Optical methods and devices

Abstract

A method for performing a multiplication operation in the optical domain using an apparatus (100), the apparatus comprising: an optical waveguide (101) and a modulation element (102) optically coupled to the optical waveguide (101), the modulation element (102) modifying the transmission, reflection or absorption characteristics of the waveguide (101) according to the state of the modulation element, wherein the state of the modulation element (102) can be adjusted by a write signal (103). The method comprises: encoding a first value into the write signal (103), mapping the first value to the state of the modulation element (102) using the write signal (103); encoding a second value into a read signal (104); generating an output signal intensity of the read signal as a transmission or reflection, wherein the product of the first value and the second value is encoded in the output signal intensity.

Description

[0001] The present invention relates to: a method and apparatus for performing multiplication; a method and apparatus for digital-to-analog conversion; a method and apparatus for adjusting the state of a phase-change material; and a method and apparatus for implementing a volatile optical storage element. Background Art

[0002] Integrated photonics offers an attractive solution for performing computational tasks on-chip using light, and phase-change materials are becoming the functional materials of choice on photonic platforms. On-chip nonvolatile memories that can be written, erased, and accessed optically are rapidly bridging the gap toward all-photonic chip-scale information processing.

[0003] In current computing systems, the storage and processing of data occur in different physical locations - memory and processor. The transfer of information between memory and processor is a well-known problem that limits the speed of computers. It has been proposed that scalar multiplication and block-by-block bitwise operations can be performed in memory elements (memelements) (electronic circuit elements that perform both information processing and storage). Such in-memory computers (including memory elements) can solve certain non-deterministic polynomial (NP) problems in polynomial (P) time by exploiting properties such as inherent parallelism, functional polymorphism, and information overhead.

[0004] Photonic devices have potential advantages over electronic implementations - they can provide even faster solutions that allow fast multiplexing using different wavelengths on a chip. In recent years, photonic memories have been disclosed, for example, in WO2017 / 046590, the disclosure of which is incorporated herein by reference. Although considerable progress has been made, there is still room for improvement in many areas. Summary of the invention

[0005] Each embodiment and aspect of the present invention may be implemented using or comprising an apparatus comprising: an optical waveguide and a modulation element optically coupled to the optical waveguide, the modulation element modifying the transmission, reflection or absorption characteristics of the waveguide according to the state of the modulation element, wherein the state of the modulation element can be adjusted by an optical signal carried by the waveguide or by an electrical signal applied to the waveguide or a resistive element located near the modulation element.

[0006] The modulation element may include a phase change material. The phase change material may be a superlattice material. The phase change material may include or be selected from GeSbTe, VO x Compounds or alloys composed of a combination of elements. x, GeTe, GeSb, GaSb, AgInSbTe, InSb, InSbTe, InSe, SbTe, TeGeSbS, AgSbSe, SbSe, GeSbMnSn, AgSbTe, AuSbTe and AlSb. The phase change material may include a mixture of compounds selected from the list. The core material of the waveguide may have an optical band gap of at least 1 eV. The core material of the waveguide may be selected from: silicon, silicon nitride, gallium nitride, gallium arsenide, aluminum nitride, magnesium oxide and diamond (polycrystalline or single crystal). The modulation element may have a thickness of less than 40nm or 20nm.

[0007] According to a first aspect of the present invention, there is provided a method for performing a multiplication operation in an optical domain using an apparatus, the apparatus comprising:

[0008] An optical waveguide and a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element can be adjusted by a written signal;

[0009] The method comprises the following steps:

[0010] encoding a first value into a write signal,

[0011] mapping the first value to a state of the modulation element using a write signal;

[0012] encoding a second value into the read signal;

[0013] An output signal intensity is generated as a transmitted or reflected read signal, wherein a product of the first value and the second value is encoded in the output signal intensity.

[0014] The write signal may be an optical signal carried by the waveguide.Mapping the first value to the state of the modulation element using the write signal may include transmitting the write signal through the waveguide.

[0015] The write signal may be an electrical signal. The waveguide may be doped and the electrical signal may be applied to the doped waveguide. The electrical signal may be applied to a resistive element proximate to the modulation element. The electrical signal may be a current pulse.

[0016] The electrical signal may cause current to flow through the waveguide or resistive element, resulting in Joule heating and transferring thermal energy from the waveguide or resistive element to the modulation element, thereby adjusting the state of the modulation element.

[0017] According to a second aspect of the present invention, there is provided a method for performing a multiplication operation in an optical domain using an apparatus, the apparatus comprising:

[0018] an optical waveguide and a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by an optical signal carried by the waveguide;

[0019] The method comprises the following steps:

[0020] encoding a first value into a write signal,

[0021] mapping the first value to the state of the modulation element using the write signal by transmitting the write signal through the waveguide;

[0022] encoding a second value into the read signal;

[0023] An output signal intensity is generated as a transmitted or reflected read signal, wherein a product of the first value and the second value is encoded in the output signal intensity.

[0024] The following optional features apply to both the first and second aspects of the invention.

[0025] Determining the result may include applying an offset correction to the output intensity.

[0026] The offset correction may correspond to the output signal strength.

[0027] Determining the result may include applying a scaling correction to the output intensity.

[0028] The first value and the second value have at least three different possible levels.

[0029] The write pulse may map a first value to a degree of amorphism of the modulating element.

[0030] The modulation element may be placed in a baseline crystallization condition prior to applying a write signal.

[0031] Placing the modulating element in a baseline crystallization condition may include using a two-step reset pulse, the first step having a higher power and a shorter duration than the second step. The reset pulse may be in accordance with the sixth aspect described below. The two-step pulse is not limited to a first step having a fixed power and a second step having a fixed power, and may take other forms. For example, a square first step may be followed by a triangular wave second step, or a two-step reset pulse with continuously varying power may be used, wherein the first step includes a high power portion and the second step includes a low power portion.

[0032] There may be a linear scaling between the first value and the product and between the second value and the product.

[0033] The output pulse intensity can be detected as the ratio of the transmitted read pulse.

[0034] The write signal may be an optical write pulse.

[0035] The read signal may be an optical read pulse.

[0036] The method may include determining a vector or matrix multiplication by performing one or more multiplication operations, wherein an output signal is produced by combining transmitted or reflected signals from more than one waveguide.

[0037] The method may comprise using an apparatus comprising more than one waveguide, each of the one or more waveguides comprising a respective modulation element.

[0038] The apparatus may further include at least one optical combiner, each combiner being configured to combine output signals generated by at least one waveguide.

[0039] The write signal may be a first write signal that maps a first value to a state of a first region of a modulation element, and the method may further include encoding a third value into a second write signal and mapping the third value to a state of a second region of the modulation element using the second write signal, wherein the output signal intensity encodes the product of the first value, the second value, and the third value and / or the sum of the first value multiplied by the second value and the first value multiplied by the third value.

[0040] The method may include encrypting or decrypting information.

[0041] The first write signal and the second write signal may propagate in different directions.

[0042] The apparatus may comprise a first waveguide defining a direction of propagation of a read signal, and at least one further waveguide for carrying a write signal substantially transversely to the direction of propagation of the read signal.

[0043] The optical waveguide may be a first optical waveguide, and the device may further include a second waveguide, which may be transverse to the first waveguide (or at any non-zero angle to the first waveguide) in the region of the modulation element, wherein the modulation element is optically coupled to both the first waveguide and the second waveguide.

[0044] According to a third aspect, there is provided an apparatus for performing a multiplication operation in an optical domain, comprising:

[0045] Optical waveguides;

[0046] a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by a written signal;

[0047] a light source configured to transmit a light signal through the optical waveguide;

[0048] a detector configured to detect the intensity of light from the waveguide;

[0049] The controller is configured as:

[0050] encoding a first value into a write signal;

[0051] encoding a second scalar value into a read signal transmitted by the light source;

[0052] determining an output pulse intensity based on a signal from the detector;

[0053] A result of the multiplication of the first value and the second value is determined based on the output intensity.

[0054] The state of the modulating element may be adjusted by an optical signal carried by the waveguide.The controller may be configured to encode the first value into a write signal transmitted by the light source.

[0055] The device may include an electrical signal generator. The state of the modulation element may be adjusted by an electrical signal generated by the electrical signal generator, the electrical signal being the write signal.

[0056] The waveguide may be doped and an electrical signal may be arranged to be applied to the waveguide.

[0057] The device may further comprise a resistive element proximate the modulation element.The electrical signal may be arranged to be applied to the resistive element.

[0058] The controller may be configured to encode the first value into the electrical signal generated by the electrical signal generator.

[0059] The electrical signal may be arranged to cause current to flow through the waveguide or resistive element, causing Joule heating and transferring thermal energy from the waveguide or resistive element to the modulation element, thereby adjusting the state of the modulation element. The electrical signal may be a current pulse.

[0060] According to a fourth aspect, there is provided an apparatus for performing a multiplication operation in an optical domain, comprising:

[0061] Optical waveguides;

[0062] a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by an optical signal carried by the waveguide;

[0063] a light source configured to transmit a light signal through the optical waveguide;

[0064] a detector configured to detect an intensity of light from the waveguide;

[0065] The controller is configured as:

[0066] encoding a first value into a write signal transmitted by a light source;

[0067] encoding a second scalar value into a read signal transmitted by the light source;

[0068] determining an output pulse intensity based on a signal from the detector;

[0069] A result of the multiplication of the first value and the second value is determined based on the output intensity.

[0070] According to a fifth aspect, there is provided a device comprising a first optical waveguide defining a propagation direction of a read signal and a modulation element optically coupled to the first optical waveguide, the modulation element modifying the transmission, reflection or absorption characteristics of the waveguide according to a state of the modulation element, wherein the state of the modulation element can be adjusted by at least one write optical signal carried by a corresponding at least one write optical waveguide, each write waveguide introducing a corresponding write signal into the modulation element in a direction different from the propagation direction of the read signal (for example, transverse to the propagation direction of the read signal).

[0071] According to a sixth aspect, there is provided a device comprising a first optical waveguide and a second optical waveguide and a modulation element, wherein the modulation element is optically coupled to both the first waveguide and the second waveguide, and the first waveguide is configured to propagate light through the modulation element in a first direction, and the second waveguide is configured to propagate light through the modulation element in a second direction different from the first direction (e.g., transverse to the read signal propagation direction).

[0072] The apparatus according to any of the third to sixth aspects may be configured to perform the method of the first aspect.

[0073] According to a seventh aspect, there is provided a method for weighting a signal light pulse using an apparatus, the apparatus comprising:

[0074] an optical waveguide and a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by an optical signal carried by the waveguide;

[0075] Among them, the method includes:

[0076] transmitting a timing light pulse through the waveguide; and

[0077] subsequently transmitting signal light pulses through the waveguide, wherein each signal light pulse produces an adjustment in the state of the modulation element weighted by a time delay between the timing light signal pulse and the corresponding signal light pulse;

[0078] An output signal intensity is generated as a transmitted or reflected read signal, which encodes the amount of adjustment of the modulation element.

[0079] The method may include performing digital-to-analog conversion, wherein the signal light pulse is a digital input signal and the output signal is an analog output signal.

[0080] The time delay between the timing light pulse and the first signal light pulse may be smaller than a thermal time constant of the modulation element.

[0081] The time delay between the timing light pulse and the first signal light pulse may be less than 25 ns.

[0082] The timing pulse and each signal light pulse may comprise the same duration and the same pulse energy.

[0083] The waveguide may be in a baseline crystalline state prior to transmitting a timing light pulse.

[0084] Each signal light pulse may increase the amount of amorphous material present in the modulating element.

[0085] The weighting of the signal light pulses may be binary such that each successive signal light pulse causes approximately half as much amorphization as the previous signal light pulse.

[0086] According to an eighth aspect, there is provided an apparatus for performing optical digital-to-analog conversion, comprising:

[0087] Optical waveguides;

[0088] a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by an optical signal carried by the waveguide;

[0089] a light source configured to transmit light pulses through the optical waveguide;

[0090] A controller is configured to use the light source to:

[0091] transmitting a timing light pulse through the waveguide, and

[0092] The signal light pulse is then transmitted through the waveguide,

[0093] The time delay between the leading edge of the signal light pulse and the leading edge of the timing light pulse is smaller than the thermal time constant of the modulation element.

[0094] The apparatus of the eighth aspect may be configured to perform the method of the seventh aspect.

[0095] According to a ninth aspect, there is provided a method of controlling volatility in an optical storage element, wherein the optical storage element comprises:

[0096] an optical waveguide, a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element can be adjusted by a written signal;

[0097] Among them, the method includes:

[0098] modifying the state of the modulation element using a write signal; and

[0099] The volatility of the modulation element is controlled using a read signal transmitted through the waveguide, the read signal having a sufficiently high power to cause the modulation element to recrystallize in a stable state.

[0100] The write signal may be an optical signal carried by the waveguide.The state of the modulating element may be modified by means of the optical write signal carried by the waveguide.

[0101] The write signal may be an electrical signal. The state of the modulation element may be modified by applying the electrical signal to the waveguide or a resistive element proximate to the waveguide and the modulation element.

[0102] According to a tenth aspect, there is provided a method of controlling volatility in an optical storage element, wherein the optical storage element comprises:

[0103] an optical waveguide, a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by an optical signal carried by the waveguide;

[0104] Among them, the method includes:

[0105] modifying the state of the modulation element using an optical write signal carried by the waveguide;

[0106] The volatility of the modulation element is controlled using a read signal transmitted through the waveguide, the read signal having a sufficiently high power to cause the modulation element to recrystallize in a stable state.

[0107] The following optional features apply to both the ninth and tenth aspects of the present invention.

[0108] The read signal may have a power sufficient to heat the modulating element to at least the crystallization temperature in a steady state.

[0109] The read signal may be substantially continuous.

[0110] The power of the read signal may be at least 1 mW, or may be at least 0.1 mW.

[0111] The method may include determining a degree of correlation between the first and second optical signals by transmitting the first and second optical signals through a waveguide simultaneously with a read signal, wherein the degree of correlation is indicated by the intensity of an output signal produced by transmitting or reflecting the read signal through the waveguide.

[0112] According to an eleventh aspect, there is provided a method of simulating a nervous system using a plurality of memory cells, wherein at least some of the memory cells are operated according to the ninth aspect or the tenth aspect.

[0113] According to a twelfth aspect, there is provided a storage system, comprising:

[0114] Optical waveguides;

[0115] a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by a written signal;

[0116] at least one light source configured to transmit an optical signal through the optical waveguide;

[0117] The controller is configured as:

[0118] applying a write signal to adjust the state of the modulation element;

[0119] A read signal is transmitted from at least one light source, the read signal having a power sufficient to cause recrystallization of the modulating element in a stable state.

[0120] The write signal may be an optical signal carried by the waveguide.The controller may be configured to transmit the write optical signal from at least one optical source to adjust the state of the modulating element.

[0121] The write signal may be an electrical signal.The controller may be configured to apply the electrical signal to the waveguide or a resistive element proximate to the waveguide and the modulation element so as to adjust the state of the modulation element.

[0122] According to a thirteenth aspect, there is provided a storage system, comprising:

[0123] Optical waveguides;

[0124] a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by an optical signal carried by the waveguide;

[0125] at least one light source configured to transmit an optical signal through the optical waveguide;

[0126] The controller is configured as:

[0127] transmitting a write optical signal from at least one light source to adjust the state of the modulating element;

[0128] A read signal is transmitted from at least one light source, the read signal having a power sufficient to cause recrystallization of the modulating element in a stable state.

[0129] The following optional features apply to both the twelfth and thirteenth aspects of the invention.

[0130] The storage system may include a detector configured to detect an intensity of light from the waveguide.

[0131] The storage system may include a plurality of modulation elements.

[0132] The storage system may include a plurality of waveguides, at least some of which include modulating elements.

[0133] The storage system can be configured to perform the method of the seventh aspect or the eighth aspect.

[0134] According to a fourteenth aspect, there is provided a method for adjusting a state of a phase change material in a device, comprising:

[0135] Optical waveguides;

[0136] a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by an optical signal carried by the waveguide;

[0137] The method includes:

[0138] A composite resetting light pulse is used to increase the crystal fraction of the modulation element, the composite resetting light pulse comprising a non-crystallizing pulse and a crystallizing pulse, the non-crystallizing pulse having a higher power and a shorter duration than the non-crystallizing pulse.

[0139] The amorphous pulse may have at least twice the power of the crystallizing pulse.

[0140] The crystallizing pulse may have a duration at least twice that of the non-crystallizing pulse.

[0141] The composite reset pulse may be a step pulse.

[0142] Any time delay between the trailing edge of the amorphous pulse and the leading edge of the crystallizing pulse may be less than the thermal time constant of the modulating element.

[0143] Before the modulation element, the amorphous pulse may have a power of at least 5 mW or at least 10 mW.

[0144] Before the modulation element, the crystallization pulse may have a power of less than 8 mW.

[0145] The total switching energy of the composite reset light pulse may be less than 3 nJ, or 2 nJ, or 1 nJ, or 800 pJ, or 600 pJ.

[0146] The duration of the composite reset light pulse may be less than 1 μs, or 500ns, or 400ns, or 300ns, or 200ns, or 150ns.

[0147] The composite reset signal may return the modulating element to a baseline state, which may be a fully crystalline state.

[0148] The power level of the crystallization pulse may be selected based on the desired degree of recrystallization of the modulation element.

[0149] According to a fifteenth aspect, there is provided an apparatus comprising:

[0150] Optical waveguides;

[0151] a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the waveguide depending on a state of the modulation element, wherein the state of the modulation element is adjustable by an optical signal carried by the waveguide;

[0152] a light source configured to transmit light pulses through the optical waveguide;

[0153] A controller is configured to use the light source to:

[0154] A composite resetting light pulse is transmitted to increase a crystal fraction of the modulation element, the composite resetting light pulse comprising a non-crystallizing pulse and a crystallizing pulse, the non-crystallizing pulse having a higher power and a shorter duration than the crystallizing pulse.

[0155] The apparatus may be configured to perform a method according to the fourteenth aspect.

[0156] According to a sixteenth aspect, there is provided an apparatus for performing a matrix multiplication operation in an optical domain, the apparatus comprising:

[0157] a first plurality of optical waveguides defining a plurality of rows;

[0158] a second plurality of optical waveguides defining a plurality of columns, wherein the first plurality of optical waveguides and the second plurality of optical waveguides are overlaid to define a plurality of crossover points;

[0159] a plurality of waveguide coupling elements, each waveguide coupling element being located proximate a respective intersection of an optical waveguide of the first plurality of optical waveguides and an optical waveguide of the second plurality of optical waveguides, each waveguide coupling element having a respective modulation element optically coupled to the waveguide coupling element,

[0160] wherein each waveguide coupling element is arranged to couple light from an adjacent one of the first plurality of optical waveguides and to couple light into an adjacent one of the second plurality of optical waveguides, wherein a transmission characteristic of the waveguide coupling element is responsive to a state of a modulation element coupled to the waveguide coupling element.

[0161] The apparatus may comprise one or more detectors arranged at the output of the second plurality of optical waveguides.

[0162] The first plurality of optical waveguides may be transverse to the second plurality of optical waveguides.

[0163] Each optical waveguide in the first plurality of optical waveguides may cross each optical waveguide in the second plurality of waveguides.

[0164] A coupled waveguide adjacent to each waveguide in the first plurality of waveguides may be configured to receive an equal proportion of the signal carried by the corresponding waveguide. A coupled waveguide adjacent to each waveguide in the second plurality of waveguides may be configured to receive an equal proportion of the signal carried by the corresponding waveguide.

[0165] The device may include a plurality of resistive elements, each of which is located adjacent to a respective modulation element. The device may include an electrical signal generator. The electrical signal generator may be arranged to provide current pulses to the resistive elements. The modulation elements may each include a phase change material. Due to the heat generated in the resistive elements, the current pulses may adjust the state of the phase change material.

[0166] The waveguide coupling element may be doped.The electrical signal generator may be arranged to provide a current pulse to the doped waveguide coupling element to adjust the state of the phase change material due to heat generated in the doped waveguide coupling element.

[0167] The apparatus may be arranged to receive an input vector encoded in the intensity of a plurality of input optical pulses, wherein each optical waveguide of the first plurality of optical waveguides receives a respective input optical pulse. The input optical pulses may have different optical wavelengths. The input optical pulses may all have the same optical wavelength.

[0168] The states of the modulation elements may encode matrix elements of a matrix that is multiplied by the input vector, wherein each modulation element encodes an element of the matrix that is multiplied by the input vector.

[0169] The apparatus may be arranged to determine an output vector resulting from the multiplication of the input vector and the matrix.Components of the output vector may be encoded in the output light intensities of the second plurality of optical waveguides.

[0170] Features of any aspect (including optional features) may be combined with features of any other aspect, as appropriate. DETAILED DESCRIPTION

[0171] Example embodiments will now be described purely by way of example with reference to the accompanying drawings, in which:

[0172] Figure 1 is a schematic diagram of a GST-based photonic storage cell in which an optical signal is used to both write and read the state of a modulation element coupled to a waveguide;

[0173] Figure 2 schematically illustrates the multiplication of two scalar numbers a and b to produce a product c according to an embodiment;

[0174] Figure 3 shows the use of a write pulse to adjust the state of a phase change material modulation element, and the resulting change in waveguide transmission;

[0175] Figure 4 shows how the state of the modulation element modulates the output pulse;

[0176] Figure 5 is a graph showing the variation of waveguide transmission with write pulses of different durations (at fixed power);

[0177] Figure 6 is a graph showing different write signals: for amorphizing an initially crystalline material; resetting an amorphous material to a fully crystalline state; and partially resetting a material from an amorphous state to a partially crystalline state;

[0178] Figure 7 is a graph showing the relationship between write pulse energy and recrystallization amount;

[0179] Figure 8 is a histogram showing programming errors for an amorphous state to a crystalline state;

[0180] Fig. 9 is a graph showing the variation in transmission over time during a write pulse that increases the amount of amorphous material in the modulating element and a reset pulse that increases the amount of crystalline material in the modulating element;

[0181] Fig.10 is a graph showing the effect of varying the time delay between a write pulse that converts a modulation element to an amorphous state and a subsequent erase pulse that returns the modulation element to a crystalline state;

[0182] Fig.11 Is from Fig.10 A graph of maximum transmission versus time delay;

[0183] Fig.12 is a graph showing the relationship between transmission change and time delay between two write pulses, each write pulse having insufficient energy to cause a change of state by itself;

[0184] Fig.13 is a graph showing the relationship between the energy of a write pulse and the resulting change in the intensity of transmitted light;

[0185] Fig.14 is a graph showing multi-stage adjustment of a device according to an embodiment with 13 different transmission levels;

[0186] Fig.15 is a histogram showing the error between the programmed transmission level and the actual transmission level of the waveguide;

[0187] Fig.16 is a set of three graphs showing no drift in transmission levels over time;

[0188] Fig.17 is a graph showing input pulse energy for writing and reading and the corresponding measured energy (through the waveguide storage unit and grating coupler);

[0189] Fig.18 is a graph showing three example multiplications;

[0190] Fig.19 is a graph showing 429 example multiplications, wherein measured results are plotted relative to expected results;

[0191] Fig. 20 It is shown Fig.19 a histogram of the distribution of errors in the multiplication shown, wherein the inset shows the errors as a function of the values ​​of the first value and the second value;

[0192] Fig.21 is a micrograph of the first waveguide and the second waveguide used to combine the results of the two multiplications;

[0193] Fig. 22 is a schematic diagram of an apparatus including eight modulation elements, the apparatus being operable to determine the product of an eight-element vector and an N×8 matrix;

[0194] Fig.23 is a schematic diagram showing the use of write signals propagating through the modulation element in different directions to adjust the state of the modulation element;

[0195] Fig.24 is a schematic diagram of a modulation element addressable by more than one waveguide, wherein six lateral waveguides are used to adjust the state of different regions of the modulation element;

[0196] Fig.25 is a schematic diagram of a 3D stacked architecture for a device, wherein modulation elements are shared between stacked waveguides;

[0197] Fig.26is a schematic diagram of each arrangement of the timing signal and the 2-bit digital signal;

[0198] Fig. 27 , Fig.28 and Fig.29 The laser currents of 520mA, 525mA and 530mA are shown respectively. Fig.26 The transmission levels produced by each arrangement shown;

[0199] Fig.30 An example device comprising a waveguide with a modulation element and a reference waveguide (without the modulation element) having a common input grating coupler is shown;

[0200] Fig.31 shows simulation results, plotting the magnitude of the Poynting vector as a shadow plot on a waveguide, where the modulating element is in an amorphous state and a crystalline state;

[0201] Fig.32 is a pair of graphs showing (top) temperature variation with time after a write pulse for low, medium, and high level read signals; and (bottom) the corresponding crystallization fraction with time;

[0202] Fig.33 is a graph showing the relationship between write signal pulse energy and transmission change;

[0203] Fig.34 is a graph showing nine programming levels for nonvolatile operation using a low power read signal;

[0204] Fig.35 is a graph showing the relationship between the maximum change in transmission for a high power read signal and the write signal pulse energy;

[0205] Fig.36 is a graph illustrating volatile operation using a high power read signal, wherein each write pulse results in a short duration (or spike) of amorphization that is quickly recrystallized by the read signal;

[0206] Fig.37 is a plot of the (logarithmically scaled) time-dependent transmission of the device after an initial write pulse that places the material in an amorphous state, with traces for a range of read signal powers;

[0207] Fig.38 is a graph showing the relationship between recovery time and read signal / probe power;

[0208] Fig.39is a plot of the (linear scale) time-dependent transmission of the device after an initial write pulse that places the material in an amorphous state, with traces for a range of read signal powers;

[0209] Fig.40 is a graph showing the relationship between the maximum change in transmission and the time delay between a pair of subthreshold write pulses, with traces for a read signal power of 1.52 mW and a read signal power of 2.37 mW;

[0210] Fig.41 is a graph of measured output optical power versus time for four different sets of write pulses (read signal after transmission through the waveguide), corresponding to: no delay, 25 ns delay, 50 ns delay, and 100 ns delay;

[0211] Fig.42 is a graph showing a curve of transmission versus time for a pulse sequence with varying relative delay amounts;

[0212] Fig.43 A device for determining the multiplication of a vector and a matrix is ​​schematically shown;

[0213] Fig.44 Schematic diagram showing the optical adjustment Fig.43 the manner in which the modulation element of the device is modulated; and

[0214] Fig.45 Schematic diagram of a waveguide coupling element with a doping functioning as a heater Fig.43 and Fig.44 part of the device.

[0215] Figure 1 An apparatus 100 is shown comprising a waveguide 101 and a modulating element 102. The modulating element 102 is optically (near field) coupled to the waveguide 101 such that an optical signal carried by the waveguide 101 interacts with the modulating element 102.

[0216] The modulation element 102 may comprise any material switchable between different states, each different state corresponding to a different optical property of the modulation element. Preferably, the modulation element 102 comprises a phase change material, such as GST. The modulation element 102 may comprise a further encapsulation layer, which may comprise ITO, for example to protect the PCM layer from oxidation.

[0217] The waveguide 101 may be, but is not limited to, a planar waveguide, such as a rib waveguide. The waveguide 101 includes a core material capable of carrying a write optical signal (or pulse) 103 to the modulation element 102 in order to adjust the state of the modulation element 102. Typically, suitable materials for the waveguide core may have a band gap of at least 1 eV.

[0218] One example of a suitable material for the core of the waveguide 101 is silicon nitride. Alternative materials include silicon, gallium nitride, gallium arsenide, diamond (single crystal or polycrystalline), and magnesium oxide, but any material with a band gap greater than 1 eV may be suitable. The waveguide core may comprise an insulating material or a semiconductor.

[0219] An air cladding may be used around the waveguide core 101. In alternative embodiments, other materials may be used. A solid phase cladding material may be used to reduce the thermal time constant of the modulation element 102.

[0220] The transmission properties of the optical waveguide 101 can be inferred by transmitting a read signal (or light pulse) 104 through the waveguide 101 and monitoring the amount of the read signal that is transmitted through (or reflected from) the waveguide 101 .

[0221] The state of the modulation element 102 can be adjusted by a write light pulse 103 carried through the waveguide 101. The write pulse 103 can be input to the waveguide at the first port 115 or the second port 116. The evanescent coupling of the write pulse 103 causes the modulation element 102 to absorb optical power. Subsequent heating of the modulation element 102 by the write pulse 103 can change the state of the modulation element 102. Since the modulation element 102 is optically coupled to the waveguide 101, changes in the optical properties of the modulation element 102 result in changes in the transmission, reflection or absorption characteristics of the optical waveguide 101.

[0222] The information in the write pulses can thereby be mapped to the state of the modulation element 102 , which in turn defines the transmission properties of the waveguide 101 .

[0223] exist Figure 1 In the example of , the write pulse has a wavelength λ=1590 nm and the read pulse has a wavelength λ=1598 nm. The length of the modulation element (along the propagation direction of the light through the waveguide 101) is 1 μm or 2 μm. The width of the waveguide is 1.3 μm and the height of the waveguide is h=165 nm (etched down from a 330 nm thick Si3N4 layer). Other geometries of waveguides and modulation elements may also be used - this is just an example.

[0224] Alternatively, or in addition to using the optical write pulse as described above, the state of the modulation element 102 can be adjusted by an electrical write signal applied to the waveguide 101 or to a separate resistive element near the modulation element. For example, the waveguide core (e.g., silicon) can be doped. In this way, the doped waveguide can act as a heater element by applying a write signal in the form of a current pulse through the doped waveguide. The current pulse causes Joule / resistance heating in the doped waveguide. The heat generated in the doped waveguide will also cause heating of adjacent modulation elements, which can be used to change the state of the modulation element in a manner similar to that described above with reference to the optical write pulse. As a further alternative, instead of or in addition to the doped waveguide, a separate resistive element can be used as a heater element. For example, a resistive element can be formed in a metal layer above the modulation element. The current pulse can be generated by an electrical signal generator controlled by a controller. The heat generated in the resistive element or the doped waveguide can be used to amorphize or crystallize the phase change material of the modulation element by a predetermined amount, for example, based on a previous calibration of how the electrical pulse energy delivered to the waveguide / resistive element affects the state of the modulation element.

[0225] In more detail (which is not intended to limit the present disclosure), one method of manufacturing the device 100 is to deposit a 3.3 μm S i O2 layer. A 330nm Si3N4 on top of the O2 layer is used to start. A photolithography tool can be used to write the photonic circuits, followed by a reflow process (e.g., 90s at 100°C). These prototype devices use a JEOL JBX-5500ZD 50kV electron beam, but a stepper or contact aligner can also be used. These examples were made using MaN-2403 negative resist, but other resists can also be used. After resist development and reflow, reactive ion etching (RIE) is performed in CHF3 / Ar / O2 to etch 165nm of Si3N4, and thus a bare photonic device is obtained. The phase change material is patterned using a second photolithography writing step using poly(methyl methacrylate) (PMMA), followed by a stripping process. A stack of 10nm GST with a 10nm ITO capping layer (to avoid oxidation) is deposited in an argon environment using an RF sputtering system (Nordiko). Before measurement, GST was crystallized on a hot plate after annealing at 250°C for 5 minutes.

[0226] Taking GST as an example, the modulation element can be crystallized from the amorphous state by annealing at a temperature above 150°C, or amorphized from the crystalline state by rapid quenching at a temperature above about 600°C. Most phase change materials (including GST) have a non-negligible imaginary refractive index in the visible and near-infrared wavelength range, and light is attenuated by different amounts depending on the phase of the material, which causes a differentiable transmission signal, thereby encoding information in it.

[0227] like Figure 3 As shown, the initial state 110 of the modulation element 102 may be crystalline (e.g., after a write pulse 103 that resets the modulation element 102 to that state). Subsequent write pulses 103 may be arranged to amorphize the modulation element 102 to a state 111 having an amorphized sub-region 106. The size of the amorphized sub-region will depend on the power of the write pulse 103.

[0228] We can define the write pulse energy P Write >E Th >E Pin , where E Th is the threshold energy for partially amorphizing the phase change material. The larger the proportion of amorphous material in the modulation element 102, the more transmissive the waveguide 101 becomes.

[0229] In the experimental examples presented in this paper, a back-propagating write and read pulse measurement configuration (such as Figure 1 ). The write pulse is used to control the phase configuration of the GST, while a continuous wave (CW) read optical signal is used to read out the transmission state of the modulation element 102. The read signal 104 uses a sufficiently low energy / power so that the state of the modulation element 102 is not modified by the read signal 104. By controlling the power of the pump pulse to write (amorphize) to any higher transmission level, multiple and non-volatile transmission levels are achieved due to the mixing between the amorphous GST and the crystalline GST. For erasing (recrystallization), two methods can be used: i) a series of pulses with decreasing energy; or ii) a single multi-step pulse (e.g., two steps). Any level can be reached starting from any other (i.e., from fully crystalline to fully amorphous), and the number of levels is limited by the geometry of the GST cell and the available signal-to-noise ratio of the detection arrangement.

[0230] Figure 2 represents the two numbers a and b to be multiplied. The number a is mapped to the transmission property T of the waveguide 101 using a write pulse 103 which amorphizes a region 106 of the modulation element 102 and leaves the remaining region 107 in a crystalline state. The write pulse P Write The energy of the write signal 103 has a substantially linear mapping with the transmission T of the waveguide 101. The read signal 104 is attenuated inversely proportional to the transmission T of the waveguide, thereby generating an output signal 105 corresponding to the multiplication of the write signal 103 and the read signal 104. The output pulse P out =(P Write )×P in is to map the multiplicand a to T and the multiplier b to P in Such processing is more efficient than the multiplication performed by sequential addition in conventional electronic implementations.

[0231] exist Figure 4 The process is shown in FIG. 1 , which shows that at a constant power level P in The first write signal is a high power write signal for the completely amorphous modulation element 102, resulting in a maximum transmission 112T of the waveguide. max The second write signal is a low power write signal, resulting in the modulation element remaining fully crystalline, corresponding to the minimum transmission 113T of the waveguide 101 min The output signal 105 obtained by multiplying the read pulse 104 by the first write signal is higher than the output signal 105 obtained by multiplying the read pulse 104 by the second write signal.

[0232] The operating parameters of the example device were explored to reduce energy consumption and increase operating speed. The write pulse duration was varied to achieve different transmission levels while maintaining constant power. Figure 5 Results obtained for a 1 μm long modulation element are shown. The transmission change ΔT is plotted as a function of pulse duration as series 132 and the energy corresponding to each pulse duration is plotted as series 131 .

[0233] For pulses of duration longer than 45 ns, there is saturation due to the finite size of the modulation element 102, where no more amorphous material can be obtained without using higher powers. Therefore, longer pulses represent a waste of energy, as the modulation element 102 will not amorphize further and may even be ablated. From these results, it can also be observed that the change induced by a pulse of 25 ns is equivalent to 75% of the maximum achievable transmission, which is a good balance between maximum contrast between states and reducing switching energy. Longer modulation elements 102 require larger pulse widths to reach saturation, as there will be larger areas to be amorphized. It was found that for GST modulation elements between 1 μm and 4 μm long, pulses of 25 ns are sufficient to achieve clear transmission contrast between levels, limited only by the measured SNR.

[0234] Energy consumption can be further reduced by using an uninterrupted erase signal to return the amorphous elements from an arbitrary level to a (baseline) fully crystalline state. This can be achieved by using a two-step pulse.

[0235] Figure 6Some different write signals are shown. Write signal 103a is a single level signal of short duration (35ns in this example) for transitioning from a crystalline state 90 to a more (or completely) amorphous state 95. Erase signal 109 is a write signal intended to return the modulating element to a completely crystalline (baseline) state. Erase signal 109 comprises a two-step pulse, comprising a first step with a first power level and a short duration (e.g. 35ns), in which the material is amorphous, and a second step with a lower power level and a longer duration (e.g. 100ns), in which the material is crystallized. Write signal 103b is also a two-step pulse, comprising a first step with a first power level and a short duration (e.g. 35ns), in which the material is amorphous, and a second step with a lower power level and a longer duration (e.g. 100ns), in which the material is crystallized. The write signal preferably includes any time interval between the first and second steps. The first step is selected to amorphize the material. The second step is selected to crystallize the material by an amount corresponding to the power level of the second step. In this way, the state of the modulating element can be changed between a crystalline state and a fully amorphous state using a pulsed write signal.

[0236] Figure 7 The relationship between the energy of the second recrystallization portion of a two-step write pulse for recrystallization as a function of the transmission change from a fully amorphous state is shown. The error associated with the recrystallization process is largest at the intermediate level where the sensitivity to the recrystallization energy is highest, but a generally linear relationship is observed, with higher energy write pulses (corresponding to higher powers in the second step) resulting in more state transitions. Figure 8 The error in programming levels from an amorphous state to different degrees of crystallinity is shown. This error limits the number of levels that can be accurately programmed.

[0237] Fig. 9 Both a short duration pulse for amorphization and an example two-step pulse for making the modulation element more crystalline are shown. A curve 144 showing the measured output power of the write signal (after propagation through the waveguide 101) is shown, as well as a curve 141 showing the transmission change ΔT (relative to the baseline fully crystalline state). At t = -100ns, the modulation element is fully crystalline. At t = 0ns, a narrow high power (about 14mW input power, corresponding to about 5.5mW detected after propagation) write pulse 143a (about 25ns) is used to amorphize the modulation element 102. The initial drop in transmission can be attributed to free carrier absorption, followed by a sharp increase in transmission once the narrow pulse is complete. The rate at which the transmission increases after the amorphization write pulse depends on the rate of thermal equilibrium - absorption decreases when equilibrium is reached.

[0238] At t = 300 ns, a two-step erase / recrystallization pulse is initiated. This two-step pulse includes a first high-power (about 14 mW), short-duration (about 25 ns) step that amorphizes the modulation element 102. Then, the pulse switches to a second step with lower power and longer duration (about 5.5 mW, approximately 0.4 times that of the first step), during which the crystallization process occurs in the modulation element 102 (while it is maintained at 150 °C < T < 600 °C). The second step is at a high enough power to prevent rapid quenching. In this example, the duration and power of the second step are long enough (about 100 ns) to return the modulation element to the baseline state. The total switching energy of this two-step pulse is approximately 577.4 pJ.

[0239] This single two-step pulse can replace the 19 individual 100 ns pulse schemes used in the prior art (Ríos, C. et al. Integrated all-photonic non-volatile multi-level memory. Nat. Photonics 9, 725–732 (2015)), where the switching energy of each individual pulse in the erase sequence ranges from 370 pJ to 600 pJ, for a total of approximately 9.5 nJ, and the duration is 3.8 μs (erasing from the highest transmission level to the lowest transmission level). Thus, the two-step method illustrated here is more than 100 times more energy-efficient and 25 times faster in terms of speed.

[0240] In terms of the operating speed of the write / erase cycle, it can be observed that Fig. 9 it takes approximately 200 ns (including the pulse duration) to obtain a stable transmission level for both the write pulse and the erase pulse. However, this time varies with the pulse width: the shorter the pulse, the shorter the time required for the material to cool and the refractive index to stabilize, and its time scale is dominated by the thermo-optic effect. Using a 200 ns pulse interval and considering the cooling time of the erase pulse, the device can operate at 2.5 MHz even if the effect of the time interval between the write pulse and the erase pulse on the level transition has not been optimized.

[0241] Fig.10 Shows the effect of changing the time delay between the write pulse that converts to the amorphous state and the subsequent erase pulse that returns the element to the crystalline state. Fig.11 Plots the maximum (normalized) transmission of the curve from Fig.10 A delay of about 200 ns or 250 ns is sufficient to saturate the transmission of the modulation element at its steady-state value (due to the thermo-optic effect).

[0242] Further improvements in speed and energy can be achieved by reducing the pulse width to even shorter times, especially write pulses which can be picosecond or even femtosecond pulses, thereby reducing the dead time between the two pulses.

[0243] Delays between pulses shorter than that required for thermal equilibrium (in this example, less than about 250 ns) can be used for correlation. For example, if pulses below the switching threshold (the energy required to cause amorphization) are close enough in time, they can still change the state of the device. Fig.12 This effect is shown in , where a pair of write pulses with energies too small to cause a change of state does cause a change in transmission when the time delay between pulses is 25 ns or less.

[0244] Fig.13 shows the write pulse energy 151 for Fig.14 The relationship between the energy of the multi-stage modulation (conversion from a crystalline baseline state to a more amorphous state with a short write pulse) is shown. A remarkable linear response is shown - the linear fit 152 corresponds to the data 151. For large energies, the linearity suffers due to saturation, which means that the modulation element 102 is in its most amorphous state. Fig.13 The onset of this saturation was observed at write energies greater than 210 pJ in . A 2 μm long modulation element was used in these experiments.

[0245] Fig.14 The operation of the device according to an embodiment is shown, where 13 clearly distinguishable levels are written (and read) randomly. The number of levels is limited only by the SNR and the confidence interval. Curve 161 shows the variation of the transmittance ΔT over time when different levels are written to the modulating element.

[0246] Fig.15 The error distribution of the programming level as an error histogram (expected ΔT-actual ΔT) is shown. To study the error in reaching the programmed transmission level, a combination of write pulses and erase pulses was used to reach 10 different transmission levels in 20 consecutive sequences. The experiment was repeated three times. Fig.15 The result of subtracting the actual transmission level after a particular transition from the original programmed level is plotted in Figure 2. After several switching cycles during the conditioning process, the programmed level is considered to be an average level. The average error is very small (about 10 -16 ), and the standard deviation of the error is 0.35. A confidence interval for each transmission level can be established so that each level is uniquely distinguished. The minimum difference in transmission level between programmed states is determined by the SNR, but also by variations in pump pulse power due to fluctuations in the electro-optical conversion. Fig.15A histogram of error data 157 and a normal distribution 156 fit to the data are shown.

[0247] Fig.16 Shows up to 10 4 s, thus demonstrating the stability of the programmed transmission level and the low level of photodrift. An arbitrary sequence of transmission levels was written and erased in two 2 μm GST modulating elements. Subsequently, the device was held at an intermediate transmission level for a longer period of time. Fig.16 a) shows the measured transmission 171 under multi-level operation of a cell written (up-converted) using 50 ns pulses with energies in the range of 350 pJ to 600 pJ and erased (down-converted) using a series of pulses with decreasing power. The highlighted area 172 corresponds to a constant measurement of about 8.5 h with a CW read signal (inside the waveguide) of 0.1 mW. The transmission level measured after the long period is the same as the transmission level measured before.

[0248] Fig.16 b) shows the Fig.16 a) Similar measurement, where trace 173 shows the measured transmission during multi-stage operation. Fig.16 In b), the highlighted area 174 corresponds to switching off the read signal for about 1.5 h. A drift is observed between 4600 s and 4800 s, which is corrected by sending the pulse energy to the level at which the memory was originally set.

[0249] Fig.16 c) shows a different device also including a 2 μm long GST modulating element ( Fig.16 a and Fig.10 b)) Multi-level operation. The write signal is a 25ns pulse with energy in the range of 200pJ to 360pJ. Fig.16 a and Fig.16 b) The writing step and the erasing step are performed in the same way. During the highlight area 176, the read signal is turned off for about 2 h. In this case, the CW read signal power is reduced to 0.05 mW, which is sufficient to avoid drift.

[0250] The mechanical drift of the sample stage was observed to be due to the relaxation of the micromotor holding the device in optical alignment over time. However, once the chip was placed in a stable position, the transmission level remained the same as before for the case where the probe was kept on. 4s constant measurement without measurable drift, a property that can be attributed to the fact that the crystalline phase, which is more stable than the amorphous state, determines and dominates the light absorption. This drift-free process represents a big advantage of photonic memory computing over its electrical analog, which experiences very significant resistance drifts over time, preventing (or at least making it very difficult) to achieve reliable levels. Moreover, the same specific transmission level is retrieved after the measurement: the multi-level regulation is also preserved over time.

[0251] For the case when the read signal is turned off, a drift of close to 9% is observed once the read signal is turned on again. This drift is due to relaxation of the material when the probe is removed, assuming that the probe itself heats the material to a constant temperature, causing a thermo-optical effect that changes the value of the complex refractive index without crystallizing the material. Once the read signal is turned on, the multi-level adjustment is maintained. The same write signal can be applied again to return to the same level at which the memory was initially prepared. Drift can be avoided by simply keeping the read signal turned on at a low power when not actively reading (e.g. 0.05mW, which is half the active read signal power). With this continuous low power signal, material relaxation is negligible, as Fig.16 c) as shown.

[0252] Fig.17 The relationship between the input pulse energy and the corresponding measured energy (measured after the waveguide and grating coupler) is shown. Fig.13 As shown, Fig.17 The measurements in 181, 182 were performed using a waveguide in a multi-level tuned transmission baseline. Line 183 marks the transition to a pulse energy that induces a switch to a partially amorphous state (after writing a specific amorphous state, the memory is erased down to the crystalline baseline again before the next pulse).

[0253] Fig.18 The multiplication a×b=c is shown, where a,b,c∈{0,1}. The same device with a 2 μm long GST modulation element and the single write and erase scheme described above is used. The multiplicand a is mapped to the transmittance of the waveguide T=ΔT+T0, where ΔT corresponds to the change in transmission, which is P Write A linear function of the pulse (such as Figure 7 ), and T0 is the baseline transmission level (fully crystallized). Subsequently, the multiplier b is mapped to the second pulse P in The result of the multiplication is calculated from the output of this latter pulse, which is equivalent to P out =T×P in By tuning the pulse power at the EOM, P is generated in the above manner. Write and P in Both (see Materials and Methods).

[0254] Fig.17 Shows the input pulse energy for the multiplicand a and the multiplier b, highlighting the energy that causes phase switching. The measured energy corresponds to the output pulse energy after propagating through the GST cell and passing through a grating coupler. In these demonstrations, P Write ∈ {180, 354} pJ or equivalently, T ∈ {0, 0.143} (see Figure 7 ), and P in ∈ {0, 112.8} pJ. Fig.17 The linear response of the storage device shown is significant and allows for easy mapping of a scalar to the pulse energy without relying on a fitting function.

[0255] Fig.18 Shows three multiplications, plotting the measured P in values 191, 192, 193 over time and the measured P out values 195, 196, 197. The time delay between the pulses is due to the difference in the optical path between the reference pulse and the pulse coupled into the photonic chip, both of which are obtained from the pump pulse using a 90 / 10 beam splitter.

[0256] In the first multiplication, the modulation element 102 is set to the maximum transmission level T = 0.143 by a 354 pJ write signal (corresponding to a = 1). A read pulse 191 with P 1 in = 112.8 pJ at 0 < t < 35 ns (corresponding to b = 1) is multiplied by the write signal, resulting in an output pulse 195 with a value of approximately 10 pJ at 35 < t < 70 ns (corresponding to c = 1) P out .

[0257] In the second multiplication, the modulation element 102 is set to the minimum transmission level T = 0 by a 180 pJ write signal (corresponding to a = 0). A read pulse 192 with P 1 in = 112.8 pJ at 0 < t < 35 ns (corresponding to b = 1) is multiplied by the write signal, resulting in an output pulse 196 with a value of approximately 8.5 pJ at 35 < t < 70 ns (corresponding to c = 0) P out . The result when multiplied by T = 0 corresponds to a level - specific offset.

[0258] In the third multiplication, the modulation element 102 is set to the maximum transmission level T = 0.143 by a 354 pJ write signal (corresponding to a = 1). A read pulse with P 2 inThe read pulse 193 of 38.9 pJ is multiplied by the write signal, resulting in an output pulse 197P having a value of approximately 3.5 pJ at 35 < t < 70 ns (corresponding to c = 0.4). out .

[0259] In Fig.18 , the output power P out has different energies, which can be measured and then rescaled to obtain the results of three corresponding multiplications: 1×0 = 0, 1×1 = 1, and 1×0.4 = 0.4. Note that the lowest transmission level among the three transmission levels corresponding to 0.4 is actually less than the level for 0. This is due to the fact that even in the fully crystalline state, GST does not absorb all the light from the read signal even in the low transmission state (unless a longer modulation element is used to increase the light attenuation). Therefore, there is an offset given by the horizontal baseline T0 that must be subtracted from each multiplication to enable an accurate linear rescaling of the c ∈ {0,1} results.

[0260] Fig.19 Shows 429 c = a×b multiplications plotted as a scatter sequence 200. These are obtained using 13 different, equally spaced values for T (achieved using P Write ∈ {180,354} pJ), thus creating 13 values for the multiplicand a, and using 33 different values for P in ∈ {0,112.8} pJ, thus creating 33 scalars corresponding to b. Before changing the level again, P Write is sent first to establish the transmission level T, followed by 33 P in pulses. Based on the mapping of the input parameters a and b, the measured value of c is plotted relative to the exact value of c (inferred from the P out signal). The exact value is calculated from the linear fit obtained during the characterization of the device and subsequent mapping of both the multiplicand and the multiplier (a and b) to {0,1}. The measured value corresponds to the average of the output pulse energy, corrected for the offset, and normalized to {0,1}.

[0261] Fig. 20 is Fig.19 a histogram 210 of the errors of the multiplications shown, where the inset 220 illustrates the relationship between the error and a and b. The line 212 on the histogram corresponds to a normal distribution fit of the data 211, which has a mean = 0.0016 and a standard deviation of 0.023. The error grows approximately linearly with the a and b values, which explains the spread of P out for c values close to 1.

[0262] Although the result of the multiplication is not accurate due to factors such as fluctuations in the T value, as above Fig.15 As shown, this multiplication operation has proven useful in application areas such as machine learning. In addition, in application areas where arbitrarily high precision is required, mixed precision computation can be employed, in which low-precision multiplication units (depending on the implementation) are used in combination with high-precision units (which can be conventional). In addition, the horizontal non-volatility means that the multiplicand is fixed until the next pulse stimulus changes its state. In architectures including several scalar multiplication units, this property can be exploited to compute matrix-vector multiplications or to find solutions to linear systems of equations using iterative Krylov subspace methods (such as the conjugate gradient method or the generalized minimum residual method). They can also be used for forward and backward propagation during training of deep neural networks. Using such an approach, the input matrix A can be mapped to the photonic storage unit and an iterative algorithm is used to compute the matrix with A∈R N×N and b,x∈R N The solution x of Ax=b.

[0263] The present disclosure provides a proof of concept for the multiplication of two scalar numbers computed using phase change photonic memory. This can be achieved using the interaction of two optical signals, each representing a number to be multiplied with a modulation element near-field coupled to a photonic waveguide - one optical signal having energy above the switching threshold and the other having energy below the switching threshold. Such a device can have a substantially linear response, which helps to avoid the need for a fitting function (compared to pseudo-ohmic electrical phase change memory devices). In addition, an erase mechanism is disclosed in which only a single pulse is required; compared to the energy-decreasing pulse sequence used in the prior art. This is an important advance because the duration of the erase operation can thus be reduced from microseconds to about 100ns, and the total energy from up to tens of nJ to the sub-nJ region. In addition, it has been demonstrated that the change in transmission saturates when increasing the duration of the pump pulse (with fixed power); by optimizing the pulse length, it has been demonstrated that in a memory cell comprising 1μm and 2μm long GST modulation elements, a single 25ns pulse is sufficient to reach a level distinguishable from a fully crystalline (baseline) state. It has been shown that devices according to embodiments can be used at up to 10 4 s with negligible transmission fluctuations, and the SNR, the error in achieving the programmed level, and the noise are ultimately limited by the quality of the readout electronics used in the system. These results confirm the potential of phase-change materials in the photonic hardware computing paradigm. Although there is much room for improvement, the capabilities disclosed herein hold promise for all-optical nonvolatile data storage, all-optical and electro-optical switching, and for performing optical computing tasks with collocated memory and processing.

[0264] Measurement setup

[0265] In the results discussed above, all optical read, write and erase signals are guided within the waveguide. To avoid interference, two different C+L CW tunable laser sources are used, and wavelengths of 1598nm (TSL-550, Santec) and 1590nm (N7711A, Keysight) are selected for the read signal and the erase / write signal, respectively. The erase / write pulse and the multiplicand pulse are then generated using an electro-optic modulator (Lucent Technologies, 2623NA), which is controlled by a 100MHz electrical pulse generator (AFG 3102C, Tektronix). The pulse is further power amplified by a low-noise erbium-doped fiber amplifier (AEDFA-CL-23, Amonics). Both the erase / write pulse and the read signal are coupled into the photonic device using an integrated grating coupler having a transmission peak at 1598nm and a coupling efficiency of about 20%. The reverse propagation scheme (wherein the erase / write signal propagates in the opposite direction to the read signal) is used to simplify the separation of the signal. A tunable filter (OTF-320, Santec) is introduced into the optical line to further suppress the noise caused by reflection. At one output of the device, a 90 / 10 beam splitter is used to split the CW read signal into two beams to measure time resolution and long-term transmission using a 200kHz low-noise optical receiver (NewFocus, 2011) and a 125MHz photodetector (NewFocus, 1811), respectively. At another output, a 1GHz photodetector (NewFocus, 1611) is used to monitor the transmitted pulse.

[0266] Fig.21 An apparatus comprising a first waveguide 101a and a second waveguide 101b is shown. A first input grating coupler 301a is coupled to a first end of the first waveguide 101a, and a second input grating coupler 301b is coupled to a first end of the second waveguide 101b. An output grating coupler 302 is coupled to a second end of both the first waveguide 101a and the second waveguide 101b. Each waveguide 101a, 101b comprises a GST modulation element 102a, 102b, respectively. The apparatus can be used to combine the results of two multiplications, for example to approximate the multiplication of a matrix and a vector.

[0267] For example, a first waveguide can be used to multiply a (a write signal encoded as the transmission state of the first waveguide) and b (a read signal modulated by the transmission state of the first waveguide). A second waveguide can be used in a similar manner to multiply c (a write signal encoded as the transmission state of the second waveguide) and d (a read signal modulated by the transmission state of the second waveguide). The results of the multiplication of the first waveguide and the second waveguide will be combined at the output grating coupling to give a×b+c×d. A second device using the same read signals b and d can be used in a similar manner to determine f×b+g×d, where f and g are encoded into the transmission state of the second device. In this way, calculate:

[0268]

[0269] can be calculated (or approximated).

[0270] As an alternative to using a second device, the same device may be used to compute the first and second rows of the output vector at different times.

[0271] Fig. 22 An apparatus for determining the multiplication between a higher dimensional matrix and a vector is shown. Fig. 22 The device in has 8 input coupling gratings 301 and 8 corresponding modulation elements 102, and 8 of these devices can be used to determine the product of an N×8 matrix and a 1×8 vector. The outputs from each pair of modulation elements 102 are combined at a first horizontal combiner 108a. The outputs from the first horizontal combiner 108a are combined at a corresponding second horizontal combiner 108b. The outputs from the second horizontal combiner are combined at an output combiner 108c. The same device can be used to determine the multiplication of each of the N columns of the matrix with the vector by encoding each of the N columns as a set of 8 write pulses. Each set of pulses can be sent / multiplied at different times.

[0272] The examples discussed above have used write signals from a single direction, but it is also possible to use write pulses from more than one direction, thereby encoding more than one item of information in the modulating element. Fig.23 , in which a first write pulse P1 propagating through the waveguide 101 in a first direction is used to write the non-crystalline region 106a at a first end of the modulation element 102, and a second write pulse P2 propagating through the waveguide 101 in a second opposite direction is used to write the non-crystalline region 106b at a second opposite end of the modulation element 102.

[0273] In this way, simple modulation elements can be used to multiply 3 or more numbers, such as:

[0274] P out =P inT(P1)T(P2)

[0275] Taking into account the offset (T is actually T+T0), we can write:

[0276] P out =P in (T(P1)+T o )(T(P2)+T′ o )

[0277] =P in T(P1)T(P2)+P in T(P1)T′ o +P in T(P2)T′ o +P in T o T′ o

[0278] The first term in the expanded expression corresponds to three multiplications, while the next two correspond to the addition of two multiplications. The last term represents noise that can be removed or used for security applications. One can envision calculations that cannot be decoded without knowledge of the transmission offset of the waveguide. A waveguide can be designed with a specific transmission offset to provide a specific "key" property to the waveguide (e.g., through trimming of the modulation element).

[0279] Fig.24 An extension of this concept is shown, in which the modulation element 102 can be used to carry the write signals 1031 to 103 n The write signal 1031 to 103 n The state of the modulation element can be adjusted using an optical signal. In this example, there are six lateral waveguides for writing to the modulation element 102 in a direction transverse to the propagation direction of the read signal 104. This multiply addressed modulation element can be used with each region performing a separate calculation, which is measured by the common read signal 104 (based on the output signal 105). Optionally, depending on the number of waveguides addressing the modulation element 102, this type of device can be used to perform many numbers of multiplications and additions. This device can be used as a neuron in stochastic computing, where each part of the amorphous modulation element provides a weight for a given task.

[0280] Fig.25 A 3D stacked structure for a device is shown, wherein a first waveguide 101a and a second waveguide 101b cross at a modulation element 102. The modulation element 102 may be sandwiched between waveguide cores, thereby coupling to both, and / or placed outside one or both of the waveguides 101a, 101b, such that at least a portion of the modulation element 102 is not coupled to both waveguides 101a, 101b.

[0281] Fig.43 An apparatus 500 is shown for determining the multiplication of a vector and a matrix and specifically for determining in this example an output vector corresponding to the multiplication of an input 3×1 vector and a 3×3 matrix. Thus, the apparatus implements the calculation GxP=b:

[0282]

[0283] The device consists of a plurality of low-loss waveguide cross structures. In this example implementing 3×3 matrix multiplication, the device consists of three parallel input row waveguides 502a, 502b and 502c (rows 1 to 3, respectively) crossed with three output column waveguides 504a, 504b and 504c (columns 1 to 3, respectively), which are generally perpendicular to the input waveguides, but can be at any tilt angle.

[0284] Input vector components P1, P2 and P3 are encoded in the intensities of three optical input pulses at unique wavelengths λ1, λ2 and λ3 introduced into input traveling waveguides 502a, 502b and 502c respectively.

[0285] Adjacent each waveguide crossing is a waveguide coupling element 506. The waveguide coupling element evanescently couples a portion of the light intensity from the adjacent running waveguide, wherein the portion coupled depends on the length of the portion of the waveguide coupling element that is placed immediately adjacent to and extends generally parallel to the adjacent running waveguide. Thus, the fraction can be accurately set during the design and fabrication phase of the device. Each waveguide coupling element has a modulation element 508 disposed thereon in a manner similar to that described above with reference to, for example, Figure 1 The modulation elements consist of a phase change material, such as GST. In a device implementing a 3×3 matrix, there are a total of 9 waveguide coupling elements and 9 associated modulation elements. The matrix element G is encoded in the transmission state of the modulation element. mn .

[0286] The fraction of the light intensity coupled from row m into the waveguide coupling element at the intersection of row m and column n is given by the coupling efficiency η nm The fraction of the light intensity coupled from the waveguide coupling element into column n at the intersection of row m and column n is given by the coupling efficiency η' nm By choosing η nm =1 / 3,η nm =1 / 2 and η nm =1, input light intensity P m is evenly divided among the three coupling elements on a given row m. Typically, the coupling efficiency η is chosen nm , so that:

[0287]

[0288] Where N is the dimension of the vector transform implemented by the device (eg, N=3 for a device implementing a 3×3 matrix transform), n indexes the column number, and m indexes the row number.

[0289] The output 510a of the first column 504a is used to determine the vector element b1, the output 510b of the second column 504b is used to determine the vector element b2, and the output 510c of the third column 504c is used to determine the vector element b3. Fig.43 For the device shown, the light output of the first column will be given by:

[0290]

[0291] The vector elements b1, b2 and b3 can be directly obtained by rescaling the detected light output intensities of the first, second and third columns, respectively, to take into account a common scale factor of 1 / 9. This scale factor can be determined by a previous characterization of the device. In the general case where there is no common scale factor to multiply each component P1, P2 and P3 of the above equation, but a different scale factor for each term, the output of each column can be spectrally resolved based on a previous calibration of the device in order to factor out the scale factor for each term separately. This is one reason why it may be desirable to use different wavelengths to encode the vector elements P1, P2 and P3.

[0292] The modulation element 508 may be optically or electrically switched in the manner generally described herein. If the modulation element is to be optically switched, the coupling efficiency η' is preferably selected to be nm , so that:

[0293]

[0294] where m indexes the row number as before, and η' nm In this way, the modulation element can be used as reference Fig.44 The overlapping light pulses are individually optically addressed. Specifically, in this example, two input light write pulses 520, 522, each having a power P and the same wavelength, are sent into the device - one input light write pulse goes into row 2, and one input light write pulse goes into column 3. The pulses may have a duration in the range from 0.5ps to 10ps. For example, the pulses may have a duration of 1ps. The pulses are sent into the device with a relative delay so that they will overlap in time inside the modulation element to be switched. Fig.44 In the example, to implement the matrix element G 32 The modulation element 524 is the target of the optical writing pulse. Because the coupling efficiency η' is selected according to the above expression nm, so the matrix element G is realized 32 The modulation element of row 2 will receive 2 / 3×P, while the other modulation elements associated with row 2 and column 3 will receive only 1 / 3×P. In this way, if P is selected so that 2 / 3×P is above the threshold required to change the state of the modulation element, but 1 / 3×P is below the threshold, then only matrix element G is realized. 32 The modulation element will be affected by the optical writing pulse.

[0295] If the modulating element is switched electrically rather than optically, it may not be necessary to select n' as described above. nm If directional waveguide coupling elements are used, then η' can be chosen for all coupling elements nm =1, and still select η according to the above expression nm In this manner, when the output 510a of the first column 504a is used to determine the vector element b1, the output 510a of the first column 504a will be given by:

[0296]

[0297] where there are corresponding expressions for the second and third columns. In this case, the weight of each component P1, P2 and P3 is 1 / 3, as opposed to 1 / 9 in the previous example. The use of directional waveguide couplers can also increase the overall efficiency of the device.

[0298] Fig.45 Schematically shows Fig.43 and Fig.44 A portion of a device configured for electrical switching of a modulation element. Fig.45 , an electrical signal generator 534 is configured to provide a current pulse for switching the modulation element 508 of the waveguide coupling element 506. An electrical interconnect 532 in the metal layer transmits the generated current pulse to the doped portion 536 of the waveguide coupling element through a pair of vias 530a and 530b. As described above, the current pulse will cause Joule heating in the doped waveguide, thereby affecting the state of the modulation element 508. In embodiments where a resistive element is used as a heater instead of the doped portion of the waveguide coupling element, the arrangement of the electrical signal generator, interconnects, and vias may be similar to Fig.45 The arrangements shown are essentially the same, with the resistive element being located adjacent to or above the modulation element in, for example, a metal or polysilicon layer.

[0299] It should be understood that reference Figure 43 to Figure 45 The described apparatus is scalable to arbitrarily large matrix and vector dimensions. In this way, a scalable architecture for performing matrix-vector multiplication in the optical domain is provided.

[0300] Digital to Analog Conversion

[0301] similar Figure 1 The device can be used to realize digital-to-analog conversion.

[0302] Fig.26 One way this can be achieved is shown based on the temporal sensitivity of the modulation element. A timing pulse 221 is provided prior to the digital word to be converted. The temporal proximity to the timing pulse weights the amount of state adjustment (e.g., amorphization from an initial crystalline state) produced by the subsequent write pulse. The most significant bit 231 results in a greater degree of amorphization because the previous timing pulse has warmed the modulation element. The temporal gap between the timing pulse 221 and the least significant bit means that it results in a smaller amount of state change (compared to its own most significant bit).

[0303] For a device like that already described, it was found that pulses of 10 ns separated by 16 ns (between leading edges) resulted in clearly distinguishable transmission levels (determined with reference to the output power of the CW read signal through the waveguide).

[0304] Fig. 27 The transmission levels for a laser current of 520 mA are shown, which are produced by: 200 timing pulse alone, 201 timing pulse and 01 sequence, 202 timing pulse and 10 sequence, and 203 timing pulse and 11 sequence. The transmission levels match the analog numbers 0, 1, 2, and 3 well. Fig.28 and Fig.29 Similar results are shown for laser currents of 525 mA and 530 mA, respectively.

[0305] Tunable Volatility

[0306] The examples given previously assume that the read signal (which may be a pulsed or CW signal) is of sufficiently low power that it does not affect the state of the modulation element 102, but this is not necessarily the case.

[0307] In emerging applications, particularly photonic and neuromorphic computing, it may be desirable to have both volatile (short-term transient) and nonvolatile (long-term static) memory operation, for example to mimic the behavior of biological neurons and synapses. Phase change materials, particularly chalcogenides, perovskites, and metal oxides have enabled recent demonstrations of reflective displays, all-photonic memories, and tunable metamaterials. No single class of materials operating in both a volatile and nonvolatile manner has been demonstrated in the prior art (not only in the photonic domain, but even in the electronic domain).

[0308] Control of the optical properties of photonic devices has been demonstrated by employing materials such as chalcogenides, metal oxides, and even silicon itself. Non-volatile, reversible switching enabled by phase change materials (PCMs) is the basis of technologies like rewritable optical discs, reflective displays, and tunable metasurfaces. Such conversions rely on initiating physical reconstruction of the atomic structure (e.g., amorphous to crystalline conversion), which in turn leads to significant changes in optical properties. Volatile photonic devices have been realized by using volatile metal oxides (such as VO2), which provide a semiconductor-to-metal phase transition at around 66°C, accompanied by significant changes in optical properties. Although materials like VO2 are good candidates for volatile reconfigurable photonics, devices that can selectively operate in both volatile and non-volatile modes are more desirable. A single device that exhibits both behaviors and operates under the right conditions can be used for data storage and computing simultaneously - essentially having the ability to mimic the mammalian brain, which requires both short-term plasticity (STP) and long-term potentiation (LTP).

[0309] It will be appreciated that LTP is essential for long term storage, whereas STP is necessary for temporal processing of information such as filtering and correlation detection.PCM memory cells in artificial neural networks have been used in the electrical domain to achieve storage and computation by emulating leaky "integrate-and-fire" neurons.

[0310] In this disclosure, reference is shown Figure 1 Devices of the type described having a modulating element coupled to an optical waveguide can also be configured to exhibit tunable volatility by using higher power optical read signals. Thus, both non-volatile multi-level storage and volatile computation-related detection in a single integrated photonic device can be achieved.

[0311] One example of a suitable device includes a 1 μm long modulating element 102 ( Figure 1 L GST ), the modulation element 102 comprises a GST covered by a 10 nm indium tin oxide (ITO) layer. The modulation element 102 is arranged on top of the Si3N4 photonic waveguide 101 (eg Figure 1 ). The ITO capping layer passivates the GST and prevents oxidation.

[0312] Fig.30 A device is shown having a first waveguide 101b and a second waveguide 101c. The first waveguide 101b has a modulation element 102b arranged thereon and is configured such that light propagating in the first waveguide 101b is optically coupled to the modulation element 102b (as already described above). The second waveguide 101c is a reference waveguide and does not include a modulation element. A central input grating 301 is provided which splits the input light into the two waveguides 101b, 101c.

[0313] The second reference waveguide 101c allows the total transmission of the first waveguide 101b and the two grating couplers (301 and 302b or 302 and 302c) to be determined without absorption losses from the modulation element 102b. Fig.24 Inset zoomed-in optical image including modulation element 102b (in the form of a GST strip transverse to Si3N4 waveguide 101a). To optimize the interaction between the light mode and the modulation element 102b, the sample device was annealed at 250°C for 10 minutes to crystallize the GST of the modulation element 102, which increases light absorption. Light pulses (e.g., 50ns or less) can be used to switch the material between its amorphous (low absorption) state and crystalline (high absorption) state (as already discussed in detail herein).

[0314] Fig.31 Results obtained by finite-difference time-domain (FDTD) simulations calculating the transmission of light through the waveguide 101 when the modulating element / GST ribbon 101 is in an amorphous state and a crystalline state are shown. Fig.31 A top view of the power flow in the x-direction through the waveguide 101 (edge ​​defined by the solid line) in the region of the GST strip (edge ​​defined by the dashed line) is shown. The magnitude of the normalized Poynting vector is indicated by shading.

[0315] The resulting transmissions for the amorphous and crystalline GST are 96.2% and 46.5%, respectively. While this would ideally give a relative change in transmission of over 100%, in practice it is not possible to amorphize the entire area of ​​GST within the optical mode accessible range using the example implementation used for the proof of principle herein due to the non-uniform mode distribution in the lateral direction. This causes the center of the modulating element / GST 102 to be exposed to light at material temperatures above the melting temperature (T m ). Increasing the optical power in the waveguide 101 will increase the area of ​​amorphization, but if the temperature at the center of the GST / modulation element 102 exceeds the damage threshold, the material may undergo irreversible changes (e.g., ablation). This is not the case in 1 μm long devices ( Figure 1 L GST ) limits the maximum achievable change in relative transmission to about 20%, but larger contrasts can be achieved using devices with wider GST bands (i.e. longer modulating elements measured in the propagation direction).

[0316] Fig.32Thermodynamics of GST starting from a crystalline state is shown. The first graph (top) shows the temperature of the modulation element 102 over time, and the second graph shows the corresponding crystallization fraction, where 1 represents the crystalline state. Curves corresponding to low power read signals 401, 411, medium power read signals 402, 412 and high power read signals 403, 413 are shown. Each curve 401 to 403 and 411 to 413 shows the temperature of the modulation element during a write pulse ( Fig.26 The write pulse encounters the crystalline GST and is at least partially absorbed, which rapidly raises the temperature of the material. If the pulse energy is high enough, the temperature of the GST will exceed T during the pulse duration. m , and at the glass transition temperature (T g ) is rapidly quenched below, leaving the GST in the affected area in a non-crystalline state.

[0317] If an optical read signal (or probe signal) is used to read out the state of the material, some of the read signal will also be absorbed and converted to heat, depending on the transmission of the GST modulation element 102. For a low-power probe, the transmission state of the modulation element 102 can be read in a way that does not affect the physical state of the material - this corresponds to traces 401 and 411 - with a low-power read signal. This reading method results in a non-volatile memory effect that has been previously reported, which is useful for storing long-term data with a retention time of more than 10 years.

[0318] However, for medium-power read signals / probes, the absorbed optical power can heat the GST to T g Near or above T, which causes recrystallization to occur after the initial write pulse 405, as shown by traces 402, 412. Due to the heating generated by the CW read signal, the modulation element here starts at an elevated temperature. In the case of a continuously applied moderate power read signal, the state of the modulation element 102 is volatile, and the retention time depends nonlinearly on the power of the read signal and the transmission state of the GST modulation element 102 after the write signal / pulse. High read signal powers tend to cause a more rapid return to the crystalline state. If the power of the read signal is further increased (as shown by traces 403 and 413), the temperature of the GST can approach T during the steady state. m In case of high read signals, the initial crystallization fraction may be less than 1 due to the heating effect of the read signal.

[0319] To demonstrate both volatile and non-volatile behavior of the example device, multiple transmission levels were defined by varying the write pulse energy for a fixed pulse duration of 50 ns. Fig.33The effect of such a write signal on a GST modulating element starting in a crystalline state is shown. Eight clear transmission levels are shown, plus a baseline with no write pulse (i.e. ΔT=0%), corresponding to a memory cell with nine unique levels. The low power read signal (P after the initial grating coupler 301) is shown. read =510 μW) is used to monitor the state of the GST modulation element 102 in real time. Fig.34 The non-volatility level corresponding to each write pulse energy is shown. 6 s, and materials studies of GST memory cells have estimated retention times of more than 10 years. The number of levels that can be achieved is ultimately limited by the signal-to-noise ratio of the optical readout and how reliably the energy of the write signal pulse can be controlled.

[0320] Volatile behavior was produced by increasing the probe power to 2.54 mW and sending a 50 ns write signal with the same pulse energy as before. Fig.35 Shown with Fig.33 A similar trend, but a significant threshold is observed around a pulse energy of 275 pJ (corresponding to a switching energy of 47.9 pJ). This is likely due to the GST modulating element 102 being partially amorphized and melted by the relatively high power read signal, which reduces light absorption and reduces the impact of the write pulse below a certain energy. Fig.36 Shown with Fig.34 A real-time trace of a similar read probe is shown, but with volatile spike behavior due to GST recrystallization from a high power read signal. At each write pulse, the transmission is briefly increased by the material of the modulation element being amorphized, but shortly after each spike 421 in the recording light transmission, a relatively high power read signal returns the modulation element to a crystalline state.

[0321] To further determine the effect of read signal power on the recrystallization kinetics of the example device, the write signal pulse energy can be fixed while varying the read signal power. Fig.37 The normalized time-dependent transmission of the example device at different read signal powers is plotted on a logarithmic scale. Curves 431 to 439 correspond to powers of 1.29 mA, 1.47 mA, 1.65 mA, 1.84 mA, 2.02 mA, 2.21 mA, 2.39 mA, 2.57 mA, and 2.76 mA, respectively. As before, ΔT = (TT min ) / T min , where T minis the transmission of the read signal when the device is in a fully crystalline state. After the initial write pulse at 0 seconds, the GST modulation element 102 is in an amorphous state, ΔT is maximum, and the temperature is at a minimum due to low light absorption. However, a portion of the read signal is still absorbed by the modulation element 102, which heats the GST material and causes crystal growth to occur at a rate that depends on the material temperature.

[0322] As GST crystallizes, the light absorption of the read signal increases and a positive feedback loop drives the material back to its crystalline state. If the read signal power is high enough to cause partial melting, the steady-state temperature T is when GST is fully crystallized. steady state will be greater than T min This makes ΔT>0 in the steady state, and this Fig.37 As can be observed for probe powers greater than 1.84 mW (i.e., curves 435 to 439). Once the material is fully crystallized, the absorption of the read signal is at a maximum, and the read signal partially remelts the GST until at T steady state Thermal equilibrium is achieved at ΔT>0.

[0323] A clear trend is observed in the recovery time of the materials, which we have defined as ΔT equal to ΔT max The amount of time required for 10% of Fig.37 denoted by the dotted line in ).

[0324] Fig.38 A curve showing the recovery time τ according to the read signal power is shown, with the index τ(P) = Ae -γP The measurements 442 and the fit 441 to the data are shown in the form of , where A and γ are the fit parameters and P is the read signal power. These results show optical control of the data retention time over six orders of magnitude.

[0325] To illustrate the effect of a write pulse on the recovery time of an example device, the read signal power may be fixed and the write pulse energy may be varied. Fig.39 The results of tests conducted in this way are shown in Figure 1. Both the maximum transmission and the recovery time decrease with decreasing write pulse energy. This can be explained by the difference in light absorption of partially amorphous versus fully amorphous modulation elements. The lower the write pulse energy, the higher the fraction of GST that remains in the crystalline state, resulting in higher absorption and faster recovery times. Fig.39 This trend is clearly seen in , where both the recovery time and the peak transmission decrease with decreasing write pulse energy.

[0326] The ability to operate an optical waveguide including a light-controlled modulation element in a non-volatile manner can enable computing using the nonlinear properties of phase change switching.

[0327] Fig.40 is a plot of the peak response of an example device of a medium power probe and a high power probe when two 50 ns write pulses separated by different time delays coincide at the modulation element. Delays less than about 40 ns result in a change in transmission, while delays greater than about 40 ns do not result in a change in transmission due to heating above the threshold amorphization temperature caused by power overlap.

[0328] Fig.41 The measured optical power of four separate write pulses with different time delays is shown. If we integrate the optical power, we see that the total energy remains constant at E regardless of the time delay between the two write pulses. pulses =340±17pJ (switching energy is 59±3pJ). However, the peak power of the combined two write pulses does vary with increasing time delay. When the device is operated in a regime where the peak power of a single write pulse is close to but below the threshold required to amorphize GST, no response occurs. However, by overlapping the two write pulses, the peak power is doubled and is able to induce amorphization, which results in increased transmission. This nonlinear response allows us to use the transmission of the device to calculate the correlation between the two light pulses.

[0329] Fig.42 This is illustrated with transmission traces 471 to 479 of pulse trains having different time intervals. Each pulse train includes 10 50 ns write pulses with a 500 Hz repetition rate, with the spacing between pulse trains varying from 0 ns to 50 ns in 5 ns increments (trace 471 corresponds to 0 ns delay, and trace 472 corresponds to 5 ns, etc.). Although in practice the repetition rate may be much higher, it is instructive to see the response of the example device between the individual write pulses in the pulse train.

[0330] By varying the time delay between the two pulse trains, we see a changing temporal response of our device. At no time delay (trace 471), the transmission remains nearly constant for the duration of the entire pulse train, with a small visible spike in the transmission where overlapping write pulses occur. As the time delay between the two pulse trains increases, the amplitude and duration of the transmission spike decreases until they no longer overlap (trace 473, 10ns delay). As the time delay is further increased (trace 477, 30ns), the transmission response disappears, indicating that the two pulse trains are no longer correlated in time. This ability to detect correlated events between multiple inputs is known to occur in biological neurons and has broad importance for training neural networks and quantifying correlations between random signals in machine learning applications.

[0331] although Figure 37 to Figure 39 The response time shown is quite long compared to the time scale of the write pulses, but one can still clearly resolve the 5 ns time delay difference between the two write pulses caused by the high-speed melting process by which the GST is amorphized using optical pulses (e.g. Fig.42 ).

[0332] According to the present disclosure, both volatile and non-volatile behavior are possible, demonstrating that the best of both worlds can be obtained with a single element. By varying the optical power of the read signal, an exponential decrease in the data retention time of the modulating element was observed, allowing retention times to range from years (i.e., non-volatile) to milliseconds (i.e., volatile). Both operating modes were implemented in an optical platform capable of multi-level data storage and computing pulse correlations. By operating the device in a volatile manner, timing differences as low as 5ns between two pulses could be resolved. Similar behavior occurred between two multiple pulse trains, showing that volatile photonic storage elements of the type disclosed herein can be used to compute correlations between two optical signals. These results demonstrate that photonics utilizing non-volatile elements can also be configured as volatile elements, and therefore provide a promising platform for all-optical data storage and computing.

[0333] The above examples are not intended to limit the scope of the present invention, which should be determined with reference to the appended claims.

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Claims

1. A method for performing a multiplication operation in an optical domain using an apparatus, the apparatus comprising: an optical waveguide and a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption property of the optical waveguide according to a state of the modulation element, wherein the state of the modulation element can be adjusted by a written signal; Wherein, the method comprises the following steps: encoding a first value into the write signal, mapping the first value to a state of the modulation element using the write signal; encoding a second value into the read signal; generating an output signal intensity as a transmitted or reflected read signal, wherein a product of the first value and the second value is encoded in the output signal intensity; and Apply a transmission offset correction to the output signal intensity by subtracting the transmission baseline from the output signal intensity.

2. The method according to claim 1, wherein: The modulation element is optically near-field coupled to the optical waveguide.

3. The method according to claim 1, wherein: Determining the result includes applying a scaling correction to the output intensity.

4. The method according to claim 1, wherein: The first value and the second value have at least three different possible levels.

5. The method according to claim 1, wherein: The modulating element includes a phase change material.

6. The method according to claim 5, wherein: The write signal maps a value of the write signal to a degree of amorphism of the modulation element.

7. The method according to claim 5, wherein: The modulation element is placed in a baseline crystallization condition prior to application of the write signal.

8. The method according to claim 1, wherein: There is a linear scaling between the first value and the product and between the second value and the product.

9. The method according to claim 1, wherein: The output pulse intensity is detected as the ratio of the transmitted read pulse.

10. The method according to claim 1, wherein: The read signal is an optical read pulse.

11. The method of claim 1 , comprising determining vector or matrix multiplication by performing more than one multiplication operation, wherein: The output signal is generated by combining the transmitted and / or reflected signals from more than one optical waveguide.

12. The method of claim 1, comprising using an apparatus comprising more than one optical waveguide, each of the more than one optical waveguides comprising a respective modulating element.

13. The method according to claim 1, wherein: The apparatus also includes at least one optical combiner, each combiner being configured to combine output signals generated by more than one optical waveguide.

14. The method according to claim 1, wherein: The optical waveguide is a first optical waveguide and the device further comprises a second optical waveguide, wherein the second optical waveguide is transverse to the first optical waveguide in the region of the modulation element and wherein the modulation element is optically coupled to both the first optical waveguide and the second optical waveguide.

15. The method according to claim 1, wherein: The state of the modulation element is adjustable by an optical signal carried by the optical waveguide, and the step of mapping the first value to the state of the modulation element using the write signal comprises transmitting the write signal through the optical waveguide.

16. The method according to claim 15, wherein: The write signal is an optical write pulse.

17. The method according to claim 15, wherein: When the modulation element includes a phase change material and the modulation element is placed in a baseline crystallization condition before applying the write signal, placing the modulation element in the baseline crystallization condition includes using a two-step reset pulse, the first step having a higher power and a shorter duration than the second step, and having a delay of less than 5ns between the first step and the second step.

18. The method according to claim 15, wherein: The write signal is a first write signal that maps the first value to a state of a first region of the modulation element, and the method further comprises: A third value is encoded into a second write signal, and the third value is mapped to a state of a second region of the modulation element using the second write signal, wherein the output signal intensity encodes the product of the first value, the second value and the third value and / or the sum of the first value multiplied by the second value and the first value multiplied by the third value.

19. The method according to claim 18, wherein: The first write signal and the second write signal propagate in different directions.

20. The method according to claim 18, wherein: The device comprises a first optical waveguide defining a direction of propagation of a read signal, and at least one further optical waveguide for carrying a write signal in a direction different from the direction of propagation of the read signal.

21. The method according to claim 1, wherein: The write signal is an electrical signal.

22. The method according to claim 21, wherein: The optical waveguide is doped and the electrical signal is applied to the doped optical waveguide.

23. The method according to claim 21, wherein: The electrical signal is applied to a resistive element proximate to the modulation element.

24. The method according to claim 22, wherein: The electrical signal causes current to flow through the optical waveguide, resulting in Joule heating and transferring thermal energy from the optical waveguide to the modulation element, thereby adjusting the state of the modulation element.

25. The method according to claim 23, wherein: The electrical signal causes current to flow through the resistive element, resulting in Joule heating and transferring thermal energy from the resistive element to the modulation element, thereby adjusting the state of the modulation element.

26. The method according to claim 21, wherein: The electrical signal is a current pulse.

27. An apparatus for performing the method according to any one of claims 1 to 26, comprising: Optical waveguides; a modulation element optically coupled to the optical waveguide, the modulation element modifying a transmission, reflection or absorption characteristic of the optical waveguide according to a state of the modulation element, wherein the state of the modulation element is adjustable by a written signal; a light source configured to transmit a light signal through the optical waveguide; a detector configured to detect the intensity of light from the optical waveguide; The controller is configured as: encoding a first value into the write signal, encoding a second scalar value into a read signal transmitted by the light source; determining an output pulse intensity based on a signal from the detector; determining a result of multiplying the first value by a second value based on the output intensity; and Apply a transmission offset correction to the output signal intensity by subtracting the transmission baseline from the output signal intensity.

28. The device according to claim 27, wherein The state of the modulating element is adjustable by an optical signal carried by the optical waveguide, and the controller is configured to encode a first value into a write signal transmitted by the optical source.

29. The device according to claim 27, further comprising an electrical signal generator, wherein: The state of the modulation element can be adjusted by an electrical signal generated by the electrical signal generator, and the electrical signal is the write signal.

30. The device according to claim 29, wherein The optical waveguide is doped and the electrical signal is arranged to be applied to the optical waveguide.

31. The apparatus of claim 29, further comprising a resistive element proximate to the modulation element, wherein The electrical signal is arranged to be applied to the resistive element.

32. The device according to claim 29, wherein: The controller is configured to encode a first value into the electrical signal generated by the electrical signal generator.

33. The device according to claim 30, wherein: The electrical signal is arranged to cause current to flow through the optical waveguide, resulting in Joule heating and transfer of thermal energy from the optical waveguide to the modulation element, thereby adjusting the state of the modulation element.

34. The device according to claim 31, wherein The electrical signal is arranged to cause current to flow through the resistive element, resulting in Joule heating and transfer of thermal energy from the resistive element to the modulating element, thereby adjusting the state of the modulating element.

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