer matrix) is:

[0054]

[0055] Where a is the one-way round-trip amplitude transmission in the resonator structure, which is the same for resonator structure 222 and resonator structure 224; t is the transmission coefficient such that t 2 represents the transmission coefficient between the first waveguide 202a and the resonator structure 222, t 1 represents the transmission coefficient between the resonator structure 222 and the resonator structure 224, and the inner cavity t 0 represents the transmission coefficient between the second waveguide 202b and the resonator structure 224; θ is the phase of the light propagating in the resonator structure, which is controlled to be the same for the resonator structure 222 and the resonator structure 224. In Equation 2, k 2 represents the coupling coefficient between the first waveguide 202a and the resonator structure 222, and k 1 represents the coupling coefficient between the first waveguide 202b and the resonator structure 224. As described above, in some examples, the resonator structures 224 and 222 may be substantially identical, in which case k 2 Can be used with k 0 However, the embodiments disclosed herein are not limited to the same resonator structure, so k 0 and k 2 For different applications, t 0 and t 2 Can be the same or different.

[0056] To control the phase θ, the refractive index of the waveguides forming the resonator structures 222 and 224 can be changed by utilizing a phase shifting mechanism similar to the phase shifting mechanism 234 discussed above. For example, the first resonator structure 222a and the second resonator structure 224a can include a first phase shifting mechanism 226a and a second phase shifting mechanism 228a disposed thereon, respectively, and the resonator structure 222b and the resonator structure 224b can include a first phase shifting mechanism 226b and a second phase shifting mechanism 228b disposed thereon, respectively. Similarly, the resonator structure 222c and the resonator structure 224c can include a first phase shifting mechanism 226c and a second phase shifting mechanism 228c disposed thereon, respectively. The first phase shifting mechanism 226a-226c is collectively referred to herein as the first phase shifting mechanism 226, and the second phase shifting mechanism 228a-228c is collectively referred to herein as the second phase shifting mechanism 228. The phase shifting mechanisms 226 and 228 can be configured to change the effective refractive index of the waveguides of the corresponding resonator structures. Phase shifting mechanisms 226 and 228 may be implemented by thermo-optical tuning (e.g., a resistor coupled to a waveguide that generates heat based on an applied voltage), electro-optical tuning (e.g., coupling a PN diode to a waveguide), metal oxide semiconductor capacitor (MOSCAP) tuning, etc. As described below, phase shifting mechanisms 226 and 228 may be controlled independently or collectively to change the effective refractive index of the respective resonator structures to tune the resonance of the respective resonator structures. By tuning the resonance, the intensity (e.g., amplitude) of light coupled to and coupled out of each resonator structure may be adjusted. In various examples, the resonance of each resonator structure 222 and the resonator structure 224 may be tuned simultaneously to have the same transmission response to detuning.

[0057] Figure 4 Depicted are example transmission responses of a signal mixing component according to example implementations disclosed herein. Figure 4 A transmission response graph 410 is shown at the output of an example signal mixing component 220, where normalized transmission is plotted as a function of phase detuning in radians. In this example, the coupling coefficient (k) between the resonator structure 222 and the resonator structure 224 is 1 ) is about 0.114. Figure 4 It can be seen that signal mixing component 220 can be used to achieve any intensity transmission coefficient from 0 to 1 through phase detuning (eg, tuning of the resonant frequencies of resonator structure 222 and resonator structure 224 ), which can be used to implement a unitary matrix using lattice 200 .

[0058] Although Figure 2 Resonator structure 232 is depicted as being smaller than 224 and / or resonator structure 222, but this is for illustrative purposes only. The figures are not intended to be drawn to scale, and Figure 2(and other figures of the present disclosure) are not intended to be limiting. Thus, the perimeter of the resonator structure 232 can be equal to, greater than, or less than the perimeter of the resonator structure 224 and / or the resonator structure 222, as desired for a given application. In the illustrative example, the perimeter of the resonator structure 232 can be substantially the same as the perimeter of the resonator structure 224 and / or the resonator structure 222, thereby resonating at the same frequency as the resonator structure 224 and / or the resonator structure 222. This allows the resonator structure 232 to have the same resonant frequency as the resonator structure 224 and / or the resonator structure 222, thereby operating on the same wavelength of light.

[0059] As described above, the phase shifting mechanism may affect the energy consumption of the lattice 200. For example, when the phase shifting mechanism is implemented as a resistive heater for thermo-optical tuning, the energy consumption of the phase shifter represents a majority of the energy consumed by the lattice 200 and thus affects the energy consumption of the mesh network implementing the lattice 200. Therefore, some embodiments disclosed herein can be used to reduce the number of phase shifting mechanisms included in the lattice, thereby reducing the energy consumption of the lattice. Figure 5 and Figure 6 Example implementations are provided.

[0060] Figure 5 An example of another implementation of a lattice according to the presently disclosed technology is depicted. Figure 5 A lattice 500 is depicted, which is substantially similar to lattice 200, except as otherwise specified herein. In particular, lattice 500 provides a single resonator structure implementation of a signal mixing component. Figure 5 The reference numerals in the figure refer to Figure 2 Like reference numerals in the Figure 2 The description provided here applies to Figure 5 Similar reference numerals in FIG.

[0061] For example, the lattice 500 is optically coupled between the first waveguide 202a and the second waveguide 202b. The first input signal 240a and the second input signal 240b may be injected into the first waveguide 202a and the second waveguide 202b, respectively, and the first output signal 250a and the second output signal 250b are output from the first waveguide 202a and the second waveguide 202b, respectively.

[0062] The lattice 500 includes a plurality of sublattices, illustratively shown as sublattices 510a to 510c (individually referred to herein as sublattices 510 as illustrative examples, or collectively referred to herein as sublattices 510). The sublattices 510 each include a signal mixing component and a phase tuning component. For example, the sublattices 510a-510c include signal mixing components 520a to 520c (individually referred to herein as signal mixing components 520 as illustrative examples, or collectively referred to herein as signal mixing components 520) and phase tuning components 230a to 230c. Although Figure 5 Three sub-lattices 510 are shown in the lattice 500, but this is for illustration purposes only. Any number of sub-lattices 510 may be included in the lattice 500. As described above, the sub-lattices 510 include resonator structures that can be tuned to configure each sub-lattice 510 to operate on a different wavelength of light, thereby associating a different wavelength of light with each sub-lattice 510.

[0063] As described above, each sub-lattice 510 includes a phase tuning component 230 and combines Figure 2 The description of the phase tuning component 230 provided is applicable to Figure 5 Thus, each of the phase tuning components 230 includes a resonator structure 232 and a phase shifting mechanism 234 disposed thereon. The corresponding phase tuning component 230 of a given sub-lattice 510 can control the phase difference between optical signals propagating on the first waveguide 202a and the second waveguide 202b at a wavelength corresponding to the given sub-lattice 510.

[0064] Each sub-lattice 510 also includes a signal mixing component 520, which can be substantially similar to the signal mixing component 220, unless otherwise specified herein. For example, the signal mixing components 520a-520c include resonator structures 224a-224c, respectively, that are optically coupled to the second waveguide 202b. Figure 5 In the example of , the signal mixing components 520a-520c are also optically coupled to the counter-propagation coupling portions 524a-524c (referred to as counter-propagation coupling portions 524 or coupling portions 524 individually herein as illustrative examples, or collectively referred to as counter-propagation coupling portions 524 or coupling portions 524 herein) via waveguide crossovers 522a-522c (referred to as waveguide crossovers 522 individually herein as illustrative examples, or collectively referred to as waveguide crossovers 522 herein) of the waveguide 202a. A waveguide crossover refers to a continuous waveguide including: one portion of the waveguide crosses another portion of the waveguide. The waveguide crossover exhibits low loss, so that an optical signal in one portion of the waveguide does not enter another portion of the waveguide (or the amount of entry is negligible).

[0065] For example, each waveguide intersection 522 is formed by a first waveguide 202a and a coupling portion 524. Light on the first waveguide 202a entering the waveguide intersection 522 propagates in a first direction toward the output end of the lattice 500 and enters the coupling portion 524. The first waveguide 202a turns in the opposite direction (e.g., toward the input end of the lattice 500) at the coupling portion 524. The coupling portion 524 is as close as possible to the resonator structure 224 so as to optically couple the light from a portion of the first waveguide 202a into the resonator structure 224, and vice versa. Since the first waveguide 202a is along the opposite direction of the coupling portion 524, the light in the coupling portion 524 propagates in the opposite direction relative to the first input signal 240a, so that the light propagates toward the input end of the lattice 500. In this way, the light in the waveguide intersection 522 can be coupled into the resonator structure 224, which mixes the optical signal from the second waveguide 202b with the light from the first waveguide 202a. The mixed optical signal can then be provided back to the second waveguide 202b and the first waveguide 202a, which propagates downstream to the output. In examples disclosed herein, the propagation losses in the waveguide crossing 522 can be lower than the propagation losses in the resonator structure (such as the resonator structure 224), for example, less than 0.1 dB per crossing.

[0066] Figure 5 The electric field transmission matrix (T MT_Signle_MRR )for:

[0067]

[0068] Where a is the one-way round-trip amplitude transmission in the resonator structure 224; t is the transmission coefficient, such that t 0 represents the transmission coefficient between the second waveguide 202b and the resonator structure 224; θ is the phase of the light propagating in the resonator structure 224; j is an imaginary number; and k 0 is the coupling coefficient between the second waveguide 202b and the resonator structure 224. In this example, the coupling coefficient k 0 Also shown is the coupling coefficient between the resonator structure 224 and the first waveguide 202a at the coupling portion 524. However, in other embodiments, the coupling between the resonator structure 224 and the second waveguide 202b need not be the same as the coupling between the resonator structure 224 and the coupling portion 524.

[0069] As above combined Figure 2 As described, the refractive index of the waveguide forming the resonator structure 224 can be varied by controlling the phase θ using the phase shifting mechanism 228. By tuning the resonance, the intensity of light coupled into and out of the resonator structure 224 can be adjusted.

[0070] Figure 6 An example of another implementation of a lattice according to the presently disclosed technology is depicted. Figure 6 A lattice 600 is provided that is substantially similar to lattice 200, except as otherwise specified herein. In particular, similar to lattice 500 above, lattice 600 provides a single resonator structure implementation of a signal mixing component. Figure 6 The reference numerals in the figure refer to Figure 6 Like reference numerals in the Figure 2 The description provided here applies to Figure 6 Similar reference numerals in FIG.

[0071] For example, the lattice 600 is optically coupled between the first waveguide 202a and the second waveguide 602b. The second waveguide 602b can be substantially similar to the second waveguide 202b, except that the second waveguide 602b can include a taper 604 and a reverse taper 606. The taper 604 increases the width of the second waveguide 602b from the first width to the second width (w d ), while the reverse taper 606 reduces the width from the second width to a third width, which can be the same as or different from the first width. In various examples, the first width and the third width are less than the second width (w d ). The first input signal 240a and the second input signal 240b may be injected into the first waveguide 202a and the second waveguide 202b, respectively, and the first output signal 250a and the second output signal 250b are output from the first waveguide 202a and the second waveguide 202b, respectively.

[0072] Lattice 600 includes a plurality of sub-lattices, illustratively shown as sub-lattice 610a and sub-lattice 610b (individually referred to herein as sub-lattice 610 as an illustrative example, or collectively referred to herein as sub-lattice 610). Sub-lattices 510 each include a signal mixing component and a phase tuning component. For example, sub-lattices 610a and 610b include signal mixing component 620a and signal mixing component 620b (individually referred to herein as signal mixing component 620 as an illustrative example, or collectively referred to herein as signal mixing component 620) and phase tuning components 230a and 230b. Although Figure 6 Two sub-lattices 610 are shown in the figure, but this is for illustration purposes only. Any number of sub-lattices 610 may be included in the lattice 600. As described above, the sub-lattices 610 include resonator structures that can be tuned to configure each sub-lattice 610 to operate on a different wavelength of light, thereby associating a different wavelength of light with each sub-lattice 610.

[0073] As described above, each sub-lattice 610 includes a phase tuning component 230 and combines Figure 2The description provided for the phase tuning component 230 also applies to Figure 6 Thus, each phase tuning component 230 includes a resonator structure 232 and a phase shifting mechanism 234 disposed thereon. Each phase tuning component 230 of a given sub-lattice 610 can control the phase difference between optical signals propagating on the first waveguide 202a and the second waveguide 602b at a wavelength corresponding to the given sub-lattice 610.

[0074] Each sub-lattice 610 also includes a signal mixing component 620, which can be substantially similar to the signal mixing component 220, unless otherwise specified herein. For example, the signal mixing components 620a and 620b include first resonator structures 224a and 224b, respectively, optically coupled to the first waveguide 202a and the second waveguide 602b. Figure 6 Directional couplers 625a and 625b (individually referred to herein as directional couplers 625 or collectively referred to herein as directional couplers 625 as illustrative examples) are illustrated and are implemented to provide coupling light between the corresponding resonator structure 224 and the second waveguide 602b. Each directional coupler 625 can be based on the coupling coefficient (k) between the second waveguide 602b and the corresponding resonator structure 224. 0 ) and the resonant frequency of the resonator structure 224 to evanescently couple light from the second waveguide 602b into the corresponding resonator structure 224, and vice versa. The third width (w ) of the second waveguide 602b within the directional coupler 625a (and similarly within the directional coupler 625b) d ) may be related to the width (w) of the waveguide forming the second resonator structure 224a (and similarly the resonator structure 224b) c This configuration may facilitate coupling due to the phase mismatch between the optical signal on the second waveguide 602b and the optical signal on the resonator structure 224.

[0075] exist Figure 6In the example of, the second resonator structure 224a and the resonator structure 224b are coupled to the first waveguide 202a by reverse couplers 623a and reverse couplers 623b (referred to as reverse couplers 623 individually herein as illustrative examples, or collectively referred to as reverse couplers 623 herein) respectively. The reverse couplers include periodic perturbations over the length L of the couplers. The periodic perturbations are configured to reflect optical signals propagating at one wavelength while transmitting optical signals of other wavelengths. For example, reverse coupler 623a can be used to reflect optical signals propagating at a first wavelength corresponding to sublattice 610a and optical signals of other wavelengths to be transmitted downstream. The reflected optical signal is then coupled into the resonator structure 224a and propagates in the same direction (e.g., counterclockwise) as the optical signal coupled from the second waveguide 602b into the second resonator structure 224a.

[0076] In an example embodiment, each reverse coupler 623 may include a wavelength-specific reflector 621 including a pair of Bragg gratings of approximately equal period, respectively coupled to the first waveguide 202a and the resonator structure 224. The pair of Bragg gratings includes a small amplitude perturbation (e.g., about tens of microns) relative to the width of the corresponding waveguide. Figure 6 As shown, the waveguide 202a may have a width w at least within the back coupler 623a. a , and the waveguide of the resonator structure 224a may have a width w at least within the backcoupler 623a. b , the width can be larger than w a . A first Bragg grating 627 may be disposed on the waveguide 202a having a grating period Λ and a grating amplitude h1 (e.g., an amplitude perturbation). A second Bragg grating 629 may be provided that is coupled to the waveguide of the second resonator structure 224a having a grating period Λ (which may be substantially equal to the grating period of the grating 627) and a grating amplitude h2 (which may be less than h1). The Bragg grating 629 on the resonator structure 224a may be used as an anti-reflection grating for suppressing Bragg reflections of the grating 627. The grating 629 may be disposed out of phase with respect to the grating 627 (e.g., the perturbation of the grating 629 is aligned with the perturbation of the grating 627). In an example embodiment, w a can be 450nm and w bCan be 550nm, Λ can be 318nm, h1 can be about 30nm, and h2 can be about 40nm. However, h2 does not need to be greater than h1, and can be smaller depending on the application. The length L of each Bragg grating 627 and 629 can be 159nm and include 40 gratings. The period Λ of each grating determines which wavelengths are reflected, and the period selection controlled in this way can be used to tune the wavelength that will be reflected by each Bragg grating pair. Although the above example is provided with reference to the reverse coupler 623a, another reverse coupler 623 can have a substantially similar configuration, except that the period Λ is selected according to the desired wavelength of each sub-lattice 610.

[0077] Figure 6 The electric field transmission matrix (T MT_Signle_MRR ) is represented by the above equation 3. Therefore, as described above in conjunction with Figure 2 As described, the refractive index of the waveguide forming the resonator structure 224 can be varied by controlling the phase θ using the phase shifting mechanism 228. By tuning the resonance, the intensity of light coupled into and out of the resonator structure 224 can be adjusted.

[0078] Figure 7 Depicted is another example transmission response of a signal mixing component according to example implementations disclosed herein. Figure 7 A transmission response graph 710 is shown at the output of an example signal mixing component implemented using a single resonator structure, where normalized transmission is plotted as a function of phase detuning (θ) expressed in radians. The signal mixing component can be implemented, for example, as signal mixing component 520 or signal mixing component 620. Figure 7 It can be seen that the signal mixing component can be used to achieve any intensity transmission coefficient from 0 to 1 through phase detuning (e.g., tuning of the resonant frequency of the resonator structure 224), which can be used to implement a unitary matrix using lattices 500 and / or 600.

[0079] FIG. 8A to FIG. 10B are schematic diagrams of various optical systems that may be used to perform various multiplication processes on a plurality of different matrices in accordance with embodiments disclosed herein. FIG. 8A to FIG. 10B Each comprises the following: an input layer configured to provide an input signal, the input signal comprising an optical signal encoded according to an input matrix; a weight matrix core, the weight matrix core configured to apply a weight matrix to the input signal; and an output layer configured to detect an output signal, the output signal comprising an output optical signal encoded with an output matrix, the output matrix representing the weight matrix applied to the input matrix.

[0080] Feedforward neural networks cascade multiple layers to improve approximation capabilities, where information moves in one direction from the input layer to the output layer. For the i-th layer, the input and output relationship can be expressed as:

[0081] Y i =f i (W i X i ) Equation 4

[0082] Wherein, Y represents the i-th output matrix; W represents the i-th weight matrix; X represents the i-th input matrix; and f represents an element-by-element nonlinear activation function. In the case of the optical devices shown in Figures 8 to 10, the elements Y and X can be encoded into the amplitude of the optical signal included in the input signal, such as the first and second input signals 140a, the first and second input signals 140b, the first and second input signals 240a, and the first and second input signals 240b. The element W can be a learned weight for performing a linear transformation on the input matrix X.

[0083] The different configurations shown in Figures 8 to 10 can be used to perform various matrix multiplication functions to apply a weight matrix W to an input matrix X. For example, Fig. 8A Describes the process used to perform Figure 8B An optical system 800 is shown with multiple matrix-vector multiplication (MVM) operations 850 . Fig. 9A Describes the use of Fig. 9B An optical system 900 is shown with a set of inputs to perform multiple MVM operations 950 . Fig. 10A Describes the method for executing Fig. 10B The optical system 1000 is shown as one or more general matrix multiplication (GEMM) operations 1050. In each case, the weight matrix kernel can be constructed by cascading multiple lattices (e.g., Figure 1 Lattice 100, Figure 2 Lattice 200, Figure 5 Lattice 500 and / or Figure 6 lattice 600) to implement.

[0084] refer to Fig. 8A and Figure 8B, the MVM operation 850 includes multiplying an input vector 852 by a plurality of weight matrices 854. The input vector 852 may be an nx1 vector, and the weight matrix 854 may be an m set of nxn weight matrices 854a-854n including weight values ​​to be applied to the input vector 852 as entries, where m and n are integers greater than zero. Applying the weight matrix 854 to the input vector 852 produces an output vector 856 including an m set of output vectors 856a-n, which are the product of each matrix 854a-854n and the input vector 852. Although three weight matrices (e.g., m=3) are illustrated herein, any number of weight matrices may be included in the weight matrix 854.

[0085] To implement operation 850, optical system 800 includes an input layer 830 that receives an input signal from a light source (such as a comb laser or other light source known in the art). The light source can transmit multiple input signals 832a-832n to multiple waveguides 822a-822n. Each input signal 832a-832n can include m number of optical signals, each optical signal propagating at a different wavelength. The number of waveguides 822a-822n can correspond to the number of items in input vector 852, and the number of optical signals at different wavelengths can correspond to the number of weight matrices 854a-854n.

[0086] The optical system 800 includes a plurality of broadband modulators 834a-834n disposed on a plurality of waveguides 822a-822n. The broadband modulators 834a-834n can be configured to modulate the amplitude of the input signals 832a-832n according to the terms of the input vector 852. For example, the broadband modulator 834a can be configured to modulate the amplitude of the input signals 832a-832n according to the first term (x 1 ) to modulate the amplitude of the optical signal constituting the input signal 832a. As a broadband modulator, the broadband modulator 834a can modulate the optical signal at each different wavelength according to the first term. Similarly, the broadband modulators 834b-n can modulate the optical signal at each different wavelength according to the second to nth terms (e.g., x in this example) of the input vector 852. 2 to x 4 ) to modulate the amplitude of the optical signals included in the input signals 832b-832n. The amplitude of the modulated optical signals encodes each optical signal using the terms of the input vector 852. The broadband modulators 834a-834n may be implemented as, for example, but not limited to, Mach-Zehnder modulators, electro-absorption modulators, etc. The control circuit 860 may be communicatively coupled (e.g., via a wired or wireless interface) to control the modulator 834a based on the terms of the input vector 852. The control circuit 860 may be implemented as a combination of the following: Fig.12 The computer system 1200 is discussed.

[0087] The encoded input signal is provided to a weight matrix core 820 (also referred to as a crossbar array). The weight matrix core 820 includes a plurality of lattices 824a-824n arranged in a cascade structure. The plurality of lattices 824a-824n may be implemented as any one of lattices 100, lattices 200, lattices 500, or lattices 600. Each lattice 824a-824n may be tuned according to an entry in the weight matrix 854. For example, each lattice 824a-824n may include m number of sub-lattices, as described above in conjunction with Figure 1 , Figure 2 , Figure 5 and Figure 6 Each sub-lattice including one or more resonant structures as described above can be tuned for different wavelengths of the m optical signals. The signal mixing components and phase tuning components of the sub-lattice can then be detuned to apply weights according to the entries of the weight matrix 854.

[0088] For example, a first group of sublattices of lattices 824a-824n can be tuned to a first wavelength corresponding to weight matrix 854a. The signal mixing components and phase tuning components of the first group of sublattices can be detuned according to the terms of weight matrix 854a. Therefore, the first group of sublattices can apply weight matrix 854a to input vector 852 by modulating an optical signal at a first wavelength encoded with the terms of input vector 852 based on the detuning of the signal mixing components and the phase tuning components. Similarly, a second group of sublattices of lattices 824a-824n can be tuned to a second wavelength corresponding to weight matrix 854b, and an m-th group of sublattices of lattices 824a-824n can be tuned to an m-th wavelength corresponding to weight matrix 854n. Therefore, each lattice includes one sublattice in each of the first, second, and m-th groups of sublattices.

[0089] In various examples, the control circuit 860 can be used to tune the lattice. For example, the control circuit 860 can adjust the voltage bias applied to the phase shifting mechanism coupled to the resonator structure of the lattice 824a-824n. The phase shifting mechanism can be as described above in conjunction with Figure 2 , Figure 5 and Figure 6 The phase shift mechanism 226, the phase shift mechanism 228 and / or the resonator structure 232 discussed. The control circuit 860 can issue a control command to a voltage source 862 that applies a voltage bias to the phase shift mechanism. The voltage bias can be selected to adjust the phase shift mechanism, thereby changing the effective refractive index of the waveguide coupled to the phase shift mechanism. By changing the effective refractive index of the waveguide, the resonator structure formed by the waveguide can be tuned to different wavelengths of the m optical signals. In order to implement the terms of the weight matrix 854, each phase shift mechanism can be detuned by adjusting the voltage bias accordingly according to the weight of each term.

[0090] Thus, the input vector 852 can be multiplied by different sets of weights to obtain multiple outputs. For example, the output signal from the weight matrix core 820 is propagated to the detection layer 840 for determining the entries of each output vector 856a-856n based on the amplitude of the output signal at each wavelength. Fig. 8A In the example shown, the detection layer 840 includes a plurality of demultiplexers 842a-842n coupled to a subset of the outputs of the waveguides 822a-822n. The number of demultiplexers 842a-842n can be half the number of waveguides 822a-822n (e.g., half the number of items in the input vector 852). Each of the demultiplexers 842a-842n can be configured to filter each wavelength to a separate output waveguide coupled thereto. The demultiplexers 842a-842n can be provided as coarse wavelength division multiplexing (CWDM) demultiplexers, which can be implemented as deinterleavers, reverse couplers, etc. Each of the demultiplexers 842a-842n can be operated to separate the output signals into separate output waveguides according to different wavelengths. For example, the demultiplexers 842a-842n receive weighted signals from the weight matrix core 820 and separate (e.g., filter) each optical wavelength to different output waveguides. Thus, each optical signal on each output waveguide indicates an entry of the output vector 856 corresponding to each wavelength.

[0091] The detection layer 840 also includes photodetectors 844a-1 to 844m-n coupled to the demultiplexers 842a-842n. The photodetectors 844a-1 to 844m-n detect optical signals on corresponding output waveguides, wherein the amplitude of each detected signal represents an item of the output vector 856. For example, the demultiplexer 842a is coupled to a first subset of the photodetectors 844a-1 to 844m-n. As described above, the demultiplexer 842a filters the output from the weight matrix core 820 into different wavelengths of light, each of which is provided to one of the photodetectors 844a-1 to 844m-n via a corresponding output waveguide. Thus, the photodetector 844a-1 detects the amplitude of light at a first wavelength representing the first item of the output vector 856a, while the photodetectors 844b-1 and 844m-1 detect the amplitude of light broadcast at a second wavelength and an m-th wavelength representing the first item of the output vector 856b and the output vector 856n, respectively. Similarly, photodetectors 844a-844n detect the amplitude of light at a first wavelength representing the nth term of output vector 856a, while photodetectors 844b-n and 844m-n detect the amplitude of light at a second wavelength and an mth wavelength representing the nth term of output vector 856b and output vector 856n, respectively.

[0092] Thus, the optical system 800 can be used to multiply multiple weight matrices 854 by the input vector 852 in parallel (e.g., simultaneously) to determine multiple output vectors 856. Thus, an n-port device (e.g., an optical system 800 having n number of input ports) that can perform any nxn unitary linear transformation can be implemented by arranging multiple lattices 824a-824n in various grid configurations. Since the resonator structure of the lattices 824a-824n is a narrowband device, as described above, by tuning the signal mixer and phase tuning components, different weight matrices can be constructed for each port by utilizing multiple wavelengths. Therefore, multiple MVM operations can be performed simultaneously, thereby reducing computation time.

[0093] In an example embodiment, the optical system 800 can be used for convolutional neural network (CNN) applications. For example, a feature detector implemented as a CNN may include a two-dimensional (2-D) weight array (e.g., a weight matrix). A grayscale image used as an input may have a monochrome channel defining the entries of an input vector 852. Multiple filters for detecting multiple features may be implemented as weights in a weight matrix. Features may be, for example, but not limited to, edges, curves, shapes, etc. Therefore, each filter may be implemented as a 2-D weight array, wherein each 2-D weight array is implemented as a single weight matrix in a weight matrix 854. Each filter may then be applied to an input image using the optical system 800 to perform a dot product of an input image (e.g., input pixel values) and multiple filters (e.g., weight matrix 854). Traditionally, an MZI-based ONN for the above implementation may process one filter at a time. However, the embodiments disclosed herein may obtain the results of multiple multiplication operations in parallel, which improves computational density and reduces computational time.

[0094] As mentioned above, Fig. 9A An optical system 900 is depicted that may be implemented to perform MVM on a set of input vectors. Fig. 9B An operation 950 is depicted by which a set of m weight matrices 954 are applied to a set of m input vectors 952 to produce an output vector 956, where m is an integer greater than one. The weight matrices 954 include a set of m weight matrices 954a-954n, and the set of m input vectors include input vectors 952a-952n.

[0095] To implement the multiple MVM operation 950, the optical system 900 includes an input layer 930 that receives an input signal from a light source (such as a comb laser or other light source known in the art). The light source can emit multiple input signals 932a-932n to multiple waveguides 922a-922n. Each source signal 932a-932n can include m number of optical signals, each optical signal propagating at a different wavelength. The number of waveguides 922a-922n can correspond to the number n of items in the input vector 952, and the number of optical signals at different wavelengths can correspond to the number m of weight matrices 954a-954n.

[0096] The input layer 930 includes a plurality of narrowband modulators 934a-1 to 934m-n, each of which is configured to modulate the amplitude of input signals 932a-932n at different wavelengths according to the terms of the input vector 952. The terms of the input vector 952 can be encoded onto the input signal by modulating the input signal 932a-932n. For example, each input vector 952a-952n can be associated with a different wavelength of light (e.g., the input vector 952a can correspond to a first wavelength, the input vector 952b can correspond to a second wavelength, and the input vector 952n can correspond to the mth wavelength). The first subset 934a of the narrowband modulator can be configured to modulate the light of the first wavelength on each of the source signals 932a-932n according to the terms of the input vector 952a. The second subset 934b of the narrowband modulator can be configured to modulate the light of the first wavelength on each of the source signals 932a-932n according to the terms of the input vector 952b. The mth subset 934m of narrowband modulators may be configured to modulate the mth wavelength of light on each of the source signals 932a-932n according to the terms of the input vector 952n.

[0097] Each waveguide 922a-922n corresponds to each row of the input vector 952a-952n, such that a given narrowband modulator coupled to a given waveguide modulates an optical signal according to the entry of the row of the input matrix corresponding to the given waveguide, wherein the modulated optical signal propagates at a wavelength corresponding to the input matrix. That is, for example, narrowband modulator 934a-1 modulates an optical signal at a first wavelength according to a first entry of input vector 952a, narrowband modulator 934b-1 modulates an optical signal at a second wavelength according to a first entry of input vector 952b, and narrowband modulator 934m-1 modulates an optical signal at an m-th wavelength according to a first entry of input vector 952n. Similarly, narrowband modulators 934a-n modulate the optical signal at the first wavelength according to the nth term of input vector 952a, narrowband modulators 934b-n modulate the optical signal at the second wavelength according to the nth term of input vector 952b, and narrowband modulators 934m-n modulate the optical signal at the mth wavelength according to the nth term of input vector 952n. Thus, the terms of input vector 952 can be encoded onto the optical signal separated into separate wavelength channels.

[0098] The optical system 900 may include a control circuit ( Fig. 9A ), such as Fig. 8A The control circuit 860 can be used to control the modulators 934a-1 to 934m-n according to the terms of the input vector 952.

[0099] The encoded input signal is supplied to a weight matrix core 920 (also referred to as a crossbar array). The weight matrix core 920 may be substantially similar to the weight matrix core 820. As such, the weight matrix core 920 includes a plurality of lattices 924a-924n, each of which may be implemented as any one of the lattices 100, lattices 200, lattices 500, or lattices 600. Each lattice 924a-924n may be tuned according to the entries in the weight matrix 954. For example, each lattice 924a-924n may include m number of sub-lattices, as described above in conjunction with Figure 1 , Figure 2 , Figure 5 and Figure 6 Each sub-lattice including one or more resonant structures as described above can be tuned for different wavelengths of the m optical signals. The signal mixing components and phase tuning components of the sub-lattice can then be detuned to apply weights according to the entries of the weight matrix 954. As discussed above, the control circuit can issue control commands for tuning the lattices 924a-924n according to the entries of the weight matrix 954.

[0100] Thus, a set of input matrices 952 can be multiplied by a set of weights to obtain an output vector 956. For example, the weighted output signals from the weight matrix core 920 are propagated to the detection layer 940 for determining the entries of the output vector 956 based on the amplitudes of the weighted output signals detected by the plurality of photodetectors 944a-944n. The photodetectors 944a to 944n detect the optical signals on the corresponding waveguides. The optical signals on each waveguide are accumulated at each photodetector 944a-944n, and the amplitudes detected by each photodetector 944a-944n represent the corresponding entries of the output vector 956.

[0101] According to an example, the maximum number of lattices used to construct an N-dimensional unitary matrix can be (N-1)*(N / 2) lattices. In an example embodiment, the input image can be a color image, which can be represented as three input vectors (e.g., input vector 952) corresponding to the red, green, and blue (RGB) channels of the input image. A weight matrix (e.g., weight matrix 954) can represent the weights of each color channel. Weight matrix 954 can be multiplied by each input vector 952, and the sum of each output detected at the detection layer 940 (e.g., the total amplitude on each waveguide) provides an entry for output vector 956.

[0102] For a traditional RGB image, the original image may include three color channels. A convolutional layer of a neural network may be provided to calculate the output of the neurons connected to the local region in the input, wherein each calculation is a dot product between the weight of the input image and the local region. The weight matrix for each color channel may be unique and is therefore implemented as a set of three weight matrices. Each item in the output vector may be calculated by element-wise multiplying each color channel of the input region with the corresponding filter (e.g., weight matrix) and summing the multiplications. According to this illustrative example, the optical system 900 may be configured to implement all RGB channel convolutions in one computation cycle by performing all three color channel calculations in parallel. Therefore, the computational efficiency may be increased threefold compared to conventional MZI-based ONNs.

[0103] As mentioned above, Fig. 10A An optical system 1000 is depicted that may be implemented to perform a GEMM. Fig. 10B An operation 1050 is depicted by which a set of m weight matrices 1054 are applied to a set of m input matrices 1052 to produce a set of m output matrices 1056, where m is an integer greater than zero. Fig. 10BIn the example of , the group of m weight matrices 1054 includes weight matrices 1054a-1054n, and the group of m input vectors includes input matrices 1052a-1052n. Therefore, the optical system 1000 can be implemented to perform a single GEMM operation (e.g., m=1) or multiple GEMM operations (e.g., m>1) in parallel.

[0104] In this case, the optical system 1000 utilizes WDM and multiple FSR to encode the input matrix 1052 into an input signal, which can be supplied to the resonator-based weight matrix core 1020. By utilizing WDM and multiple FSR, the optical system 1000 can perform GEMM through parallel photon processing. The weight matrix core 1020 can be implemented using multiple lattices (such as the lattices 100, 200, 500 and / or 600 discussed above). The weight matrix core 1020 can be encoded with a weight matrix 1054 so that when the input matrix set 1052 is input into the weight matrix core 1020, the input matrix set 1052 is multiplied with the weight matrix 1054 to produce an output matrix 1056.

[0105] exist Fig. 10A In the illustrative example of , the optical system 1000 includes an input layer 1030 that receives an input signal from a light source, such as a comb laser or other light source known in the art. The input signals (shown as signals 1032a to 1032n in FIG. 10) can each include multiple optical signals at multiple wavelengths (e.g., an initial resonant wavelength and at least ±(k-1) resonant wavelengths corresponding to the multiple FSRs of the resonator structure included in the weight matrix core 1020). For example, Fig. 10A Depicts the first FSR group (FSR 1 ) to the nth FSR group (FSR n ), where the number of FSRs corresponds to the number n of rows in the input matrix set 1052 (e.g., the number of rows in the input matrix 1052a, 1052b, or 1052n). Each FSR group includes m number of wavelengths corresponding to the m number of input matrices constituting the input matrix set 1052. The first FSR group may correspond to an initial resonant wavelength of a resonator structure including a sub-lattice of the weight matrix core 1020, and the second to nth FSR groups correspond to the n number of FSRs of the resonator structure.

[0106] The entries of the input matrix set 1052 can be encoded into a plurality of optical signals of the input signals 1032a-1032n, and the encoded optical signals can be supplied to the waveguides 1022a-1022d as inputs of the weight matrix core 1020. For example, the input layer 1030 includes a plurality of narrowband modulators configured to encode each optical signal using entries from the input matrix set 1052. For example, the input layer 1030 includes a plurality of narrowband modulator groups 1033a-1033n, each narrowband modulator group corresponding to an FRS group (e.g., the narrowband modulator group 1033a corresponds to the FSR 1 , and the narrowband modulator group 1033n corresponds to FSR n ). Each narrowband modulator group includes a plurality of subgroups 1034a-1 to 1034m-n of narrowband modulators. Each subgroup of narrowband modulators includes n number of narrowband modulators configured to modulate an optical signal at a certain wavelength. For example, the narrowband modulators of subgroup 1034a-1 are configured to modulate an optical signal at a first wavelength, and the narrowband modulators of subgroup 1034m-1 are configured to modulate an optical signal at an m-th wavelength, wherein the first wavelength and the m-th wavelength are FSR 1 The narrowband modulators of the subgroup 1034a-n are configured to modulate the optical signal at the nth resonant wavelength in the first wavelength, and the narrowband modulators of the subgroup 1034m-n are configured to modulate the nth resonant wavelength in the mth wavelength (e.g., FSR n ) under the optical signal.

[0107] Therefore, the entries of each input matrix 1052a-1052n can be encoded into multiple optical signals by modulating the optical signal by separating the signal according to both wavelength and FSR group. For example, each waveguide 1022a-1022n corresponds to a column of the input matrix 1052a-1052n, and each FSR group corresponds to a row. In addition, each wavelength corresponds to the input matrix 1052a-1052n. In this way, each narrowband modulator can be controlled to modulate the optical signal according to the entry of the input matrix 1052 corresponding to the narrowband modulator.

[0108] The encoded optical signal is supplied as an input signal to the weight matrix core 1020. The weight matrix core 1020 may be substantially similar to the weight matrix core 1020 and include a plurality of lattices 1024a-1024n implemented as any of the lattices 100, lattices 200, lattices 500, or lattices 600. Each lattice 1024a-1024n may be tuned according to an entry in the weight matrix 1054. For example, each lattice 1024a-1024n may include m number of sub-lattices, as described above in conjunction with Figure 1 , Figure 2 , Figure 5 and Figure 6 Each sub-lattice including one or more resonant structures as described above can be tuned for different wavelengths of m optical signals. In this way, the resonator structure can operate at a resonant frequency and n number of FSRs. The signal mixing components and phase tuning components of the sub-lattice can then be detuned so that weights are applied according to the entries of the weight matrix 1054.

[0109] Thus, a set of input matrices 1052 can be multiplied by a set of weights to produce a set of output matrices 1056. For example, the weighted output signals from the weight matrix core 1020 are propagated to the detection layer 1040 for determining the entries of the output matrix 1056 based on the amplitude of the weighted output signals detected by the plurality of photodetectors 1044a-1044n. The outputs from the weight matrix core 1020 are supplied to a set of demultiplexers 1042a-1042n, which are provided as coarse wavelength division multiplexing (CWDM) demultiplexers that can be implemented as deinterleavers, reverse couplers, etc. The demultiplexers 1042a-1042n can be operated to separate the output signals into separate output waveguides according to different FSR groups. Once separated (e.g., filtered) according to the FSR groups, each FSR group can be separated (e.g., filtered) into separate output waveguides according to the wavelengths included in the corresponding FSR group (e.g., as shown in the example of demultiplexer 1042b). Photodetectors 1044a to 1044n detect the optical signal of each wavelength on the corresponding output waveguide. The optical signal on each output waveguide is accumulated at each photodetector 1044a-1044n, and the amplitude detected by each photodetector 1044a-1044n represents the corresponding entry of the output matrix 1056.

[0110] Therefore, by exploiting the multiple FSRs of the resonator structure, the MVM of a single photonic core can be extended to a GEMM operation as discussed above. Fig. 10B In the illustrative example of , the weight matrix 1054 is provided as a 3×n×n tensor that is multiplied by the 3×n×k tensor as the input matrix set 1052, which produces a 3×n×k tensor as the output matrix 1056. As discussed above, due to the periodicity of the resonance, each resonator structure in the weight matrix core 1020 has a wavelength (λ 1 ) and one or more resonant wavelengths corresponding to the multiple FSR resonances (e.g., λ 1 +Δλ,…,λ 1+(k-1)Δλ, where Δλ is the FSR). By tuning the resonance of the resonator structure, the amount of optical power on each waveguide can be reduced, which increases the weight of the optical signal on the waveguide. The response of the resonant structure to different FSRs can be substantially similar, allowing the same weight value to be applied to each resonant wavelength. As discussed above, the inputs to the weight matrix kernel 1020 include the vector {x in column 1 of the input matrix 1052. 11 , …, x n1}, the vector consists of all WDM wavelength channels λ 1 , 1 +Δλ,…,λ 1 +(n-1)Δλ is encoded in the corresponding input waveguides 1022a-1022n. The depth of the input volume (eg, input matrix 1052a and input matrix 1052b) can be determined by the WDM wavelength channel λ 1 , 2 and λ 3 Parallel encoding. The encoded input signals are then weighted as discussed above and selected by demultiplexers 1042a-1042n at each output port. Thus, by encoding the k columns of X into k FSR groups, encoding the 3 depth channels of the input matrix set 1052 in 3 wavelengths, and detecting a different signal at each output port, the MVM between the weight matrix 1054 and the input matrix set 1052 (e.g., parallelization of the GEMM between the input matrix set 1052 and the weight matrix 1054) can be implemented in a single device (e.g., optical system 1000).

[0111] Fig.11 FIG. 1 illustrates example computing components that may be used to implement an ONN according to various embodiments. Referring now to FIG. Fig.11 , the computing component 1100 may be, for example, a server computer, a controller, or any other similar computing component capable of processing data. Fig.11 In the example implementation of FIG. 1 , computing component 1100 includes a hardware processor 1102 and a machine-readable storage medium 1104 .

[0112] The hardware processor 1102 may be one or more central processing units (CPUs), semiconductor-based microprocessors, and / or other hardware devices suitable for fetching and executing instructions stored in the machine-readable storage medium 1104. The hardware processor 1102 may fetch, decode, and execute instructions, such as instructions 1106-1114, to control processes or operations for the ONN. As an alternative or in addition to fetching and executing instructions, the hardware processor 1102 may include one or more electronic circuits, such as a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or other electronic circuits, including electronic components for performing the functions of one or more instructions.

[0113] A machine-readable storage medium, such as machine-readable storage medium 1104, may be any electronic, magnetic, optical, or other physical storage device that contains or stores executable instructions. Thus, machine-readable storage medium 1104 may be, for example, a random access memory (RAM), a non-volatile RAM (NVRAM), an electrically erasable programmable read-only memory (EEPROM), a storage device, an optical disk, or the like. In some embodiments, machine-readable storage medium 1104 may be a non-transitory storage medium, wherein the term "non-transitory" does not encompass transient propagating signals. As described in detail below, machine-readable storage medium 1104 may be encoded with executable instructions (e.g., instructions 1106-1114).

[0114] The hardware processor 1102 may execute instructions 1106 to tune the resonance of the multiple resonator structures of the weight matrix core to multiple resonant wavelengths. FIG. 8A to FIG. 10B As described, it is possible to provide a plurality of lattices (such as Figure 1 Lattice 100, Figure 2 Lattice 200, Figure 5 Lattice 500 and / or Figure 6 The weight matrix core of the lattice 600 of FIG. 600 is shown in FIG. 600. Each lattice includes one or more sub-lattices, which include one or more resonator structures. A bias (e.g., a voltage bias) may be applied to a phase shift mechanism (e.g., phase shift mechanism 226, 228, and / or 234) coupled to the resonator structure to tune the resonator structure to a desired resonant frequency (e.g., resonant wavelength).

[0115] The hardware processor 1102 may execute instructions 1108 to adjust the resonance of the plurality of resonator structures to detune the resonance with respect to the plurality of resonant wavelengths according to the entries of the plurality of weight matrices. Each of the plurality of weight matrices may be associated with a resonant wavelength in the plurality of resonant wavelengths. For example, as described above in conjunction with FIG. 8A to FIG. 10BAs described, a plurality of weight matrices may be provided, each weight matrix including terms of learned weights. Each weight matrix may be associated with a resonant wavelength set by tuning at instruction 1106, such that each lattice includes a sub-lattice corresponding to the weight matrix. Based on the terms of each weight matrix, the resonant frequency of the resonator structure of each lattice may be detuned to act on an optical signal encoded with input data according to the weights of the corresponding weight matrix.

[0116] The hardware processor 1102 may execute the instruction 1110 to input a plurality of first optical signals at a plurality of resonant wavelengths to a plurality of waveguides, each first optical signal being encoded with information according to one or more input matrices. A plurality of resonator structures are optically coupled between adjacent waveguides in the plurality of waveguides, and the plurality of first optical signals are supplied to the plurality of waveguides. FIG. 8A to FIG. 10B Example implementations of the first optical signals are provided so that the implementations disclosed herein can be used to perform various multiplication processes on various matrices. Multiple first optical signals can be encoded with data representing entries of a single matrix or vector to perform multiple matrix-vector multiplications on a single input (e.g., Fig. 8A and Figure 8B As another example, the plurality of first optical signals may be encoded with data representing entries of a plurality of vectors to perform a matrix-vector multiplication operation on a plurality of inputs (eg, Fig. 9A and Fig. 9B As yet another example, the plurality of first optical signals may be encoded with data representing entries of a set of matrices for performing multiple general matrix multiplication operations (eg, Fig. 10A and Fig. 10B ).

[0117] The hardware processor 1102 may execute instructions 1112 to detect the optical power output from the plurality of resonator structures. FIG. 8A to FIG. 8B As described, the outputs from the weight matrix core can be demultiplexed into separate outputs based on the resonant frequency and the optical power detected for each output.

[0118] Hardware processor 1102 may execute instructions 1114 to generate one or more entries of an output matrix based on the detected optical power. FIG. 8A to FIG. 10B As depicted, the detected optical power from instruction 1112 represents an entry in the result matrix, which may be used to construct the output of the multiplication operation as described above.

[0119] Fig.12A block diagram of an example computer system 1200 is depicted in which various embodiments described herein may be implemented. The computer system 1200 includes a bus 1202 or other communication mechanism for communicating information, one or more hardware processors 1204 coupled to the bus 1202 for processing information. The one or more hardware processors 1204 may be, for example, one or more general purpose microprocessors.

[0120] The computer system 1200 also includes a main memory 1206, such as a random access memory (RAM), cache, and / or other dynamic storage device, coupled to the bus 1202 for storing information and instructions to be executed by the processor 1204. The main memory 1206 may also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 1204. Such instructions, when stored in a storage medium accessible to the processor 1204, cause the computer system 1200 to become a special-purpose machine customized to perform the operations specified in the instructions.

[0121] The computer system 1200 further includes a read only memory (ROM) 1208 or other static storage device coupled to the bus 1202 for storing static information and instructions for the processor 1204. A storage device 1210, such as a magnetic disk, optical disk, or USB thumb drive (flash drive), is provided and coupled to the bus 1202 for storing information and instructions.

[0122] The computing system 1200 may include a user interface module for implementing a GUI, which may be stored in a mass storage device as executable software code executed by one or more computing devices. By way of example, this module and other modules may include components such as software components, object-oriented software components, class components, and task components, processes, functions, properties, programs, subroutines, program code segments, drivers, firmware, microcode, circuits, data, databases, data structures, tables, arrays, and variables.

[0123] Generally, the words "component", "engine", "system", "database", "data storage", etc. as used herein may refer to logic implemented in hardware or firmware, or to a set of software instructions written in a programming language such as, for example, Java, C or C++, which may have entry points and exit points. Software components may be compiled and linked into an executable program, installed in a dynamic link library, or may be written in an interpreted programming language such as BASIC, Perl or Python. It will be understood that software components may be called from other components or from themselves, and / or may be called in response to detected events or interrupts. Software components configured for execution on a computing device may be provided on a computer-readable medium such as an optical disc, a digital video disc, a flash drive, a disk, or any other tangible medium, or may be provided as a digital download (and may be stored originally in a compressed format or an installable format that needs to be installed, decompressed or decrypted before execution). Such software code may be stored in part or in whole on a memory device of an executing computing device for execution by the computing device. Software instructions may be embedded in firmware such as an EPROM. It will be further understood that hardware components may include connected logic units such as gates and flip-flops, and / or may include programmable units such as programmable gate arrays or processors.

[0124] The computer system 1200 may implement the techniques described herein using customized hard-wired logic, one or more ASICs or FPGAs, firmware, and / or program logic that is combined with the computer system to make or program the computer system 1200 into a special-purpose machine. According to one embodiment, the techniques herein are performed by the computer system 1200 in response to one or more processors 1204 executing one or more sequences of one or more instructions contained in the main memory 1206. Such instructions may be read into the main memory 1206 from another storage medium, such as storage device 1210. Execution of the sequences of instructions contained in the main memory 1206 causes the one or more processors 1204 to perform the process steps described herein. In alternative embodiments, hard-wired circuits may be used in place of or in combination with software instructions.

[0125] As used herein, the term "non-transitory medium" and similar terms refer to any medium that stores data and / or instructions that cause a machine to operate in a particular manner. Such non-transitory media may include non-volatile media and / or volatile media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 1210. Volatile media include dynamic memory, such as main memory 1206. Common forms of non-transitory media include, for example, floppy disks, floppy disks, hard disks, solid-state drives, magnetic tapes or any other magnetic data storage media, CD-ROMs, any other optical data storage media, any physical media with a pattern of holes, RAM, PROMs and EPROMs, flash EPROMs, NVRAMs, any other memory chips or cartridges, and networked versions of these media.

[0126] Non-transient media are distinct from transmission media but can be used in conjunction with transmission media. Transmission media participate in the transfer of information between non-transient media. For example, transmission media include coaxial cables, copper wire, and optical fiber, which includes the wires that comprise bus 1202. Transmission media can also take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications.

[0127] Computer system 1200 also includes a communication interface 1218 coupled to bus 1202. Communication interface 1218 provides bidirectional data communication coupled to one or more network links, and the one or more network links are connected to one or more local networks. For example, communication interface 1218 can be an integrated services digital network (ISDN) card, a cable modulator, a satellite modulator, or a modulator for providing a data communication connection to a telephone line of a corresponding type. As another example, communication interface 1218 can be a local area network (LAN) card for providing a data communication connection to a compatible LAN (or a WAN component communicating with a WAN). Wireless links can also be implemented. In any such implementation, communication interface 1218 sends and receives an electrical signal, an electromagnetic signal, or an optical signal carrying a digital data stream representing various types of information.

[0128] A network link typically provides data communication through one or more networks to other data devices. For example, a network link can provide a connection through a local network to a host computer or to data devices operated by an Internet Service Provider (ISP). The ISP in turn provides data communication services through the global packet data communication network now commonly referred to as the "Internet". Both the local network and the Internet use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link and through the communication interface 1218 (which carry digital data to and from the computer system 1200) are example forms of transmission media.

[0129] Computer system 1200 can send messages and receive data, including program code, through one or more networks, network links, and communications interface 1218. In the Internet example, a server can transmit the requested code for an application program through the Internet, an ISP, a local network, and communications interface 1218.

[0130] The received code may be executed by processor 1204 as it is received, and / or stored in storage device 1210 or other non-volatile storage for later execution.

[0131] Each of the processes, methods and algorithms described in the previous sections can be implemented in a code component executed by one or more computer systems or computer processors including computer hardware and automated in whole or in part by these code components. The one or more computer systems or computer processors can also operate to support the execution of related operations in a "cloud computing" environment, or operate as "software as a service (SaaS)". These processes and algorithms can be implemented in part or in whole in a dedicated circuit. The various features and processes described above can be used independently of each other, or can be combined in various ways. Different combinations and sub-combinations are intended to fall within the scope of the present disclosure, and some method boxes or process boxes can be omitted in some embodiments. The methods and processes described herein are also not limited to any particular order, and the boxes or states related to these methods and processes can be executed in other appropriate orders, or can be executed in parallel, or in some other way. Boxes or states can be added to or removed from the disclosed example embodiments. The execution of certain operations or processes can be distributed to computer systems or computer processors so that they do not reside only in a single machine, but are deployed across multiple machines.

[0132] As used herein, circuits can be implemented using any form of hardware, software or a combination thereof. For example, one or more processors, controllers, ASIC, PLA, PAL, CPLD, FPGA, logic components, software routines or other mechanisms can be implemented to form circuits. In an embodiment, various circuits described herein can be implemented as discrete circuits, or described functions and features can be shared partially or entirely between one or more circuits. Although various features or functional elements can be described or advocated individually as separate circuits, these features and functions can also be shared among one or more common circuits, and this description should not require or imply that separate circuits are needed to implement such features or functions. In the case of using software to implement circuits in whole or in part, this software can be implemented to operate together with a computing system or a processing system that can perform the functions described about the software.

[0133] As used herein, the term "or" may be interpreted in an inclusive or exclusive sense. Furthermore, descriptions of resources, operations, or structures in the singular should not be construed to exclude the plural. Unless expressly stated otherwise, or understood otherwise within the context as used, conditional language (such as, among others, "may," "might," "could," or "might") is generally intended to convey that certain embodiments include and other embodiments do not include certain features, elements, and / or steps.

[0134] Unless expressly stated otherwise, the terms and phrases used in this document and their variations should be interpreted as open-ended and not restrictive. Adjectives such as "traditional," "customary," "normal," "standard," "known," and terms of similar meaning should not be interpreted as limiting the items described to items available for a given time period or before a given time, but should be understood to cover traditional, customary, normal, or standard technologies that may be available or known now or at any time in the future. In some cases, the presence of broad words and phrases (such as "one or more," "at least," "but not limited to," or other similar phrases) should not be understood to mean that narrower cases are intended or required where such broad phrases may not be present.

Claims

1. An optical device for implementing an optical neural network, the optical device comprising: a plurality of waveguides configured to receive a plurality of first optical signals propagating at a plurality of wavelengths; as well as a lattice disposed between a first waveguide and a second waveguide of the plurality of waveguides, the lattice being configured to perform a linear transformation on each of the first optical signals to output a plurality of second optical signals at a plurality of wavelengths, the lattice comprising: a plurality of signal mixing components optically coupled to the first waveguide and the second waveguide of the plurality of waveguides, each signal mixing component corresponding to a different wavelength of the plurality of wavelengths and configured to mix first optical signals at the different wavelengths on the first waveguide and the second waveguide; as well as A plurality of phase tuning components, each of which corresponds to a different wavelength among the plurality of wavelengths, is configured to adjust the phase of a mixed optical signal at the different wavelength among the plurality of wavelengths and output a second optical signal among the plurality of second optical signals.

2. The optical device according to claim 1, wherein: At least one signal mixing component of the plurality of signal mixing components comprises one or more resonator structures and one or more phase shifting mechanisms coupled to the one or more resonator structures, the one or more phase shifting mechanisms being adapted to tune a resonant frequency of the one or more resonator structures.

3. The optical device according to claim 2, wherein: The one or more phase shifting mechanisms include at least one of: a resistive heater, a PN diode, and a metal oxide semiconductor capacitor.

4. The optical device according to claim 1, wherein: At least one signal mixing component of the plurality of signal mixing components comprises a resonator structure and a phase shifting mechanism coupled to the resonator structure, the phase shifting mechanism being adapted to tune a phase of an output of the at least one signal mixing component.

5. The optical device according to claim 1, wherein: Each of the plurality of signal mixing components includes a series-coupled dual-ring microring resonator having a first microring resonator optically coupled to the first waveguide and a second microring resonator optically coupled to the first microring resonator and the second waveguide.

6. The optical device according to claim 1, wherein: Each of the plurality of signal mixing components includes a first microring resonator optically coupled to the first waveguide and the second waveguide, wherein the first microring resonator is coupled to the second waveguide via a back-coupler.

7. The optical device of claim 1, wherein: The second waveguide includes a plurality of waveguide crossings, and wherein each of the plurality of signal mixing components includes a first microring resonator optically coupled to the first waveguide via the waveguide crossings and optically coupled to the second waveguide.

8. The optical device of claim 1, further comprising: a weight matrix kernel adapted to apply one or more weight matrices to an input signal, the input signal comprising the first optical signal, the weight matrix kernel comprising: A plurality of lattices are disposed in a cascade configuration between adjacent ones of the plurality of waveguides, the plurality of lattices including the lattice disposed between the first waveguide and the second waveguide, each of the plurality of lattices comprising one or more resonator structures tuned according to terms of the one or more weight matrices.

9. A method for implementing an optical neural network, comprising: tuning resonances of a plurality of resonator structures of a weight matrix core to a plurality of resonant wavelengths; adjusting the resonances of the plurality of resonator structures to detune the resonances with respect to the plurality of resonant wavelengths according to entries of a plurality of weight matrices, each of the plurality of weight matrices being associated with a resonant wavelength of the plurality of resonant wavelengths; inputting a plurality of first optical signals at the plurality of resonant wavelengths to a plurality of waveguides, each first optical signal being encoded with information according to one or more input matrices, wherein the plurality of resonator structures are optically coupled between adjacent waveguides of the plurality of waveguides; detecting optical power output from the plurality of resonator structures; and One or more entries of an output matrix are generated based on the detected optical powers.

10. The method of claim 9, wherein: Tuning the resonance of multiple resonator structures includes: A plurality of biases are applied to a plurality of phase shifting mechanisms coupled to the plurality of resonator structures.

11. The method of claim 10, wherein: Adjusting the resonance of the plurality of resonator structures comprises: The plurality of biases applied to the plurality of phase shifting mechanisms are adjusted according to the entries of the plurality of weight matrices.

12. The method of claim 9, wherein: The weight matrix core includes a plurality of lattices, and each lattice includes a subset of the plurality of resonator structures, and wherein tuning the resonance of the plurality of resonator structures includes: The resonance of each resonator structure in each subset of resonator structures is tuned to the plurality of resonant wavelengths.

13. A weight matrix kernel, comprising: a plurality of waveguides, each waveguide configured to receive a plurality of first optical signals propagating at a plurality of wavelengths and output a plurality of second optical signals; as well as a plurality of lattices disposed between adjacent waveguides of the plurality of waveguides, each lattice comprising a plurality of sub-lattices, each sub-lattice corresponding to a wavelength of the plurality of wavelengths, wherein each sub-lattice comprises: a signal mixing component optically coupled to the adjacent waveguides of the plurality of waveguides, the signal mixing component configured to mix first optical signals at the wavelengths corresponding to the respective sub-lattices on the adjacent waveguides; and A phase tuning component is configured to adjust a phase of the mixed first optical signal at the wavelength corresponding to the corresponding sub-lattice and output a second optical signal among the plurality of second optical signals.

14. The weight matrix kernel of claim 13, wherein: The plurality of first optical signals are encoded according to one or more input matrices.

15. The weight matrix kernel of claim 14, wherein: The signal mixing component includes at least one resonator structure, wherein the at least one resonant structure is configured to mix the first optical signals on the adjacent waveguides based on detuning a resonant frequency of the at least one resonator structure.

16. The weight matrix kernel of claim 14, wherein: The phase tuning component includes a resonator structure configured to adjust the phase of the mixed first optical signal based on detuning a resonant frequency of the resonator structure.

17. The weight matrix kernel of claim 16, wherein: Detuning the resonant frequency is based on entries of a plurality of weight matrices associated with the plurality of wavelengths.

18. The weight matrix kernel of claim 13, wherein: The signal mixing component includes a series-coupled dual-ring microring resonator having a first microring resonator optically coupled to a first waveguide of the adjacent waveguides and a second microring resonator optically coupled to the first microring resonator and a second waveguide of the adjacent waveguides.

19. The weight matrix kernel of claim 13, wherein: The signal mixing component includes a first microring resonator optically coupled to the adjacent waveguides, wherein the first microring resonator is coupled to one of the adjacent waveguides via a back-coupler.

20. The weight matrix kernel of claim 13, wherein: A first waveguide of the adjacent waveguides includes a waveguide crossover, and wherein the signal mixing component includes a first microring resonator optically coupled to a second waveguide of the adjacent waveguides and optically coupled to the waveguide crossover.

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