Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/06—Physical realisation, i.e. hardware implementation of neural networks, neurons or parts of neurons
  • G06N3/067—Physical realisation, i.e. hardware implementation of neural networks, neurons or parts of neurons using optical means
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/04—Architecture, e.g. interconnection topology
  • G06N3/0464—Convolutional networks [CNN, ConvNet]
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
  • G02F1/21—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference
  • G02F1/212—Mach-Zehnder type
• • G—PHYSICS
  • G02—OPTICS
  • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
  • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
  • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
  • G02F1/21—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference
  • G02F1/225—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference in an optical waveguide structure
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
  • G06F16/90—Details of database functions independent of the retrieved data types
  • G06F16/901—Indexing; Data structures therefor; Storage structures
  • G06F16/9017—Indexing; Data structures therefor; Storage structures using directory or table look-up
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/08—Learning methods

Definitions

• This disclosure relates to systems and methods for half-digital and full-digital high precision digital optical processing.
• Deep learning architecture scales in complexity and craves computing power to address massive data, mainly for matrix-vector multiplications (MVMs).
• MVMs matrix-vector multiplications
• TPU tensor processing unit
• microelectronics are encountering fundamental bottlenecks on speed, energy consumption, heating, and interconnect delay, which can no longer be resolved by scaling.
• a typical neural network either optical or analogue, contains linear and nonlinear operations.
• Linear operations include the convolutional and fully connected layers.
• Nonlinear operations include the activation and softmax layers.
• Most of the computation time is spent on the linear layers, up to about 90%. Therefore, current artificial intelligence (Al) or neural network processors are mainly designed to optimize the linear operation process, that is, matrix multiplication, for example.
• Al artificial intelligence
• One of the state-of-the-art Al processors is the Google’s TPU.
• the core component of the Google’s TPU is the matrix multiplication unit, which also consumes most of the computation time and power consumption.
• matrix multiplication units are essentially multipliers, adders and shifters, so that the computation speed is limited by the electrical clock rate, resulting in a computing speed limit of a few GHz.
• the clock speed is accelerated, it may lead to timing violations and power consumption spikes.
• a matrix multiplication refers to multiplications between digital signals, and more generally to the family of arithmetic logic circuits.
• a digital multiplication may preferably be performed by digital circuits following digital multiplier architectures such as the Baugh-Wooley algorithm, Wallace trees, or Dadda multipliers.
• digital multipliers implemented with digital circuits quickly requires complex architectures which are both energy costly and speed inefficient. These architectures impose a limit in the processing speed of digital multiplications.
• PICs photonic integrated circuits
• PIC-based ONNs are physical implementations of an analogue neural network (ANN) using ultrafast optical integrated components. PIC-based ONNs demonstrations have shown great potential to surpass their digital microelectronic counterparts in calculating speed (> 10 3 ), energy consumption (> 10 2 ), and computing density (> 10 2 ). Despite these great potentials, there are great scientific and technical challenges for ONNs. First and foremost, these ONNs are all based on analogue computing architectures (analogue ONNs) where the input data and weight are carried on the light intensities. There is one major scientific challenge for this analogue computing architecture: insufficient signal-to-noise ratio due to accumulated noise and crosstalk in the system.
• the intensity of the optical signals is usually limited to a precision of around 4 bits at desired high speed. Instead, a 16-bit calculation precision is practically required for reasonable training convergence and many demanding convolutional neural network (CNN) applications such as autonomous driving, high-definition image processing, and 3D computer vision.
• CNN convolutional neural network
• analogue ONN are also incompatible with microelectronics so extra expensive, high-resolution and energy consuming data processing is required, such as digital-to-analogue conversion (DAC) and/or analogue-to-digital conversion (ADC). Therefore, breakthrough technologies are needed to solve challenges in ONN, including calculation precision, compatibility with microelectronics.
• DAC digital-to-analogue conversion
• ADC analogue-to-digital conversion
• a digital optical computing processing unit configured to perform analogue-digital convolutions by processing at least a first and a second electrical digital signal and a first optical signal preferably comprising at least two wavelengths.
• the digital optical computing processing unit may comprise a first waveguide for carrying the first optical signal; a light source configured to deliver the first optical signal comprising at least two wavelengths to the first waveguide; at least a first and a second electrical-to-optical transducer preferably arranged in series and preferably comprised in the first waveguide, configured to be biased by at least a first and a second weight, wherein the at least first and second electrical digital signals modulate the first optical signal in the at least first and second electrical-to-optical transducers, respectively, and wherein the first electrical-to-optical transducer is configured to modulate a first wavelength and the second electrical-to- optical transducer is configured to modulate a second wavelength; and a first optical-to- electrical transducer arranged at a first output of the first waveguide, and wherein the first optical-to-electrical transducer is configured to output a first electrical output signal based on the first optical signal.
• the digital optical computing processing unit may comprise an optical calculation unit that can comprise a first waveguide for carrying the first optical signal; at least a first and a second electrical-to-optical transducer preferably arranged in series and comprised in the first waveguide, configured to be biased by at least a first and a second weight, wherein the at least first and second electrical digital signals modulate the first optical signal in the at least first and second electrical-to-optical transducers, respectively, and wherein the first electrical-to-optical transducer is configured to modulate a first wavelength and the second electrical-to-optical transducer is configured to modulate a second wavelength.
• the optical calculation unit may comprise at least one optical device and/or at least one electrical-to-optical device that would perform analogue-digital convolutions.
• the first and second electrical-to-optical transducers are configured to modulate the first optical signal with the at least first and second electrical digital signals, therefore enabling the digital optical computing processing unit to process calculations with electrical digital signals instead of electrical analogue signals.
• electrical digital signals are more robust to noise than analogue signals. Therefore, robustness to signal-to-noise ratio is improved compared to an optical processing unit that may use electrical analogue signals.
• the first electrical output may be a first electrical digital output signal, which can be easier to detect, process and adjudicate than an analogue signal.
• the digital optical processing unit reduces costs, saves energy and simplifies system complexity.
• the at least first and second electrical-to-optical transducers can be biased or loaded by a first and a second weight, which may give a possibility of multiplying the at least first and second electrical digital signals with the at least first and second weights, respectively.
• the first optical signal is then being modulated on each wavelength by electrical digital signals being a result of several multiplications between the at least first and second electrical digital signals and the at least first and second weights in the at least first and second electrical-to-optical transducers arranged on the first waveguide.
• the first optical-to-electrical transducer is then configured to output a first electrical output signal based on the first optical signal.
• the first optical-to-electrical transducer may advantageously be wavelengthindependent. Therefore, the first electrical output comprises a sum of the several multiplications between the at least first and second electrical digital signals and the at least first and second weights, respectively, which can be defined as a convolution operation.
• the digital optical processing unit is configured to process convolution operation between digital signals and weights, wherein weights can be either analogue signals or digital signals that can be converted to analogue signals.
• FIG. 1A-B show schematic views of an embodiment of the digital optical computing processing unit configured to perform analogue-digital convolutions.
• a first light source here a multi-wavelength light source is configured to generate a first optical signal comprising at least two wavelengths, and feed this first optical signal into a first waveguide.
• the first waveguide comprises 9 electrical-to-optical transducers, connected in series, and more specifically in this embodiment, 9 micro-ring resonators.
• Each of the micro-ring resonators are biased by a weight, and each of the micro-ring resonators are configured to modulate the first optical signal, each one on a different wavelength with electrical digital signals, which in this embodiment, has an 8-bit precision and represents data from an image.
• the electrical digital signals are digital representations of the data input to be processed by the digital optical computing processing unit.
• the data input to be processed is data from an image, preferably information contained in at least one pixel.
• the electrical digital signals are encoding the data input in a form of a binary word.
• Di is a first electrical digital signal, which is a digital representation of the decimal number “39” in a form of a binary word with a length of 8-bit, where “39” may represent the intensity of a corresponding pixel from the image, since the image is in a grayscale format.
• Di is a first electrical digital signal, which is a digital representation of the decimal number “39” in a form of a binary word with a length of 8-bit, where “39” may represent the intensity of a corresponding pixel from the image, since the image is in a grayscale format.
• the decimal number “39” is then coded or encoded within a binary word “00100111” which is equal to “39”.
• the person skilled in the art would understand that any other digital representations can be achieved by increasing the number of bits within the binary word, or by reducing the number of bits within the binary word, depending on the resolution that the user of the digital optical computing processing unit wants to achieve.
• All the wavelengths, namely Ai- A2-...- Ag, are then summed up in a first optical-to-electrical transducer, specifically in this embodiment, a photodetector, arranged at a first output of the first waveguide.
• the first electrical signal based on the first optical signal is a multi-level signal due to the 9 wavelengths summed up at each symbol period.
• this multi-level signal is then converted to a binary signal, which represents the convolution result between a matrix comprising 9 electrical digital signals, namely Di-D x -...-Dg and a kernel matrix comprising 9 weights, namely Wn-W xy -...-W33.
• the digital optical processing unit may compute convolutions faster and may consume less power than the electrical computing scheme. This is due to the convolution being performed in the optical domain rather than in the electrical domain. By performing the convolution operation with digital electrical signal, a better robustness to noise is achieved compared to analogue counterparts, such as optical neural networks using analogue signals as input signals.
• the present disclosure relates to a digital optical computing processing unit configured to perform analogue-digital continuous convolutions by processing at least a first, a second and a third electrical digital signal and a first optical signal preferably comprising at least two wavelengths.
• the digital optical computing processing unit may comprise a first waveguide; a light source configured to deliver a first optical signal comprising at least two wavelengths to the first waveguide; a primary electrical-to-optical transducer preferably comprised in the first waveguide, wherein the first optical signal is modulated by the at least first electrical digital signal in the primary electrical-to-optical transducer; at least a first and a second electrical-to-optical transducer preferably arranged in series and preferably comprised in the first waveguide, and further arranged in series with the primary electrical-to-optical transducer, wherein the at least first and second electrical-to-optical transducer are configured to be biased or modulated or loaded by at least a first and a second weight, and wherein the at least first and second electrical digital signals modulate the first optical signal in the at least first and second electrical-to-optical transducers, respectively, and wherein the first electrical-to-optical transducer is configured to modulate a first wavelength and the second electrical-to-optical trans
• the digital optical computing processing unit configured to perform analogue-digital continuous convolutions may comprise the same features than the digital optical computing processing unit configured to perform analogue-digital convolutions as described herein. At least one difference can be the first waveguide portion which can be configured to disperse the first optical signal or to introduce a wavelength-dependent time delay in the first optical signal, thereby enabling the digital optical computing processing unit to be configured to advantageously perform continuous convolutions between analogue and digital signals.
• the at least two wavelengths comprised in the first optical signal are then dispersed or delayed in time by any other known methods, thereby delayed in time with each other.
• the at least two wavelengths are both modulated by the at least first electrical digital signal with the primary electrical-to-optical transducer. The at least two wavelengths are then modulated by the same electrical digital signal, i.e.
• the digital optical computing processing unit configured to perform analogue-digital continuous convolutions can then enable a time-delayed interleaving technique.
• the time-delayed interleaving technique may allow a continuous processing of data on the at least two wavelengths.
• time-delayed interleaving technique it can be understood as time, wavelength and/or spatial dimensions are interleaved. This maximize the processing speed of the digital optical processing unit, thereby enabling more data to be processed in a given amount of time, or preferably more convolutions between analogue and digital or digital and digital signals to be performed.
• Fig. 2 shows a schematic view of an embodiment of the digital optical computing processing unit configured to perform analogue-digital continuous convolutions.
• a light source here a multi-wavelength light source is configured to generate a first optical signal comprising at least two wavelengths, namely Ai- A2-...- Ag, and feed this first optical signal into a first waveguide.
• the first waveguide comprises; a primary electrical-to-optical transducer, namely a Mach-Zehnder modulator, in series with 9 electrical-to-optical transducers, connected in series, and more specifically in this embodiment, 9 micro-ring resonators.
• the Mach-Zehnder modulator is configured to modulate the first optical signal with at least a first electrical digital signals, namely dj.k, where j and k are dimensions of a matrix comprising j*k electrical digital signals.
• the at least two wavelengths are then passing through a first waveguide portion, namely a dispersive waveguide, configured to disperse the first optical signal, therefore generating a time delay between each of the wavelengths comprised in the first optical signal.
• Each of the wavelengths are then further modulated by a weight matrix, namely Wjj, where i and j are dimensions of a matrix comprising i*j weights.
• the first optical-to-electrical transducer specifically in this embodiment, a photodetector, arranged at a first output of the first waveguide.
• the first electrical signal based on the first optical signal is a multi-level signal due to the 9 wavelengths summed up at each symbol period. This multi-level signal is then converted to a binary signal, which represents the convolution result between the matrix dj.k and the matrix Wj,j.
• This digital optical computing processing unit can advantageously process more convolution in a faster way by using both a primary electrical-to-optical transducer, such as a Mach-Zehnder, and high-speed modulation inputs of micro-ring resonators, such as a different convolution between two submatrixes can be performed at each symbol period of the system.
• a primary electrical-to-optical transducer such as a Mach-Zehnder
• micro-ring resonators such as a different convolution between two submatrixes can be performed at each symbol period of the system.
• different weights can also be applied at each symbol period of the system, which makes this digital optical computing processing unit adapted for processing convolution where kernel matrixes containing weights may be different when convolving it with the data from the same source.
• the digital optical computing processing unit may comprise a first waveguide; a light source configured to deliver a first optical signal comprising at least two wavelengths to the first waveguide; a primary electrical-to-optical transducer preferably comprised in the first waveguide, wherein the first optical signal can be modulated by the at least first electrical digital signal in the primary electrical-to-optical transducer; at least a first and a second electrical-to-optical transducer preferably arranged in series and preferably comprised in the first waveguide, and further arranged in series with the primary electrical-to-optical transducer, and wherein the at least second and third electrical digital signals modulate the first optical signal in the at least first and second electrical-to-optical transducers, respectively, and wherein the first electrical-to-optical transducer is configured to modulate a first wavelength and the second electrical-to-optical transducer is configured to modulate a second wavelength; a first waveguide portion configured to disperse the first optical signal or introduce a wavelength-dependent time delay in the
• the digital optical computing processing unit configured to perform digital-digital multiplications may comprise the same features than the digital optical computing configured to perform analogue-digital continuous convolutions as described herein. At least one difference is that the first waveguide portion which is configured to disperse the first optical signal or preferably to introduce a wavelength-dependent time delay in the first optical signal is arranged after the at least first and second electrical-to-optical transducers. This enables a digital multiplication between the at least first with the at least second and third electrical digital signals.
• the at least second and third electrical digital signals are elements and/or symbols of a secondary electrical digital signal.
• the digital multiplication as referred herein is the digital multiplication between the at least first electrical digital signal and the secondary electrical digital signal.
• digital-digital multiplication(s) refers to a multiplication between two digital numbers, preferably two binary numbers, or two multi-level digital signals/numbers.
• the multi-level digital signals may allow more data per symbol, therefore allowing a multiplication between two numbers with less symbols to be processed by the digital optical processing unit.
• the digital multiplication performed by the digital optical computing processing unit configured to perform digital-digital multiplications outperforms the digital multiplier architectures since it is advantageously using features of electrical-to-optical transducers and/or photonic circuits in order to perform digital-digital multiplications.
• the first optical signal can be independently modulated on each of the at least one wavelength, with a time delay between the wavelengths generated by the first waveguide portion.
• FIG. 3A-B show an illustration of a multiplication between two binary words, namely “0110” and “1011”, where the first binary word “0110” needs to be multiplied by each of the symbol or bit of the second binary word “1011”, while each multiplication results need to be shifted by one symbol or bit with the previous one.
• a binary word can be obtained which represents the result of the multiplication between the two binary words.
• each of the multiplications between the first binary word and each of the symbol or bit of the second binary word can be performed on each wavelength, as shown in Fig. 3B.
• the sum of all of these multiplications can be performed by the first optical-to-electrical transducer, which may preferably be wavelength-independent.
• Fig. 13 shows a schematic view of an embodiment of the digital optical processing unit.
• the digital optical processing unit comprises optical devices such as a light source and an optical calculation unit.
• the light source as described herein, can be configured to generate a first optical signal comprising at least two wavelengths.
• the optical calculation unit can be configured to convert the at least first and second electrical digital signals into at least a first and a second optical signals.
• the optical calculation unit can be configured to process the digital signal inputs, which may be the at least first and second electrical digital signals, with the weight control signals, which can be the at least first and second weights.
• the optical calculation unit may comprise at least two electrical-to-optical conversion units.
• the at least two electrical-to-optical conversion units may comprise the at least first and second electrical-to-optical transducers.
• the optical calculation unit may comprise the first waveguide, the at least first and second electrical-to-optical transducers configured to be biased by the at least first and second weight, and/or the primary electrical-to-optical transducer.
• the digital optical processing unit further comprises a signal post-processing unit, wherein the signal post-processing unit comprises at least one analogue-to-digital converter (ADC), at least one multiplier and at least one full-adder.
• a shift circuit can be any combination of electrical delays, thereby shifting binary data either to the left or to the right.
• Shift circuits can come in two types: serial-in/serial-out (SISO) and serial-in/parallel-out (SIPO).
• SISO circuits binary data is shifted in serially (bit by bit) and comes out in the same manner.
• SIPO circuits binary data is shifted in serially but comes out in parallel (all bits at once).
• shift registers which may comprise flip-flops connected in series.
• a clock signal can determine when binary data is shifted, and the direction of shifting (left or right) can be controlled by at least one shift control input.
• Fig. 13 may or may not be drawn to scale and that elements of similar structures or functions are represented by like reference numerals throughout the figures. It should also be noted that Fig. 13 is intended to facilitate the description of the embodiments. Fig. 13 is not intended as an exhaustive description of the invention or as a limitation on the scope of the invention.
• the present disclosure further relates to a method for a hybrid optical- electrical convolution between an input data matrix of size i x j and kernel matrix of size i x j comprising the steps of providing an optical signal having i x j different optical carriers, such as i xj different wavelengths; modulating the optical signal with i xj digital data signals, such that an nth of the i x j optical carriers is modulated with an nth of the i x j digital data signals, wherein the i x j digital data signals are a digital representation of i x j elements of the input data matrix; modulating the optical signal with the kernel matrix such that the kernel matrix applies weights on the i x j optical carriers; summing the i x j optical carriers in a wavelength-independent optical-to- electrical transducer on a per symbol level thereby generating an electrical output signal, wherein the electrical output signal represents the convolution between the input data matrix and the kernel matrix.
• the present disclosure further relates to a method for a hybrid optical-electrical convolution between an input data matrix of size i x j and kernel matrix of size i x j comprising the steps of providing an optical signal having i x j different optical carriers, such as i x j different wavelengths; modulating the optical signal with i x j digital data signals, wherein the i xj digital data signals are a digital representation of the i x j elements of the input data matrix, and such that each of the i x j optical carriers is modulated with the i x j digital data signals, thereby obtaining i x j optical data signals; providing a time delay between the i x j optical data signals, such that each of the i x j optical data signals are delayed in time between each other; modulating the i x j optical data signals with the kernel matrix such that an nth element of the kernel matrix applies a nth weight on a nth of the i x
• the present disclosure further relates to a method for hybrid optical- electrical multiplication of a first digital signal comprising j symbols with a second digital signal comprising k symbols, comprising the steps of providing an optical signal having i different optical carriers, such as i different wavelengths and wherein i is larger or equal than j, and wherein j is larger than or equal to k; modulating the optical signal with the first digital signal, such that each of the i optical carriers is modulated with the first digital signal, thereby defining i optical digital signals; modulating each of the i optical digital signals with a nth of the k symbols on a nth of the i optical carriers; providing a time delay between the i optical digital signals, such that each of the i optical digital signals are separated in time; summing the i optical carriers in a wavelength-independent optical-to-electrical transducer on a per symbol level thereby generating an electrical output signal, wherein the electrical output signal represents the multiplication between the first digital signal and the second digital signal.
• convolution may refer to an operation between two matrices wherein each of the elements in the same position of the two matrices are multiplied and all the multiplications are summed.
• the digital optical computing processing units disclosed herein may be configured to carry out any of the presently disclosed convolution and multiplication methods.
• the presently disclosed convolution and multiplication methods may comprise any of the features of the presently disclosed digital optical computing processing units.
• electrical digital signals may refer to digital binary words.
• the person skilled in the art would understand that the electrical digital signals can represent inputs to the digital optical computing processing units and the methods, as disclosed herein.
• the inputs can be encoded into digital signals, thereby encoded into digital binary words or digital vectors.
• analogue signals are fundamentally vulnerable to noise and crosstalk.
• electrical digital signals By using electrical digital signals, a better performance against noise and a higher calculation precision can be achieved, while releasing constraints on the architecture, such as high-speed, high-level digital- to-analogue converters that are used in the analogue optical computing systems.
• Figs. 1A-B show schematic views of an embodiment of the digital optical computing processing unit configured to perform analogue-digital convolutions
• Fig. 2 shows a schematic view of an embodiment of the digital optical computing processing unit configured to perform analogue-digital continuous convolutions
• Figs. 3A-C show illustrations of an example of a multiplication between two binary numbers and a schematic view of an embodiment of the digital optical computing processing unit configured to perform digital-digital multiplication
• Figs. 4A-E show a schematic view of an embodiment of a micro-ring resonator and graphs illustrating a micro-ring resonator transmission curves with different biases, transmission loss at a given wavelength, and residual power after the micro-ring resonator at the given wavelength for different bias voltages,
• Figs. 5A-H show schematic views of an embodiment of a micro-ring resonator and different graphs illustrating the resulting optical amplitude of an optical signal being modulated by a micro-ring resonator biased with different weights, by an electrical digital signal having a peak-peak amplitude of Vpp,
• Figs. 6A-C show a drawing and a schematic view of an embodiment of a digital optical processing unit with parallel waveguides
• Fig. 7 shows a schematic view of an embodiment of the digital optical processing unit where the at least first, second and third electrical digital signals are modulated by a carrier wave
• Figs. 8A-B show graphs representing statistical summaries of correlation between root-mean square error (RMSE) or signal error rate (SER) and signal to noise ratio (SNR), for a PAM-16 modulation scheme, a QAM-16 modulation scheme and an analogue scheme,
• RMSE root-mean square error
• SER signal error rate
• SNR signal to noise ratio
• Figs. 9A-L show an example of the LUT working principle as used in the disclosed digital optical processing unit
• Fig. 10 shows a schematic view of an embodiment of the digital optical computing processing unit configured to perform analogue-digital continuous convolutions
• Figs. 11 A-B show a drawing and a schematic view of an embodiment of a digital optical processing unit with parallel waveguides
• Figs. 12A-G show a modified national institute of standards and technology (MNIST) dataset validation with the digital optical processing unit
• Fig. 13 shows a schematic view of an embodiment of the digital optical processing unit.
• the first electrical output signal is a first electrical digital output signal.
• the first electrical digital output signal can be a multi-level digital output signal.
• the first electrical digital output may be generated by the first optical-to-electrical transducer, based on the first optical signal. Since the first optical signal can be modulated by at least a first and a second electrical digital signal, the first electrical output signal may be advantageously digital.
• the first electrical output signal By having the first electrical output signal being digital, an easier processing of the first electrical output signal can be achieved with common reshaping, filtering or equalizing techniques known in the art. These techniques can be achieved by a digital signal processing system.
• Digital signal processing (DSP) systems may include the following features:
• Equalizers compensate for channel impairments in high-speed communication systems, such as distortion and attenuation.
• Clock and data recovery systems extract the clock signal from a high-speed data stream, allowing data to be accurately sampled and processed.
• Signal generators generate high-frequency signals that can be used for testing and calibration of high-speed systems.
• Time-domain reflectometers locate faults in high-speed transmission lines by measuring the reflection of signals at the point of discontinuity.
• Modulation and demodulation systems modulate data onto high-frequency carrier signals and to demodulate received signals back to baseband.
• Error correction systems correct errors that occur in high-speed data transmission due to noise and interference.
• At least one signal processing unit configured to convert the first electrical digital output signal to a binary signal may be further comprised in the digital optical computing processing unit.
• the at least one signal processing unit may comprise electrical/electronic circuits able to convert a digital signal into a binary signal.
• the digital signal may be a multi-level digital signal, therefore a processing unit may be needed to convert the multi-level digital signal into a binary digital signal.
• a binary digital signal is easier to handle by common electronic processing units such as field- programmable gate array (FPGA).
• the at least one signal processing unit may comprise electronic signal processing circuits that can be suitable for decoding a multilevel electrical digital signal to a binary signal.
• an output of the first electrical-to-optical transducer is connected to an input of the second electrical-to-optical transducer.
• the first and the second electrical-to-optical transducers may have an input and an output, wherein the input and the output are connected to each other.
• the input and the output may be connected by a waveguide or may directly be connected.
• the electrical-to- optical transducer is symmetric, such as the input can be the output and vice versa.
• “arranged in series” may mean that the output of the first electrical-to-optical transducer is connected to the input of the second electrical-to- optical transducer.
• first electrical-to-optical transducer can be arranged in series with the primary electrical-to-optical transducer, while not necessarily being connected to each other, but sharing the same optical signal, i.e. the first optical signal on the first waveguide.
• the at least first and second electrical-to-optical transducer can be arranged in parallel.
• the first waveguide comprising at least two wavelengths could be split into at least two secondary waveguides, where each of the secondary waveguides comprise one wavelength of the at least two wavelengths.
• the at least first and second electrical-to- optical transducer can be wavelength-independent electrical-to-optical transducer since the at least first and second electrical-to-optical transducer would be respectively arranged on one of the secondary waveguides.
• the secondary waveguides could then be recombined into a first output waveguide by combining the at least two wavelengths in the first output waveguide.
• the primary electrical-to-optical transducer is wavelengthindependent.
• the primary electrical-to-optical transducer may be configured to modulate all the wavelengths comprised in an optical signal passing through it with the same information/data.
• the optical signal may comprise at least two wavelengths, such as two, ten, fifty or more wavelengths.
• the primary electrical-to-optical transducer may advantageously be a Mach-Zehnder modulator (MZM) or an electro-absorption modulator (EAM).
• MZM Mach-Zehnder modulator
• EAM electro-absorption modulator
• a MZM is an interferometric structure made from a material with strong electro-optic effect (such as LiNbO3, GaAs, InP). Applying electric fields to the arms changes optical path lengths of the optical signal passing through it resulting in phase modulation.
• the at least one signal processing unit can further comprise an electrical signal processing unit, wherein the electrical signal processing unit comprises at least one multiplier and at least one full-adder.
• the at least one multiplier and the at least one full-adder can be used to generate a binary signal out of a multi-level electrical digital signal.
• Fig. 6A-C show an illustration of the different steps processed by the at least one signal processing unit.
• Fig. 6A shows the first electrical output signal.
• the first electrical output signal is a multi-level signal.
• the first electrical output signal is split by groups of 8 symbols in order to be processed.
• the first electrical output signal is then arranged in time with one clock period difference between successive symbols as shown in Fig. 6B.
• the digital optical computing processing unit can further comprise a look-up table (LUT).
• LUT look-up table
• the LUT method is widely used in optical communications, where it is used to map detected values to real data values. It may be a relatively simpler and may save energy consumption.
• a LUT may be implemented in a field-programmable gate array (FPGA). By implementing the LUT in a FPGA, this makes the LUT flexible in a way such that detected values can be mapped to different real data values in the table of the LUT. If logic circuit would be used as a LUT, the output of the logic circuit mapping the detected values to the real data values would be fixed by the architecture and the connection(s) of the logic circuit.
• the FPGA may offer a flexibility to the LUT that the logic circuit may not provide.
• the LUT is configured to store the at least first and second weights.
• the LUT can be configured to store a digital representation of the at least first and second weights.
• the at least first and second normalized weight value may be arranged such that there are equally separated between each other, on a specific weight range.
• the multi-level signal obtained from the convolution may have equally spaced levels. This would advantageously ease the detection of the levels of the multi-level signal, while enabling the LUT to match the at least first and second weights with the at least first and second normalized weight value.
• the LUT may allow a greater resolution of possible weight values, while the multi-level signal may be kept with equally spaced levels.
• Fig. 9C illustrates the mapping relationship that can exist between the weight value and the PAM-4 signal, as further described in Figs. 9E-F. If the different levels of the PAM-4 signal are detected, the corresponding weight value can be mapped with the corresponding levels.
• Fig. 9G shows a convolution kernel matrix of a size 3x3. In many applications, multiple kernels need to be processed on the same input data. Therefore Fig.
• the digital optical computing processing unit configured to perform analogue-digital convolutions can further process at least a fourth and a fifth electrical digital signals, and the digital optical computing processing unit configured to perform analogue-digital convolutions may further comprise: a second waveguide; a second light source, configured to deliver a second optical signal comprising at least two wavelengths to the second waveguide; at least a third and a fourth electrical-to-optical transducer arranged in series and comprised in the second waveguide, configured to be biased by at least a third and a fourth weight, wherein the at least fourth and fifth electrical digital signals modulate the second optical signal in the at least third and fourth electrical-to-optical transducers, respectively, and wherein the third electrical-to-optical transducer is configured to modulate a third wavelength and the fourth electrical-to-optical transducer is configured to modulate a fourth wavelength; a second optical-to-electrical transducer arranged at a second output of the second waveguide, and wherein the second optical- to-electrical
• the digital optical computing processing unit configured to perform analogue-digital convolutions can further process at least a fourth and a fifth electrical digital signals.
• the digital optical computing processing unit configured to perform analogue-digital convolutions can then perform convolutions on two parallel and distinct paths, therefore increasing the speed by a factor of two.
• the same would apply by having an additional set of similar features, which would increase the processing/computing speed of the digital optical computing processing unit by a factor proportional to the similar features added to the system.
• Figs. 11 A-B show a drawing and a schematic view of an embodiment of a digital optical processing unit with parallel waveguides.
• FIG. 11A shows a 3D view of an embodiment of a digital optical processing unit where multiple waveguides are comprised in the digital optical processing unit, therefore parallelizing the operations of convolution and/or multiplication as described in the present disclosure.
• Fig. 11 B shows a schematic view of an embodiment of a digital optical processing unit with parallel waveguides where main functions are divided into categories, namely multi-wavelength laser, micro-ring arrays, photon detectors and electrical interface.
• the multi-wavelength lasers are the light source as described in the present disclosure
• the micro-ring arrays are the at least first, second, third and fourth electrical-to-optical transducers as described in the present disclosure
• the photon detectors are the first and second optical-to-electrical transducer
• the electrical interface are the at least one processing unit and the at least one signal processing unit as described in the present disclosure.
• Fig. 10 shows a schematic view of an embodiment of the digital optical computing processing unit configured to perform analogue-digital continuous convolutions.
• a carrier wave oscillating at a frequency fi is comprised in the digital optical computing processing unit.
• An IQ modulation/demodulation system is also comprised in the digital optical computing processing unit, thereby allowing the electrical digital signals to be both modulated on the carrier wave and in quadrature with each other.
• the electrical digital signals are pixels of an image. For instance, Xi and X2 are modulated by the carrier wave and are in quadrature between each other, Xi being modulated by cos(fi*2TTt) and X2 being modulated by sin(fi*2TTt).
• X n are multiplied by W1, W2, ... W n , respectively, where W1, W2, ... W n are normalized weights, as described in the present disclosure.
• These signals generated by the multiplication of the electrical digital signals and the weights are modulating the optical signal generated by the comb laser.
• the resulting multiplication between Xi and W1 modulates the optical signal on one wavelength
• the resulting multiplication between X2 and W2 modulates the optical signal on a second wavelength and so forth.
• the optical signal is detected by a photodiode at the end of the waveguide.
• the photodiode converts the optical signal into an electrical output signal, which is then processed by a processing unit such as a FPGA and a QAM output is obtained.
• a LUT can match the obtained normalized weights to the actual weights, in order to generate a resulting digital data. Then the resulting digital data is processed by a processing unit in order to be converted into binary data, thereby generating the final result.
• the digital optical computing processing unit configured to perform analogue-digital continuous convolutions can further process at least a fourth, a fifth and a sixth electrical digital signals, and the digital optical computing processing unit configured to perform analogue-digital continuous convolutions can further comprise: a second waveguide; a second light source, configured to deliver a second optical signal comprising at least two wavelengths to the second waveguide; a secondary electrical- to-optical transducer comprised in the second waveguide, wherein the second optical signal is modulated by the at least fourth electrical digital signal in the secondary electrical-to-optical transducer; at least a third and a fourth electrical-to-optical transducer preferably arranged in series and comprised in the second waveguide, and further arranged in series with the secondary electrical-to-opti
• the digital optical computing processing unit configured to perform digital-digital multiplications can further process at least a fourth, a fifth and a sixth electrical digital signals, and the digital optical computing processing unit configured to perform digitaldigital multiplications can further comprise: a second waveguide; a second light source configured to deliver a second optical signal comprising at least two wavelengths to the second waveguide; a secondary electrical-to-optical transducer comprised in the second waveguide, wherein the second optical signal is modulated by the at least fourth electrical digital signal in the secondary electrical-to-optical transducer; at least a third and a fourth electrical-to-optical transducer preferably arranged in series and comprised in the second waveguide, and further arranged in series with the secondary electrical-to-optical transducer, wherein the at least third and fourth electrical-to-optical transducers can be configured to be biased or loaded by at least a third and a fourth weight, wherein the at least third and fourth electrical digital signals modulate the second optical signal in the at least third and fourth electrical-to
• the second waveguide may have at least one property or any combinations of properties as described herein regarding the first waveguide.
• the second electrical output signal can have at least one property or any combinations of properties as described herein regarding the first electrical output signal.
• the secondary electrical-to- optical transducer may have at least one property or any combinations of properties as described herein regarding the primary electrical-to-optical transducer.
• the second light source can be the first light source.
• the first wavelength can have the same wavelength than the third wavelength and/or the second wavelength may have the same wavelength than the fourth wavelength.
• the second optical signal may have at least one property or any combinations of properties as described herein regarding the first optical signal.
• the at least third and fourth electrical-to-optical transducer can have at least one property or any combinations of properties as described herein regarding the at least first and second electrical-to-optical transducer.
• the digital optical computing processing unit may further comprise a splitter configured to split a light source such as the first optical signal and the second optical signal can be generated from the light source.
• the light source may be configured to provide an optical signal to the first and the second waveguide, wherein the optical signal is the first optical signal and/or the second optical signal.
• the second light source can be the first light source.
• the at least fourth, fifth and sixth electrical digital signals may have at least one property or any combinations of properties as described herein regarding the at least first, second and third electrical digital signals.
• the second waveguide portion can have at least one property or any combinations of properties as described herein regarding the first waveguide portion.
• Fig. 12A-G show a modified national institute of standards and technology (MNIST) dataset validation with the digital optical processing unit.
• MNIST task is a preferred tool for verifying image recognition.
• the task is to distinguish 10 handwritten digits for classification.
• the model is pre-trained, such as the kernel matrix is known and implemented in the digital optical processing unit.
• Fig. 12A shows the 10,000 images of the handwritten digital MNIST test dataset used to perform the convolutional layer processing, with each image having a pixel resolution of 28x28. The result of the processing of the images is shown in Fig.
• Fig. 12B where the pixel resolution is down to 26x26, because of the stride step of the convolution.
• Four 3x3 kernel matrixes are used in this example, which gives 26x26x4 pixel matrixes of 10,000 images.
• the remaining networks is processed with electronic hardware as shown in Fig. 12C, where decisions are made.
• the results are then compared with the results obtained from a processing unit, such as a computer.
• the results are substantially equivalent in each prediction classification as shown in Figs. 12D-E.
• the deviation is on the order of one in a thousand.
• the diagonal prediction accuracy data are extracted and compared, as shown in Fig. 12F, and is substantially identical.
• Fig. 12G shows the comparison between standard expected result and the digital optical processing unit calculation result.
• the resulting distribution converge linearly, with only individual points distributed outside.
• the present disclosure may relate to a method for a hybrid optical- electrical convolution between an input data matrix of size i x j and kernel matrix of size i x j comprising the steps of providing an optical signal having i xj different optical carriers, such as i xj different wavelengths; modulating the optical signal with i xj digital data signals, such that an nth of the i x j optical carriers is modulated with an nth of the i x j digital data signals, wherein the i x j digital data signals are a digital representation of i x j elements of the input data matrix; modulating the optical signal with the kernel matrix such that the kernel matrix applies weights on the i x j optical carriers; summing the i x j optical carriers in a wavelength-independent optical-to- electrical transducer on a per symbol level thereby generating an electrical output signal, wherein the electrical output signal represents the convolution between the input data matrix and the kernel matrix.
• the optical-to-electrical transducer may be wavelength-independent.
• the optical-to- electrical transducer may be configured to optically convert all the wavelengths from an optical signal passing through it to an electrical signal, with the same modulation data.
• i is larger than j, preferably lower than j, more preferably equal to j.
• the i xj different wavelengths may be equally spaced between each other.
• the i xj different wavelengths can have different corresponding frequencies, and the different frequencies can define a frequency comb.
• the i x j digital data signals can be binary words.
• the input data matrix can contain coded elements from an image, where the coded elements may be digital representation of pixels.
• the digital representation of pixels can be a binary code.
• the binary code may be a 2-bit binary code, preferably a 4-bit binary code, more preferably a 8-bit binary code, even more preferably a 16-bit binary code, most preferably a 32-bit binary code, yet preferably a 64-bit binary code.
• the kernel matrix may be a convolution matrix, where the convolution matrix can be a matrix used for blurring, sharpening, embossing or edge detecting.
• the kernel matrix can be a 3 x 3 matrix, preferably a 4 x 4, more preferably a 6 x 6, even more preferably a 16 x 16 matrix.
• the optical signal can be generated by a laser source.
• the laser source may be configured to generate at least two optical wavelengths.
• the i x j digital data signals can comprise at least two symbols.
• the i x j digital data signals may be binary data signals, preferably multi-level digital data signals, such as PAM signals.
• the PAM signals may comprise 2, 4, or more levels.
• Binary data signals may be binary signals containing data.
• the weights can be comprised between -1 and 1.
• the weights can be any values comprised between -1 and 1, including -1 and 1.
• the wavelength-independent optical-to-electrical transducer can be a photodiode.
• the wavelength-independent optical-to-electrical transducer can be any type of photodetector.
• the method for a hybrid optical-electrical convolution between an input data matrix of size i x j and kernel matrix of size i x j can be carried out by the optical digital processing unit configured to perform analogue-digital convolutions as described herein.
• the present disclosure may relate to a method for a hybrid optical- electrical convolution between an input data matrix of size i x j and kernel matrix of size i x j comprising the steps of providing an optical signal having i x j different optical carriers, such as i xj different wavelengths; modulating the optical signal with i xj digital data signals, wherein the i x j digital data signals are a digital representation of the i x j elements of the input data matrix, and such that each of the i x j optical carriers is modulated with the i x j digital data signals, thereby obtaining i x j optical data signals; providing a time delay between the i x j optical data signals, such that each of the i x j optical data signals are delayed in time between each other; modulating the i x j optical data signals with the kernel matrix such that an nth element of the kernel matrix applies a nth weight on a nth of the i x j optical
• the optical-to-electrical transducer may be wavelength-independent.
• the optical-to- electrical transducer may be configured to modulate all the wavelengths from an optical signal passing through it, with the same modulation data.
• the i x j digital data signals can be binary words. i can be larger than j, preferably lower than j, more preferably equal to j.
• the i x j different wavelengths can be equally spaced between each other.
• the i x j different wavelengths may have different corresponding frequencies, and the different frequencies can define a frequency comb.
• the time delay may be relative to a symbol data rate.
• the j symbols and/or the k symbols may modulate the i optical carriers at the symbol data rate.
• the symbol data rate can be the inverse of a symbol data period.
• the time delay can be 100 % of the symbol data period, preferably comprised between 100 % and 110 % of the symbol data period, more preferably comprised between 100 % and 150 % of the symbol data period, even more preferably comprised between 100 % and 200 % of the symbol data period.
• the input data matrix can contain coded elements from an image.
• the coded elements may be digital representation of pixels.
• the digital representation of pixels can be a binary code.
• the binary code may be a 2-bit binary code, preferably a 4-bit binary code, more preferably a 8-bit binary code, even more preferably a 16-bit binary code, most preferably a 32-bit binary code, yet preferably a 64-bit binary code.
• the kernel matrix can be a convolution matrix, wherein the convolution matrix may be a matrix used for blurring, sharpening, embossing or edge detecting.
• the kernel matrix can be a 3 x 3 matrix, preferably a 4 x 4, more preferably a 5 x 5, even more preferably a 6 x 6 matrix, most preferably a 16 x 16 matrix.
• the optical signal may be generated by a laser source.
• the laser source can be configured to generate at least two optical wavelengths.
• the i x j digital data signals may comprise at least two symbols.
• the i x j digital data signals can be binary data signals, preferably multi-level digital data signals, such as PAM signals.
• the PAM signals may comprise 2, 4, or more levels.
• Binary data signals may be binary signals containing data.
• the weights may be comprised between -1 and 1.
• the weights can be any values comprised between -1 and 1, including -1 and 1.
• the wavelength-independent optical-to-electrical transducer can be a photodiode.
• the wavelength-independent optical-to-electrical transducer can be any type of photodetector.
• the method for a hybrid optical-electrical convolution between an input data matrix of size i x j and kernel matrix of size i x j may be carried out by the digital optical processing unit configured to perform analogue-digital continuous convolutions as described herein.
• the present disclosure may relate to a method for hybrid optical- electrical multiplication of a first digital signal comprising j symbols with a second digital signal comprising k symbols, comprising the steps of providing an optical signal having i different optical carriers, such as i different wavelengths and wherein i is larger or equal than j, and wherein j is larger or equal than k; modulating the optical signal with the first digital signal, such that each of the i optical carriers is modulated with the first digital signal, thereby defining i optical digital signals; modulating each of the i optical digital signals with a nth of the k symbols on a nth of the i optical carriers; providing a time delay between the i optical digital signals, such that each of the i optical digital signals are separated in time; summing the i optical carriers in a wavelengthindependent optical-to-electrical transducer on a per symbol level thereby generating an electrical output signal, wherein the electrical output signal represents the multiplication between the first digital signal and the second digital signal.
• the optical-to-electrical transducer may be wavelength-independent.
• the optical-to- electrical transducer may be configured to optically convert all the wavelengths from an optical signal passing through it to an electrical signal, with the same modulation data.
• the i different wavelengths can be equally spaced between each other.
• the i different wavelengths may have different corresponding frequencies, and the different frequencies can define a frequency comb.
• the time delay may be relative to a symbol data rate.
• the j symbols and/or the k symbols can modulate the i optical carriers at the symbol data rate.
• the symbol data rate may be the inverse of a symbol data period.
• the time delay can be 100 % of the symbol data period, preferably comprised between 90 % and 110 % of the symbol data period, more preferably comprised between 50 % and 150 % of the symbol data period, even more preferably comprised between 50 % and 200 % of the symbol data period.
• the first digital signal and/or the second digital signal can be a multi-level digital signal or a binary signal.
• Each of the i optical digital signals can be multi-level digital signals or binary signals.
• the optical signal may be generated by a laser source.
• the laser source can be configured to generate at least two optical wavelengths.
• the first digital signal can be a multiplier and the second digital signal can be a multiplicand.
• the first digital signal can be a multiplicand and the second digital signal can be a multiplier.
• the j symbols and/or the k symbols can be multi-level symbols or bits, which may be two-level symbols.
• the wavelength-independent optical-to-electrical transducer may be a photodiode.
• the wavelength-independent optical-to-electrical transducer can be any type of photodetector.
• the method for hybrid optical-electrical multiplication can be carried out by the digital optical processing unit configured to perform digital-digital multiplications as described herein.
• a digital optical computing processing unit configured to perform analoguedigital convolutions by processing at least a first and a second electrical digital signal and a first optical signal comprising at least two wavelengths, the digital optical computing processing unit comprising: a first waveguide for carrying the first optical signal; at least a first and a second electrical-to-optical transducer comprised in the first waveguide, configured to be biased by at least a first and a second weight, wherein the at least first and second electrical digital signals modulate the first optical signal in the at least first and second electrical- to-optical transducers, respectively, and wherein the first electrical-to- optical transducer is configured to modulate a first wavelength and the second electrical-to-optical transducer is configured to modulate a second wavelength.
• the digital optical computing processing unit according to item 1, further comprising a light source configured to deliver a first optical signal comprising at least two wavelengths to the first waveguide.
• a first optical-to-electrical transducer arranged at a first output of the first waveguide, and wherein the first optical-to-electrical transducer is configured to output a first electrical output signal based on the first optical signal.
• a digital optical computing processing unit configured to perform analoguedigital continuous convolutions by processing at least a first, a second and a third electrical digital signal and a first optical signal comprising the at least two wavelengths, the digital optical computing processing unit comprising: a first waveguide for carrying the first optical signal; a primary electrical-to-optical transducer comprised in the first waveguide, wherein the first optical signal is modulated by the at least first electrical digital signal in the primary electrical-to-optical transducer; at least a first and a second electrical-to-optical transducer comprised in the first waveguide, and further arranged in series with the primary electrical-to-optical transducer, wherein the at least first and second electrical-to-optical transducer are configured to be biased by at least a first and a second weight, and wherein the at least first and second electrical digital signals modulate the first optical signal in the at least first and second electrical-to-optical transducers, respectively, and wherein the first electrical-to-optical transducer is configured
• the digital optical computing processing unit according to any one of items 6-7, further comprising a first optical-to-electrical transducer arranged at a first output of the first waveguide, and wherein the first optical-to-electrical transducer is configured to output a first electrical output signal based on the first optical signal.
• a digital optical computing processing unit configured to perform digital-digital multiplications by processing at least a multiplier and a multiplicand, wherein the multiplicand comprises at least a first electrical digital signal, and the multiplier comprises at least a second and a third electrical digital signal, and a first optical signal comprising at least two wavelengths
• the digital optical computing processing unit comprising: a first waveguide for carrying the first optical signal; a primary electrical-to-optical transducer comprised in the first waveguide, wherein the first optical signal is modulated by the at least first electrical digital signal in the primary electrical-to-optical transducer; at least a first and a second electrical-to-optical transducer comprised in the first waveguide, and further arranged in series with the primary electrical-to-optical transducer, wherein the at least second and third electrical digital signals modulate the first optical signal in the at least first and second electrical-to-optical transducers, respectively, and wherein the first electrical-to-optical transducer is configured to modulate a first
• the digital optical computing processing unit according to item 11 , further comprising a light source configured to deliver a first optical signal comprising at least two wavelengths to the first waveguide.
• first optical-to-electrical transducer arranged at a first output of the first waveguide, and wherein the first optical-to-electrical transducer is configured to output a first electrical output signal based on the first optical signal.
• the at least second and third electrical digital signals are respectively at least a first and a second bit of the multiplier.
• wavelength-dependent time delay is a time delay between the at least two wavelengths.
• the waveguide portion is comprised in the first waveguide and arranged after the at least first and second electrical-to-optical transducers.
• the at least first and second electrical-to-optical transducer are configured to be biased by the at least second and third electrical digital signals, thereby modulating the first optical signal with the at least second and third electrical digital signals.
• the first electrical output signal is a first electrical digital output signal.
• the digital optical computing processing unit further comprises at least one signal processing unit configured to convert the first electrical digital output signal to a binary signal.
• the primary electrical-to-optical transducer is a Mach-Zehnder modulator (MZM) or an electro-absorption modulator (EAM).
• MZM Mach-Zehnder modulator
• EAM electro-absorption modulator
• the at least first and second electrical-to-optical transducers are wavelength-dependent.
• the digital optical computing processing unit according to any one of the preceding items, wherein the at least first and second electrical-to-optical transducers are configured to have a passband bandwidth comprised between 5 and 100 GHz, preferably between 10 and 70 GHz, more preferably between 20 and 60 GHz, even more preferably between 30 and 50 GHz.
• the digital optical computing processing unit according to any one of the preceding items, wherein the at least first and second electrical-to-optical transducers are at least a first and a second micro-ring resonator or at least a first and a second cascaded Mach-Zehnder.
• the digital optical computing processing unit according to any one of the preceding items, wherein the digital optical computing processing unit further comprises a digital-to-analogue converter (DAC) configured to convert the at least first and second electrical digital weight signals into at least a first and a second electrical analogue weight signals.
• DAC digital-to-analogue converter
• 34 The digital optical computing processing unit according to item 33, wherein the at least first and second electrical analogue weight signals are at least a first and a second bias signal.
• the at least first and second bias signals are configured to bias the at least first and second heater modulators of the at least first and second electrical-to-optical transducers, respectively.
• the at least first, second and third electrical digital signals represents at least a first and a second pixel information of an image.
• the at least first, second and/or third electrical digital signal comprises at least one symbol.
• the digital optical computing processing unit according to item 41 wherein the dispersive waveguide portion is a photonic crystal or a chirped Bragg grating.
• the digital optical computing processing unit according to any one of the preceding items, wherein the digital optical computing processing unit further comprises a phase modulator.
• the digital optical computing processing unit according to item 48 wherein the phase modulator is configured to generate a frequency comb light source.
• the digital optical computing processing unit according to any one of the preceding items wherein the at least two wavelengths are separated from one another by a frequency spacing.
• the digital optical computing processing unit according to item 50 wherein the frequency spacing is a comb frequency spacing.
• the digital optical computing processing unit according to any one of the preceding items, wherein the at least first, second and third electrical digital signal are multi-level digital signals and/or binary signals.
• digital optical computing processing unit according to any one of the preceding items, wherein the digital optical computing processing unit further comprises a carrier wave generator.
• each one of the at least one carrier wave has an oscillating frequency.
• the carrier wave generator is an electronic oscillator, such as a feedback oscillator or a negative-resistance oscillator.
• each of the at least first, second and third electrical digital signals are modulated by one of the at least one carrier wave.
• the digital optical computing processing unit according to any one of the preceding items, wherein the digital optical computing processing unit further comprises at least one digital-to-analogue converter, wherein the at least one digital-to-analogue converter is configured to convert the at least first, second and third electrical digital signals into at least a first, a second and a third electrical analogue signals.
• the digital optical computing processing unit according to any one of the preceding items, wherein the at least first, second and third electrical analogue signals are modulated by the at least one carrier wave, thereby generating at least a first, a second and a third carrier-modulated electrical signals.
• the digital optical computing processing unit according to item 61 , wherein the at least first, second and third carrier-modulated electrical signals are modulated in quadrature or orthogonal between each other.
• the digital optical computing processing unit according to any one of the preceding items, wherein the digital optical computing processing unit further comprises an IQ modulation system.
• the digital optical computing processing unit according to item 63, wherein the IQ modulation system is configured to modulate the at least first, second and third carrier-modulated electrical signals in quadrature or orthogonal between each other.
• the first electrical output signal is modulated according to a quadrature-amplitude modulation (QAM).
• QAM quadrature-amplitude modulation
• the digital optical computing processing unit wherein the quadrature-amplitude modulation is a quadrature-phase-shift-keying (QPSK) modulation, preferably a 8-QAM, more preferably a 16-QAM, even more preferably a 32-QAM, most preferably 64-QAM, yet preferably a 128-QAM, yet more preferably a 256-QAM, yet even more preferably 512-QAM, yet most preferably 2 N -QAM, where N is an integer.
• QPSK quadrature-phase-shift-keying
• the at least one signal processing unit comprises an analogue-to-digital converter (ADC) configured to convert the first electrical output signal into a first electrical digital output signal.
• ADC analogue-to-digital converter
• the digital optical computing processing unit according to any one of the preceding items, wherein the at least one signal processing unit further comprises digital signal processing filters and/or analogue or digital equalizers.
• the at least one signal processing unit further comprises an electrical signal processing unit, wherein the electrical signal processing unit comprises at least one multiplier and at least one full-adder.
• the digital optical computing processing unit according to any one of items 71- 74, wherein the LUT is implemented in a field-programmable gate array (FPGA). 76. The digital optical computing processing unit according to any one of the preceding items, wherein the LUT is configured to match the at least first and second weights with at least a first and a second normalized weight value.
• FPGA field-programmable gate array
• the digital optical computing processing unit according to any one of the preceding items, wherein the digital optical computing processing unit is configured for further processing at least a fourth and a fifth electrical digital signals and a second optical signal comprising at least two wavelengths, the digital optical computing processing unit further comprises: a second waveguide for carrying the second optical signal; at least a third and a fourth electrical-to-optical transducer comprised in the second waveguide, configured to be biased by at least a third and a fourth weight, wherein the at least fourth and fifth electrical digital signals modulate the second optical signal in the at least third and fourth electrical-to-optical transducers, respectively, and wherein the third electrical-to-optical transducer is configured to modulate a third wavelength and the fourth electrical-to-optical transducer is configured to modulate a fourth wavelength.
• the digital optical computing processing unit according to item 78 further comprising a second light source, configured to deliver a second optical signal comprising at least two wavelengths to the second waveguide;
• the digital optical computing processing unit according to item 78, further comprising a second optical-to-electrical transducer arranged at a second output of the second waveguide, and wherein the second optical-to-electrical transducer is configured to output a second electrical output signal based on the second optical signal.
• the digital optical computing processing unit according to any one of the preceding items, wherein the digital optical computing processing unit is configured for further processing at least a fourth, a fifth and a sixth electrical digital signals and a second optical signal comprising at least two wavelengths, the digital optical computing processing unit further comprises: a second waveguide for carrying the second optical signal; a secondary electrical-to-optical transducer comprised in the second waveguide, wherein the second optical signal is modulated by the at least fourth electrical digital signal in the secondary electrical-to-optical transducer; at least a third and a fourth electrical-to-optical transducer comprised in the second waveguide, and further arranged in series with the secondary electrical-to-optical transducer, wherein the at least third and fourth electrical-to-optical transducers are configured to be biased by at least a third and a fourth weight, wherein the at least fifth and sixth electrical digital signals modulate the second optical signal in the at least third and fourth electrical-to-optical transducers, respectively, and wherein the third electrical-to-
• the digital optical computing processing unit according to any of the preceding items, wherein the digital optical computing processing unit is configured for further processing at least a fourth, a fifth and a sixth electrical digital signals and a second optical comprising at least two wavelengths, the digital optical computing processing unit further comprises: a second waveguide for carrying the second optical signal; a secondary electrical-to-optical transducer comprised in the second waveguide, wherein the second optical signal is modulated by the at least fourth electrical digital signal in the secondary electrical-to-optical transducer; at least a third and a fourth electrical-to-optical transducer comprised in the second waveguide, and further arranged in series with the secondary electrical-to-optical transducer, wherein the at least third and fourth electrical-to-optical transducers are configured to be biased by at least a third and a fourth weight, wherein the at least third and fourth electrical digital signals modulate the second optical signal in the at least third and fourth electrical-to-optical transducers, respectively, and wherein the third electrical-to-to-
• the digital optical computing processing unit according to item 86 further comprising a second light source configured to deliver a second optical signal comprising at least two wavelengths to the second waveguide.
• the digital optical computing processing unit according to item 86 further comprising a second optical-to-electrical transducer arranged at a second output of the second waveguide, and wherein the second optical-to-electrical transducer is configured to output a second electrical output signal based on the second optical signal.
• the digital optical computing processing unit according to any one of the preceding items, wherein the second optical signal has at least one property or any combinations of properties as presented regarding the first optical signal.
• the digital optical computing processing unit according to any one of the preceding items, wherein the at least third and fourth electrical-to-optical transducer has at least one property or any combinations of properties as presented regarding the at least first and second electrical-to-optical transducer.
• the digital optical computing processing unit further comprises a splitter configured to split a light source such as the first optical signal and the second optical signal is generated from the light source.
• the second light source is the first light source.
• a method for a hybrid optical-electrical convolution between an input data matrix of size / x j and kernel matrix of size / x j comprising the steps of: providing an optical signal having / x j different optical carriers, such as / x j different wavelengths; modulating the optical signal with / x j digital data signals, such that an nth of the / x j optical carriers is modulated with an nth of the / x j digital data signals, wherein the / x j digital data signals are a digital representation of / x j elements of the input data matrix; modulating the optical signal with the kernel matrix such that the kernel matrix applies weights on the / x j optical carriers; summing the / x j optical carriers in an optical-to-electrical transducer on a per symbol level thereby generating an electrical output signal, wherein the electrical output signal represents the convolution between the input data matrix and the kernel matrix.
• the binary code is a 2-bit binary code, preferably a 4-bit binary code, more preferably a 8-bit binary code, even more preferably a 16-bit binary code, most preferably a 32-bit binary code, yet preferably a 64-bit binary code.
• the kernel matrix is a convolution matrix
• the convolution matrix is a matrix used for blurring, sharpening, embossing or edge detecting.
• a method for a hybrid optical-electrical convolution between an input data matrix of size / x j and kernel matrix of size / x j comprising the steps of: providing an optical signal having / x j different optical carriers, such as
• the method according to any one of items 119-128, wherein the coded elements are digital representation of pixels. .
• the binary code is a 2-bit binary code, preferably a 4-bit binary code, more preferably a 8-bit binary code, even more preferably a 16-bit binary code, most preferably a 32-bit binary code, yet preferably a 64-bit binary code.
• the kernel matrix is a convolution matrix, wherein the convolution matrix is a matrix used for blurring, sharpening, embossing or edge detecting.
• the kernel matrix is a 3 x 3 matrix, preferably a 4 x 4, more preferably a 5 x 5, even more preferably a 6 x 6 matrix, most preferably a 16 x 16 matrix.
• the optical signal is generated by a laser source.
• the laser source is configured to generate at least two optical wavelengths.
• the / x j digital data signals comprises at least two symbols. 137.
• the method according to any one of items 119-136, wherein the / x j digital data signals are binary data signals, preferably multi-level digital data signals.
• a method for a hybrid optical-electrical multiplication of a first digital signal comprising j symbols with a second digital signal comprising k symbols comprising the steps of: providing an optical signal having / different optical carriers, such as / different wavelengths and wherein / is larger or equal than J, and wherein j is larger or equal than ; modulating the optical signal with the first digital signal, such that each of the / optical carriers is modulated with the first digital signal, thereby defining / optical digital signals; modulating each of the / optical digital signals with a nth of the k symbols on a nth of the / optical carriers; providing a time delay between the / optical digital signals, such that each of the / optical digital signals are separated in time; summing the / optical carriers in a wavelength-independent optical-to- electrical transducer on a per symbol level thereby generating an electrical output signal, wherein the electrical output signal represents the multiplication between the first digital signal and the second digital signal.

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