Energy-efficient nonlinear optical micro-device arrays

Abstract

A nonlinear optical microdevice array that enables low energy and massively parallel nonlinear optical control with incoherent light. Optical computing has been a goal long sought after, because it allows for massively parallel information processing. The major roadblock has been the difficulty to achieve efficient optical nonlinearity that is required in controlling one light by another light beam. A semiconductor pn junction and electro-optical modulator (e.g., liquid crystal or micromirror array) are integrated at a single pixel scale, to achieve artificial optical nonlinearity that is highly parallel (with millions of pixels), extremely energy efficient (at sub picojoule level), and compatible with incoherent LED light sources.

Description

ENERGY-EFFICIENT NONLINEAR OPTICALMICRO-DEVICE ARRAYSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to, and the benefit of, U.S. provisional patent application serial number 63 / 743,668 filed on January 10, 2025, incorporated herein by reference in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with Government support under Contract No.DE-AC02-05CH11231 awarded by the U.S. Department of Energy. The government has certain rights in the invention.BACKGROUND

[0003] 1. Technical Field

[0004] The technology of this disclosure pertains generally to optical devices for nonlinear optical control, and more particularly to a liquid crystal electro- optical modulator integrated at a single pixel scale for achieving artificial optical nonlinearity that is highly parallel.

[0005] 2. Background Discussion

[0006] As digital computation approaches an energy efficiency bottleneck, particularly in fields, such as artificial intelligence and neural networks, alternative computational architectures are gaining attention. In the realm of physics-based computational approaches, all optical neural networks have emerged as a promising and energy conscious alternative. These all-optical networks use linear optics to implement fundamental mathematical operations, such as matrix multiplications, which are the building blocks of inference tasks. Optical implementations of matrix multiplication already offers significant energy savings on a per-operation basis. However, the widespread adoption of all optical neural networks is hindered by the lack of energy efficient optical nonlinearities. Photons, due to their inherent noninteracting nature, necessitate the mediation of photonic nonlinearitiesUCLBL-2023-160-03-PCT -1-through an induced polarization within a solid medium, known as polaritons. Polaritons interact weakly enabling higher order optical processes (nonlinearities) especially when incident electric fields approach the scale of interatomic forces.

[0007] The efficiency of these nonlinear processes is governed by the coupling strength between the electric field of the incident light and the medium (the so-called nonlinear coefficients) and is inherently limited. To enhance the efficiency of optical nonlinearities various strategies are employed. Typically, the medium is engineered such that the coherence length or time of the nonlinearity is enhanced through phase, and / or quasiphase, matching and cavities. Alternatively, the coupling strength of the nonlinearity is boosted by confinement into a smaller mode volume or through leveraging resonant enhancements and vanishing susceptibilities. However, it is worth noting that these approaches put strict constraints on the characteristics of the light source driving the optical nonlinearity, particularly regarding its wavelength and coherence.

[0008] There are numerous applications in which incoherent light nonlinearity can be an important factor. However, to date it does not appear that a technology for creating an effective optical nonlinearity using incoherent light is available.

[0009] Accordingly, a need exists for obtaining optical nonlinearity using incoherent light. The present disclosure fulfills that need and provides additional benefits over existing systems.BRIEF SUMMARY

[0010] An engineered optical nonlinearity in which the light-detecting element is integrated into the same structure as the electro-optical modulator (EOM), wherein carriers generated in the photodetector provide in-situ modulation of the EOM. By engineering device parameters, such as capacitance, enables generation of optical nonlinearities with energy budgets on the order of 30 fJ per nonlinear activation. The EOM may be implemented in a number of different ways, such as a liquid-crystal EOM, or a mirror EOM, or other EOM types, without departing from the teachings of the present disclosure. In oneUCLBL-2023-160-03-PCT -2-embodiment, the device integrates liquid-crystal EOM and Si pn-junction at the pixel level in a silicon-compatible platform, toward enabling energy efficient and highly parallel optical nonlinear device arrays that can operate with incoherent light such as LEDs.

[0011] Further aspects of the technology described herein will be brought out in the following portions of the specification, wherein the detailed description is for the purpose of fully disclosing preferred embodiments of the technology without placing limitations thereon.BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The technology described herein will be more fully understood by reference to the following drawings which are for illustrative purposes only:

[0013] FIG. 1 A is a cross-section pictorial view of a Nonlinear Optical Microdevice Array (NOMA), according to at least one embodiment of the present disclosure.

[0014] FIG. 1 B is a schematic of the NOMA seen in FIG. 1 A, according to at least one embodiment of the present disclosure.

[0015] FIG. 1 C is a graph of voltage-dependent reflectance for the NOMA of FIG. 1 A, according to at least one embodiment of the present disclosure.

[0016] FIG. 1 D is a waveform diagram of applied voltage in the active and erase phases for the NOMA of FIG. 1 A, according to at least one embodiment of the present disclosure.

[0017] FIG. 2A and FIG. 2B depict wide field images representing the state of every pixel in NOMA at a given time delay, as captured according to at least one embodiment of the present disclosure.

[0018] FIG. 2C is a graph of reflectance over time at different pump light intensities, as determined for at least one embodiment of the present disclosure.

[0019] FIG. 2D is an image rendition demonstrating an achieved contrast value of four, according to at least one embodiment of the present disclosure.

[0020] FIG. 2E is a graph of contrast mapping determined for at least one embodiment of the present disclosure.

[0021] FIG. 2F is a graph of contrast variation showing a pixel-to-pixelUCLBL-2023-160-03-PCT -3-representation of contrast variation under various illumination conditions for at least one embodiment of the present disclosure.

[0022] FIG. 3A is a graph of output intensity as a function of incident intensity for at least one embodiment of the present disclosure.

[0023] FIG. 3B is a graph of reflectance with respect to incident light intensity as determined for at least one embodiment of the present disclosure.

[0024] FIG. 3C and FIG. 3D are graphs of single pulse nonlinearity as characterized according to at least one embodiment of the present disclosure.

[0025] FIG. 3E and FIG. 3F are histograms showing comparative pixel values as obtained according to at least one embodiment of the present disclosure.

[0026] FIG. 4A and FIG. 4B are cross-section views of a single NOMA pixel as implemented with pn junction, and with p-i-n junction, respectively, according to embodiments of the present disclosure.

[0027] FIG. 5A and FIG. 5B are cross-section views of NOMA pixel operation using micromirrors (MMs), comparing operation without and with illumination, respectively, according to an embodiment of the present disclosure.

[0028] FIG. 6 is a rendition of a microscope image of NOMA, with an inset showing a single pixel, depicting the metallic region, which is the Al mirror, according to an embodiment of the present disclosure.

[0029] FIG. 7 is a cross-section view of fabricated NOMA pixels, according to an embodiment of the present disclosure.

[0030] FIG. 8 is a graph characterizing LC birefringence using voltagedependent Cross-Polarized (CP) reflectance of the LC cell, according to an embodiment of the present disclosure.

[0031] FIG. 9 is a current-voltage relation of the Si PD under dark conditions, according to an embodiment of the present disclosure.

[0032] FIG. 10 is an equivalent circuit for a NOMA pixel, according to an embodiment of the present disclosure.

[0033] FIG. 11 is a diagram of a portion of a NOMA configured for light selfmodulation, with the input beam as a linearly polarized pulse, and the output beam as the CP reflected pulse, according to an embodiment of the present disclosure.

[0034] FIG. 12 is a plot of ReLU-like input-output relationship a NOMA pixel,UCLBL-2023-160-03-PCT -4-according to an embodiment of the present disclosure.

[0035] FIG. 13 are voltage waveforms, as synchronized square waves, in the active and erase phases for a NOMA pixel, according to an embodiment of the present disclosure.

[0036] FIG. 14 is a block diagram of a pump-probe experiment from light emitting diodes as directed onto NOMA, according to an embodiment of the present disclosure.

[0037] FIG. 15 are graphs of CP reflectance dynamics of NOMA at increasing pump energies, according to an embodiment of the present disclosure.

[0038] FIG. 16 are graphs of pump dependent CP reflectance at different Vc voltages, with an insert illustrating expected linear relationship between switching energy Esw and Vc, according to an embodiment of the present disclosure.

[0039] FIG. 17 is a graph of average output energy versus input energy across more than 10,000 NOMA pixels, showing nonlinear dependence, as shown fitted in relation to a ReLU function, according to an embodiment of the present disclosure.

[0040] FIG. 18 is a histogram of switching energy shown in a normal distribution with a mean ( / z) of 280 fJ, and a standard deviation (a) of 18 fJ, determined for an embodiment of the present disclosure.

[0041] FIG. 19 is a pair of image renditions comparing a reference image and a contrast enhanced image in response to NOMA operation, according to an embodiment of the present disclosure.

[0042] FIG. 20 are histograms for the images of FIG. 19, demonstrating a four-fold increase in image contrast using NOMA, as determined for an embodiment of the present disclosure.

[0043] FIG. 21 is an image rendition and block diagram of a Multilayer Optical Neural Network (ML-ONN) used for binary classification, according to an embodiment of the present disclosure.

[0044] FIG. 22 is a scatter plot illustrating performance of the linear operation of the ML-ONN measured outputs against ground truth of 80 random Matrix- Vector Multiplications (MVMs), according to an embodiment of the present disclosure.UCLBL-2023-160-03-PCT -5-

[0045] FIG. 23 is a scatter plot characterizing the RMSE of the full ML-ONN, including the nonlinear activation between MVMs, along with an inset showing an error histogram, according to an embodiment of the present disclosure.

[0046] FIG. 24 shows image renditions of a circuit dataset with, and without non-linearities, and indicating a classification accuracy over 97%, according to an embodiment of the present disclosure.

[0047] FIG. 25 shows image renditions of an exclusive-OR (XOR) dataset with, and without non-linearities, and indicating a classification accuracy over 97%, according to an embodiment of the present disclosure.

[0048] FIG. 26A is a rendition of an image showing a fabricated NOMA device having 750 x 700 pixels, according to an embodiment of the present disclosure.

[0049] FIG. 26B is a diagram showing vertical design areas for the NOMA device of FIG. 26A, according to an embodiment of the present disclosure.

[0050] FIG. 27A through FIG. 27C are circuit diagrams of NOMA operation in different phases, according to an embodiment of the present disclosure.

[0051] FIG. 28A is an optical layout of a test configuration for characterizing the nonlinear response of NOMA under two pulse and single pulse conditions, according to an embodiment of the present disclosure.

[0052] FIG. 28B are time traces of NOMA with three periods of active and erase phases at different pump energies, according to an embodiment of the present disclosure.

[0053] FIG. 29A and 29B are plots of switch energy of optical ReLU as tuned by Vc, according to an embodiment of the present disclosure.

[0054] FIG. 30A is an image rendition of a camera image of over 10,000 NOMA pixels, according to an embodiment of the present disclosure.

[0055] FIG. 30B depicts a curve of optical nonlinear response for the NOMA pixels of FIG. 30A, according to an embodiment of the present disclosure.

[0056] FIG. 30C is a threshold energy distribution of NOMA pixels, according to an embodiment of the present disclosure.

[0057] FIG. 31 A and FIG. 31 B depict results from endurance testing of four NOMA neurons, according to an embodiment of the present disclosure.

[0058] FIG. 32 is an optical layout of an implemented two-layer all opticalUCLBL-2023-160-03-PCT -6-neural network, according to an embodiment of the present disclosure.

[0059] FIG. 33A and FIG. 33B are plots of non-linear responses from the neurons of the ML-ONN, according to an embodiment of the present disclosure.

[0060] FIG. 34A through FIG. 34D are optical inference results before, and after, fine tuning toward improving ML-ONN inference accuracy, according to an embodiment of the present disclosure.DETAILED DESCRIPTION

[0061] 1. Introduction

[0062] The present disclosure describes an engineered nonlinearity that operates with incoherent light. In the literature, alternative methods for engineering effective optical nonlinearities have been explored through a hybrid electro-optical approach. This hybrid approach involves using a photodetector to measure the incident light intensity on an Electro-optical Modulator (EOM), such as a Mach-Zehnder interferometer (MZI) or a liquid crystal device. The output of the photodetector output is then electronically amplified and used as the input bias for the EOM to introduce an intensity dependent phase shift on the incident light. In this case, the need for electronic amplification limits the efficiency of the nonlinear operation.

[0063] The next step on realizing this device is integrating the light-detecting element into the same structure as the EOM, which allows carriers generated in the photodetector to in-situ modulate the EOM. Careful engineering of the device parameters, such as capacitance, enables optical nonlinearities with energy budgets on the order of 30 fJ per nonlinear activation. Examples of this approach have employed pn-junctions as the photodetector and a variety of EOMs, such as micro ring resonators and photonic crystal cavities, toward aiding the EOM to achieve effective nonlinearities.

[0064] The present disclosure, however, adopts a new device architecture that integrates liquid-crystal EOM and Si pn-junction at the pixel level in a silicon- compatible platform. This architecture now enables the creation of energy efficient and highly parallel optical nonlinear device arrays that can operate with incoherent light such as LEDs. In this approach arrays of devices areUCLBL-2023-160-03-PCT -7-created, herein called pixels, that contain a photodiode directly interfaced with a mirror (e.g., Aluminum) inside a liquid crystal cell. In conjunction with the broadband reflectivity of the mirror, liquid crystal transparency and the high responsivity of the Si photodiode in the visible wavelength, the device outlined herein presents a visible wavelength agnostic nonlinear optical device that can operate with incoherent light sources.

[0065] 2. Device Structure and Equivalent Circuit

[0066] FIG. 1A illustrates an example embodiment 10 of the disclosed Nonlinear Optical Microdevice Array (NOMA), in which the EOM comprises a liquid crystal (LC) layer 14 sandwiched between a conductively coated transparent material (for example glass coated with Indium Tin Oxide (ITO glass) 12 (cover substrate) as an n-type semiconductor that exhibits excellent transmittance and conductivity. Substrate 16 is shown of p-type Si, within which are first n-type wells 24, and second n-type wells 25, over which is at least one layer of dielectric, such as comprising SiO2 and / or AI2O3.

[0067] In at least one embodiment of the NOMA, each silicon pixel in the array comprises a pixel area having a conductive mirror 18, such as an aluminum (Al) layer, over the dielectric layer(s) 20 (e.g., SiO2 and / or AI2O3). Beneath at least a portion of the area of each mirror are first n-wells 24 within the p-Si substrate. These first n-Si n-wells establish a crucial pn junction, supplied with voltage V226, with the underlying p-type substrate, allowing the combination to function as a sensitive photodetector. In addition, there are second n-wells 25 as bars between the mirror regions connecting to multiple pixels in the array. This pn junction 28 is between lower substrate 16 and the cover substrate 12, and is seen as voltage Vi 30.

[0068] In at least one embodiment, the lower substrate portion (below liquid crystal (LC) layer 14) may also be fabricated using p-i-n diodes, in which there is an undoped intrinsic semiconductor (i-Si) layer between the p-type and n- type semiconductor regions. A principle advantage for a p-i-n diode structure is its lower dark current and lower resistance which would make the device perform more energy efficient optical nonlinear activations; at the cost of slightly increasing fabrication complexity. The differences between the p-n and p-i-n implementations are described in regard to FIG. 4A and FIG. 4B.UCLBL-2023-160-03-PCT -8-

[0069] The conductive (e.g., Al) mirror serves a dual purpose. It both efficiently reflects incoming light, while it also contributes to the formation of a liquid crystal capacitance (C / c) in conjunction with the upper ITO electrode. Beneath these mirrored regions 18 lies dielectric material(s) 20 (e.g., SiO2 / Al2O3). The second set of n-wells 25 collectively forms another capacitance (Cox). Importantly, each of these second n-wells extends across a row of pixels, connecting to a common metal pad, whereby the Al of the mirror extends 22 through the dielectric 20 at these contact points.

[0070] By regulating the potential applied to this second n-well, an additional degree of control over the voltage across the LC capacitor is obtained. In at least one embodiment, the bottom side of the silicon substrate is coated in an ohmic material, exemplified herein as a platinum (Pt) contact 32, Pt with its large work function, forms an Ohmic contact with the p-type substrate.Alternatively, the underside can be connected as the lower contact, if the substrate has sufficient conductivity.

[0071] These structures are shown in the array 10 of silicon pixels. The device capitalizes on the electro-optical properties of LC to modulate incident light, offering control over phase, polarization, or intensity. Concurrently, the silicon pixel absorbs a fraction of the incoming light, generating a charge field across the LC. This synergy empowers the NOMA device to achieve optical self-modulation and optical-electrical-optical modulation.

[0072] FIG. 1 B illustrates an example embodiment 50 of equivalent circuit for the NOMA shown in FIG. 1A. During device operation, the p-type substrate is established as the common ground 51 while applying voltage Vi 64 to the ITO electrode and voltage V252 to the supplementary n-well. The figure shows the series nature of the liquid crystal capacitance (C / c) 56, and n-well to oxide capacitance (Cox) 54. The localized pn junction, active under incident light, is represented as a diode capacitance CPd 58 in parallel with a current source IR 60. The parameter CPd represents the reverse capacitance of the local pn junction, which is determined by the depletion region width. The diffusive capacitance is ignored because the junction is working mainly under a reverse bias. The parameter F?s62 represents the series resistance, including the resistance associated with the ITO layer, bulk silicon, and metal-siliconUCLBL-2023-160-03-PCT -9-contacts. Notably, Rstypically falls within the range of several kilo-ohms per square centimeter (k / cm2). A summary of the estimated capacitance values within each pixel is presented in Table 1.

[0073] By way of example and not limitation, the example NOMA device is configured with each pixel being 20 pm by 20 pm, and the device is patterned by way of example with a total of 700 by 750 pixels. Consequently, the overall dimensions of this NOMA spans 14 mm by 15 mm. The area of the Al mirror in this example is approximately 60% of the total area of a pixel. The cell gap size is 3 pm, which is enough to generate a 2n phase retardation for visible light.

[0074] It should be appreciated that the number of pixels can be extended to an arbitrary number in each direction of the array. Regarding the size of each pixel, it will be recognized that as the pixels are made larger, device performance generally suffers (both in terms of energy per operation and number of operations per unit area).

[0075] Moving in the direction of smaller pixels, such as smaller than 20 urn, device performance increases. The examples presented of 20 urn pixels were selected for simplifying device fabrication. It should also be noted, however, that there are at least two physical limits on how small one could make one of these pixels. (1) At much smaller pixel sizes, such as less than about 1 to 5 urn, individual pixels could start to effect each other, beyond which making the pixels smaller wouldn’t improve performance. The exact size would certainly depend on device parameters such as the liquid crystal material utilized and / or the thickness of the liquid crystal cell. (2) Ultimately the highest number of operations one could achieve with this sort of free- space approach is set by the diffraction limit of the light that is being utilized, which could be sub 1-um. Fabricating even smaller pixels then wouldn’t enable any performance gains. Accordingly, a preferred range of pixel sizes is on the order of 5 to 20 pm, but other sizes below and above this are also possible.

[0076] 3. Electro-Optical Modulator Characteristics

[0077] 3.1. Liquid Crystal Characteristics

[0078] The experimental setup utilized LC-VAST-05 as its nematic liquidUCLBL-2023-160-03-PCT -10-crystal material which is characterized by its negative dielectric constant. It should be appreciated that other forms of liquid crystal may be utilized, such as ferroelectric liquid crystal (FE LC) as the EOM. It will be appreciated that the operation and fabrication is similar to that of nematic liquid crystal; however, the response time using FE LC is about 10 microseconds, and thus operates more rapidly that nematic LC which requires milliseconds. Both the upper and lower substrate surfaces receive a thin SiO2 layer through e-beam evaporation (not shown in the figure). It will be appreciated that the ITO glass 12 receives a layer of SiO2 on it, and for the sake of simplicity we will call this SiO2 layer ‘side A’ and is referred to as the upper substrate. The lower substrate with layers 16, 18, 20 and so forth in FIG. 1A, also receives a thin layer of SiO2 on top of this “lower substrate”.

[0079] Initially, the liquid crystal molecules align vertically, driven by van der Waals interactions with the SiO2 surfaces. The application of an electric field induces a rotational response within the liquid crystal, promoting alignment parallel to the substrate to minimize free energy. Incident light with polarizations parallel or perpendicular to the liquid crystal's principal axis, experience distinct refractive indices, leading to a phase delay between the two linear polarization components. When the liquid crystal (LC) is oriented at a 45 degree angle with respect to the incident polarization, it functions as a half-wave plate, effectively capable of converting the parallel-polarized incident light to a perpendicular polarized-reflected light.

[0080] FIG. 1C is a graph 70 showing voltage-dependent reflectance behavior of the disclosed liquid crystal cell. In this test, a p-polarized incident light is utilized while a DC voltage is applied across the LC cell. The principal axis of LC molecules is 45 degrees to the incident polarization. The experiment measured the s component of the reflected light as a function of V1. The observed threshold voltage of +2.2V closely aligns with the calculated value derived from the Ericksen-Leslie theory. The graph shows the reflectance curves for red 72, green 74 and blue 76 wavelengths of the light. It can be seen in the figure that reflectance differences between these wavelengths starts increasing dramatically when LC voltage increases, such as extending beyond 3 volts.UCLBL-2023-160-03-PCT -11-

[0081] 3.2. Micromirror array Characteristics

[0082] The EOM of the present disclosure may also comprise a layer which utilizes other forms of light modulation, for example a micromirror array. It will be appreciated that the use of a micromirror array can provide a few orders of magnitude in speed improvement over using the LCD material.

[0083] In this embodiment, the EOM comprises a micro mirror (MM) array which can be actuated electrostatically. The angular or vertical position of the MM is controllable through the potential applied to the underlying electrode, while the mirror itself remains grounded. The MM and its control electrode are separated by a few micrometers, creating a capacitance (Cmm) analogous to the Cic in the LC configuration. This control electrode is connected to a photodiode. Given the high voltage required to drive the MM (typically around 100V), a PIN diode is the preferred choice. This is due to its smaller capacitance relative to Cmm, facilitated by the greater distance between its anode and cathode (several hundred micrometers). Compared to LC EOMs, MMs offer a markedly faster operational speed. For instance, while nematic LC EOMs commonly have refresh rates under 100 Hz, MMs can be driven at frequencies up to several hundred kHz. The operation of the EOM which comprises a MM array is described in Section 9.

[0084] 4. Device Operation

[0085] FIG. 1 D illustrates a plot 90 of applied voltages for active and erase phases. The device operates in two distinct phases: the active phase and the erase phase. During the active phase, a positive bias is applied to the upper ITO electrode, causing the pn junction to become reverse-biased. This configuration facilitates the concentration of photo-generated carriers within the bulk silicon, directing them towards the n-well where they accumulate on the Al mirror. This accumulation creates an electric field across the LC capacitor. Conversely, in the erase phase, both Vi and V2 are set to zero to discharge the accumulated carriers. Thus, an external bias is applied through points marked as 26 and 30 in FIG. 1A. These voltages can be applied utilizing conventional power supplies and control electronics. It should be noted that the external bias does not need to be zero volts, as it is only required to be below the threshold voltage of the liquid crystal (which is aUCLBL-2023-160-03-PCT -12-physical parameter) so as to erase the state of the cell.

[0086] Within the active phase, the charging of the liquid crystal capacitor involves two stages: a rapid initial step and a subsequent gradual step. When Vi and V2 are initially applied, the LC capacitor charges to an initial voltage, Vi, given by:"This stage arises in a time scale of T~7?S(C0X / / CZC), where Coxl / Clcrepresents the equivalent series capacitance of Coxand Clc. Considering that Rsis on the order of kilohms per square centimeter (kQ / cm2) and values for Coxand Clcare around several nanofarads per square centimeter (nF / cm2), the charging time occurs on the timescale of several microseconds (ps).

[0087] The capacitance of Clcis then slowly charged to Vi and the charging time is limited by the reverse current lRof the pn junction. In the absence of light, the reverse current IR is on the order of a femtoampere (fA) per pixel so this charging time T2~ Cox+ CZC)1 / / Ris in the order of seconds. In this testing, the operation period T is 200 ms, which means« T « T2- Consequently, the LC voltage remains a relative constant value of Vi in the active phase under dark conditions. However, when exposed to illumination, the increase of reverse current IRleads to a more rapid charging of the LC capacitor to V-i.

[0088] The fundamental concept behind achieving optical nonlinearity involves configuring Vi to be smaller than Vth and Vi to be larger than Vth. This configuration ensures that the reflectance of the LC cell remains close to zero in the absence of light while the reflectance of the LC cell increases significantly upon exposure to light. Building upon this principle, two distinct types of nonlinear operations can be achieved, as illustrated in FIG. 1 D which shows light-to-light modulation 92 and single-pulse modulation 94.

[0089] In the light-to-light modulation scenario 92, two short-pulse light sources are provided, one acting as the pump and the other as the probe. The pump light is incident at the onset of the active phase, rapidly charging the LC capacitor to Vi. Subsequently, the LC undergoes rotational changes, enabling measurement of the reflectivity of probe light as a function of theUCLBL-2023-160-03-PCT -13-pump light energy and time delay between pump and probe. In the singlepulse modulation scenario 94, a long pulse that spans almost the entire active phase is utilized. The initial portion of this pulse is responsible for charging the LC capacitor, subsequently modulating the reflectance of the latter part of the pulse. Elements of the above will be described in more details below.

[0090] 5. Device Fabrication

[0091] By way of example and not limitation, the silicon substrate of the present disclosure was fabricated using conventional planar processing techniques as commonly used for integrated circuit manufacturing. To create pn junctions, thermal diffusion of phosphorus is carried out within a 6-inch p- type substrate, under a POCI3 atmosphere at a temperature of 840°C.Subsequently, a dielectric layer stack is established through the deposition of 15 nm AI2O3 at 250°C by Atomic Layer Deposition (ALD) and 530 nm SiO2 at 350°C by Plasma Enhanced Chemical Vapor Deposition (PECVD). Notably, the ALOs / Si interface hosts a substantial built-in charge density, which effectively passivates minor carrier recombination in the silicon, reducing the reverse current of the pn junction.

[0092] Following the formation of the dielectric stack, the wafer undergoes a patterning and etching process to create contact vias for the Al mirrors. This is followed by Al sputtering and patterning. Then 100 nm Pt is sputtered on the back side of the wafer to establish an ohmic contact. In parallel, the glass substrate is cleaned with a piranha solution and then a 200nm ITO transparent thin film is deposited via sputtering at temperature of 500°C. The sheet resistance of the ITO film after sputtering is approximately 20 Q / sq. Subsequently, both the silicon and glass substrates are coated with a 40 nm SiO2 layer via e-beam evaporation which serves as the alignment layer for the liquid crystal.

[0093] The glass substrate is then diced into the desired sized pieces (e.g., 23mm x 25mm), while the silicon substrate is also diced into the desired sized pieces (e.g., 20mm x 22mm). The diced components are thoroughly cleaned using acetone / IPA sonication and O2 plasma. The assembly of the cell is achieved by bonding the silicon and glass pieces together using a UV curing adhesive (e.g., NOA 68). The cell gap is controlled by the inclusion ofUCLBL-2023-160-03-PCT -14-microspheres (Micropearl SP-203, Sekisui, Chemical Co., Ltd, Japan) with a diameter of 3 micrometers within the UV adhesive.

[0094] Subsequently, the cell is filled with nematic liquid crystal LC-VAST14- 5g (made by INSTEC, USA) utilizing a capillary effect. Finally, the filling hole is sealed using a UV adhesive, completing the assembly process.

[0095] 6. Pump Probe Testing

[0096] FIG. 2A through FIG. 2F depicts various results from pump-probe testing. To distinguish between the contributions of the voltage induced effect and the photocurrent effect, time resolved testing was performed. A pump probe test was designed which is capable of optically probing the device dynamics at the characteristic time scale of the liquid crystal molecules.Moreover, short pulses (e.g., approximately 2 ms duration) were generated from colored LEDs (both for the pump and probe beams) as our light sources to emphasize the pronounced nonlinearity under incoherent illumination. A variable time-delay was electronically introduced and scanned between the pump and probe LED pulses, while synchronizing a camera with the probe pulse to record changes in reflectivity induced by the pump.

[0097] In FIG. 2A and FIG. 2B wide field images 130, 150, were captured each representing the state of every pixel in NOMA at a given time delay. This allowed us not only to measure the average behavior of all pixels but also to investigate pixel-to-pixel variations in the dynamics.

[0098] In FIG. 2C is depicted the average behavior 170 of the 2000 pixels that lie in the image, showing reflectance over time at different pump light intensities. In the absence of pump light illumination (lowest curve), the probe reflectivity increased from 7% to 10% with a time constant of 8 ms as the liquid crystal responded to the applied electric field (2.5V). This behavior is consistent with the sub-threshold response of the liquid crystal cell, where a slight rotation of the liquid crystal angle occurs. As the intensity of the pump light increased the higher and darker curves in FIG. 2C were obtained which represent the saturated value of the reflectivity rising and eventually reaching a plateau value of 40.6% (top curve).

[0099] The light induced change was quantified in NOMA reflectivity by defining a reflection contrast AT? = Rpump-on / Rpump-off-UCLBL-2023-160-03-PCT -15-

[0100] In FIG. 2D contrast is demonstrated 190 and shows a sharp saturation with respect to pump pulse energy, with an achieved contrast value of approximately 4. Although, with better performing LCD materials, and pn junctions with lower leakage current, a contrast of at least 30 has been achieved.

[0101] In FIG. 2E is depicted contrast mapping 210. To further investigate the response at the pixel level, the wide field image was segmented into a regular grid, each grid containing only one pixel of NOMA. The saturated contrast value of a given pixel was mapped. Across the 2000 pixels in the image, a normal distribution is seen of the responses.

[0102] Given the statistically significant sample size in regard to contrast, mean and the standard deviation were employed for the normal distributions. Similar to the aggregate response, the pixel-to-pixel contrast sharply increased with increasing pump intensity. The pixel-to-pixel variation remained low at low pump intensities, while at high pump intensities a greater variation in pixel response was evident for fluences below the saturation limit (approximately 1 p J per pixel).

[0103] In FIG. 2F is seen a pixel-to-pixel representation 230 of contrast variation under various illumination conditions. The pixel-to-pixel variation stems from both the inhomogeneity in the pump pulse front and the inherent heterogeneity in the device dynamics which could be mitigated by refining the device preparation steps.

[0104] In applications, such as all-optical computation and optical neural networks, although some degree of heterogeneity in the response of individual computing elements (for example individual pixels) is acceptable and even leveraged through hardware-aware training, however, achieving uniform and consistent responses across multiple pixels is generally desirable. This becomes increasingly important at scale as cascading errors can significantly impede computation. To this end, it is envisioned that the pixel-to-pixel variation, as measured in these tests, is a good starting point for future applications.

[0105] 7. Single-Pulse Nonlinearity Testing

[0106] In these tests longer pulses (e.g., 80 ms) were utilized to explore theUCLBL-2023-160-03-PCT -16-capability of an extended light pulse to self-modulate. It is expected that the initial portion of the light pulse (e.g., first 10ms) will generate sufficient photocurrent in the photodiode which has been demonstrated to introduce a robust nonlinearity. Subsequently, it is expected that the introduced nonlinearity will modulate the remaining portion of the light pulse.

[0107] One could also describe this nonlinearity as a four-wave mixing process where the initial part of the optical pulse (E1 ) creates an electric field (E2) which modulates the remainder of the pulse (E3). As a result, the reflected beam (E4) exhibits a nonlinear relationship with the incident beam.

[0108] FIG. 3A through FIG. 3D demonstrate results from single-pulse nonlinearity testing.

[0109] In FIG. 3A is shown output intensity 310 as a function of incident intensity. The distinctive signature of this nonlinearity is depicted in this figure showing the relationship between reflected light intensity (output intensity) and incident light intensity (input intensity) which resembles a leaky ReLu function.

[0110] In FIG. 3B reflectance 330 is shown with respect to incident light intensity. To quantify this nonlinearity, the reflected intensity was normalized with the input and the reflectivity of NOMA calculated as a function of the incident intensity. It can be seen in the figure that at low input light intensities, the reflectivity of NOMA is marginal at approximately 7%. However, at higher incident intensities, the reflectivity increases to 40% and eventually saturates. The saturated reflectivity is primarily limited by the fill factor of the Al mirror and the Fresnel losses at the interfaces of the device stack, both of which hold potential for improvement in future designs. Similar to the two-pulse experiment, the nonlinearity exhibits a rapid saturation at higher incident intensities, yielding a contrast ratio of around 15.

[0111] In FIG. 3C and FIG. 3D a single pulse nonlinearity 350, 370 being demonstrated showing incident intensity 350 and reflected intensity 370 with a simple application, in which we enhanced the contrast of a binary grayscale image (created using a linear SLM) after interaction with NOMA. Grayscale values are shown here and their resultant input intensities. Due to reproduction limitations of the patent office these grayscale images could not be shown. Specifically, in FIG. 3C incident light intensity is depicted as aUCLBL-2023-160-03-PCT -17-function of the grayscale of spatial light modulator (SLM). In FIG. 3D the intensity of light reflected from NOMA is depicted as a function of SLM grayscale. The difference between figure these two figures indicates that the device of the present disclosure performs image thresholding since the region with small grayscale will appear even darker.

[0112] FIG. 3E and FIG. 3F illustrate pixel value histograms depicting the results of image contrast enhancement from the disclosed NOMA device. Compared with the dark regions of the reference image, the contrast enhanced image shows a significantly darker background while the bright regions retain their average brightness. Quantitatively, the image processed with nonlinearity exhibits a contrast four times greater than that of the reference image. It will be noted that the actual images could not be shown due to the reproduction limitations of the patent office.

[0113] 8. Implementation with p-n versus p-i-n Structures

[0114] FIG. 4A illustrates an embodiment 410 a single NOMA pixel using pn junctions. The figure depicts a platinum bottom contact 412, over which is the P-Si 414, into which are seen N-Si wells. Over this is the SiO2 / Al2O2 dielectric 418. An Al mirror 422 is connected through the dielectric into the N-Si well, with the mirror and the SiO2 / Al2O2 dielectric 418 covered with a layer of Al SiO2420. Over this area is the Liquid Crystal (LC) material 424, above which is seen the ITO glass 428 with underside coating of Al SiO2426. The schematic is shown here with Gnd, Vi , V2, the diode junction, and CLC and Cox.

[0115] FIG. 4B illustrates an embodiment 450 a single NOMA pixel using p-i-n junctions. This method of fabrication simplifies the design of the pixel by removing the additional n-doped well underneath the mirror and only requires the application of Vi , instead of both Vi and V2. Material changes are made, such as for the ohmic contact into the p-doped region, such as using a metal such as Platinum (Pt). Therefore, Pt instead of Al, would serve as the mirror material, and Al would serve as the bottom contact to the n-doped region.

[0116] The figure depicts an Al bottom contact 452, over which is an N+ Si layer 454, above which is intrinsic Si (i-Si) region 456, into which P-Si wells 458 are formed. Over this is an SiO2 dielectric 460, upon which is mirror of PtUCLBL-2023-160-03-PCT -18-464, which extends down into the P-Si well. The mirror and the SiO2 dielectric 418 are covered with a layer of oblique-evaporated Al SiO2462 as an alignment layer of liquid crystals. Over this area is the Liquid Crystal (LC) material 466, above which is seen the ITO glass 470 with underside coating of Al SiO2468. The schematic is shown here with Gnd, Vi , the diode junction, and CLC and Cox.

[0117] 9. Operation of a NOMA Device with MM EOM

[0118] FIG. 5A and FIG. 5B illustrate an example embodiment 510, 550 of operating a non-linear optical micro-device arrays (NOMAs) with MM mirrors in different lighting conditions; and has an operation which parallels that of NOMAs with LC EOMs.

[0119] In FIG. 5A is seen an example structure with an Al bottom contact 512, over which is an N+ Si layer 514, above which is intrinsic Si (i-Si) region 516, into which P-Si wells 518 are formed. Over the P-Si well is a control electrode 520, The MM 524 is retained on a support structure 522, which should typically comprise an electrically conductive material. The schematic is shown here with Gnd, Vi, the diode junction PD, and CMM.

[0120] Initially, as seen in embodiment 510 of FIG. 5A, the MM is in a grounded state and the junction is reverse biased, with Vi applied to the cathode of the PIN junction. Because the capacitance of the MM (Cmm) is significantly larger than that of the photodiode (Cpd), the initial voltage on Cmm is minimal, keeping the MM in its neutral position as seen in FIG. 5A.

[0121] In FIG. 5B the left hand of embodiment 550 is shown being activated in response to exposure to a light pulse 552, whereby the PIN junction generates a photocurrent, which charges Cmm and consequently displaces the MM support structure to a new position 522’, in response to which the mirror is displaced in a vertical and / or angular movement. It should be appreciated that the support structure can be shaped / configured to provide a desired movement profile in response to activation, and this is dependent upon the application to which the NOMA device is to be used.

[0122] It should be appreciated that the structure shown above is but one example of using a different form of EOM in the present disclosure, while many other such constructions are possible without departing from theUCLBL-2023-160-03-PCT -19-teachings of the present disclosure.

[0123] 10. Additional Background Material

[0124] As all-purpose digital computation, particularly for artificial intelligence and deep neural networks, reaches an energy bottleneck, alternative physicsbased computational architectures are attracting increasing attention. Among these, Optical Neural Networks (ONNs) are a promising alternative due to their high parallelism, energy efficiency, and minimal latency. Highly parallel linear operations, such as matrix multiplications and convolutions, can readily be implemented using linear optical transformations in ONNs, that have almost negligible dissipation. On this important metric, ONNs offer substantial energy savings per linear operation compared to cutting-edge all-digital counterparts. However, achieving efficient optical nonlinearity poses inherent challenges, leading ONNs to often rely on hybrid systems that incorporate electronic nonlinear activations. These hybrid ONNs require preamplifiers and analog-to-digital converters to process weak optical signals that increase latency and power expenditure per operation. To realize deep ONNs with low energy consumption, the development of a sub-picojoule optical nonlinearity is important.

[0125] Recently, a “receiverless” approach has been proposed for energyefficient optical modulation, which obviates the need for power-hungry electronics by in-situ integration of a photodiode (PD) with an electro-optical modulator (EOM). In this configuration, a portion of the input light generates photocarriers, which directly charge (or discharge) the EOM, thereby modulating the remaining part as the output. This process facilitates light selfmodulation, with energy consumption that scales with the capacitance of the PD and the EOM. Following this approach, optical nonlinear operation with switching energy on the order of femtojoule per activation has been demonstrated in integrated photonics circuits by integrating femto-farad capacitance PDs and EOMs such as InGaAsP photonic crystals or micro-ring resonators. However, integrated photonic devices face scalability challenges and lack compatibility with incoherent light, strongly restricting their use in large-scale ONNs in ambient light scenarios.

[0126] A free-space counterpart of the “receiverless” optical nonlinearity hasUCLBL-2023-160-03-PCT -20-the potential to address the scalability concerns by harnessing the immense parallel computing capabilities afforded by free-space light propagation.Furthermore, free-space ONNs have compelling applications in object detection and sensing where conventional neural networks are routinely employed to run inference on digitized camera images. In such applications, free-space ONNs could remove the need for the digitization step and run inference directly on the ambient light. Previously, Liquid Crystal Light Valves (LCLVs) have been developed for controlling a read beam with a write beam by placing a photosensitive film next to a Liquid Crystal (LC) EOM layer, with a dielectric mirror separating the two. With LCLVs, the sigmoid-like nonlinear dependence of the read beam intensity on the write beam intensity has been demonstrated and applied to the early research on ONNs. More recently, self-modulation of light has been realized by resistively coupling the LC layer to 2D material phototransistor arrays, but the energy consumption is well above picojoule per operation levels. To the best of our knowledge, a femtojoule-Rectified Linear Unit (ReLU) for self-activation of the input patterns - the predominant nonlinear function in contemporary deep neural networks - has never been realized.

[0127] In this study, an energy-efficient and highly parallel Nonlinear Optical Microdevice Array (NOMA) is presented for use in free-space optical computation. Each pixel of the device contains a silicon (Si) PD capacitively coupled to an LC cell, allowing for nonlinear activations at the femtojoule scale. By leveraging the mature fabrication processes for Si-based integrated circuits and liquid crystal display technologies, the disclosed design readily enables the fabrication of devices with millions of pixels. Through the characterization of NOMA, an optical ReLU nonlinearity is presented operating on an incoherent optical beam. In addition, a demonstration of practical applications of this optical ReLU is presented in two optical processing tasks: real-time image contrast enhancement and nonlinear activation within a multilayer optical neural network.

[0128] 10.1. Device Structure and Working Principle

[0129] FIG. 6 illustrates 610 a microscopic image rendition of NOMA, with an inset showing a single pixel, depicting the metallic region which is the AlUCLBL-2023-160-03-PCT -21-mirror. The n-doped region outlining the photodiode (PD) is indicated by dashed lines and the additional n-doped region underneath the Al mirror is outlined by the vertical dashed lines. The NOMA was fabricated comprising 750x700 pixels, each with a dimension of 20 pm x 20 pm. It should be recognized, however, that the present disclosure is not limited as to size or number of pixels. The materials and methods section of the supplementary text describes the detailed structure and the fabrication process for the entire device.

[0130] FIG. 7 schematically illustrates 630 a cross-section view of the NOMA structure. The device consists of a Liquid Crystal (LC) layer, represented by rods 631 between an ITO-covered glass 640 and a Si substrate 638 with PDs. Both substrates are coated with SiO2633 for LC alignment (AL). Upon illumination, PD charges the LC cell, leading to rotation of the LC molecules and modulation of reflected light through LC birefringence.

[0131] Within each pixel there is a Si PD 632 connected to an Al mirror 634 while the LC material 636 fills the gap formed between the Si substrate 638 and the indium tin oxide (ITO)-coated glass 640. The Si substrate 638 is grounded, while a source voltage Vs642 is applied to the ITO electrode. An additional n-doped region 644 beneath the Al mirror serves as a global electrode for a control voltage Vc646. Both Vsand Vcare non-negative to ensure a reverse-biased PD. For optimal optical modulation, a vertically aligned nematic LC with a large contrast ratio was employed.

[0132] FIG. 8 illustrates 710 optical intensity modulation of the LC cell as characterized using Cross-Polarized (CP) reflectance as a function of VLC. Characterization is shown of the LC birefringence using voltage-dependent cross-polarized (CP) reflectance of the LC cell with = 680nm, showing a threshold voltageat 2.8V. In this configuration, the LC cell acts as a tunable half-wave plate placed between two crossed polarizers. At low bias, the LC cell appears dark as LC molecules are aligned parallel to the propagation direction of the incident beam and no change in the polarization state of the incident beam occurs. At a threshold bias (Vtfl) of 2.8V, the LC molecules start to tilt, causing the incident beam to attain ellipticity and the LC cell appears brighter. The measured value closely approximates theUCLBL-2023-160-03-PCT -22-theoretical value of 2.2V predicted by the Freedericksz transition theory, considering the mismatch in electrode work functions (0.4V, between Al and ITO). As the bias is increased above Vtfl, a clear maximum in reflectance occurs where the polarization of the incident beam is completely rotated to the perpendicular polarization. The LC cell exhibits a contrast ratio of 120, providing a broad optical modulation range. As the Si PD provides in-situ optical-to-electrical feedback, low dark current and high optical responsivity are crucial for energy-efficient nonlinear operations.

[0133] FIG. 9 illustrates 730 that by employing an AI2O3 passivation layer, a low junction dark current of 10 nA / cm2is achieved. The plots show a currentvoltage relationship of the Si PD under dark conditions. The measured PD is the one formed between the auxiliary n-doped region and substrate. The inset of FIG. 9 shows the relation between photocurrent and light intensity, indicating a responsivity (F?) of 0.3 A / W. Given that the PD area in each pixel is approximately 100 pm2, the dark current per pixel is around 10 fA. The responsivity of the disclosed PD was measured as 0.3 A / W (A=680nm), indicating efficient collection of photocarriers.

[0134] FIG. 10 illustrates a simple circuit model 750 of a NOMA pixel that will be used in a later section to describe the dynamics of the optical ReLU nonlinearity. Capacitance CLC752 denotes the capacitance between the Al mirror and the ITO electrode. Capacitance Cox756 denotes the capacitance between the Al mirror and the n-doped region beneath it. Capacitance Cp758 represents the junction capacitance.

[0135] Thus, the model is exemplified with three main elements: (1) an LC capacitor (CLC) 752 which forms between the Al mirror and the ITO electrode; (2) a Si PD 754 which can be described by an ideal diode in parallel with a junction capacitor Cp758; (3) an oxide dielectric capacitor (Cox) 756 which forms between the Al mirror and the additional n-doped region. The estimated capacitance values of each are shown in Table 2.

[0136] FIG. 11 illustrates 770 that upon illumination, part of the incident light is reflected by the aluminum (Al) mirror, while the remainder is absorbed by the Si PD. The figure shows the configuration of NOMA for light self-modulation. The input beam is a linearly polarized pulse, and the output beam is the CPUCLBL-2023-160-03-PCT -23-reflected pulse. The photocarriers generated in the Si PD accumulate on the Al mirror, altering the voltage across the LC cell (VLC). Consequently, the orientation of the LC molecules change, which then modulates the reflected light through the LC’s birefringence. Under dark or weak illumination, the VLCremains below Vth, so the NOMA remains in the “OFF” state with a low CP reflectance. Thus, the energy of the CP-reflected light (output energy) is suppressed. On the other hand, for incident light with a high pulse energy, the LC capacitor is charged above Vth, so the NOMA is switched to the “ON” state, characterized by a high CP reflectance. In this state, the output energy exhibits a linear dependence on the input energy.

[0137] FIG. 12 illustrates 790 input-to-output characteristics of the NOMA device. The figure shows the ReLU-like input-output relationship. For incident light with a small pulse energy, the NOMA remains in the “OFF” state and the transmitted light energy through the polarizer (output energy) is suppressed. For incident light with large pulse energy, the NOMA is switched to the “ON” state, characterized by a high CP reflectance. These behavior characteristics mimic the ReLU function, where the output remains zero for low input values and increases linearly with higher inputs.

[0138] 10.2. Optical Switching Dynamics

[0139] In FIG. 13 through FIG. 16 are shown optical switching characteristics and dynamics of the NOMA.

[0140] FIG. 13 illustrates 810 the manner in which NOMA is periodically operated between an active and erase phase. The figure depicts waveforms of ;, Vc, and the resulting LC capacitor voltage VLC. Both Vsand Vcare synchronized square waves, characterized by an active and erase phase. In the active phase, an intense optical pulse can charge the VLCfrom below- threshold initial value Vtto above-threshold value l^, resulting in NOMA switching from the “OFF” to the “ON” state. In the erase phase, the LC capacitor is discharged, setting it to the default “OFF” state.

[0141] More particularly, during the active phase, the LC capacitor first charges to an initial voltage Vt, which is determined by the capacitance divider: Vt= where Ctot= CLC+ Cox+ Cp. This chargingUCLBL-2023-160-03-PCT -24-process is performed on a time scale of = RsCtot, where Rsis the series resistance of bulk silicon and the contact. Given that Rsis approximately ~106ohm and Ctotis around 20 fF, occurs on the timescale of microseconds. Under dark conditions, the LC capacitor slowly charges to Vswhere the charging time (T2) is set by the dark current IRof the Si PD. Given that IRis in the order of 10 fA / pixel, T2is in the order of seconds.

[0142] Tests were performed applying a square wave of Vsand Vcwith a period T of milliseconds, which is determined by the LC’s response time.Considering« T / 2 « T2, the LC voltage remains relatively constant at Vj under a dark condition during the T / 2 millisecond active phase. Under light illumination, the photocarriers generated in the PD leads to a rapid charging of the LC capacitor to 1 - Voltage Vswas maintained above Vthand Vcadjusted so that V remains below Vth, ensuring the LC is in the “OFF” state without light, but can readily transition to the “ON” state under sufficient light illumination. In the erase phase, voltage Vsis kept below Vthand Vcset to 0V, dissipating the accumulated charges in the LC capacitor and reverting the device to the default “OFF” state.

[0143] The optical switching energy Eswis determined by the amount of photocarriers (Qph) needed to fully charge the LC and oxide capacitors, which can be estimated from the disclosed circuit model, as:

[0144] where a is the optical-to-electrical coefficient andand Vcrespectively denote the changes of source and control voltage between the active and erase phases. Considering the responsivity of silicon PD (0.3 A / W), fill factor of Al electrode, and transmission loss through the ITO layer, a is approximately 0.1 C / J. Given that both Coxand CLCare in the range of femtofarad, Qphis estimated to be in the tens of femtocoulombs. Thus, the optical switching energy for each pixel is calculated to be in the hundreds of femtojoule range. Regarding the electronic energy consumed during the switching process, it essentially comprises the work done by the voltage sources, which can be calculated as Eeiectronic= CLCV2+ C0XV2. This indicates that the electric switching energy is on the same scale of the opticalUCLBL-2023-160-03-PCT -25-switching energy.

[0145] FIG. 14 illustrates a block diagram of a pump-probe experiment (see FIG. 28A for an optical layout), where pump 856 ( = 630nm) and probe 854 pulses ( = 680nm) from light emitting diodes (LEDs) are directed onto the NOMA. Using Analog Outputs (AOs) 852 from a Data Acquisition (DAQ) card, the light pulses are synchronized with the applied bias, such that the pump arrives at the rising edge of the bias, while the probe pulse is time- delayed. Dynamics in the CP reflectance of NOMA is measured using a polarized beam splitter (PBS) 860 with a low-pass filter (LP) 862 in a widefield microscope geometry. The total intensity of the reflected light is measured using a photodiode (PD) 864 and Analog Inputs (Al) 866 are digitized by DAQ.

[0146] More particularly, toward investigating the dynamics of the optical switching process, these pump-probe experiments were carried out and are capable of optically probing the device dynamics at the characteristic time scale of the LC molecules. Short pulses (e.g., 2 ms duration) were generated from colored LEDs for both pump and probe lights. The pump light is synchronized with the electrical signal's rising edge, which charges the LC cell and initiates optical switching. The probe light measures the CP reflectance of the device as a function of time delay between the pump and probe. To ensure that the observed dynamics are only from the pump-induced changes, a probe pulse energy (80 fJ / pixel) below the threshold energy of NOMA was utilized with probe pulse durations (2 ms) much shorter than the liquid crystal response time (~10ms). CP reflectance was mapped as a function of l^, Vc, and pump energy (Epump). Using these results, the capacitances were quantified in this circuit model to identify the optimal conditions for efficient optical nonlinearity.

[0147] FIG. 15 illustrates 830 a time trace of CP reflectance at increasing pump energies at Vs= 4V and Vc= 4.5V. The dynamics of CP reflectance of NOMA at increasing pump energies (lighter shades) Epump(l^ = 4V and Vc= 4.5V) largely follow the outline of the voltage pulse with a rise and fall time limited by the LC. More specifically, for sub-threshold pump energies (i.e. , 0 and 106 fJ / pixel), CP reflectance traces show a negligible increase afterUCLBL-2023-160-03-PCT -26-pumping, indicating that the device remains in the “OFF” state. In contrast, at a higher pump energy, the CP reflectance increases notably after pumping and reaches a plateau. With increasing pump energy, the plateau value rises from 0.8% to a maximum of 29%, showing a large modulation range of 35 between the “OFF” and “ON” states. Optical switching was further characterized by measuring the CP reflectance at a fixed probe time delay at 60 ms, at which point the CP reflectance reaches its plateau.

[0148] FIG. 16 illustrates 890 measured CP reflectance as a function of Epumpat different Vc(with Vsfixed at 4V), with the insert depicting the expected linear relationship between switching energy Eswand Vc, showing a minimum Eswat 60 fj / pixel.

[0149] The derived switching energy Esw(defined as the pump energy at which the CP reflectance reaches 95% of its saturation level) shows a linear dependence on Vc, consistent with the disclosed circuit model (Eq. 1). From the slope and intersection of the linear fit Cox= 6.5 fF / pixel and CLC= 5.8 fF / pixel are derived, which are close to their estimated values seen in Table 2.

[0150] 10.3. Femtojoule Optical ReLU for Image Contrast Enhancement

[0151] In FIG. 17 through FIG. 20 is a demonstration of the optical ReLU and image contrast enhancement.

[0152] FIG. 17 illustrates a graph 910 output with respect to input of the optical ReLU function using a single, yet extended LED light pulse (e.g., 50 ms) synchronized with the rising edge of the electrical pulses. In this test the voltages were set at Vs= 4V and Vc= 5.5V. The distinct signature of the optical nonlinearity is depicted in the figure, where the relationship between CP reflected light energy (output energy) and incident light energy (input energy) resembles a ReLU function with a switching energy of 280 fj / pixel. At low input energies, the reflectivity of NOMA is marginal at around ~1%. At higher input energies, the reflectivity increases to 24% and saturates. The saturated reflectivity is limited by the fill factor of the Al electrode and the optical losses at the interfaces of the device stack. Analogous to the response to short pulses, the switching energy value of the ReLU function can be manipulated by adjusting Vc(see FIG. 9A and 9B in Section 11). This additional tunability is useful in applications where the optical input variesUCLBL-2023-160-03-PCT -27-dynamically, enabling the device to maintain optimal performance across a variety of scenarios.

[0153] To further investigate the response at the individual pixel level, wide- field images of NOMA were captured and pixel-by-pixel dynamics tracked. The wide field images were segmented into a regular grid, each grid containing only one pixel of NOMA (see FIG. 10A in Section 11).

[0154] FIG. 18 illustrates statistics 930 from the 10,201 NOMA pixels. The ReLU function has a normal distribution of the switching energy with a mean value of 280 fJ and a standard deviation of 18 fJ. In applications such as ONNs, some degree of heterogeneity in the response of individual pixels is acceptable and even leveraged through hardware-aware fine-tuning of the models. Yet, achieving uniform and consistent response across many pixels is generally desirable as cascading errors can potentially impede computation, especially for deep neural networks.

[0155] To demonstrate the ReLU functionality and large-scale uniformity, a contrast enhancement task was performed on a binary grayscale image through interaction with more than 15,000 NOMA pixels.

[0156] FIG. 19 illustrates image contrast enhancement from image 950 to enhanced image 960. As a baseline, an image 950 reflected from NOMA was captured under a linear response. A linear response of the device was assured by setting Vs= -4V to forward bias the Si PD, which maintains the LC cell in the "ON" state. To capture the contrast-enhanced image 960, the voltages Vs= 4V and Vc= 5.5V were set to ensure that NOMA is under a ReLU response.

[0157] The example image was that of a “Cal” logo, which consists of two regions: the logo region, chosen to be bright, and the background, chosen to be dark. It should be noted that the original color images were converted here to grayscale for this patent application. Investigating the two regions separately, in terms of their pixel values, reveals histograms with a mean ( / z) and standard deviation (a) value for the reference image. Compared with the dark regions of the reference image, the contrast enhanced image shows a darker background while the bright regions retain their average brightness.

[0158] FIG. 20 illustrates bar graphs 970, 980 showing image enhancement inUCLBL-2023-160-03-PCT -28-a quantitative manner for images 950 and 960 in FIG. 19. Comparing bar charts 970 and 980, it can be seen that the non-linearly enhanced image exhibits a contrast four times greater than that of the reference image. The ability of NOMA to selectively amplify the contrast of specific image regions showcases its potential in applications such as real-time image processing and optical edge computing. In these cases, the nonlinear layer prunes or maintains connections between successive layers in the network. In spirit, this contrast enhancement task can be thought of as one such application where we have already demonstrate more than 10000 nonlinear connections with potential to expand into deep neural networks with more than one hidden layer.

[0159] 10.4. Multilayer Optical Neural Network with ReLU Activations

[0160] FIG. 21 to FIG. 25 provide evidence of using ReLU non-linearity with a neural network.

[0161] The role of ReLU nonlinearity was highlighted by demonstrating a Multi-Layer Optical Neural Network (ML-ONN). The implemented ML-ONN consists of two fully connected linear layers linked by the NOMA, serving as the nonlinear activation layer. ML-ONN was leveraged to address two distinct binary classification tasks characterized by nonlinear decision boundaries.

[0162] FIG. 21 illustrates 1010 processing of an image 1020 having a nonlinear decision boundary, and determining ground truth for one such boundary, separating the two-dimensional space defined by the input vector x = (x1,x2) °faPointin two-dimensional space from an image having two different colored regions within which is a circular boundary to be determined. It should be noted that the original image of 1012 had a center of a first color, which transitioned through a white region to a second color on its peripheral area.

[0163] In this example the ONN 1018 was configured with two inputs 1014, 1016, four hidden neurons 1018, and two output neurons 1020, 1022 with the goal of learning these nonlinear decision boundaries. The ML-ONN maps the input vector x to an output vector y = (y1,y2) through two transformation matrices and one ReLU nonlinear activation. The class of the input point (first (e.g., red) or second color (e.g., blue)) was determined by comparing theUCLBL-2023-160-03-PCT -29-magnitudes of yrand y2, or more precisely, calculating the posterior probabilities with the SoftMax function 1024 with outputs 1026, 1028.

[0164] In this optical implementation, x was encoded into light intensity, and the weight matrices (VF® & VF®) into the reflectivity of spatial light modulators (SLM). An optical fan out was used to implement Matrix Vector Multiplications (MVMs). The supplementary information of Section 11 contains a detailed description of the optical layout (FIG. 32) as well as the test and validation of the implemented optical hardware in supplementary section S4.

[0165] Firstly, the operational precision of the linear and non-linear layers in the ML-ONN are quantified. Capabilities of linear operation are evaluated for the ML-ONN by performing random MVMs on the SLMs.

[0166] FIG. 22 illustrates 1030 measured light intensities after the multiplication operation versus the theoretical values. Performance of the linear operation of the ML-ONN is shown as a scatter plot of measured outputs against ground truth of 80 random matrix-vector multiplications (MVM). In an ideal implementation, the measured output of the MVM and the ground truth fall on a line with slope of 1 , marked by the line in the figure. The inset panel within the graph depicts an error histogram illustrating the scatter around this ideal implementation line. The histogram is characterized by a root mean squared error (RMSE) of 1.2%.

[0167] Based on this comparison, a root mean square uncertainty of 1.2% was determined in our optical MVM implementation. This error rate indicates an effective calculation precision of 6.2 bits for the exemplified linear operations.

[0168] Then an optical inference experiment was performed with the complete ML-ONN depicted in FIG. 21 across two binary classification datasets, namely circle and XOR.

[0169] FIG. 23 illustrates 1050 measured light intensity versus the theoretical values. Scatter plots characterizing the RMSE of the full ML-ONN, including the nonlinear activation between MVMs, along with the error histogram (inset). RMSE rates for two classification tasks on two datasets (Circle and XOR) are characterized as 3.3% and 1.7% respectively.UCLBL-2023-160-03-PCT -30-

[0170] More specifically, the comparison shows that the root mean square uncertainty increases to 1.7 ~ 3.3% when we include a nonlinear activation through NOMA, resulting in an effective calculation precision of 5 bits.

[0171] FIG. 24 and FIG. 25 show inference results of the circle and XOR classifications respectively, where the shaded regions show the underlying decision boundaries.

[0172] FIG. 24 illustrates 1070 a circular dataset with non-linearity, and 1090 without non-linearity.

[0173] FIG. 25 illustrates 1110 an exclusive-OR (XOR) dataset with nonlinearity, and 1130 without non-linearity.

[0174] For XOR and circle datasets, the test accuracy stands at 97% and 100% respectively. In contrast, the inference accuracy without nonlinearity is only 50% (random chance) for both datasets. The poor accuracy in the absence of nonlinearity is not surprising as the network without optical nonlinearity essentially functions as a linear regression model, incapable of capturing the inherent nonlinear decision boundary of these datasets.

[0175] 10.5. Discussions

[0176] In this study, NOMA was implemented to provide an energy-efficient optical nonlinearity by integrating Si PD and LC EOM at a single pixel level. The NOMA can achieve an optical ReLU function with switching energy down to 100 fJ across more than half a million pixels. It was further demonstrated that NOMA provides energy efficiency, uniform nonlinear response, and compatibility with incoherent light through an image contrast enhancement task and the optical ReLU function was highlighted in a binary classification task for deep ML-ONNs. In contrast with the state-of-the-art analog optoelectronic neural networks, NOMA eliminates the need for shuttling signals back and forth between optical and electrical domains, which should enable neural networks having more than one hidden layer to operate in a more energy efficient manner. Further improvements to the switching energy can be achieved by decreasing EOM and PD capacitance, which is ultimately limited by the circuit Johnson noise. For instance, by reducing the pixel pitch from the current 20 pm to 3 pm (comparable to the state-of-art liquid crystal on silicon technology) and employing a smaller-capacitance PIN junction asUCLBL-2023-160-03-PCT -31-the photodiode, the capacitance of a single pixel can be as low as 100 aF, enabling optical modulation at sub-femtojoule switching energies.

[0177] In these investigations switching times are found to be on the order of milliseconds for providing energy efficient nonlinearity. At these switching times, a NOMA-based optical neural network can be used as a ‘drop-in’ energy efficient replacement for digital neural networks in applications where the inference task is frame rate limited. Such situations arise in a broad range of image recognition tasks, including applications in autonomous vehicles and facial recognition. Furthermore, a NOMA-based optical nonlinearity can be utilized in image compression as an efficient optical encoder layer that alleviates bandwidth challenges associated with large images. Still further, an energy efficient optical nonlinearity, such as the disclosed NOMA, can enable the development of optical neuromorphic computation platforms that mimic biological functions, such as visual perception.

[0178] NOMA initially addressed a fundamental challenge of nonlinearity within the all-optical neuromorphic computing framework, which generally requires high energy efficiency, scalability, and broadband compatibility. The disclosed approach may provide a catalyst to the development of large-scale deep optical neural networks for intelligent edge computing and sensing in the future.

[0179] 11. Additional Information and Results

[0180] FIG. 26A is a rendition 1210 of an image showing a fabricated NOMA device having 750 x 700 pixels. By way of example and not limitation, each pixel of the NOMA array contains a rectangular Al mirror in this example occupies approximately AA[= 240 pm2or 60% of the total pixel area. The Al mirror is connected to photodiode (e.g., Si PD) through a 4 pm2contact via. The area of the Si PD APD= 100 pm2. Beneath the Al mirror a 6pm wide additional n-doped region extends across the column of pixels and connects to a common Al electrode at the edge of the device.

[0181] FIG. 26B is a diagram 1250 of design areas for the NOMA device of FIG. 26A, showing aluminum (Al) mirror 1252 and SiPD 1254 areas.

[0182] The vertical structure of the device seen in FIG. 26B, consists of an ITO glass and a Si backplane, forming an LC cell with an approximateUCLBL-2023-160-03-PCT -32-thickness of d = 3 pm. Given the LC’s refractive index anisotropy (An = ne- n0) of about 0.1 , the retroreflected light's maximum path difference (AL) between the ordinary (o) and extraordinary (e) light is roughly 0.6 pm (AL = 2dAn), corresponding to a 1 ,8TT phase retardation for a wavelength of 670nm. This phase shift is sufficient for providing a full-range intensity modulation which typically requires a phase modulation between 0 and IT.

[0183] By way of example and not limitation, conventional planar fabrication techniques were utilized for fabricating the silicon substrate. To define the Si PD, a 6-inch p-type Si wafer (e.g., p = 10 - 20ohmcm, Silicon Valley Microelectronics, USA) was doped using phosphorus thermal diffusion under a POCh atmosphere at 840°C. A dielectric stack was established on the Si substrate in this example through the deposition of 15nm AI2O3 at 250°C by Atomic Layer Deposition (ALD) and 530nm SiO2 at 350°C by plasma- enhanced chemical vapor deposition (PECVD). Notably, the ALOs / Si interface hosts a substantial built-in charge density, which effectively passivates minor carrier recombination at the surface, reducing the surface leakage current of the Si PD. Following the formation of the dielectric stack, the wafer underwent a patterning and etching process to create contact vias for Al mirrors. This was followed by 200 nm Al sputtering and patterning. After this, an ohmic contact was established to the p-type Si using 100 nm Pt that was sputtered on the back side of the wafer. ITO glass (e.g., MSE Supplies LLC) was utilized that has a sheet resistance of around 30-60 ohm / cm2. In this example, both the silicon and ITO substrates were coated with 40 nm SiO2 utilizing oblique e-beam evaporation, which served as the alignment layer for the LC. The Si and ITO pieces were bonded together using a UV curing adhesive (e.g., OG142, Fiber Optic Center, USA). The cell gap was controlled using microspheres (e.g., Micropearl SP-203, Sekisui Chemical Co., Ltd, Japan) with a diameter of 3 pm which were placed along the periphery of the chip within the UV adhesive. The sealed cell were filled through a small fill port at the edge of the bonded chips with nematic LC (e.g., LC-VAST14, INSTEC, USA) utilizing the capillary effect to uniformly form the LC layer. Finally, the fill port was sealed using the same UV adhesive, completing the assembly process.UCLBL-2023-160-03-PCT -33-

[0184] 11.1 Working Principle of NOMA.

[0185] 11.1.1. Circuit Model

[0186] FIG. 27A through FIG. 27C illustrate operational steps 1310, 1330, 1350 of a lumped-element circuit model explaining the working principle of NOMA.

[0187] FIG. 27A illustrates 1310 this model in which the liquid crystal (LC) capacitor 1316 is connected to the cathode of the silicon photodiode 1318 (Si PD). A positive source voltage Vsis applied to the LC capacitor 1316 while the anode of Si PD is grounded, ensuring the Si PD is reversed biased. The capacitance of the photodiode is depicted as 1320. A control voltage Vc1312 is used to control the initial voltage of the LC capacitor through the capacitive coupling of a capacitor 1314 (e.g., oxide capacitor).

[0188] In this disclosure NOMA is operated periodically in the active phase and the erase phase, with FIGs 27A through 27C illustrating the phases.

[0189] In the active phase, voltages are set to Vs> Vthand Vc> 0.

[0190] FIG. 27A illustrates 1310 the case of the NOMA without illumination, in c +c cwhich the LC capacitor initially charges to Vt= — — — Vs— —Vc, which is ot otdetermined by the capacitance divider. To ensure that the voltage across the LC remains below the threshold Vth, we maintain Vc>Cvpreventing the LC molecule rotation. As a result, the NOMA remains in “OFF” state with a low cross-polarized (CP) reflectance.

[0191] FIG. 27B illustrates 1330 the case of NOMA with illumination. The figure again shows liquid crystal (LC) capacitor 1336, photodiode 1338, capacitor 1334, photodiode capacitance 1340, voltage sources 1332, 1337 and ground 1342.

[0192] Pre-charge current flows from the voltage sources into the capacitors, and with illumination, the photocurrent generated by the photodiode 1338 drains the junction capacitor, transferring charge to the LC capacitor 1336. As the LC capacitor voltage surpasses Vth, LC molecules begin to rotate, thus the NOMA is switched to “ON” state with high CP reflectance.

[0193] FIG. 27C illustrates 1350 the case of NOMA with illumination. The figure again shows liquid crystal (LC) capacitor 1356, photodiode 1358,UCLBL-2023-160-03-PCT -34-capacitor 1354, photodiode capacitance 1360, voltage sources 1352, 1357 and ground 1362. In the erase phase, voltage Vsis reduced below Vthand Vcset to 0V. A forward biased pn junction current in photodiode 1358 discharges the voltage of LC capacitor 1358 and capacitor 1354 to Vsand ground, respectively. During this process, the discharge current flows from the capacitors back to the voltage sources. As a result, NOMA is reset to “OFF” state.

[0194] 11.1.2. Capacitance Estimation

[0195] Based on device geometry, the capacitance is estimated for each component of the pixel: CLC, Coxand Cp. For the LC capacitor formed between the Al mirror and the ITO electrode, the area ALCis approximately 240|im2with a thickness dLCof 3|im. The dielectric constant ELCvaries between 3.7 and 8.6 as the orientation of LC molecule changes from parallel to perpendicular to the electric field, resulting CLCvalue ranging from 2.6 fF to 6.1 fF. The influence of the alignment layer is considered negligible because its thickness is only 3% of the LC gap.

[0196] For the oxide capacitor, which forms between the Al mirror and the underlying additional n-doped region, the area Aoxis about 100|im2in this example. The total dielectric stack thickness is characterized by an effective SiO2 thickness: deff= dsi0+£si°2dA1 0= 0.54|im. Then the estimated CeoxAl2O32 3is 6.4 fF.

[0197] Using the abrupt junction model, the capacitance of Si PD can be estimated. Given the substrate resistivity of 10 - 20Hcm, the p-type doping concentration is approximately Na= 1015cm3. The peak doping concentration of phosphorus thermal diffusion is approximately Nd= 1020cm3. Thus, the junction build-in potential Vbi= 0.9V. At zero bias, the junction depth xj is derived to be l.l|im. The junction area comprises the top-view doping area of 100|im2, and a periphery area calculated as the product of the doping area’s perimeter and junction depth. Thus, the total junction area is approximately 140|im2, and the estimated junction capacitance at zero bias is 12 fF. The disclosure summarizes these capacitances in Table 2.UCLBL-2023-160-03-PCT -35-

[0198] 11.2. S2-Optical Nonlinearity Experiments.

[0199] 11.2.1. Optical Layout

[0200] A suite of experiments were performed on NOMA aimed at demonstrating its nonlinear properties using, by way of example and not limitation, the optical setup described below.

[0201] FIG. 28A illustrates 1410 an optical setup containing multiple beam paths (e.g., two beam paths), exemplified as pump path 1412 and probe path 1416, that in this example utilize colored Cree LEDs (pump= 630 nm and ^probe=680 nm) as their light source, and which can pass through various reflectors 1416 and various lenses 1417. Each LED of these illumination paths is driven by a laser diode driver (e.g., Thorlabs, LDC205C) which can be modulated with an analog input.

[0202] A beam splitter 1420 was utilized for combining the pump and probe pulses. Using the transmitted beam path through this beam splitter, the incident probe intensity was monitored on NOMA 1424 using a photodiode (e.g., Thorlabs, SM05PD1A). The pump pulse was focused onto the back focal plane of a 4X microscope objective 1422 (e.g., AmScope Plan 4 / 0.10) to create a uniform illumination across the field of view of NOMA 1424.

[0203] The probe beam path enters a PBS 1419, with one split of the beam directed to a reflective Spatial Light Modulator 1418 (SLM) (e.g., SDE1024, Cambridge Correlators) in an intensity modulation configuration. A uniform bright image was displayed on the SLM and imaged onto NOMA 1424 using a lens and the same 4X microscope objective 1422. The light reflected by NOMA is collimated by the 4X objective and reflected by a polarized beam splitter (PBS) 1421. The CP reflected light can be either imaged, through reflectors and / or lenses, onto a CMOS camera 1426 (e.g., Allied Vision, 1800) or focused onto a photodiode 1428 (e.g., Thorlabs, SM05PD1A). The pump beam is blocked by a long-pass filter 1430.

[0204] 11.2.2. Pump-probe Measurements

[0205] The NOMA is periodically driven in its active and erase phases by applying a square wave of Vsand Vc. The pump light is synchronized with the rising edge of the voltages and the probe light is time-delayed relative to the pump light. The CP reflected light intensity can be measured, such as afterUCLBL-2023-160-03-PCT -36-filtering by filter 1431 , by either the CMOS camera or a photodiode 1432. The time delay was controlled between the arrival time of the pump and probe pulses as well as their duration (2 ms) and intensity using a data acquisition circuit (e.g., data acquisition card, such as National Instruments, NI-9264). In this example the same data acquisition circuit was utilized to generate the voltages necessary for NOMA operation (Vcand l^) as well as a camera trigger pulse synchronized to the probe arrival time. The exposure time of the camera was set to match the probe pulse duration. In at least one embodiment, for a given time delay, NOMA was operated at 5 Hz for 1 second, which constitutes 4 “ON”- “OFF” cycles. The results of the pumpprobe experiments for time delays that span the entire “ON” cycle are shown in FIG. 2C previously described in Section 6.

[0206] FIG. 28B illustrates a longer time trace 1450 that contains four periods of active and erase phases.

[0207] 11.2.3. Tunable Optical ReLU with Single Pulse

[0208] For single pulse nonlinearity experiments that show the all-optical ReLU response (such as seen in FIG. 3A described in Section 7) a similar optical setup was used as the one outlined for the pump-probe experiments, but was only focused on the probe beam path. In this test, 50 ms was used as the probe pulse duration and CP reflected light energy versus incident energy was monitored using the photodiodes.

[0209] FIG. 29A and FIG. 29B illustrate graphs 1470, 1490 of switch energy of the optical ReLU. In FIG. 29A, the reflected versus incident energy (inputoutput relationship) shows a clear dependence on the control voltage (7C) at a source voltage (1 ) of 4V in this example. It was observed that at low Vc, the input-output relationship exhibits a near-linear behavior. An increase in Vcleads to a notable suppression of output energy, particularly at low input energy levels. To quantitatively describe this optical nonlinearity, an Exponential Linear Unit (ELU) function was employed to fit the experimental data. The ELU function is expressed as:><

[0210] In the above, x represents the incident energy, R denotes the “ON”UCLBL-2023-160-03-PCT -37-state reflectance, and Eswdenotes the switching energy. The ELU function offers a better depiction of the gradual switching process of the NOMA cell compared to the ReLU function, which has a discontinuous first derivative at the threshold.

[0211] In FIG. 29B, switching energy Eswas a function of Vc, was extracted based on the ELU fit, which showed a linear dependence: Esw —+ 31 (fj). The slope of the linear line is in notable agreement with that obtained in pump-probe experiments (64 fJ / V, such as seen in the inset of FIG. 16). These results demonstrate the tunability of the implemented NOMA which can be useful in applications where incident light intensity varies, including all- optical neural networks and image processing. In these applications, the control voltage of the optical nonlinearity can be dynamically tuned to run computations under varying illumination conditions without the need to substantially modify the optical system.

[0212] 11.2.4. Homogeneity of Optical ReLU

[0213] Using the same approach outlined in the preceding section, the response of NOMA was evaluated at each individual pixel to quantify the pixel-to-pixel variations of the optical nonlinearity.

[0214] FIG. 30A illustrates a wide-field image 1510 of NOMA response. For this purpose, instead of using a photodiode to integrate the total reflected energy, the CMOS camera was utilized to capture this image. The wide-field image contains 10,201 NOMA pixels. The wide-field image was segmented into grids, in this representation, each grid square of which contains a single NOMA pixel and monitored the input-output relationship of each grid separately.

[0215] FIG.30B illustrates output energy with respect to incident energy showing optical non-linear response 1530. For a given Vcand l^, the pixel-to- pixel variations were captured using the switching energy as determined by the ELU fit. The distribution of the switching energy is shown in the histogram of FIG. 3B as described in the main text.

[0216] FIG. 30C illustrates 1550 switching energy across the 10,201 NOMA pixels, which was spatially uniform albeit with several defects which can be improved upon in future iterations of the fabrication process.UCLBL-2023-160-03-PCT -38-

[0217] 11.2.5. Long-term Dynamic Stability

[0218] The long-term dynamic stability of the nonlinear layer is a more crucial factor, compared to static noise, for achieving high accuracy in ONNs, as dynamic noise - such as phase jitter in SLMs, power fluctuations in light sources, and drift in optical alignment - poses more substantial challenges. To assess the long-term dynamic stability of the NOMA, an endurance test was conducted by periodically alternating the device between active and erase phases. During each active phase, an optical pulse with a duration of 50 ms was illuminated onto four regions of NOMA. Each region had 10 NOMA pixels, representing a neuron. Every 20 cycles, a camera (e.g., Charge-Couple Device (CCD) camera) captured the reflected image to monitor the CP reflected pulse energy, representing the neuron outputs.

[0219] FIG. 31 A illustrates that the outputs 1612 of all neurons remained consistent over the tested 4000 switching cycles. The inset histogram 1614 demonstrates that the dynamic deviation was below 0.33%. Furthermore, the ReLU-like optical nonlinear response of the four neurons was measured before and after the endurance test.

[0220] FIG. 31 B illustrates performance 1630, 1650, 1670, 1690 of each of the four NOMA neurons, wherein the nonlinear performance is seen to be almost identical, with a deviation of less than 1%, indicating stable performance over time.

[0221] 11.3. S3-Optical Neural Network Demonstration

[0222] 11.3.1. Setup of the Optical Neural Network

[0223] A Multilayer All-Optical Neural Network (ML-AONN) was designed that implements a two-layer fully connected neural network, specifically the mathematical operation y =

[0224] FIG. 32 illustrates 1710 the optical layout of the above AONN, which is exemplified as having two Matrix-Vector Multiplication (MVM) operations and one nonlinear activation function. The MVMs were implemented with two amplitude-only liquid crystal SLMs while the nonlinear activation was achieved using NOMA. The illumination source 1711 is described below in section 11.3.1.1.

[0225] The first MVM computes the input for the hidden layer neurons asUCLBL-2023-160-03-PCT -39-follows:represents the two columns of n1). Vectorandd separately onto two rectangle arrays displayed on the SLM1 1712 (e.g., SDE1024, Cambridge Correlators, UK). Lenses L1 1720 and L2 1722, both exemplified with focal length of 20 cm, were used to collimate the light reflected from the two rectangle array patterns of SLM1 1722 through PBS1 1714 and to mirrors 1716, 1718, respectively. The two patterns, one reflected by mirror M3 1723, were combined by a Beam Splitter 1724 (BS1) and projected, through BS2 1726, PBS2 1728, through a 4X microscope objective 1730 onto NOMA 1732. In addition, another path from BS2 1726 is through lens 1748 to camera 1750 for alignment purposes, whereby the camera monitors the alignment between the SLM and the NOMA pixels.

[0226] The test ensured that the image on NOMA was an equal sum of intensities from each of the patterns(i = 1,2), thus optically implementing the above equation.

[0227] The nonlinear operation a = f z) was implemented by leveraging the ReLU-like response of NOMA, as depicted in FIG. 3A in Section 7. Following the nonlinear activation, optical fan-out from PBS2 1728 was employed to generate two copies of a using a multi-lens array (MLA). These copies were then imaged through PBS2 1736 onto SLM2 1738 (e.g., SXRD-211, SONY, Japan). SLM2 1738 displayed two rectangle arrays with each array encoding the reflectance proportional to a row ofThus, the reflected light represents the element-wise multiplication between each row of W and the output of the hidden layer, resulting in° a. The optical patterns ofand s2were collimated and imaged (exemplified with lens L4 1740, mirror M4 1742 and lens L5 1744, onto a low noise camera 1746 (e.g., a low noise CCD camera, such as PIXIS 400, Princeton Instrument, USA). The two lenses (L4 and L5) are exemplifies as each having a focal length of 10 cm. The image was captured and the values ofUCLBL-2023-160-03-PCT -40-and s2were evaluated (processed) 1747 by averaging the intensity over the corresponding light spots. The final output scores, y and y2, were computed as the summation ofand s2, respectively. By way of example and not limitation, in these experiments, the light pulse has a duration of 62.5 ms at a repetition rate of 10 Hz. Camera 1746 had an exposure time of 1.1s, integrating 10 pules per inference.

[0228] Currently the weighting in the first layer and the summation in the second layer are performed using a digital computer. With improved engineering, both operations could be implemented optically.

[0229] 11.3.1.1. Weighting Operation in the First Layer

[0230] This operation of illumination 1711 in FIG. 32 can be implemented optically, by way of example and not limitation, using two LEDs, where the intensity of each LED represents one of the elements of the input vector x = ^x1,x2). Each LED illuminates a separate region of SLM1 1712, which displays two rectangular arrays. The reflectance of these arrays encodes the columns of the first layer weight matrix:The reflected light from these arrays thus results in an intensity distribution proportional to the weighted outputs, W^xt(i = 1,2).

[0231] 11.3.1.2. Summation Operation in the Second Layer

[0232] This operation can be implemented optically with a cylindrical lens that focuses the vertically aligned rectangular patterns of stinto a line, whose intensity corresponds to the summation of sf.”

[0233] Although some operations in our ML-ONN are currently carried out electronically, our setup successfully demonstrates key optical operations, including optical summation (layer 1), optical weighting (layers 1 and 2), and optical fan-out (layer 2). Most importantly, with the NOMA serving as the nonlinear layer, there is no need to convert optical signals into the digital domain for nonlinear operations and then back into the optical domain. This capability enables true cascaded optical signal processing, paving the way for scalable deep optical neural networks.

[0234] 11.3.2. Linear Layer Calibration

[0235] Due to potential deviations from ideal behavior caused by nonuniformUCLBL-2023-160-03-PCT -41-illumination and imaging aberrations, we first calibrated the two linear operations. For the first linear layer, we applied an element wise correction matrix C1to the true weight matrix IV®, resulting in a calibrated weight matrix W ' = C1o IV®. The appropriate values of the correction matrix were found by replacing the NOMA with a CCD camera to directly image the output of the first linear layer. For the second linear operation, a similar approach was employed using calibration matrix C2resulting in W ' = C2° IV®. To test the precision of the linear operations, we conducted an MVM experiment. Weused these values to calculate to form our ground truth.Experimentally, we ensured that NOMA was operating in a linear regime by setting Vc= OV, Vs= 3.6V and ran MVMs with the calibrated weight matrices to get experimental outputs. The relation between experimental outputs and the ground truth for the linear operations is seen in FIG. 22. The error rate of the two linear operations after calibration defined by a root mean squared error (RMSE) is 1.2%, which corresponds to a noise equivalent bit of 6.2 bit for the linear operations (NEB = - log2RMSE).

[0236] 11.3.3. Nonlinear Layer Calibration

[0237] Next, the nonlinear response of NOMA was calibrated. For these experiments, NOMA was operated at Vs= 3.6V and Vc= 5.5V, with IV® and wasscanned from 0 to 1. Thus, the input of hidden neurons varied from 0 to 2. The output of hidden neurons was measured with the CCD camera.

[0238] FIG. 33A illustrates 1770 that the output of the four neurons behaves almost identically, indicating a uniform response of NOMA. To fit the nonlinear response, a modified ELU function was utilized as shown below in Eq. (S3).

[0239] FIG. 33B illustrates 1790 a comparison between the ELU function of Eq. (S1), compared with the modified ELU function below, which adds a quadratic term in both the linear and the exponential portion of the ELU, thereby resulting in an improved fitting result.UCLBL-2023-160-03-PCT -42- >

[0240] 11.3.4. ML-ONN Training and Weight Fine-Tuning

[0241] The training of ML-ONN consists of two parts: (1 ) digital training and (2) weight fine tuning with the hardware feedback.

[0242] First step was digitally training a neural network with the same structure as the ML-ONN (two input neurons, four hidden neurons, and two output neurons). The nonlinear activation function was Eq. (S3) with parameters determined by the curve fitting shown in FIG. 33B. During the training, the weight matrix IVT) and U2)was constrained as non-negative. Cross-entropy loss was used and an Adam optimizer to update the weights. Table 3 summarizes the hyperparameters used to train on the two datasets (XOR and circle). In post-training, robustness of the weights at each epoch was assessed by evaluating inference accuracy across various computational precisions. Selected of weights demonstrating a high inference accuracy, particularly those performing well at a 4-bit precision, for implementation in the ML-ONN.

[0243] After completing digital training, the trained weights were applied for both layers obtained by the digital model and measured the experimental outputs of the second layer for the training data points, denotedand expS2

[0244] FIG. 34A through FIG. 34D illustrate how weight fine tuning improves ML-ONN inference accuracy.

[0245] FIG. 34A illustrates 1810 the optical inference results before fine tuning, as having an accuracy of 88%.

[0246] FIG. 34B illustrates 1820, 1830 how there was still a linear relationship between s1 and s2, despite that the experimental values deviated from the theoretical valuescalculated by the digital model.

[0247] To address this mismatch, a linear fitting was performed between the experimental and theoretical values:Then the weight matrix was modified of the second layer aswhere C is the fitted coefficient matrix.UCLBL-2023-160-03-PCT -43-

[0248] FIG. 34C illustrates 1840 the optical inference results after fine tuning, as having an accuracy of 97%.

[0249] FIG. 34D illustrates 1850, 1860, that after weight fine-tuning, the measured outputs showed improved alignment between the experimental and theoretical values.

[0250] The disclosed fine-tuning approach is similar to a layer-by-layer fine- tuning process using experimentally collected data, which has been successfully implemented in previous optical neural networks training processes. This method effectively compensates for static non-uniform ities in the optical setup and converges rapidly, eliminating the need for exhaustive parameter searches. Additionally, the disclosed digital model is finely calibrated to match the physical response of the described NOMA, by ensuring that (i) without nonlinearity, the two-layer neural network performs matrix-vector multiplications with high precision, and (ii) the nonlinear behavior of the hidden neurons in our digital model closely mimic the actual behavior of the device.

[0251] 12. General Scope of Embodiments

[0252] Embodiments of the present technology may be described herein with reference to flowchart illustrations of methods and systems according to embodiments of the technology, and / or procedures, algorithms, steps, operations, formulae, or other computational depictions, which may also be implemented as computer program products. In this regard, each block or step of a flowchart, and combinations of blocks (and / or steps) in a flowchart, as well as any procedure, algorithm, step, operation, formula, or computational depiction can be implemented by various means, such as hardware, firmware, and / or software including one or more computer program instructions embodied in computer-readable program code. As will be appreciated, any such computer program instructions may be executed by one or more computer processors, including without limitation a general purpose computer or special purpose computer, or other programmable processing apparatus to produce a machine, such that the computer program instructions which execute on the computer processor(s) or other programmable processing apparatus create means for implementing theUCLBL-2023-160-03-PCT -44-function(s) specified.

[0253] Accordingly, blocks of the flowcharts, and procedures, algorithms, steps, operations, formulae, or computational depictions described herein support combinations of means for performing the specified function(s), combinations of steps for performing the specified function(s), and computer program instructions, such as embodied in computer-readable program code logic means, for performing the specified function(s). It will also be understood that each block of the flowchart illustrations, as well as any procedures, algorithms, steps, operations, formulae, or computational depictions and combinations thereof described herein, can be implemented by special purpose hardware-based computer systems which perform the specified function(s) or step(s), or combinations of special purpose hardware and computer-readable program code.

[0254] Furthermore, these computer program instructions, such as embodied in computer-readable program code, may also be stored in one or more computer-readable memory or memory devices that can direct a computer processor or other programmable processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory or memory devices produce an article of manufacture including instruction means which implement the function specified in the block(s) of the flowchart(s). The computer program instructions may also be executed by a computer processor or other programmable processing apparatus to cause a series of operational steps to be performed on the computer processor or other programmable processing apparatus to produce a computer- implemented process such that the instructions which execute on the computer processor or other programmable processing apparatus provide steps for implementing the functions specified in the block(s) of the flowchart(s), procedure (s) algorithm(s), step(s), operation(s), formula(e), or computational depiction(s).

[0255] It will further be appreciated that the terms "programming" or "program executable" as used herein refer to one or more instructions that can be executed by one or more computer processors to perform one or more functions as described herein. The instructions can be embodied in software,UCLBL-2023-160-03-PCT -45-in firmware, or in a combination of software and firmware. The instructions can be stored local to the device in non-transitory media, or can be stored remotely such as on a server, or all or a portion of the instructions can be stored locally and remotely. Instructions stored remotely can be downloaded (pushed) to the device by user initiation, or automatically based on one or more factors.

[0256] It will further be appreciated that as used herein, the terms processor, hardware processor, computer processor, central processing unit (CPU), and computer are used synonymously to denote a device capable of executing the instructions and communicating with input / output interfaces and / or peripheral devices, and that the terms processor, hardware processor, computer processor, CPU, and computer are intended to encompass single or multiple devices, single core and multicore devices, and variations thereof.

[0257] From the description herein, it will be appreciated that the present disclosure encompasses multiple implementations of the technology which include, but are not limited to, the following:

[0258]

[0259] A nonlinear optical microdevice array (NOMA) apparatus, comprising:(a) a lower substrate, having wells forming a p-n or p-i-n junction; (b) a dielectric layer over the lower substrate and its wells; (c) an array of conductive mirrors disposed over the dielectric layer; (d) wherein between each conductive mirror are wells configured as bars which extend across a row of the conductive mirrors and make electrical contact with each conductive mirror, wherein each conductive mirror area is a silicon pixel; (e) wherein each of the wells establishes a p-n or p-i-n junction with its underlying substrate, allowing the combination to function as a sensitive photodetector; (f) a conductively coated transparent material as an n-type cover substrate; and (g) an electro-optical modulator (EOM) layer sandwiched between the conductively coated transparent material and the conductive mirror.

[0260] A nonlinear optical microdevice array (NOMA) apparatus, comprising:(a) a lower substrate, having wells forming a p-n or p-i-n junction; (b) a dielectric layer over the lower substrate and its wells; (c) an array ofUCLBL-2023-160-03-PCT -46-conductive mirrors disposed over the dielectric layer; (d) wherein between each conductive mirror are wells configured as bars which extend across a row of the conductive mirrors and make electrical contact with each conductive mirror, wherein each conductive mirror area is referred to as a silicon pixel; (e) wherein each the local well establishes a p-n or p-i-n junction with its underlying substrate, allowing the combination to function as a sensitive photodetector; (f) a conductively coated transparent material as an n-type cover substrate; and (g) an electro-optical modulator EOM layer sandwiched between the conductively coated transparent material and the conductive mirror.

[0261] The apparatus of any preceding implementation, wherein the EOM layer comprises a liquid crystal (LC) material.

[0262] The apparatus of any preceding implementation, wherein the LC material comprises a nematic liquid crystal material, or a ferroelectric liquid crystal (FE LC) material.

[0263] The apparatus of any preceding implementation, wherein the EOM layer comprises a micromirror array.

[0264] The apparatus of any preceding implementation, wherein the lower substrate is configured with p-i-n junctions, the lower substrate comprising a bottom layer of N+ Si over which is intrinsic Si (i-Si), and contains p-type wells.

[0265] The apparatus of any preceding implementation, wherein a first voltage is exhibited between the well bars of p-wells, and the n-type cover substrate.

[0266] The apparatus of any preceding implementation, wherein each of the conductive mirror reflects incoming light, and contributes to the formation of a EOM capacitance (CMM) in conjunction with the n-type cover substrate.

[0267] The apparatus of any preceding implementation, wherein the lower substrate is configured with p-n junctions, the lower substrate comprising a p- type substrate with n-type wells.

[0268] The apparatus of any preceding implementation, wherein the lower substrate is further configured with n-type wells beneath each conductive mirror.

[0269] The apparatus of any preceding implementation, wherein a first voltageUCLBL-2023-160-03-PCT -47-is exhibited between the well bars of n-wells, and the n-type cover substrate, and wherein a second voltage is applied to each n-type well beneath its associated conductive mirror.

[0270] The apparatus of any preceding implementation, wherein each of the conductive mirror reflects incoming light, and also contributes to the formation of an EOM capacitance (CMM) in conjunction with the n-type cover substrate.

[0271] The apparatus of any preceding implementation, wherein the apparatus provides an engineered nonlinearity configured for operating with an incoherent light input.

[0272] The apparatus of any preceding implementation, wherein the apparatus operates in either an active phase or an erase phase, with the active phase entered into when a positive bias is applied to the upper ITO electrode, causing the junction to become reverse-biased, while the erase phase arises when there is insufficient reverse-bias and accumulated carriers are discharged.

[0273] The apparatus of any preceding implementation, wherein the mirror comprises an Al or Pt material.

[0274] The apparatus of any preceding implementation, wherein the dielectric layer comprises a stack of dielectric materials.

[0275] The apparatus of any preceding implementation, wherein the dielectric layer comprises SiO2 and / or AI2O3 layers.

[0276] The apparatus of any preceding implementation, wherein an underside of the lower substrate is coated with an ohmic material, creating an ohmic contact with the lower substrate.

[0277] The apparatus of any preceding implementation, wherein the ohmic material comprises Al or Pt.

[0278] The apparatus of any preceding implementation, wherein each silicon pixel is on the order of approximately 5 x 5 pm to 20 x 20 pm.

[0279] The apparatus of any preceding implementation, wherein each silicon pixel absorbs a fraction of incoming light, generating a charge field across the EOM which allows achieving optical self-modulation and optical-electrical- optical modulation, to provide control over phase, polarization, and / or intensity in generating optical nonlinearities.UCLBL-2023-160-03-PCT -48-

[0280] The apparatus of any preceding implementation, wherein the electro- optical modulator EOM layer comprises a liquid crystal (LC) material.

[0281] The apparatus of any preceding implementation, wherein the LC material comprises a nematic liquid crystal material, or a ferroelectric liquid crystal (FE LC) material.

[0282] The apparatus of any preceding implementation, wherein the electro- optical modulator EOM layer comprises a micromirror array.

[0283] The apparatus of any preceding implementation, wherein the lower substrate is configured with p-i-n junctions, the lower substrate comprising a bottom layer of N+ Si over which is intrinsic Si (i-Si), contains p-type wells.

[0284] The apparatus of any preceding implementation, wherein a voltage Vi is exhibited between the well bars of p-wells, and the n-type cover substrate.

[0285] The apparatus of any preceding implementation, wherein each the conductive mirror reflects incoming light, and also contributes to the formation of a EOM capacitance (CMM) in conjunction with the n-type cover substrate.

[0286] The apparatus of any preceding implementation, wherein the lower substrate is configured with p-n junctions, the lower substrate comprising a p- type substrate with n-type wells.

[0287] The apparatus of any preceding implementation, wherein the lower substrate is also configured with n-type wells beneath each conductive mirror,

[0288] The apparatus of any preceding implementation, wherein a voltage Vi is exhibited between the well bars of n-wells, and the n-type cover substrate, and wherein a voltage V2 is applied to each n-type well beneath its associated conductive mirror;

[0289] The apparatus of any preceding implementation, wherein each conductive mirror reflects incoming light, and also contributes to the formation of an EOM capacitance (CMM) in conjunction with the n-type cover substrate.

[0290] The apparatus of any preceding implementation, wherein the apparatus provides an engineered nonlinearity that can operate with an incoherent light input.

[0291] The apparatus of any preceding implementation, wherein the apparatus operates in either an active phase or an erase phase, with the active phase entered into when a positive bias is applied to the upper ITOUCLBL-2023-160-03-PCT -49-electrode, causing the junction to become reverse-biased, while the erase phase arises when there is insufficient reverse-bias and accumulated carriers are discharged.

[0292] The apparatus of any preceding implementation, wherein the mirror comprises an Al or Pt material.

[0293] The apparatus of any preceding implementation, wherein the dielectric layer comprises a stack of dielectric materials.

[0294] The apparatus of any preceding implementation, wherein the dielectric layer comprises SiO2 and / or AI2O3 layers.

[0295] The apparatus of any preceding implementation, wherein an underside of the lower substrate is coated with an ohmic material, creating an ohmic contact with the lower substrate.

[0296] The apparatus of any preceding implementation, wherein ohmic material comprises Al or Pt.

[0297] The apparatus of any preceding implementation, wherein each silicon pixel is on the order of approximately 5 x 5 pm to 20 x 20 pm.

[0298] The apparatus of any preceding implementation, wherein each silicon pixel absorbs a fraction of the incoming light, generating a charge field across the EOM which allows achieving optical self-modulation and optical-electrical- optical modulation, to provide control over phase, polarization, and / or intensity in generation of optical nonlinearities.

[0299] As used herein, the term "implementation" is intended to include, without limitation, embodiments, examples, or other forms of practicing the technology described herein.

[0300] As used herein, the singular terms "a," "an," and "the" may include plural referents unless the context clearly dictates otherwise. Reference to an object in the singular is not intended to mean "one and only one" unless explicitly so stated, but rather "one or more."

[0301] Phrasing constructs, such as “A, B and / or C”, within the present disclosure describe where either A, B, or C can be present, or any combination of items A, B and C. Phrasing constructs indicating, such as “at least one of” followed by listing a group of elements, indicates that at least one of these groups of elements is present, which includes any possibleUCLBL-2023-160-03-PCT -50-combination of the listed elements as applicable.

[0302] References in this disclosure referring to “an embodiment”, “at least one embodiment” or similar embodiment wording indicates that a particular feature, structure, or characteristic described in connection with a described embodiment is included in at least one embodiment of the present disclosure. Thus, these various embodiment phrases are not necessarily all referring to the same embodiment, or to a specific embodiment which differs from all the other embodiments being described. The embodiment phrasing should be construed to mean that the particular features, structures, or characteristics of a given embodiment may be combined in any suitable manner in one or more embodiments of the disclosed apparatus, system, or method.

[0303] As used herein, the term "set" refers to a collection of one or more objects. Thus, for example, a set of objects can include a single object or multiple objects.

[0304] Relational terms such as first and second, top and bottom, upper and lower, left and right, and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.

[0305] The terms "comprises," "comprising," "has", "having," "includes", "including," "contains", "containing" or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, apparatus, or system, that comprises, has, includes, or contains a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, apparatus, or system. An element proceeded by "comprises . . . a", "has . . . a", "includes... a", "contains . . . a" does not, without more constraints, preclude the existence of additional identical elements in the process, method, article, apparatus, or system, that comprises, has, includes, contains the element.

[0306] As used herein, the terms "approximately", "approximate", "substantially", "essentially", and "about", or any other version thereof, are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which theUCLBL-2023-160-03-PCT -51-event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. When used in conjunction with a numerical value, the terms can refer to a range of variation of less than or equal to ± 10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1 %, less than or equal to ±0.5%, less than or equal to ±0.1 %, or less than or equal to ±0.05%. For example, "substantially" aligned can refer to a range of angular variation of less than or equal to ±10°, such as less than or equal to ±5°, less than or equal to ±4°, less than or equal to ±3°, less than or equal to ±2°, less than or equal to ±1 °, less than or equal to ±0.5°, less than or equal to ±0.1°, or less than or equal to ±0.05°.

[0307] Additionally, amounts, ratios, and other numerical values may sometimes be presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified. For example, a ratio in the range of about 1 to about 200 should be understood to include the explicitly recited limits of about 1 and about 200, but also to include individual ratios such as about 2, about 3, and about 4, and sub-ranges such as about 10 to about 50, about 20 to about 100, and so forth.

[0308] The term "coupled" as used herein is defined as connected, although not necessarily directly and not necessarily mechanically. A device or structure that is "configured" in a certain way is configured in at least that way, but may also be configured in ways that are not listed.

[0309] Benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature or element of the technology described herein or any or all the claims.

[0310] In addition, in the foregoing disclosure various features may be grouped together in various embodiments for the purpose of streamlining theUCLBL-2023-160-03-PCT -52-disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments require more features than are expressly recited in each claim. Inventive subject matter can lie in less than all features of a single disclosed embodiment.

[0311] The abstract of the disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.

[0312] It will be appreciated that the practice of some jurisdictions may require deletion of one or more portions of the disclosure after the application is filed. Accordingly, the reader should consult the application as filed for the original content of the disclosure. Any deletion of content of the disclosure should not be construed as a disclaimer, forfeiture, or dedication to the public of any subject matter of the application as originally filed.

[0313] The following claims are hereby incorporated into the disclosure, with each claim standing on its own as a separately claimed subject matter.

[0314] Although the description herein contains many details, these should not be construed as limiting the scope of the disclosure, but as merely providing illustrations of some of the presently preferred embodiments. Therefore, it will be appreciated that the scope of the disclosure fully encompasses other embodiments which may become obvious to those skilled in the art.

[0315] All structural and functional equivalents to the elements of the disclosed embodiments that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the present claims. Furthermore, no element, component, or method step in the present disclosure is intended to be dedicated to the public regardless of whether the element, component, or method step is explicitly recited in the claims. No claim element herein is to be construed as a "means plus function" element unless the element is expressly recited using the phrase "means for". No claim element herein is to be construed as a "step plus function" element unless the element is expressly recited using the phrase "step for".UCLBL-2023-160-03-PCT -53-Table 1Estimated Capacitance Values within each Pixel‘effective thicknessUCLBL-2023-160-03-PCT -54-Table 2Estimated Capacitance Values within NOMA‘effective thickness“junction depth at zero reverse biasUCLBL-2023-160-03-PCT -55-Table 3Hyper Parameters Used in Digital TrainingUCLBL-2023-160-03-PCT -56-

Claims

CLAIMSWhat is claimed is:

1. A nonlinear optical microdevice array (NOMA) apparatus, comprising: (a) a lower substrate, having wells forming a p-n or p-i-n junction;(b) a dielectric layer over the lower substrate and its wells;(c) an array of conductive mirrors disposed over the dielectric layer;(d) wherein between each conductive mirror are wells configured as bars which extend across a row of the conductive mirrors and make electrical contact with each conductive mirror, wherein each conductive mirror area is a silicon pixel;(e) wherein each of the wells establishes a p-n or p-i-n junction with its underlying substrate, allowing the combination to function as a sensitive photodetector;(f) a conductively coated transparent material as an n-type cover substrate; and(g) an electro-optical modulator (EOM) layer sandwiched between the conductively coated transparent material and the conductive mirror.

2. The apparatus of claim 1 , wherein the EOM layer comprises a liquid crystal (LC) material.

3. The apparatus of claim 2, wherein the LC material comprises a nematic liquid crystal material, or a ferroelectric liquid crystal (FE LC) material.

4. The apparatus of claim 1 , wherein the EOM layer comprises a micromirror array.

5. The apparatus of claim 1 , wherein the lower substrate is configured with p-i-n junctions, the lower substrate comprising a bottom layer of N+ Si over which is intrinsic Si (i-Si), and contains p-type wells.UCLBL-2023-160-03-PCT -57-6. The apparatus of claim 5, wherein a first voltage is exhibited between the well bars of p-wells, and the n-type cover substrate.

7. The apparatus of claim 5, wherein each of the conductive mirror reflects incoming light, and contributes to the formation of a EOM capacitance (CMM) in conjunction with the n-type cover substrate.

8. The apparatus of claim 1 , wherein the lower substrate is configured with p-n junctions, the lower substrate comprising a p-type substrate with n-type wells.

9. The apparatus of claim 8, wherein the lower substrate is further configured with n-type wells beneath each conductive mirror.

10. The apparatus of claim 9, wherein a first voltage is exhibited between the well bars of n-wells, and the n-type cover substrate, and wherein a second voltage is applied to each n-type well beneath its associated conductive mirror.

11. The apparatus of claim 9, wherein each of the conductive mirror reflects incoming light, and also contributes to the formation of an EOM capacitance (CMM) in conjunction with the n-type cover substrate.

12. The apparatus of claim 1, wherein the apparatus provides an engineered nonlinearity configured for operating with an incoherent light input.

13. The apparatus of claim 11 , wherein the apparatus operates in either an active phase or an erase phase, with the active phase entered into when a positive bias is applied to the upper ITO electrode, causing the junction to become reverse-biased, while the erase phase arises when there is insufficient reverse-bias and accumulated carriers are discharged.

14. The apparatus of claim 1, wherein the mirror comprises an Al or Pt material.UCLBL-2023-160-03-PCT -58-15. The apparatus of claim 1 , wherein the dielectric layer comprises a stack of dielectric materials.

16. The apparatus of claim 1, wherein the dielectric layer comprises SiO2 and / or AI2O3 layers.

17. The apparatus of claim 1 , wherein an underside of the lower substrate is coated with an ohmic material, creating an ohmic contact with the lower substrate.

18. The apparatus of claim 17, wherein the ohmic material comprises Al or Pt.

19. The apparatus of claim 1 , wherein each silicon pixel is on the order of approximately 5 x 5 pm to 20 x 20 pm.

20. The apparatus of claim 1 , wherein each silicon pixel absorbs a fraction of incoming light, generating a charge field across the EOM which allows achieving optical self-modulation and optical-electrical-optical modulation, to provide control over phase, polarization, and / or intensity in generating optical nonlinearities.UCLBL-2023-160-03-PCT -59-

Images