WO2022256905A1

WO2022256905A1 - System and method for optically performing computations using a photonic modulator

Info

Publication number: WO2022256905A1
Application number: PCT/CA2021/050802
Authority: WO
Inventors: Enxiao LUAN; Armaghan Eshaghi
Original assignee: Huawei Technologies Canada Co., Ltd.
Priority date: 2021-06-11
Filing date: 2021-06-11
Publication date: 2022-12-15

Abstract

A system for optically multiplying two inputs and involving a Mach-Zehnder configuration. In one configuration, a signal is split to propagate in two similar Mach-Zehnder arms, each with a tunable phase shifter and a tunable attenuator. The two modulated optical signals are interferometrically combined to produce the multiplication results. Other combinations of Bragg grating, attenuator, and Mach-Zehnder device are also described. Phase shifters can be implemented with various kinds of Bragg gratings, resonators and photonic crystals, and phase shift can be tuned via carrier density or thermal tuning. By including a 3-dB directional coupler at the input, parts of a signal carrying multiple wavelength peaks can be reflected by the Bragg grating and be redirected to other multipliers. Outputs of multipliers can be collected by balanced photodetectors.

Description

SYSTEM AND METHOD FOR OPTICALLY PERFORMING COMPUTATIONS USING A PHOTONIC MODULATOR

CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This is the first application filed for the present invention.

FIELD OF THE INVENTION

[0002] This invention pertains generally to the field of optical computation and in particular, to systems and methods of performing a multiplication operation, for example involving a dot product operation between two vectors, using optical elements.

BACKGROUND

[0003] The von Neumann architecture is widely used for conventional personal computers. This architecture essentially consists of a central processor and some memory, and is suitable for running sequential, procedure-based programs. However, such an architecture is inefficient for computational models that are distributed, massively parallel, and adaptive, including neural networks in machine learning (ML) for artificial intelligence (AI), and neuromorphic computing. To address the shortcomings of conventional computer architecture and to improve computing speed and power consumption efficiency of neural networks, newer research has focused on tailored computing architectures.

[0004] Moore’s law, a principle of information-technology that has been observed since 1960s, is becoming less applicable, as electronic computing reaches the nanoscale. As a solution, photonics, which is becoming a mature industrial reality, is being considered with regards to high speed, high throughput data communication and switching infrastructures. In the field of optical communication, photonic solutions have evolved along similar lines, namely in terms of increasing transmission speeds and energy efficiency. For these reasons, implementations of neural networks with optical devices are being investigated. The improvements allowed by photonics are largely due to the large parallelism allowed by the many optical degrees of freedom, including wavelength, polarization, mode, and high connectivity. Microring resonator (MRR) modulators (MRM) and Mach-Zehnder interferometer (MZI) modulators (MZM), are optical modulation candidates that can be investigated for high-throughput data communication in modem data centers. Fortuitously, they can also be employed as key elements to implement the neurons of a neural network system.

[0005] However, current proposed solutions for optically performing computations, such as vector multiplications, are subject to significant limitations. For example, some systems involve a plurality of MRRs arranged in series, each MRR being operated to implement a different component of a respective one of a pair of vectors being multiplied together. However, the different MRRs are spaced apart significantly, leading to operational difficulties due to manufacturing limitations such as spatial variations across a silicon photonics chip.

[0006] Therefore, there is a need for a system and method for optically performing computations, such as vector multiplications, that obviates or mitigates one or more limitations in the prior art.

SUMMARY

[0007] Embodiments of the present disclosure consists of systems and methods for optically performing computations, such as vector multiplications, using one or a set of photonic modulators. Each of the modulators can be localized on a device, for example on a photonic integrated circuit, which performs an element-by-element multiplication. Multiple such elements can be cascaded to perform vector multiplications, such as dot products. Such multiplications can also be used to perform matrix multiplications.

[0008] In accordance with an embodiment of the present disclosure, there is provided a photonic device, which may be used for photonically multiplying two values together. The device includes Mach-Zehnder interferometer (MZI) and one or more optical attenuators. The device may further include at least one optical fdter. The MZI includes an input, a first output, a second output, and at least one controllable phase shifter. The MZI is configured, via operation of the at least one phase shifter along with interferometric operation of the MZI, to cause a first controllable portion of an optical signal presented at the input to be produced at the first output, and a second controllable portion of the optical signal presented at the input to be produced at the second output. Each of the optical attenuators is configured to modulate, directly or indirectly, an intensity of the first portion and the second portion. The modulation of intensity of the first portion and the second portion is by substantially a same amount. The MZI and the optical attenuators, and the at least one optical filter, where present, are co-located. This facilitates provision of a compact photonic device, which in turn facilitates reliable fabrication.

[0009] In various embodiments, the at least one optical filter is present and configured to transmit, from at least one portion of an optical signal, a range of optical wavelengths and to reflect the remaining optical wavelengths to a back-reflection path. The at least one optical filter is placed at a location (i.e. prior to the attenuators) which allows it to filter the at least one portion of an optical signal before it is transmitted through the one or more attenuators. The at least one optical filter may be a Bragg grating. There are several alternatives for placement of the optical filters. The at least one optical filter may be integrated with a corresponding one of the controllable phase shifters. The optical filter may be a single optical filter located prior to the MZI input. The phrase “prior to” is used to describe order relative to the flow of optical signals through the photonic device, where such optical signals are processed by the photonic device to implement a multiplication for example.

[0010] The attenuators, generally placed after the optical filter or else integrated with the optical filter(s) (when present), can be a pair of attenuators each disposed in a respective arm of the MZI, or a single attenuator operative to attenuate signals in both arms of the MZI. Alternatively, the pair of attenuators, or a single attenuator operatively coupled to two waveguides, can be located after the MZI outputs. As yet another alternative, a single attenuator can be located following an output of the optical filter and prior to the input of the MZI. [0011] In various embodiments, the MZI input includes a directional coupler such as a 3 dB directional coupler. The directional coupler has two input ports and two output ports, with each output port connected to a respective MZI waveguide arm. One of the input ports receives an optical signal having multiple components at different wavelengths. A Bragg grating internal to the MZI reflects light outside of a particular band, and this reflected light is output by the other one of the input ports. (The Bragg grating also transmits light within the particular band.) This other one of the input ports can be coupled to one or more subsequent instances of the photonic device, each of which admits a different particular band of wavelengths and reflects light outside of this particular band. This allows for a cascade configuration of photonic devices, each of which can perform a multiplication operation. The outputs of the multiplication operations can be summed together using one or more balanced photodetectors.

[0012] In some embodiments, the photonic device can include, as input, a contra directional coupler (CDC). The CDC can be placed prior to the MZI for example. The CDC acts as the optical filter to admit (transmit) light within a particular band, while also reflecting light outside of the particular band via one of its ports. The admitted (transmitted) light can be processed as described above in order to perform a multiplication. The reflected light can be provided to subsequent instances of the photonic device for processing thereby, according to a cascade configuration.

[0013] The photonic device may be configured to implement a multiplication by operation of the at least one phase shifter to produce a pair of output signals having a difference in intensity which represents a multiplier in the multiplication, and further by operation of the one or more optical attenuators to pass the output signals in proportion to a multiplicand in the multiplication. The photonic device may further include a balanced photodetector (BPD) having a pair of inputs directly or indirectly coupled to the outputs of the MZI. The BPD is configured to produce an indication of a difference in intensity between optical signals produced by the photonic device via said first output and said second output. [0014] In accordance with an embodiment of the present disclosure, there is provided a photonic device made up of a plurality of photonic devices as described above (with optical fdters) and arranged in a cascade configuration. The optical filters of each of the photonic devices are configured to transmit light in a separate wavelength range and to reflect light outside of that wavelength range toward one or more other ones of the plurality of photonic devices. The transmitted light is transmitted toward further parts of the photonic device, while the reflected light is transmitted away from further parts of the photonic device and toward other photonic devices, where present. The overall photonic device can further include a readout device having one or more balanced photodetectors (BPDs). The readout device is configured to produce a result signal which is based on a plurality of differences, each difference being a difference in intensity between optical signals produced by a respective one of the component photonic devices via said first output and said second output of said one of the component photonic devices.

[0015] In various embodiments, each of the component photonic devices is configured to implement a respective multiplication by operation of the at least one phase shifter thereof to produce a pair of output signals having a difference in intensity which represents a respective multiplier in the multiplication and by operating the one or more optical attenuators thereof to pass light in proportion to a respective multiplicand in the multiplication. The result signal is indicative of a sum of these differences in intensity, in order to perform a dot product operation between a first vector comprising the multipliers and a second vector comprising the multiplicands.

[0016] In accordance with an embodiment of the present disclosure, there is provided a method, in a photonic device. The method includes operating a Mach-Zehnder interferometer comprising an input, a first output, a second output, and at least one controllable phase shifter, to cause a first controllable portion of an optical signal presented at the input to be produced at the first output, and a second controllable portion of the optical signal presented at the input to be produced at the second output. The method further includes operating one or more optical attenuators to modulate, directly or indirectly, an intensity of the first portion and the second portion, said modulation of intensity of the first portion and the second portion being by substantially a same amount. The Mach-Zehnder interferometer and the optical attenuators are co-located. In some embodiments, the method further includes admitting the optical signal presented at the input into the Mach-Zehnder interferometer and the optical attenuators, and reflecting light accompanying the optical signal and having a different range of wavelengths than the optical signal, said reflecting comprising directing said light accompanying the optical signal toward one or more further photonic devices.

[0017] Embodiments have been described above in conjunctions with aspects of the present disclosure upon which they can be implemented. Those skilled in the art will appreciate that embodiments may be implemented in conjunction with the aspect with which they are described, but may also be implemented with other embodiments of that aspect. When embodiments are mutually exclusive, or are otherwise incompatible with each other, it will be apparent to those skilled in the art. Some embodiments may be described in relation to one aspect, but may also be applicable to other aspects, as will be apparent to those of skill in the art.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Fig. 1 illustrates a microring resonator (MRR) modulator (MRM), in accordance with the prior art.

[0019] Fig. 2a illustrates an MRR modulator as used in a weight bank of a broadcast & weight (B&W) architecture, in accordance with the prior art.

[0020] Fig. 2b illustrates transmission curves as functions of bias voltages, at the drop port and through port of an MRR modulator in a B&W architecture, in accordance with the prior art. [0021] Fig. 3a illustrates transmission curves displaying the optical cross-talk issue, when operating a signal at a given wavelength, in accordance with the prior art.

[0022] Fig. 3b illustrates the optical modulation amplitude (OMA) of an MRR’s resonant peak, as the resonant wavelength peak of an adjacent MRR is shifted, in accordance with the prior art.

[0023] Fig. 4a illustrates an MRR modulator and a cross-section showing details of a PN junction and an in-resonator photoconductive heater (IRPH) within, in accordance with the prior art.

[0024] Fig. 4b illustrates an optical circuit for multiplying two values using a pair of MRR modulators and balanced photodetectors, in accordance with the prior art.

[0025] Fig. 4c shows an artificial neuromorphic network in which many MRR modulators, each one emulating a neuron, can have different resonant conditions, in accordance with the prior art.

[0026] Fig. 5a illustrates an embodiment of the present disclosure in which a Mach-Zehnder interferometer (MZI), with tunable phase shifters and attenuators, is configured to perform a multiplication operation, in accordance with embodiments of the present disclosure.

[0027] Fig. 5b illustrates an embodiment of the present disclosure in which a Mach-Zehnder interferometer (MZI) includes a separate Bragg grating, phase shifter and attenuator in each arm.

[0028] Fig. 5c illustrates an embodiment of the present disclosure in which a Mach-Zehnder interferometer (MZI) includes a separate phase shifter and attenuator in each arm, and a common Bragg grating, before the MZI input. [0029] Fig. 5d illustrates an embodiment of the present disclosure in which a Mach-Zehnder interferometer (MZI) includes a phase shifter in each arm, and before the MZI input: a common Bragg grating, and a common attenuator.

[0030] Fig. 5e illustrates an embodiment of the present disclosure in which a Mach-Zehnder interferometer (MZI) includes a separate Bragg grating and phase shifter in each arm, and attenuators that can be a common attenuator, at the output.

[0031] Fig. 5f illustrates a Mach-Zehnder interferometer (MZI) in which each arm includes a PSBG with an attenuator integrated within, in accordance with embodiments of the present disclosure.

[0032] Fig. 5g illustrates a contra directional coupler (CDC) acting as an input port for a signal having many wavelength peaks, and as an output port for the same signal, but reflected after one range of wavelengths has been transmitted further, in accordance with embodiments of the present disclosure.

[0033] Fig. 5h illustrates a Mach-Zehnder interferometer (MZI), the input of which is a CDC, in accordance with embodiments of the present disclosure.

[0034] Fig. 6 illustrates a MZI-based multiplier with Bragg gratings combined with phase shifters as well as attenuators, in accordance with embodiments of the present disclosure.

[0035] Fig. 7a illustrates details of a PN-junction-based, phase-shifted Bragg grating (PSBG), in accordance with embodiments of the present disclosure.

[0036] Fig. 7b illustrates design parameters of a phases-shifted Bragg grating (PSBG), in accordance with embodiments of the present disclosure. [0037] Fig. 7c illustrates a Bragg grating, doped at the center with a tunable PN junction allowing an input optical signal to undergo a p phase shift from either direction, in accordance with embodiments of the present disclosure.

[0038] Fig. 7d is a transmission spectrum of a PSBG, in accordance with embodiments of the present disclosure.

[0039] Fig. 7e is a graph showing the time delay associated with a resonating photon remaining in a PSBG, before it is transmitted as part of an output signal, as a function of the photon wavelength, in accordance with embodiments of the present disclosure.

[0040] Fig. 8 illustrates an MZM with a phase shifter and an attenuator in each arm, in which phase shifting can be applied through a variety of techniques, in accordance with embodiments of the present disclosure.

[0041] Fig. 9 illustrates both a regular Bragg grating and a sub-wavelength grating-based (SWG) Bragg grating, in accordance with embodiments of the present disclosure.

[0042] Fig. 10a illustrates an MZM with integrated intensity attenuators, in accordance with embodiments of the present disclosure.

[0043] Fig. 10b illustrates a cross-section of a germanium-based electro-absorption modulator (Ge-EAM), configured as an intensity attenuator, along with constituent materials, a doping configuration and dimensions, in accordance with embodiments of the present disclosure.

[0044] Fig. 10c is a cross-sectional view of a Ge-EAM, and applied electric fields, in accordance with embodiments of the present disclosure. [0045] Fig. 11a illustrates an MZM configured to perform a multiplication, highlighting the output location of a 2 x 2 directional coupler, in accordance with embodiments of the present disclosure.

[0046] Fig. lib illustrates details of a 2 x 2 directional coupler (DC) with signals propagating within from left to right, in accordance with embodiments of the present disclosure.

[0047] Fig. 12 illustrates a plurality of cascaded multipliers operating together to implement a vector multiplication (e.g. dot product) operation, in accordance with embodiments of the present disclosure.

[0048] Fig. 13a illustrates a 2 x 2 DC located at the input of a MZM, propagating one input signal towards two optical fdters, in accordance with embodiments of the present disclosure.

[0049] Fig 13b illustrates a 2 x 2 DC located at the input port of a MZM, propagating and recombining a split signal reflected from two optical fdter from right to left via a back- propagating path, in accordance with embodiments of the present disclosure.

[0050] Fig. 14 illustrates how three cascaded multiplication devices can be connected to balanced photodetectors and a controller, to produce the summation of a dot product, in accordance with embodiments of the present disclosure.

[0051] It will be noted that throughout the appended drawings, like features are identified by like reference numerals.

DETAILED DESCRIPTION

[0052] Silicon photonics is an emerging technology that can be used to build large-scale photonic integrated circuits (PICs) for multiple functions into a single package. Most silicon PICs can be manufactured with mature fabrication facilities, namely complementary metal oxide semiconductor (CMOS) foundries, which can offer mass production at low cost. An optical signal can be modulated by being transmitted through a tunable waveguide element, usually through carrier density tuning or thermal tuning, which can be respectively realized by adding a PN-doping region in the waveguide core or a metal heater on top of the waveguide.

[0053] Embodiments of the present disclosure provide a means for optically multiplying two numbers, where each number is encoded as an electrical input to an optical element. A first multiplier can be encoded as an electrical signal to at least one tunable phase shifter, and a second multiplier (a multiplicand) can be encoded as an electrical signal to a tunable attenuator. Once processed by the optical elements, the resulting optical signal can represent the product of the two input numbers.

[0054] By cascading a plurality of modulators in accordance with an embodiment, a plurality of separate multiplications can be performed. Each multiplication can be performed by manipulating optical signals of a different wavelength. The resulting signals can be read together to indicate the sum of the multiplications. If the original electrical inputs represent vector components of two vectors, the sum of the multiplications can represent the dot product of the two vectors.

[0055] Embodiments include a configuration of optical elements, generally referred to as a Mach-Zehnder interferometer (MZI) or alternatively a Mach-Zehnder modulator (MZM), for performing the multiplication of two multipliers, and further embodiments include a cascade of MZMs, for performing from one input optical signal, a plurality of multiplications. Other configurations are also described. By co-locating the elements for multiplying two values together in a same optical circuit, such as on a common PIC, or in a same optical circuit of a common PIC containing many optical circuits, a single integrated element-by-element multiplier is provided. A cascade of such multipliers can be used to perform vector or matrix multiplications, such as dot products. The integrated nature of the configuration can mitigate implementation problems due to spatial variation of characteristics within a photonic integrated circuit. Such variations can arise due to manufacturing imperfections and can otherwise affect device performance.

[0056] Before describing the invention in detail, a review of some of the relevant state of the art is given. Fig. 1 illustrates a microring resonator (MRR) modulator (MRM) according to the prior art. Such an MRM can be used as an optical element in a photonic multiplier for example via a broadcast and weight architecture as discussed briefly below. The cross- section image shows some fabrication details of the modulator. For optical signal modulation, either or both of a PN-junction 120 doped in the waveguide, and a metal heater 130, can be utilized.

[0057] The “broadcast-and-weight” (B&W) architecture, which can use MRR modulators, can be used for implementing neuromorphic processors to PICs as well as generalized, fully programmable network models. In the B&W approach, the output of each MRR can be assigned a unique wavelength carrier, which can wavelength division multiplexed (WDM) and broadcast. Incoming WDM signals can first be weighted by reconfigurable, continuous valued filters acting as photonic weight banks. The outputs of the weight banks can then be summed by monitoring its total power. A B&W architecture can be implemented using a bank of tunable add-drop MRR modulators recreating on-chip synaptic weights and emulating physical neurons. By modulating the refractive index (RI) of the waveguide’s core in each modulator, the transmission intensity at the drop and through ports of each modulator can change accordingly, and this can change the weights of the weight bank array individually, because a weight corresponds to a difference between an intensity at a drop port and an intensity at a port intensity (/_Drop - /n_m).

[0058] Fig. 2a illustrates a MRR modulator as used in a weight bank of a broadcast & weight (B&W) architecture. The drop 205 and through 210 ports of an add-drop ring 215 are connected to a pair of balanced-photodetector (BPD) 220. The photodetectors (PD) can individually sum the total optical power of an operational optical-band and the balanced pair of photodetectors (e.g. photodiodes) can perform a subtraction 225 between the drop port power and the through port power. In an application, the resulting output can be used to tune the refractive index of another modulator 230, which can modulate a pump signal 232 to produce an optical output 234. This configuration can allow the optical output 234 to be a function of the drop 205 and through 210 port signals.

[0059] Fig. 2b shows transmission curves as functions of bias voltages, at the drop port and through port of a MRR modulator in a B&W architecture. The upper graph shows the power 235 at the drop port 205 (with reference to Fig. 2b) and power 240 at the through port 210, at different voltages 250. The lower graph shows the difference between the two outputs i.e. the resulting weight 255.

[0060] In some embodiments, MRR modulators can be implemented using in-resonator photoconductive heaters. These are referred to as IRPH-MRRs, and the refractive index (RI) tuning scheme in such modulators is based primarily on thermo-optical modulation. In some embodiments, MRR modulators can be implemented by modulating the carrier density using a PN junction inside the MRR’s waveguide core. These are referred to as PN-MRRs. A PN junction refers to a structure comprising joined positively and negatively doped semiconductor regions, as would be readily understood by a worker skilled in the art. PN- MRRs may have a greater modulation bandwidth than IRPH-MRRs. With either an IRPH- MRR, a PN-MRR modulators, or a MRR modulator combining the two, when a bias voltage is applied, the modulator’s resonant wavelength peak can drift and because of the Lorentzian- shaped tail of a resonant peak, drifting can influence the OMA of adjacent resonant peaks. This can be referred to as optical cross-talk.

[0061] Fig. 3a shows transmission curves displaying the optical cross-talk issue, when operating a signal at a given wavelength (i.e. l₂). When cascading multiple MRR modulators in a row 305, a shifting 310 of wavelength li (usually a red shift) will also shift the Lorentzian-shaped tail, and influence 315 the OMA of the adjacent peak at l₂. This is what is referred to as optical cross-talk. The greater the number of MRR modulators the greater the cross-talk influence.

[0062] Fig. 3b shows the optical modulation amplitude (OMA) of a MRR’s resonant peak, as the resonant peak of an adjacent MRR is shifted. As a bias voltage is applied 320, the resonance peak li is shifted, the power transmitted at the l₂ MRR drop port decreases 325, and the power transmitted at the l₂ MRR through port increases 330. The detectable power difference for l cannot be greater than the OMA and available weight 335, which decreases.

[0063] To address the cross-talk issue, an absorption-based modulation scheme can be investigated. By making use of a MRR modulator fabricated on a silicon-on-insulator (SOI) platform, and a graphene-based electro-absorption modulator (EAM), the optical intensity of a MRR’s resonant wavelength peak, such as li in fig. 3a, can be tuned without the peak at /._\ being shifted. Keeping a MRR’s peak (e.g. l_\) from being shifted can prevent cross-talk.

[0064] Another solution for addressing the cross-talk issue is the development of an MRR modulator solution based on interferometric-coupling, where the coupling coefficient between the input signal and the MRR, and the coupling coefficient between the MRR and the output signal, can both be tuned to change the extinction ratio (ER) of the output signal, without the wavelength being shifted. However, controlling such a system can require complex electrical circuitry, and because of additional interferometric-coupling regions, the footprint can be large compared to that of a conventional MRR’s.

[0065] In a conventional artificial neuromorphic network or a conventional matrix multiplication accelerator, two separate MRRs, one per multiplier (i.e. one per vector or matrix entry), are required to perform a dot product operation. To achieve a dot product between two vectors, each product of two vector components can be assigned a different wavelength, and each component can be an electrical input to a separate MRR, via MRR modulation. [0066] In case of matrices, the rows or columns of each matrix can be processed as vectors, a dot product can be performed, and the results can be used to rebuild a resulting matrix. In this case, an input vector can be seen as a degenerate case of a matrix (only one row or only one column), and the matrix can be said to be “vectorized”, into as many vectors as necessary for it to be processed by the available MZMs. As will be readily understood by a worker skilled in the art, a product of two matrices A and F can be represented using a matrix C having entries Cy computed using a dot product between the i^th row of A, denoted row;(A) and the j^th column of F, denoted column_j(F), i.e.:

Cij = roW (A) columnfyF)

^{= a}il/lj + ^ai2 fl) +

and f_i} represent the entry in the i^th row and the j^th column of matrices C, A and F, respectively. It is noted that this also holds for vector and scalar cases, i.e. where a “matrix” degenerately has one column, one row, or one entry.

[0067] To implement a multiplication, each of two MRRs can be tuned with an IRPH, a PN junction, or both. Each MRR can be therefore modulated at the same resonant condition, in order to modify an output intensity accordingly. By changing the refractive index of the MRR’s waveguide core using thermal or carrier density tuning (or a combination of both), the transmission intensity of a MRR’s resonant wavelength can vary. The output intensity of the first MRR can be adjusted to represent a component <¾ of a first matrix A, and the output intensity of the second MRR can be adjusted to represent a component of a second matrix F. With multiple pairs of MRR’s in series, each pair carrying a different wavelength, the product of each pair of components a,_/fy can be obtained. A balanced-photodetector (BPD) can be used to accumulate and sum the output intensities obtained, thereby implementing a dot product operation, which may be part of a matrix multiplication operation. [0068] Fig. 4a represents a MRR modulator 405 and a cross-section 410 showing details of a PN junction and an IRPH associated therewith, to allow modulation of its refractive index and therefore its resonant wavelength.

[0069] Fig. 4b shows a configuration able to perform a multiplication operation between two scalar quantities (such as <¾ and as discussed above), using two MRR modulators 415 connected in series. A multiplication operation can be performed as part of a vector or matrix multiplication operation (e.g. as discussed above). In more detail, the balanced photodetectors (BPD, comprising two photodetectors and a transimpedance amplifier) receive output of the two MRRs 415 connected in series. The second MRR is an add-drop MRR, allowing both positive and negative values to be represented for the multiplicand (e.g . fig in a multiplication a,f_t-,). The first MRR allows positive values to be represented for the multiplier (e.g. <¾). In the illustrated configuration, the multiplier is 0.8 and the multiplicand is 0.1. The multiplicand =0.1 is represented as a difference between two values 0.55 and 0.45. In other words, for a multiplicand of y, the add-drop MRR is configured to route a first portion ( 1 -y)/2 of its input light to a first output port and to route the remaining portion (l+y)/2 of its input light to a second output port. In the present case, the first portion is equal to 55% of the input light and the second portion is equal to 45% of the input light. Because the first MRR attenuates the input light by 20%, i.e. producing an output with an intensity of 0.8 relative to an input intensity of 1 unit, the second MRR routes 45% of the input intensity of 0.8, which is equal to light with a relative intensity of 0.36, to the first (lower) output port. The second MRR also routes 55% of the input intensity of 0.8, which is equal to light with a relative intensity of 0.44, to the second (upper) output port. The BPD outputs a signal indicative of the difference 0.44-0.36=0.08. Thus, a multiplication between the multiplier 0.8 and the multiplicand 0.1 is implemented. By adding multiple such MRRs in series before the BPD, each operating at a different wavelength, with the BPD responsive to all wavelengths, a sum of plural multiplications can be performed, for example to implement a vector dot product multiplication, which may be part of a matrix multiplication. This principle is illustrated for example in Fig. 4c. [0070] Fig. 4c shows an artificial neuromorphic network in which many MRR modulators (MRMs), each one emulating a neuron, can have different resonant conditions. As discussed above, multiplication between two scalar values can be achieved by using two MRMs operated at the same wavelength. A dot product between two vectors can be achieved by multiplying multiple pairs of scalars, using corresponding pairs of MRMs operated at different wavelengths. The output intensity can be modified by using thermal or carrier density tuning in each MRM. As illustrated, there are two cascaded banks 425, 430 of four MRMs each, per row-wise photonic circuit 420. The first bank 425 is used to represent the (non-negative) entries of a first vector, and the second bank 430 is used to represent the entries of a second vector. The first and second vectors are multiplied together in accordance with a dot product operation. The first and second vectors can be rows and columns, respectively, of matrices being multiplied together.

[0071] A drawback of the aforementioned system is that because two individual MRMs are required to implement each multiplication of two vector components, fabrication variations between the two MRMs can increase with the size of the matrix multiplication (MM) to be implemented, or with the dimensions of the vectors or matrices (or vectorized matrices) to be multiplied. For example, to perform a large-scale multiplication between two vectors A and F each having 1000 components, one thousand (1000) MRMs, cascaded in a row are required to represent each vector. Two MRMs operating to modulate intensity at the same resonant peak (one from the first cascaded MRM bank and another from the second cascaded MRM bank) can be far apart from each other on the chip, which means that fabrication tolerances for imperfections can be very low. Therefore, in such a large optical MM acceleration system, additional modulations can be required to compensate for fabrication imperfections and the required energy consumption can be too great.

[0072] To address problems existing in current MRM-based optical computing systems, as mentioned above, embodiments include a device based on a single modulator that uses an intensity modulation scheme operating at a fixed (non-shifting) wavelength, and that is able to perform a multiplication between two corresponding vector (or matrix) entries (i.e. two components). By using a plurality of such devices, or by using the same device multiple times, or a combination thereof, a vector (e.g. dot product) or matrix multiplication can be performed.

[0073] To achieve a multiplication operation with an optical modulator, an embodiment can make use of a Mach-Zehnder interferometer (MZI) configuration, in which an electronically modulated phase shifter is included in at least one of the two arms (i.e. optical paths) to phase shift at least one portion of the signal, and an electronically modulated attenuator is included either before, within, or after the MZI, to modulate the intensity of both portions of the signal, whether split or combined. Modulating of intensity can refer to adjusting the intensity (e.g. amount) of light in the optical signal, for example by absorbing a controllable portion of such light. A phase shifter can be configured to be an optical filter as well, in which case it can be referred to as a phase-shifted Bragg grating (PSGB). An MZI that includes a PSBG can be referred to as a phase-shifted Bragg grating-assisted MZI (PSGB-MZI), or as a phase-shifted Bragg grating-assisted MZM (PSGB-MZM). If an optical modulator configuration also includes an electro-absorption modulator (EAM), the assembly can be referred to as a PSBG- EAM-MZI, or as a PSBG-EAM-MZM. If an optical element, such as a phase shifter or a modulated attenuator, is within the MZI, or sufficiently close for the MZI and the optical element to be considered as the same multi-element modulation device, the MZI and the optical element can be said to be co-located. Co-location, referring to two devices, can additionally or alternatively be understood to mean that the two devices are structurally integrated with one another, or adjacent to one another (e.g. not connected by an elongated waveguide), or otherwise located in the same part of a photonic integrated circuit layout. The phase shifter(s) and attenuator(s) cooperate to perform the multiplication. The phase shifter(s) steer optical signal to the two MZI outputs so that the relative amounts of signal at the two outputs represent, by way of a difference in intensity, a multiplier in the multiplication. The attenuator(s) attenuate optical signal in the two MZI outputs (or else prior to or following the MZI) in order to pass a remaining portion of such optical signal in proportion to a multiplicand in the multiplication. [0074] In another embodiment, a MZI configuration can include phase shifters that do not incorporate Bragg gratings. Instead, the input to the MZI configuration is a contra-directional coupler (CDC) operative to perform the function of a Bragg grating. (It is noted that a CDC typically includes a Bragg grating.) Because a CDC includes an optical grating, an embodiment with a CDC as input ports does not require additional optical gratings, but it can potentially include some.

[0075] In a MZM according to an embodiment, the inclusion of an index modulator such as a PN-junction within a Bragg grating can allow modulation of the Bragg grating’s refractive index, and therefore the phase shift of an optical signal propagating through it. Such a phase shift can cause a phase difference between the two arms of the MZM, and therefore modulate the intensity of the MZM at each of a pair of outputs thereof. A first vector component to be multiplied can be encoded as an electrical signal modulating a Bragg grating via a PN- junction. A phase shift can therefore correspond with the value of a component of a first vector.

[0076] Further, in an MZM according to an embodiment, an intensity attenuator such as an EAM can be inserted in each arm (or another location), in order to adjust the output intensity. A second vector component to be multiplied (the multiplicand) can be encoded as an electrical signal modulating the two EAM similarly, and thereby adjusting the signal’s intensity in each arm of the MZM arm. The amount of absorption can correspond to the value of a second vector component. An intensity attenuator is also referred to as an optical attenuator, or simply an attenuator. These attenuators are configured to modulate intensity of signals output by the MZM, i.e. at the first and second outputs thereof, as described elsewhere herein. As the MZM has two outputs, two signals are output. Generally, the attenuator(s) modulate these two signals by the same amount (which need not be precisely the same). The modulation by the attenuator(s) can be direct or indirect, depending on the attenuator placement. For example, where an attenuator is placed before the MZM, they modulate the input to the MZM, thereby indirectly modulating the signals output by the MZM. Where the attenuators are placed following the MZM, the attenuators can directly modulate the signals output by the MZM. Where the attenuators are placed within the MZM, they can be regarded as directly or indirectly modulating the signals output by the MZM, depending on the perspective taken.

[0077] In an embodiment, modulation of a signal’s output intensity can be performed without the signal’s wavelength being shifted. Therefore, cross-talk between two signals having different wavelengths can potentially be non-existent. Moreover, because a Bragg grating has little to no limitation on the free spectral range (FSR) of input signals, it can allow for large- scale implementation. Further, the footprint of a multiplication device according to an embodiment, such as a PSBG-MZM, a MZM with a CDC as an input, and other embodiments discussed, can be relatively small, and can be highly tolerant to fabrication imperfections.

[0078] By making use of interference between two optical signals having a phase difference, an embodiment simultaneously incorporating an MZM scheme and an EAM scheme in one modulator can realize a multiplication. This can effectively reduce the footprint, compared to a system based on two MRMs.

[0079] In an embodiment, a p-phase-shifter in the middle of a Bragg grating arm can generate one resonant peak within the stopband. By having a single resonant peak, the FSR limitation for multi-operational channels can be eliminated.

[0080] In embodiments, modulation can be realized by using PN-junctions and Ge-EAMs, both of which can have an EO-bandwidth larger than 50 GHz. In an embodiment performing a dot product between two vectors, each one having many components, many multiplications are required, and the high bandwidth allowed by an embodiment can allow low latency of the dot product operation as a whole.

[0081] In an embodiment, the materials used, and their manufacturing processes can be can be mature and be compatible with CMOS foundries, which can reduce fabrication complexity and costs.

[0082] In an embodiment, phase shifting and absorption (attenuation) modulation can be performed on an optical signal without the signal’s wavelength being shifted. Therefore, if multiple channels are being tuned simultaneously, overlap of one resonant peak with another can be very low, minimal or non-existent, and this can result in cross-talk between channels also being low, minimal or non-existent. Minimal cross-talk can help ensure that the intensity of each signal remains optimal.

[0083] In an embodiment, a device based on a single MZI-type modulator can perform a multiplication using an optical signal, the intensity of which can be modulated without the optical signal’s wavelength being shifted. By introducing a phase shifter, controlled for example by thermal modulation or carrier density modulation, into each arm of a symmetrical 2-arm MZI, the intensity of a signal resulting from the interference of the signals in each arm of the MZI can change according to the phase difference between the two signals, because of constructive and destructive interference when the signals recombine at the MZI output..

[0084] For implementing a multiplication, a phase shifter can be introduced in each arm of an MZI in order to cause a phase shift and corresponding intensity modulation (when interfering), according to a first encoded vector component, and an intensity absorption element, such as an electro-absorption modulator (EAM), can be introduced immediately after, in order to cause a second intensity modulation, according to a second encoded vector component. At the output of a so-modified MZI, referred to as an MZM, a 2 ^c 2 directional coupler (DC) can be added.

[0085] In an embodiment that includes a 2 ^c 2 directional coupler (DC) at the output of an MZM, the two signals modulated by phase shifters and attenuators are from an input signal to the 2 x 2 DC. The 2 x 2 DC can be designed to adjust the intensity ratio of the two signals according to their phase difference, and to produce an output that is a function of the electrical signals received by the phase shifters and attenuators. [0086] In an embodiment, a phase-shifter in one arm of an MZM, such as a PSGB, can be modulated to cause any phase difference from 0 to 2p between the two signals. In another embodiment, the phase shifters in the each arm can be modulated simultaneously in a push- pull scheme, which can also result in any phase difference from 0 to 2p. A phase difference between the two signals, being a number from 0 to 2p, can be mapped to a negative, null, or positive multiplier.

[0087] As for the intensity absorption elements (EAMs), in an embodiment, they can apply the same absorption to both signals (having a phase difference between 0 to 2p) and together cause attenuation (i.e. absorption or intensity modulation) of the combined signals anywhere from 0 to 1. This can correspond to an arbitrary positive or null multiplicand (i.e. vector component).

[0088] In another embodiment, a negative, null or positive multiplicand can be mapped with absorption modulation, if a calculation is done twice instead of only once. To do so, an intermediate absorption 5_nuii can be defined, and 5_reai can be the actual absorption. Then, the subtraction of 5_nuii from 5_reai can represent a multiplicand [B] that is negative, null or positive. With [A] as the multiplier, a multiplication can be represented as:

[A][b] = [A](B_reai — B_nuu)

[0089] To implement the above multiplication, it suffices to use an optical circuit of an embodiment to perform a first multiplication and a second multiplication:

and then subtract the second result from the first to get the result of [A] [B] .

[0090] The intensity of an optical signal recombined from two signals having a phase difference and being attenuated can represent a multiplication between a first vector (or matrix) component, implemented by a phase difference between the two signals, and a second vector (or matrix) component, implemented by absorption (i.e. attenuation).

[0091] Fig. 5a illustrates an embodiment of the present disclosure in which a single MZI is configured to perform a multiplication, using an intensity modulation scheme at a given (e.g. fixed) wavelength. An optical signal presented (e.g., introduced, input, submitted) at an input 505 of the MZI is first split by a Y junction 510 into two portions having substantially equal intensities. In practice, the Y junction may be implemented using a directional coupler, such as a 3-dB directional coupler. Each of the two portions then propagates through similar optical elements in each arm: first a tunable phase shifter 515, and then a tunable attenuator 520. Each phase shifter 515 can be tuned with a thermal or a carrier density modulation 525 and it can apply a corresponding phase shift to its respective portion of the input signal. The tunable attenuator can attenuate the phase-shifted signal according to another electrical input. Tuning of the phase shifter causes a controllable amount of phase shift to be imparted to the signal portion passing through same. The phase and intensity of the output signals 535 can be tuned according to electrical inputs to the thermal/carrier tuner 525 of the phase shifter, and to the attenuators 530. In the illustrated embodiment, the same voltage level is applied to both attenuators, in order to cause each attenuator to attenuate its respective input signal by substantially a same amount. The electrical inputs can correspond to multiplier and multiplicand of a multiplication operation. A pair of attenuators, each disposed in a respective arm of the MZI, are shown. An MZI inherently has two arms (generally formed from waveguides) for propagating light along two different paths. The pair of attenuators operate to attenuate light propagating along both of these two different paths, with each attenuator operating on light propagating along one of the two different paths.

[0092] The two arms of the MZI end at a 2x2 coupler where interference of the signals in the two arms takes place. The outputs of the 2x2 coupler, which provide the optical outputs 535, are referred to as a first output and a second output. In general, as will be readily understood by a worker skilled in the art, the MZI is operable, by control of the phase shifters, to controllably steer portions of an input optical signal to the first and second outputs. That is, a first controllable portion of optical signal can be caused to be produced (e.g., output) at the first output, and a second controllable portion (e.g., the remainder of the input optical signal) can be caused to be produced at the second output. It is well understood that an MZI can be used as an optical switch to steer all of the input signal to one of the first and second outputs. Additionally, the MZI can be operated in an intermediate region to steer part of the optical signal to the first output, and the remainder of the optical signal to the second output. This steering of parts of the optical signal to the two outputs corresponds to the above-mentioned causing of controllable portions of optical signal to be produced at the two outputs. These controllable portions of optical signal are thus produced as a pair of output signals. By suitable action of the phase shifters, the pair of output signals can be produced such that their difference in intensity represents a multiplier in a multiplication operation being performed. For example, if the pair of output signals have the same intensity, their difference is zero and the multiplier may be zero. If the difference in intensity is x, the multiplier may be proportional to x or -x, depending on which of the pair of output signals is larger.

[0093] Although Fig. 5a illustrates a balanced MZM having a phase shifter in each arm, it will be readily understood by a worker skilled in the art that a phase shifter can be implemented in only one of the two arms, in an unbalanced configuration. Either the balanced or unbalanced configuration can be operated to implement a desired phase difference between the signal portions in the two arms. In the balanced configuration, the two phase shifters may operate in a push-pull manner. It is noted, however, that a narrow bandpass optical filter (e.g. a Bragg grating) may be required in both arms, unless the optical filter is implemented before the Y-junction 510. The Y-junction 510 can be implemented using beam spliher, or using a directional coupler such as a 3-dB 2x2 directional coupler.

[0094] In embodiments, a phase shifter in each arm of an MZM can be a phase-shifted Bragg grating (PSBG), and the intensity ahenuator in each arm of an MZM can be a germanium- based electro-absorption modulator (Ge-EAM). Other types of ahenuators, for example ahenuators based on phase change materials, can be used. Each PSBG can be modulated by having a PN-junction doped within its waveguide. This can allow a modulation speed in the range of 20 to 30 GHz. A Ge-EAM can consist of a PIN-junction allowing up to 56 GHz EO- bandwidth. Thus, the phase shifter can be integrated with a Bragg grating device. This integration is such that the phase shifter is located internally within the Bragg grating structure, i.e. built into the Bragg grating structure. This integration may reduce complexity and the count of optical elements, as separate phase shifters and Bragg gratings are not required. Alternatively, a Bragg grating device can be provided on its own and a phase shifter can be provided separately. For example, output of the Bragg grating device can be coupled to an input to the phase shifter, and output of the phase shifter can be coupled to an input to the attenuator. As another example, the output of a Bragg grating can be coupled to an input to the attenuator, and the output of the attenuator can be coupled to an input to the phase shifter.

[0095] Fig. 5b illustrates an alternative embodiment, in which an optical fdter (e.g. Bragg grating) 550 is separate from the phase shifters 555.

[0096] Fig. 5 c illustrates an embodiment where a Bragg grating is located prior to the Y junction in order to avoid duplication. In a single-ended version, one of the phase shifters 555 can be omitted. Although not illustrated, one or both ahenuators 520 can be alternatively placed before one or both phase shifters 555.

[0097] Fig. 5d illustrates an embodiment where ahenuators are placed prior to the input of a MZI configuration. A technical effect of this configuration is that only a single ahenuator 520 is needed. The ahenuator can modulate (e.g., set, adjust, ahenuate, amplify, change) an intensity of the optical signal prior to it being presented at the input, thereby indirectly adjusting the intensities. A benefit of this embodiments is that the count of optical elements is reduced, and thus the system’s complexity. Notably, the single ahenuator in Fig. 5d is located following an output of an optical filter. A technical effect of this configuration is that only one ahenuator is needed, thus reducing the count of optical elements, and complexity.

[0098] Fig. 5e illustrates an embodiment where the ahenuators 520 are placed after the MZI structure. A pair of attenuators is thus provided, and located following the MZI first and second outputs. The two attenuators can, in some embodiments, be integrated together and provided using a single element. That is, a single attenuator, which is operatively coupled to a pair of waveguides following the MZI first and second outputs, can be used.

[0099] In Fig. 5e, the Bragg grating can alternatively be located prior to the input of the MZI (e.g. prior to the Y junction) as in Fig. 5c or Fig. 5d. Generally, the attenuators can be located anywhere in the structure after the Bragg grating, and the phase shifters, when not integrated with the Bragg grating, can be located anywhere in the MZI arms after the Bragg grating. When the phase shifter and Bragg grating are integrated, they are located in the MZI arms and prior to the attenuators. Here and elsewhere, the Bragg grating may be omitted if not required, for example if only one multiplier device is present in a given optical circuit, or if another means such as an optical multiplexer, or a system of multiple separate optical sources and feeds, is used to separate different optical inputs from one another.

[00100] Fig. 5f illustrates yet another embodiment, in which the attenuator is integrated into the Bragg grating structure. In an embodiment, the phase shifter can also be integrated into the Bragg grating structure, forming a structure referred to as a phase-shifted Bragg grating (PSBG) 557. An attenuator 515 may be located in the phase-change cavity of the Bragg grating, which only allows signals at the resonant wavelength to have multiple round trips within the Bragg grating structure. This can provide for a strong absorption operation for resonant wavelengths as opposed to other wavelengths.

[00101] In embodiments, the Bragg grating in Fig. 5c and Fig. 5d may be implemented using a contra-directional coupler (CDC). If the input of CDC is an optical signal having many wavelength peaks, a CDC can transmit one of the many wavelength peaks, and reflect the remaining wavelength peaks. The reflected wavelength peaks can be directed to another multiplication device having a CDC input port as well, which can transmit a second wavelength peak, and reflect the remaining peaks. By cascading many multiplication devices, each one having a CDC as an input Y-j unction, an optical signal having many wavelength peaks can be filtered at each device such that each peak of the signal is processed by a different multiplication device of the cascade.

[00102] Fig. 5g illustrates a contra-directional coupler (CDC), having four ports. The CDC further has two adjacent waveguides, with the first waveguide having two of the ports 565, 570, and the second waveguide having the other two ports. The waveguides are adjacent and sufficiently close for light coupling to occur in which light in one waveguide potentially transfers to the other waveguide. One of the ports 565 can receive input light having multiple peaks. Another one of the ports 570 (e.g. the through port) can pass a limited portion (e.g. one peak) of said received input light toward the attenuator and MZI structure. Another one of the ports 575 (e.g. the drop port) can pass the reflected remainder of the received input light (e.g. all but said one peak) toward another device.

[00103] Similarly, Figs. 5h illustrates an embodiment similar to Fig. 5d, where a Bragg grating is also implemented using a contra-directional coupler (CDC). The CDC 560 can be as in Fig. 5g. In particular, as shown in Fig. 5g, the CDC 560 allows for cascading of multiple photonic devices for example as described with respect to Figs. 12 and 14. The CDC thus operates as an optical filter which transmits some optical wavelengths received at a first port 565 (see FIG. 5g) toward the remainder of the photonic device via a second port 570, and reflects the remaining optical wavelengths via a third port 575.

[00104] It is noted that, when locating the attenuator before or within a phase shifter, Bragg grating, or both, care should be taken to ensure that the device still operates sufficiently well for all anticipated amounts of absorption. For example, if the attenuator is controlled to absorb 90% of an input optical signal, it should be verified that the Bragg grating, MZI, phase shifters, or combinations thereof following the attenuator can sufficiently and accurately manipulate the remaining 10% of optical signal as intended. In various embodiments, particularly where the attenuator has a wideband operation, at least part of the Bragg grating is typically placed before the attenuator, so that out-of-band signal is reflected toward another multiplier device without absorption. [00105] Where embodiments include a pair of attenuators (e.g. as in FIGs. 5a, 5b, 5c, 5e and 5f) coupled to a respective pair of waveguides, a single device may be provided to implement both atenuators. That is, a single atenuator structure may be coupled to both waveguides provided that crosstalk between the waveguides is acceptably low. A phase change material (PCM) may potentially be used as such as atenuator. Functionally, the single atenuator operates to atenuate optical signals in each waveguide by substantially the same amount and thus acts the same as a pair of atenuators. Structurally, the single atenuator is a single integrated device which is coupled to two waveguides instead of one.

[00106] Fig. 6 illustrates a symmetric MZM multiplier device including Bragg gratings, each incorporated with PN-junction based phase shifter. The multiplier device further includes a pair of atenuators 620, such as Ge-EAMs. A multiplication can be performed by modulating the output intensity through interference and absorption schemes within the device. First, an input signal 605 can be split in two parts 610 having substantially equal intensities. Then, each part 610 can pass through a (e.g. PN-junction based) phase shifter 615 and then a Ge- EAM 620. The materials and doping configuration of the Ge-EAMs are indicated in the figure. Then, electrical inputs to the phase shifter and the Ge-EAM can result in the two output signals from the MZM having different intensity values. The inputs to the phase shifters can be set based on a value of a multiplier, and the inputs to the Ge-EAMs can be set based on a value of the multiplicand, where the multiplier and the multiplicand are two values to be multiplied together.

[00107] In an embodiment, a phase shifter with a Bragg grating can be used (PSBG), and in another embodiment, a phase shifter can be without a Bragg grating, and the filtering function of the Bragg grating can be performed by a CDC at the input of a multiplication device.

[00108] In an embodiment, a phase shifter can be doped with a PN-junction, or a thermal heater can be added on top. Either case can allow the phase of the phase shifter’s output signal to be varied. If each arm of an MZI has such a phase shifter, the phase at each arm can be biased differently. If the phase shifter is a PSBG, the roundtrips of a resonant wavelength in a Fabry-Perot (FP) cavity within the PSBG can cause the signal variation to be more pronounced (up to at least 7-fold). A recombination of the light from the two phase shifter outputs can be achieved with a 2 x 2 directional coupler (DC), which can redistribute the light from the two MZI output ports, depending on their phase difference. By adding an electro-absorption modulator (EAM) after each phase shifter, the output intensity in both arms can be further modified, potentially at high-speed. This can facilitate a multiplication operation within the same device.

[00109] In an embodiment, a multiplication between a_ik and f_kj can be implemented, where a multiplier a_ik is either a negative or a positive number, and a multiplicand is a positive number. Further, in an embodiment, the area of a signal can be constant, or at least similar at each port, such that calculating the power at an output port is similar to calculating an intensity at the same port, because the power is intensity times area ( P = l A).

[00110] In an embodiment, the input powers at each arm can be i and P2, and after the signals have gone through phase shifters causing a Af phase shift, attenuators causing an absorption factor A, and a 3-dB directional coupler, the output powers 3 and 4 can be:

[00111] In an embodiment, signals 3 and P4 can be directed to a BPD, and therefore the signal of interest is:

P₄ — P₃ = P_tA cos (Af) [00112] In an embodiment, the MZI input 510, viewed here as a Y-junction, can split an input equally such that i = 2 = 0.5 and therefore:

[00113] By pre-selecting that cos(A^) is to be from 0 to 1, a range can be set for Af to be from 0 to p/2. In another embodiment, a range can be from — p/2 to p/2.

[00114] For a BPD to produce the same result with the same multiplier and multiplicand as the prior art of Fig. 4b (i.e. multiplier 0.8 and multiplicand 0.1), the difference in the outputs can be set to P₄ — P₃ = 0.08. To use the full range of an attenuator, the A factor can be set to 0.8 to match and correspond with multiplier a_ik = 0.8. From the above equation, the phase shift Af to be applied with phase shifters of an embodiment is:

0.8 co (Affl)

0.08 = -

Af = 0.37

[00115] Therefore, in an embodiment, a multiplication between multiplier <¾ = 0.8 and multiplicand = 0.1, can be implemented by applying a phase shift of D<r = 0.37 and an absorption of A = 0.8. By propagating the resulting output signals to a BPD, the BPD can produce the same result of 0.08 as if the originating signals had been produced by a system of the prior art having two modulators (Fig. 4b) instead of one (Fig. 6).

[00116] In view of the above, the multiplication can be implemented by operation of one or more phase shifters and one or more optical attenuators in combination. In particular, the one or more phase shifters operate to produce a pair of output signals of the MZI structure which have a difference in intensity which represents a multiplier in the multiplication. The intensities may correspond to output powers. The intensities of the pair of output signals of the MZI structure relate to the proportion of input light steered toward each MZI output. [00117] The one or more optical attenuators operate to pass light in proportion to a respective multiplicand in the multiplication. For example, the attenuators may pass a proportion of light which is an increasing (e.g. approximately linear) function of the multiplicand. That is, if an attenuator receives light of intensity x and the multiplicand is p, the multiplicand can be normalized to a value /¾? between 0 and 1, and the attenuator can be operated to pass a proportion p_N of light input thereto, so that intensity of light at the output of the attenuator is x/ v. Attenuators may absorb a portion of light input thereto and pass the remainder of the light input thereto.

[00118] Fig. 7a illustrates details of a PN-junction-based phase shifter 705, according to an embodiment. The PN-junction-based phase shifter can include a Bragg grating 707 and a PN- j unction tuner 709, which can cause an optical signal propagating in the Bragg grating 707 to undergo a tunable phase shift. By integrating the Bragg grating and the phase shifter together, a reduction in the number of required optical elements can be realized. The Bragg grating functions to admit some of the light while reflecting other light for treatment by other devices, such as other multipliers. The phase shifter functions to implement part of the required multiplication operation.

[00119] An embodiment can include an optical element causing an input signal to be phase- shifted according to a controller output, where the controller directs multiplication operations. Such an optical element can be referred to as a phase shifter.

[00120] Embodiments can include a Bragg grating. In a Bragg grating, the pitch A, the corrugation depth Ac and the Bragg length L, can be selected for the coupling strength k between the Bragg grating and the waveguide to be maximized for the resonant peak to be at a specific wavelength X_c. to have a specific stopband range D l_B. to have a specific quality factor, and to have a specific extinction ratio (ER). Relations between these values can be expressed as:

where:

An represents the index contrast between the high and low silicon parts, neff represents the effective index of the Bragg grating waveguide, n_g represents the group index of the Bragg grating waveguide, and L represents the total length of the Bragg grating.

[00121] Based on these relations, in order to obtain a strong coupling strength within a design, a long Bragg grating having a deep corrugation depth can be used.

[00122] Fig. 7b illustrates some design parameters of a Bragg grating, according to an embodiment. Design parameters can include the pitch L 710 between corrugations 710, the height of a corrugation Ac 720, and the Bragg grating’s length L 730. These parameters can be adjusted to tune output performance. The various structural parameters of the Bragg grating can be selected and implemented in order to achieve a desired operation (e.g. a desired transmission spectrum as in Fig. 7d), for example in order to select the wavelengths (e.g. center wavelength and bandwidth) which are admitted through the Bragg grating and the wavelengths which are back-reflected by the Bragg grating.

[00123] If the center of a Bragg grating is doped with a PN-junction, it can be modulated such that an input signal having a specific wavelength will undergo a controllable phase shift between 0 and p radians. A p-radian phase-shift can result in the Bragg grating acting as two adjoining Bragg gratings, each one acting as a wavelength-selective mirror, by causing photons of the specified wavelength to resonate within. [00124] Fig. 7c illustrates a Bragg grating, doped at the center with a tunable PN junction that allows an input optical signal to undergo a p-radian phase shift, according to an embodiment. Design parameters can further include the corrugation thickness a 750, the spacing b between corrugations 755, the effective refractive index i?_effi of a corrugation 760, and the effective refractive index n_e m of the spacing between corrugations 765.

[00125] When a PN junction in a doped Bragg grating is biased, photons at the resonant wavelength can go through multiple round trips. This can also occur if the tuner is a thermal heater. The multiple round trips cause the photons to have a larger group delay, which can result in a much larger phase shift. Compared to photons of other wavelengths, the increase in delay can be up to at least 7-fold, in some embodiments.

[00126] Fig. 7d is a transmission spectrum of a Bragg grating, in particular a PSBG, according to an embodiment. The wavelengths D \_B within a stopband range 770 are prominent.

[00127] Fig. 7e is a graph showing the time delay a resonating photon can remain in a Bragg grating, in particular a PSBG, before it is transmitted as part of an output signal, as a function of the photon wavelength, according to an embodiment. The wavelengths 775 correspond to those of the stopband in Fig. 7d.

[00128] In embodiments, phase shift modulation (i.e. active phase shifting) can be performed with any one of a PN junction, a PIN junction with carrier density tuning, a metal heater, and an IRPH with thermal tuning.

[00129] As for optical filtering, different kinds of optical filters can be used including Bragg gratings side-wall gratings, a “top grating”, and others. Alternatives to Bragg gratings include a microring resonators (MRR), a microdisk resonators (MDR), and a variety of one dimensional, two-dimensional, and three-dimensional photonic crystals (PHC). [00130] As with a PSBG, a resonator such as an MRR, an MDR and a PHC can also offer a specific resonant condition within a Fabry-Perot (FP) cavity within. This can allow a broadcast signal to be de-multiplexed in a single waveguide. Then, depending on the index modulation in the resonator, the phase can change accordingly, and this can be used to cause a variation between two output intensities of an MZI, thereby making it a modulator (MZM).

[00131] Fig. 8 illustrates an MZM in which phase shifting can be applied through any of a variety of techniques, according to different embodiments. In embodiments, phase shifting can be achieved with any of a side-wall grating 805, a top grating 810, a ring resonator 815 and a photonic crystal 820, and phase shift control can be achieved by modulating an index of refraction in any of these elements using any of thermal tuning 825 and carrier density tuning 830. In general, a controllable element which imparts a (e.g. electrically) controllable amount of phase shift to an optical signal can be used in one or both arms of the MZI structure, and a variety of technologies for implementing such a controllable element can be used.

[00132] In some embodiments, in order to limit or minimize the footprint of a system while maintaining adequate performance, an embodiment can include a sub-wavelength grating- based (SWG) Bragg grating architecture, instead of a regular Bragg grating. In other words, the Bragg grating can have a sub-wavelength architecture. By replacing a periodic Bragg grating with high and low index variations, achieved by changing the width, with Si and Si0₂ blocks aligned periodically to enhance the index contrast, a SWG Bragg grating can obtain a similar coupling strength but with a 2-fold reduction in length.

[00133] Fig. 9 illustrates both a regular Bragg grating and a sub-wavelength grating-based (SWG) Bragg grating. A regular Bragg grating 905 can be made of silicon (Si) blocks, having a periodic refractive index, alternating for example between ni = 2.40 910 and n₂ = 2.66 915, which is caused by periodic dimensions, alternating for example between widths of 350 nm 920 and 650 nm 925. The thickness of a pair of blocks can be for example 300 nm 930. In a SWG Bragg grating 935, each silicon block 937 can be cladded in silica Si0₂ 939. This allows the refractive indices to be modified further, by adjusting the thickness of each Si block, and/or the thickness of each S1O2 cladding. Because the thickness of each Si block and each S1O2 cladding can be thinner than a propagating wavelength, the propagating wavelength is not affected by each interface, but rather by effective interfaces between Si/SiC>2 assemblies that are spaced on the order of the wavelength. In an embodiment, the effective refractive index can alternate between ni = 2.18 940 and n₂ = 2.44 945, and the effective interfaces can be spaced 300 nm apart 950.

[00134] Compared to a conventional strip or rib waveguide, a SWG architecture can allow more freedom in tailoring the waveguide’s index, beyond thickness, width and length. Because the period of a SWG is below the Bragg condition, the propagating light is not affected by the period and neither of the two materials (e.g. Si and S1O2) can be seen as individually uniform. This can allow a SWG Bragg grating with a very small footprint to have a very wide stopband.

[00135] Embodiments of the present disclosure include at least one optical element causing a controllable amount of absorption (i.e. attenuation) of a signal. Such an element can be referred to as an attenuator, an optical intensity attenuator, an intensity attenuator, an attenuator, and in some embodiments, it is an EAM. An attenuator can operate by absorbing light, for example, in which case the attenuator can be referred to as an absorber. In various embodiments, the attenuators can be located in each arm of the MZI structure and be configured to absorb a portion of the signals propagating in said arms, for example following phase shifting.

[00136] Because of their high electro-optical speed and small footprint, electro-absorption modulators (EAMs) can be used as attenuators in embodiments of the present disclosure. A germanium-based EAM (Ge-EAM) can enable the absorption coefficient of bulk germanium (Ge) to be modulated by an applying an electric field at photon energies near the direct band gap of Ge. To simplify the fabrication of a Ge-EAM, a trapezoidal-shaped Ge sample with an asymmetric PIN junction can be designed according to conventional foundry design rules, where N⁺⁺ doping can be done on top of the Ge.

[00137] Fig. 10a illustrates a MZM and highlights the location of an intensity attenuator, according to an embodiment. In the illustrated embodiment, an attenuator 1010 is located in each MZI arm, following the integrated Bragg grating and phase shifters 707. However, as noted elsewhere, other configurations are possible.

[00138] Fig. 10b illustrates a cross-section of an intensity attenuator as in Fig. 10a, along with constituent materials, a doping configuration and dimensions, according to an embodiment using a Ge-EAM. The intensity attenuator of Fig. 10b represents an asymmetric PIN-based germanium-based electro-absorption modulator Ge-EAM system, including materials with which it can be fabricated, and a configuration that is applicable in an embodiment. Materials of a Ge-EAM can include silicon at different levels of positive doping at one terminal: P++ 1015, P+ 1020 and P 1025; and germanium at different levels of negative doping at the other terminal: N 1030, N+ 1035 and N++ 1040. P silicon 1025, intrinsic silicon 1045, intrinsic germanium 1050, and N++ germanium 1055 can form an attenuating PIN junction having dimensions shown in the figure. By applying a reverse bias across the P++ terminal 1015 and the N++ terminal 1040, a strong electric field can be generated within the PIN-Ge. Since a propagating optical field is confined to the center of Ge, the applied electric field and the optical field propagating in the EAM can overlap. As a result, the design can offer highly efficient modulation while maintaining low insertion losses at wavelengths greater than 1600 nm.

[00139] Simulations of a Ge-EAM as used in an embodiment show that an electric field applied to a Ge-EAM can be well-matched with an optical field within. This suggests that a strong modulation effect can be obtained, which in turn can result in adequate electro absorption modulation efficiency.

[00140] Fig. 10c is a cross-sectional view of a Ge-EAM as in Fig. 10a, and applied fields within, according to usage in a simulated embodiment. The left-most simulation shows an applied electric field applied externally to the Ge-EAM, and the right-most simulation shows a propagating optical field inside the Ge-EAM, according to an embodiment. A lighter shade represents a field with a greater magnitude.

[00141] In an embodiment, in order to enhance an EAM’s modulation efficiency, an EAM can be deposited onto a phase-shifting cavity of a PSBG. The roundtrip-passes of the resonant light within can cause the EAM’s efficiency to be improved.

[00142] In an embodiment, other EAM materials can be used instead of germanium (Ge). Such other materials can include indium tin oxide (ITO); graphene, which can also perform a similar function at high-speed; and non-volatile materials.

[00143] In an embodiment, a non-volatile material such as a phase change material (PCM) can be implemented as the attenuator of an EAM, and its modulation speed can depend on a writing/erasing step. However, the absorption coefficient of a PCM can be preserved without any energy consumption, and such a state can last for months without any intervention. This can be referred to as in-memory computing.

[00144] Embodiments of the present disclosure include, as a part of an MZM, an optical element causing two output signals of the MZM to be recombined, and re-emitted with different intensities. Such an optical element can be a directional coupler (DC), and in an embodiment, it can be a 3-dB 2 x 2 directional coupler.

[00145] Fig. 11a illustrates where a 2 x 2 directional coupler (DC) 1110 can be located on a MZM, according to an embodiment. To receive two output signals of an MZM according to an embodiment, a 2 x 2 DC 1110 can be located following the EAMs, as shown. Although the MZM shown includes a PSBG and an EAM within the MZI arms, other locations for an optical grating and an attenuator are possible, as shown in Figs 5b to 5f and 5h.

[00146] In embodiments, a 2 x 2 DC can be used as a recombination port for the two output signals of a MZM. For the MZM’s output signals, a 2 x 2 DC can be used as part of the structure to modulate the intensities of the two output signals, based on the applied phase shift between the two signals in the MZI arms.

[00147] Fig. lib illustrates a 2 x 2 DC, as well as example signals at selected cross-sections thereof, as viewed from the front (or back), of two input signals to the two respective ports of an output 2 x 2 DC, as they become output signals of the 2 x 2 DC. Two signals 1120, 1130, which can be the outputs of an MZM, are shown as inputs to the 2 x 2 DC. One signal is an in-phase 1130 and the other is an out-of-phase (Dp/2 phase) 1120. Two output signals Outputl 1140 and Output2 1150 are also shown. The signal intensity at the outputs changes according to the phase difference between the signals at the inputs, according to constructive or destructive interference. When the signals at the two inputs are in phase, the input can be routed substantially entirely to Outputl 1140 and to provide a peak 1125 at the operating frequency, while the signal at Output2 1150 can be substantially zero 1135 at the operating frequency.

[00148] The first cross-sectional image 1155 of the uppermost sequence of Fig. lib, show two input signals having a phase difference of p being injected at the same time in the same DC. The second cross-sectional image 1160 shows one of the two signals vanishing as it is transferred to the other waveguide. The third 1165 and fourth 1170 images show only the combined signal in the waveguide of propagation, as no signal remains in the other waveguide.

[00149] In the lowermost sequence of cross-sectional images, the first image 1175 shows two input signals, having a phase difference of 0 (i.e. same phase), injected in the DC at the same time. The second image 1180 shows one of the two signals vanishing as it is transferred to the other waveguide. The third 1185 and fourth 1190 images show only the combined signal in the waveguide of propagation, as no signal remains in the other waveguide.

[00150] In a 2 x 2 DC, the transfer of signal energy from one waveguide to the other (i.e. from the upper waveguide to the lower waveguide) is a function of the refractive index L) of each waveguide 1140, the refractive index N_s u_s of the surrounding medium 1145, the width IT 1150 of each waveguide, the separation .v_com· 1152 between the two waveguides and the distance L 1155 travelled by each signal at the waveguide separation .v_com· 1152. As two signals propagate along the z-axis of the DC, part of their energy is transferred to the adjacent arm, due to the proximity of the two waveguides. In order to simplify simulations, implementations and fabrications, each waveguide of a DC according to an embodiment can have or be assumed to have a rectangular cross-section.

[00151] An embodiment can be used in an optical neural network (ONN) and it can effectively facilitate large-scale integration. To perform a multiplication, an embodiment does not require two individual modulators. It can perform a multiplication with a scheme involving intensity -tuning of two input signals in one modulator. This configuration can reduce the footprint of a matrix multiplication (MM) accelerator. This configuration can also reduce or eliminate cross-talk resulting from wavelength-tuning, as well as FSR limitations when dealing with multiple optical channels in parallel. An embodiment can be fabricated with CMOS -compatible materials using present commercial fabrication processes, including electron-beam lithography techniques and deep UV-lithography techniques, and can be interfaced with existing optical/electrical platforms.

[00152] Embodiments of the present disclosure include large-system architectures comprising multiple instances of a multiplier as described herein. A large-system architecture can allow a B&W protocol to be used with multiplexed input signals, injected and weighted in parallel, in order to perform high throughput computing and communications.

[00153] In an embodiment, the implementation of a B&W protocol with a large-system architecture can include the capability to de-multiplex a broadcast signal from different wavelengths, and to cascade the information to a subsequent device. In an embodiment that includes an optical grating (e.g. a PSBG), the resonant wavelength (A_c) of the optical grating can be modulated by adjusting its geometric parameters, such that a Fabry-Perot (FP) cavity within can trap an input signal’s resonant wavelengths for a certain time before transmitting them, while reflecting almost 100% of the wavelengths in its stopband. This can enable an embodiment to de-multiplex and cascade signals having different wavelengths, as long as the optical signal’s wavelength is within the stopband of the device.

[00154] Fig. 12 illustrates three cascaded PSBG-EAM-MZMs, that can be used for operating on three different signal wavelengths, according to an embodiment. An input signal having three (3) peak wavelengths 1205 is directed to a first PSBG-EAM-MZM 1210. The peak with wavelength li passes through 1215 the first PSBG and the l₂ and l₃ peaks are reflected 1220. The l₂ and l₃ peaks are directed to the PSBG 1225 of a second PSBG-EAM-MZM. The l₂ peak passes through 1230 and the l₃ peak is reflected 1235 and directed to the PSBG 1240 of a third PSBG-EAM-MZM, where it passes through 1245. Although only three cascaded PSBG-EAM-MZMs are shown, more or fewer such devices can be provided in cascade. Multiple cascades can be provided in parallel. Other variations of the PSBG-EAM-MZM multiplier device, for example as described elsewhere herein, can also be used. In particular, instead of a PSBG, an embodiment can include a phase shifter and a separate optical filter, and these elements, as well as attenuators, can be at different locations within or next to the MZI configuration, as shown in Figs 5b to 5f, and 5h, and said to be co-located with the MZI.

[00155] It is noted that each multiplication device in Fig. 12 has a pair of input ports. This can be achieved by using a 2 x 2 DC (e.g. a 3 dB) as the input path splitting device in the MZI structure. A 2 x 2 DC can operate similarly to a Y-j unction by connecting one of its input ports to a light source and the other two ports to the arms of the MZI. Other embodiments as described herein can be readily configured in this way. The remaining input port can be coupled to further multiplication devices in a cascade. An optical signal which is reflected in the MZI, by one or two optical filters (e.g. Bragg gratings), can be passed to the further multiplication devices via a back-reflection path (i.e. back-propagation) through the same input 2 x 2 DC. Thus, a plurality of multiplication devices can be cascaded together by connecting one of the input ports to an optical signal source, and another one of the input ports to a next multiplication device in the cascade. As such, multiplexed signals having two or more different wavelength peaks, can pass through cascaded multiplication devices, and individually participate in a different multiplication operation.

[00156] In an embodiment including PSBGs, there can be sufficient phase control of each PSBG for the reflection of non-resonant wavelengths, and the transmission of resonant wavelengths, to be maximized at each PSBG, and allow a useful cascadability of MZMs. In some embodiments, MZMs can be cascaded via their reflected output.

[00157] For an embodiment to function as a cascade of multiplier devices (cascaded MZMs), each MZM can include a reflector for reflecting the wavelengths that are not required by the MZM to perform the multiplication. The reflected wavelengths are back-propagated (i.e. back-reflected) through the same input 2 x 2 DC used to enter the multiplication device (MZM). Generally, a reflector can be an optical fdter, and in an embodiment, it can be an optical grating such as a Bragg grating. A benefit of using a Bragg grating is that it can filter a signal by transmitting a narrow band of wavelengths, while reflecting a wide band of remaining wavelengths. Another benefit of a Bragg grating is that it can act as a phase shifter as well, and phase shifting can be modulated with a PN junction or an IPRH (thereby making the device a PSBG). Different kinds of optical filters can be used, including conventional Bragg gratings, side-wall gratings, top gratings, sub-wavelength grating-based (SWG), however, microring resonators and properly configured photonic crystals, which generally include ID, 2D and 3D optical gratings, can also perform the functions of filtering by reflection and transmission, as well as phase shifting, as they can also be tuned with a PN junction or an IPRH, making for many possible combinations, all of which are encompassed by embodiments.

[00158] Further, in an embodiment where a 2 x 2 DC is used for the input ports of an MZI, the 2 x 2 DC can be configured such that when an input signal enters the 2 x 2 DC through a first port of the DC’s first waveguide, the signal can be split in two similar portions and exit at both outputs of the 2 x 2 DC’s two waveguides, such that the portion entering the MZI’s arm 2 (e.g. the “lower” arm) is substantially the same as in arm 1 (e.g. the “upper” arm). However, the part of the input signal transferring from the input port’s waveguide to the second waveguide will undergo a p/2 phase shift. To implement a multiplier as a phase shift between the two transmitted portions, the two transmitted portions should be in-phase and therefore, a passive p/2 phase shifter should be added to one of the MZI arms before the transmitted portions recombine at the output DC. Therefore, if a 2 x 2 DC is used as the input Y-junction in any embodiment shown in Figs 5a to 5f, a passive p/2 phase shifter should be added in one of the MZI arms, at any location between that arm’s modulated (active) phase shifter, and the output Y-junction, which can be a 2 x 2 DC.

[00159] By adding a passive p/2 phase shifter in one arm of the MIZ, the phase shift caused by the input 2 x 2 DC will be cancelled, and the observed phase difference of the output signals will be due to the modulation implementing a multiplier. In other words, the intensity of a signal injected in arm 1 (e.g. the “upper” arm) of an input 2 x 2 DC can be split equally and exit at both outputs of the 2 x 2 DC, but with arm 2’s (e.g. the “lower” arm) output having undergone a p/2 phase change. Therefore, to maintain the same phase difference of signals transmitted at the output of an MZM system, an additional p/2 passive phase modulation should be applied after one of the two modulated phase shifters.

[00160] In an embodiment where the input of the MZI is from a 2 x 2 DC, and each arm of the MZI includes an optical fdter, such as a Bragg grating or a PSBG, the input DC also acts as an output DC through which portions of an input signal that are fdtered and reflected are back-propagated. Because the phase of the lower arm signal was shifted by p/2 when the original signal was split, the upper arm signal can recombine with it, undergo a similar p/2 shifting, and form an output signal similar to the original input signal (but without the transmitted portion performing the multiplication further down the MZI). The back- propagating (i.e. back-reflected) output signal reflected from the MZI can therefore be redirected to a subsequent MZI as though it was simply 100% reflected, but without the narrow band of resonant wavelengths transmitted through the optical fdter. In other words, an optical fdter transmits, from an optical signal received thereby, a range of optical wavelengths within a passband, and reflects the remaining part of the optical signal (outside the passband) on a back-reflection path. A CDC can transmit the range of optical wavelengths from an input port to a drop port, and reflect the remaining part of the optical signal via another port, for example. A MZI with integrated Bragg grating can transmit the range of optical wavelengths through the Bragg grating while reflecting the remaining part of the optical signal out of a second input port of a 2x2 coupler which forms the input stage of the MZI.

[00161] In an embodiment with a PSBG in each arm of the MZIs, a 2 x 2 DC at an MZI input can split the power of input light equally in two arms towards 2 respective PSBGs. The resonant wavelengths can be trapped by, and transmit through, the PSBGs for further intensity operations, and be shifted passively by an additional device, in order to eliminate the phase shift caused by the 2 x 2 DC. The non-transmitted light, which is from non-resonant wavelengths within the stopband, can be 100% reflected by the PSBGs, back to the input DC, now acting as an output DC. The 3-dB 2 x 2 DC at the MZI’s input introduces a phase difference of p/2 between the signals of the two arms, but that phase difference is preserved even after a signal is reflected back from a PSBG, so when they recombine after having been reflected, the non-shifted signal can now be p/2 phase-shifted itself. Because each of the two signals can undergo a p/2 phase-shift, one at splitting, the other at recombination, the resulting, reflected signal can be similar to the original input, less the bandwidth fdtered out at the PSBGs, and be redirected towards another MZM of a cascade.

[00162] To properly recombine, the two reflected signals should have the same phase difference as when they were split. If they are reflected by two similar reflectors (i.e. two similar optical fdter), this can be automatic. Otherwise, an additional passive phase shifter may be required, between the 2 x 2 DC and one of the reflectors.

[00163] For an input signal containing many wavelength peaks, wavelength de-multiplexing can be achieved with wavelength fdtering and reflection using either one optical grating before an MZI, or one optical grating in each arm of the MZI. If each arm of the MZI includes an optical grating, the input port of the MZM can be used to recombine the two reflected signals and redirect the resulting signal to the next MZM of a cascade. By using a standard 2 x 2 DC at the input of a MZM, one reflected signal can be combined to the other within the 2 x 2 DC with substantially 100% intensity (except for the power of the resonant wavelength).

[00164] In an embodiment where the input ports of an MZM is a CDC instead of a standard 2 x 2 DC, the function of filtering by reflection and transmission can be performed by the CDC and therefore, further optical filtering may not be required. In such an embodiment, an arm of an MZM can include a phase shifter without an optical filter, because optical filtering can occur at the MZM’s input CDC, and the reflected wavelengths can be redirected to the subsequent MZMs before they even enter the present MZM.

[00165] In an embodiment cascading three MZM, as shown in Fig. 12, each one of the three MZMs shown can include a contra directional coupler (CDC) at its input port, and a 2 x 2 DC at its output port. Because a CDC includes an optical grating, the MZM is not required to include a further optical filter. Multiplexed signals at three different wavelengths can pass through the cascaded MZM system, and individually participate in a different multiplication operation in a respective MZM.

[00166] In an embodiment where the input ports at each multiplication device in FIG. 12 are contra-directional couplers (CDCs), as shown in Fig. 5g, each CDC can filter the input light such that only a narrow range of wavelengths around a peak is transmitted to the multiplication devices, and the remaining part of the signal is reflected to the next multiplication devices of a cascade. In an embodiment where a CDC is used at the input instead of a 2 x 2 DC, it can be unnecessary to use a further optical filter or Bragg grating, and modulated phase shifters are not required to be PSBGs.

[00167] In an embodiment where a CDC is as the input ports of an MZM, a first port 565 can receive input light having multiple peaks. A second port 570 can pass a limited portion (e.g. one peak) of the received input light toward the MZI structure. In the MZI structure. Because of the internal optical grating of a CDC, a third port 575 can direct the reflected portion of the received input light, toward another MZI of a cascade of MZIs, and this portion can serve as the input light of that subsequent MZI, which can repeat the process. Each time a fdtering function is performed at a CDC, the signal propagating through the cascade loses a narrow band of wavelengths, as a signal peak is transmitted in each MZM to perform a multiplication operation.

[00168] In Fig 12, each of the three MZMs can perform a multiplication of two vector components from vector A = [a₁ a₂, a₃] and vector B = [/¾, ¾_< ^3]· For example, the first MZM can perform the multiplication a_L

. the second MZM can perform a₂b₂, and the third MZM can perform a₃ b₃. In an embodiment, the three outputs can then be summed together with a common balanced photodetector (BPD) with sufficiently wideband responsiveness. In another embodiment, the three outputs can be summed together using three separate BPDs and an electronic summation circuit. In either embodiment, the summation

+ a₂b₂ + a₃b₃ , by definition represents the dot product A B.

[00169] An optical filter, which can be a Bragg grating, can ensure that a transmitted multiplier is narrowband. A modulated phase shifter, which can also be a Bragg grating, can encode a component of vector A. An attenuator following a phase shifter can encode a component of vector B. Each of the multipliers 1210, 1225, 1240, operates on a narrow band of wavelengths, e.g. centered at li, l₂ and l3, respectively. The reflecting filter admits its narrow band of wavelengths into the multiplier for manipulation by the phase shifters and attenuators thereof, while reflecting back all other wavelengths for handling by other ones of the multipliers. Although Fig. 12 is illustrated with a PSGB and the configuration of Fig. 5a, any configuration from Figs 5a to 5f can perform a similar result. For example, if a CDC is used as the input Y-junction, a PSBG can be substituted with another kind of phase shifter. As other examples, an optical filter can be placed before the input Y-junction, and the attenuators can be located elsewhere within or next to the MZI.

[00170] Fig. 13a illustrates a 2 x 2 DC located at the input port of an MZM, according to an embodiment of the present disclosure. The DC includes a first waveguide adjacent to a second waveguide. The first waveguide, on top, has a first port of the DC on the left and a second port of the DC on the right. The second waveguide, on bottom, has a third port of the DC on the left and a fourth port of the DC on the right. An input signal propagates from left to right. An input optical signal 1305 is injected from the left into the first port of the DC (e.g. the “upper left” port) and is split such that the intensities of signals 1310 at the second and fourth ports on the right are substantially the same (e.g. due to the DC being a 3-dB DC). The signal produced in the lower arm can have a p/2 phase difference 1315 from the signal in the upper arm due to coupling of part of the signal from the upper waveguide onto the lower waveguide.

[00171] Fig. 13b illustrates a 2 x 2 DC located at the input port of a MZM, and acting as an output port for signals having been reflected at respective optical filters in an MZI, (e.g. PSBGs) and now propagating from right to left, according to an embodiment. Each signal, originally going from left to right, has been mostly reflected at a respective PSBG (except for the resonant wavelengths), and is now returning to the same 2 x 2 DC as signals Inputl and Input2 1320, at the second and fourth ports of the DC, going from right to left. The 2 x 2 DC can recombine the two signals as a single signal Output2 1325, having the sum of their intensities, and signal Output2 1325 at the third port of the DC, can then be redirected towards another device, such as another cascaded PSBG-MZM. As the upper signal is transferred to the lower arm, it can undergo aii/2 phase shift 1330, thereby matching the lower arm’s phase shift.

[00172] When properly configured as described, whether using 2 x 2 DCs or a CDCs as input Y-junctions, each of the three MZMs in Fig. 12 can perform a multiplication of two vector components from vector A = [ , a₂, a₃] and vector B = [b_t, b₂, b₃\. For example, the first MZM can perform the multiplication a_tb_t, the second MZM can perform a₂b₂, and the third MZM can perform a₃b₃. In an embodiment, the three outputs can then be summed together with a common balanced photodetector (BPD) with sufficiently wideband responsiveness. In another embodiment, the three outputs can be summed together using three separate BPDs and an electronic summation circuit. In either embodiment, the summation + a₂b₂ + ci₃b₃ , by definition represents the dot product A B. A cascade of MZMs according to embodiments can include any number of MZMs as described, other than three, and such a cascade is also an embodiment.

[00173] Fig. 14 illustrates how a plurality of cascaded photonic multiplication devices (MZMs) according to embodiments can be connected to balanced photodetectors at their outputs, to produce the summation in a dot product. Three photonic devices are shown in cascade, although more or fewer devices may be present in the cascade. A signal having three wavelength peaks 1205 is incident on a first MZM 1250. The MZM 1250 includes an optical filter, such as a Bragg grating, configured to transmit one of the wavelength peaks and reflect at least the other two peaks. The two reflected peaks 1220 are directed to a second MZM 1255, which is configured to transmit one of the wavelength peaks and reflect the other peak other. The reflected peak 1235 is directed to a third MZM 1260, where it is transmitted. Each optical filter transmits light in a separate wavelength range and reflects light outside of that wavelength range. The reflected light is directed toward subsequent photonic devices in the cascade.

[00174] In Fig. 14, the output of each MZM 1450, 1455, 1460, is connected to a respective pair of balanced photodetectors (BPD), 1465, 1470, 1475, each of which produces an electrical signal based on the two output signals of an MZM. The three output signals are added by a summation unit 1280, which is configured to produce a signal comprising the sum of the three input signals, and thereby completing the vector multiplication. Depending on the implementation, the outputs of the MZM can be directly coupled to the BPD, for example for the implementations of Figs. 5a-5d, 5f and 5h, or the outputs of the MZM can be indirectly coupled to the BPD, for example for the implementation of Fig. 5e where an attenuator or attenuators are located after the MZM. The BPDs and summation unit form part of a readout device which is configured to produce a result signal. Each BPD produces an input signal which is indicative of a difference in intensity between optical signals produced by the two outputs of a corresponding one of the photonic devices. The outputs of the BPDs are summed to produce the result signal.

[00175] An embodiment can implement a B&W protocol by using a 2 x 2 DC as an input port of an MZM. Another embodiment can implement a B&W protocol by using a CDC as an input port of an MZM. Each MZM can include at least one modulated phase shifter and at least one modulated attenuator, in accordance with embodiments. Such embodiments can allow cascadability, which can be used to process multiplexed signals in the wavelength domain. For optical computing acceleration and for photonic tensor cores, such embodiments can replace conventional MRM (microring modulator) systems in applications using conventional MRMs based on wavelength-shifting. Benefits of such embodiment over conventional MRMs include a smaller footprint, little to no crosstalk issue, simplified electrical circuitry, and others.

[00176] Embodiments include a pair of similar waveguides, at least one optical filter, at least one modulated phase shifter, and at least one modulated attenuator, the output of the two waveguides recombined with a 3-dB 2 x 2 directional coupler. In an embodiment, the optical filter and the modulated phase shifter can be a same optical element, and in another embodiment, they can be different elements. A modulated phase shifter can be tuned if there is a PN-junction within. In an embodiment, a modulated attenuator can include germanium and it can be a germanium electro-absorption modulator (Ge-EAM). An embodiment including these optical elements, configured an MZI configuration to modulate an optical signal can be referred to as an MZM.

[00177] Embodiments can further include a second 3-dB 2 x 2 directional coupler (DC), which can be located at the input of an MZM. The second 3-dB 2 x 2 DC can split one input signal into two similar signals, each one to be reflected by at least one optical filter. The second 3-dB 2 x 2 DC can recombine the two reflected signals into one signal, and then redirect the recombined signal to another photonic device. That is, portions of signals input into the photonic device can be partially reflected by optical filters such as Bragg gratings. The reflected portions of signals are then recombined by a DC at the photonic device input, and transmitted toward another photonic device in cascade. [00178] As an alternative to a 3-dB 2 x 2 directional coupler at the input, an embodiment can include a contra directional coupler (CDC). In comparison, a CDC can provide the function of optical fdtering, by which transmission to the MZM can be limited to peaks of certain wavelengths, and other wavelengths can be reflected. The transmitted peaks can be phase shifted by a phase shifter of the MZM to implement a multiplication, while the reflected wavelengths can be redirected to other MZMs.

[00179] As another alternative to a 3-dB 2 x 2 directional coupler, an embodiment can include a broadband adiabatic coupler. In comparison, a broadband adiabatic coupler can provide similar signal splitting and combining, for a wider range of wavelengths.

[00180] In an embodiment, a phase shifter and an optical fdter can be combined as a phase- shifted Bragg grating (PSBG), and the PSBG can be designed as a sub-wavelength grating. Such a design can have a shorter length, as well as coupling coefficients that are sufficient to implement a practical multiplication operation, in that for example, the power loss in a system can be sufficiently low to implement a multiplier with enough accuracy to represent a practical multiplication operation.

[00181] Embodiments can include a modulator (i.e. MZM) that allows modulating the output intensity of a signal without shifting its peak wavelength. With a MZM having a modulated phase shifter in at least one arm, two output signals can have a same, fixed wavelength, and their combined intensity can be modulated according to their phase difference. Because the wavelength peaks are not shifted, embodiments may not necessarily give rise to the same degree of cross-talk issues as seen in wavelength-tuning devices of prior art, and they can facilitate a large-scale integration of optical neural networks.

[00182] In embodiments, a PSBG can be used as the resonant (i.e. optical filtering) element. The stopband of a PSBG can allow one wavelength peak to resonate and other wavelengths to be reflected. For the resonant peak, there are little to no free spectral range (FSR) limitations. Therefore, if a signal’s wavelength is selected to be within the stopband of a PSBG, it will not be appreciably subjected to free spectral range (FSR) limitations. Compared with a system based on conventional MRRs, the stopband of a PSBG can allow the operation of more wavelength channels.

[00183] Embodiments can include at least one optical attenuator, either before the MZM, in each arm of the MZM, or after the MZM, in order to allow the modulation of through-power with varying levels of absorption. Such modulation can encode a number, which can be a multiplier or a multiplicand, and such a number can be a vector component of a vector undergoing a multiplication operation. The use of an optical attenuator can allow a multiplication operation to be performed with the MZM, without the signal’s wavelength being shifted. A cascade of similar MZMs can be used to perform many multiplications, and the multiplications can be summed with for example a BPD, so as to implement a dot product.

[00184] The footprint of an MZM according to embodiment can be smaller than the footprint of a conventional MRR modulator performing a similar dot product operation.

[00185] Embodiments have been described above in conjunction with aspects of the present disclosure upon which they can be implemented. Those skilled in the art will appreciate that embodiments may be implemented in conjunction with the aspect with which they are described, but may also be implemented with other embodiments of that aspect. When embodiments are mutually exclusive, or are otherwise incompatible with each other, it will be apparent to those skilled in the art. Some embodiments may be described in relation to one aspect, but may also be applicable to other aspects, as will be apparent to those of skill in the art.

[00186] Although the present disclosure has been described with reference to specific features and embodiments thereof, it is evident that various modifications and combinations can be made thereto without departing from the invention. The specification and drawings are, accordingly, to be regarded simply as an illustration of the invention as defined by the appended claims, and are contemplated to cover any and all modifications, variations, combinations or equivalents that fall within the scope of the present disclosure.

Claims

WHAT IS CLAIMED IS:

1. A photonic device comprising: a Mach-Zehnder interferometer comprising an input, a first output, a second output, and at least one controllable phase shifter, and configured, via operation of the at least one phase shifter along with interferometric operation of the Mach-Zehnder interferometer, to cause a first controllable portion of an optical signal presented at the input to be produced at the first output, and a second controllable portion of the optical signal presented at the input to be produced at the second output; and one or more optical attenuators configured to modulate, directly or indirectly, an intensity of the first portion and the second portion, said modulation of intensity of the first portion and the second portion being by substantially a same amount, wherein the Mach-Zehnder interferometer and the optical attenuators are co located.

2. The photonic device of claim 1, further comprising at least one optical filter configured to transmit, from at least one portion of an optical signal, a range of optical wavelengths and to reflect the remaining optical wavelengths to a back-reflection path, the at least one optical filter being located to filter the at least one portion of an optical signal before it is transmitted through the one or more attenuators.

3. The photonic device of claim 2, wherein the at least one optical filter comprises a Bragg grating.

4. The photonic device of claim 2 or 3, wherein the at least one optical filter has a sub wavelength architecture.

5. The photonic device of any one of claims 2 to 4, wherein at least one of the optical filters is integrated with a corresponding one of the controllable phase shifters.

6. The photonic device of any one of claims 2 to 4, wherein the optical filter is located prior to the input of the Mach-Zehnder interferometer.

7. The photonic device of any one of claims 1 to 6, wherein the controllable phase shifter includes a PN junction.

8. The photonic device of any one of claims 1 to 7, wherein the one or more attenuators comprise a pair of attenuators each disposed in a respective arm of the Mach-Zehnder interferometer.

9. The photonic device of any one of claims 1 to 7, wherein the one or more attenuators comprise a single attenuator operatively coupled to both respective arms of the Mach- Zehnder interferometer.

10. The photonic device of any one of claims 1 to 7, wherein the one or more attenuators comprises a single attenuator located following an output of the optical filter and prior to the input of the Mach-Zehnder interferometer.

11. The photonic device of any one of claims 1 to 7, wherein the one or more attenuators comprises a pair of attenuators respectively located following the first output and the second output of the Mach-Zehnder interferometer.

12. The photonic device of any one of claims 1 to 7, wherein the one or more attenuators comprises a single attenuator operatively coupled to a pair of respective waveguides following the first output and the second output of the Mach-Zehnder interferometer.

13. The photonic device of any one of claims 1 to 9, wherein an attenuator is integrated into an optical filter.

14. The photonic device of any one of claims 1 to 13, wherein the one or more attenuators comprises a germanium-based electro-absorption modulator (Ge-EAM).

15. The photonic device of any one of claims 1 to 14, wherein the input comprises a directional coupler comprising a first waveguide adjacent to a second waveguide, the first waveguide having a first port and a second port, the second waveguide having a third port and a fourth port, the directional coupler configured to produce, from a signal at the first port, a portion of the signal at the third port and a portion of the signal at the fourth port.

16. The photonic device of claim 15, wherein the directional coupler is further configured to transmit, from a reflected portion of a signal at the second port and a reflected portion of the signal at the fourth port, a recombined signal at the third port.

17. The photonic device of any one of claims 2 to 6, further comprising a passive p/2 phase shifter in one arm of the Mach-Zehnder interferometer, after the optical filter.

18. The photonic device of claim 1, further comprising a contra directional coupler comprising a first waveguide adjacent to a second waveguide, the first waveguide having a first port and a second port, the second waveguide having a third port and a fourth port, the contra directional coupler configured to operate as an optical filter for transmitting, from a received optical signal, a range of optical wavelengths from the first port to the second port and to reflect the remaining optical wavelengths from the first port to the third port.

19. The photonic device of any one of claims 1 to 18, wherein the photonic device is configured to implement a multiplication by operation of the at least one phase shifter to produce a pair of output signals having a difference in intensity which represents a multiplier in the multiplication and by operation of the one or more optical attenuators to pass the output signals in proportion to a multiplicand in the multiplication.

20. The photonic device of any one of claims 1 to 19, wherein the Mach-Zehnder interferometer comprises an input directional coupler having two inputs and two outputs, an output directional coupler having two further inputs and two further outputs, and said at least one phase shifter, wherein the two outputs of the input directional coupler are coupled, via said at least one phase shifter, to the two further inputs of the output directional coupler.

21. The photonic device of any one of claims 1 to 20, further comprising a balanced photodetector (BPD) having a pair of inputs directly or indirectly coupled to the first output and the second output of the Mach-Zehnder interferometer, respectively, the BPD configured to produce an indication of a difference in intensity between optical signals produced by the photonic device via said first output and said second output.

22. A photonic device comprising: a plurality of photonic devices according to any one of claims 2 to 6, the photonic devices arranged in cascade configuration and the respective optical filters thereof each configured to transmit light in a separate wavelength range and to reflect light outside of said wavelength range toward one or more other ones of the plurality of photonic devices.

23. The photonic device of claim 22, further comprising a readout device comprising one or more balanced photodetectors (BPDs), the readout device configured to produce a result signal which is based on a plurality of differences, each difference being a difference in intensity between optical signals produced by a respective one of the photonic devices via said first output and said second output of said one of the photonic devices.

24. The photonic device of claim 23, wherein: each of the photonic devices is configured to implement a respective multiplication by operation of the at least one phase shifter thereof to produce a pair of output signals having a difference in intensity which represents a respective multiplier in the multiplication and by operating the one or more optical attenuators thereof to pass light in proportion to a respective multiplicand in the multiplication; and the result signal is indicative of a sum of said differences, in order to perform a dot product operation between a first vector comprising said multipliers and a second vector comprising said multiplicands.

25. A method, in a photonic device, comprising: operating a Mach-Zehnder interferometer comprising an input, a first output, a second output, and at least one controllable phase shifter, to cause a first controllable portion of an optical signal presented at the input to be produced at the first output, and a second controllable portion of the optical signal presented at the input to be produced at the second output; and operating one or more optical attenuators to modulate, directly or indirectly, an intensity of the first portion and the second portion, said modulation of intensity of the first portion and the second portion being by substantially a same amount, wherein the Mach-Zehnder interferometer and the optical attenuators are co located.

26. The method of claim 25, further comprising admitting the optical signal presented at the input into the Mach-Zehnder interferometer and the optical attenuators, and reflecting light accompanying the optical signal and having a different range of wavelengths than the optical signal, said reflecting comprising directing said light accompanying the optical signal toward one or more further photonic devices.