Reverse designed optical modulator

Abstract

The optical modulator includes a modulation region, an input port, an output port, and a modulation actuator. The modulation region includes a non-uniform arrangement of two or more different materials having different refractive indices to configure the modulation region to manipulate one or more optical properties of the optical carrier in response to the modulation bias. An input port is optically coupled to the modulation region to inject an optical carrier into the modulation region. A modulation actuator is disposed near the modulation region and adapted to apply a modulation bias to the modulation region to generate a modulated wave. The modulation bias adjusts at least one of the different refractive indices of the non-uniform arrangement to provide variable control of one or more optical properties of the optical carrier. The output port is optically coupled to the modulation region to receive the modulated wave.

Description

[0001] Cross - Reference to Related Applications

[0002] This application claims the benefit of U.S. Patent Application No. 17 / 970,141, filed Oct. 20, 2022, the content of which is incorporated herein by reference. Technical Field

[0003] The present disclosure generally relates to photonic devices, and more particularly, to optical modulators. Background Art

[0004] An optical modulator is an active component that allows a user to modulate an optical signal via an applied bias. This bias is typically achieved by changing a voltage that electro - optically, thermo - optically, or mechanically - optically tunes the refractive index of a material in a certain region of an integrated device. When the bias is modulated at high speeds (e.g., gigahertz rates), information and data can be encoded and sent to a remote receiver.

[0005] Typical modulators are designed using components that are well understood by humans (e.g., a combination of waveguide - based phase shifters and directional couplers or modulating ring resonators). However, these conventional components have limitations: they have a large footprint and a limited number of “knobs” by which their performance can be improved and adjusted. Brief Description of the Drawings

[0006] Non - limiting and non - exhaustive embodiments of the present invention are described with reference to the following drawings, in which, unless otherwise indicated, the same reference numerals refer to the same parts in each view. Not all instances of an element are necessarily labeled so as not to clutter the drawings in appropriate cases. The drawings are not necessarily to scale, but rather emphasis is placed on illustrating the described principles.

[0007] Figure 1A An optically - reverse - designed modulator according to an embodiment of the present disclosure is shown.

[0008] Figure 1B An optically - reverse - designed modulator according to an embodiment of the present disclosure is shown Figure 1A in a top - view of a portion of the optically - reverse - designed modulator.

[0009] Figures 1C to 1E An optically - reverse - designed modulator according to an embodiment of the present disclosure is shown Figure 1A in a cross - sectional view of a portion of the optically - reverse - designed modulator.

[0010] Figure 1F A more detailed view of an exemplary modulation region of an optically - reverse - designed modulator according to an embodiment of the present disclosure for Figure 1A is shown.

[0011] Figure 2A Shows a loss function for inverse design of an optical modulator according to an embodiment of the present disclosure.

[0012] Figure 2B Shows an example optical modulator response curve for an inverse-designed optical modulator according to an embodiment of the present disclosure.

[0013] Figure 3 Shows a diagram illustrating an iterative process according to an embodiment of the present disclosure, by which a modulation region is optimized to reduce a loss metric.

[0014] Figure 4 Shows a flowchart detailing an example operation of an inverse-designed optical modulator according to an embodiment of the present disclosure.

[0015] Figure 5 Shows a flowchart detailing an iterative process for designing an inverse-designed optical modulator according to an embodiment of the present disclosure.

[0016] Figure 6A Shows a demonstrative simulation environment for simulating the operation of a physical device according to an embodiment of the present disclosure.

[0017] Figure 6B Shows an operation simulation of a physical device according to an embodiment of the present disclosure.

[0018] Figure 6C Shows an adjoint simulation (backpropagation) of a performance loss error through a simulation environment according to an embodiment of the present disclosure.

[0019] Figure 7A Is a flowchart showing an example time step for the operation and adjoint simulation for inverse design of an optical modulator according to an embodiment of the present disclosure.

[0020] Figure 7B Is a flowchart showing the relationship between an operation simulation and an adjoint simulation (backpropagation) according to an embodiment of the present disclosure. Detailed Description

[0021] Embodiments of systems, devices, methods of operation, and methods of design for inverse-designed optical modulators are described herein. In the following description, numerous specific details are set forth to provide a thorough understanding of the embodiments. However, those skilled in the relevant art will recognize that the techniques described herein may be practiced without one or more of the specific details or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring certain aspects.

[0022] References to "one embodiment" or "an embodiment" in the present specification mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the phrases "in one embodiment" or "in an embodiment" that appear in various places throughout the present specification do not necessarily all refer to the same embodiment. In addition, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0023] Embodiments of a reverse-designed optical modulator are described herein. The optical modulator is a photonic device capable of manipulating one or more optical properties (e.g., frequency, phase, polarization, power, or a combination thereof) of an optical carrier (e.g., a waveform that can be modulated to convey information) by applying a modulation bias (e.g., voltage, pressure, or temperature) to the optical modulator. It should be understood that the embodiments of the optical modulator described herein can be designed to overcome one or more bottlenecks of conventional optical modulators. For example, a significant performance bottleneck of conventional optical modulators is due to the non-linear relationship between the optical property being manipulated and the applied modulation bias. For example, when adjusting the bias (e.g., voltage) to modulate the power (e.g., intensity or amplitude) of the optical carrier of a conventional optical modulator, there may be a non-linear relationship. Such non-linear relationships can be attributed to the material properties and / or components (e.g., ring resonators, optical power splitters, or other optical components included in a photonic integrated circuit) of the conventional optical modulator. The non-linearity may create distortion in the transmitted signal and may limit the overall performance (e.g., data rate) of the conventional optical modulator. Additionally, it should be understood that conventional optical modulators have limited parameters by which performance can be tuned. For example, a conventional optical modulator may correspond to an optical waveguide formed of lithium niobate, which has limited parameters by which the waveguide can be tuned or designed. Therefore, a method for designing an optical modulator with a greater number of tunable parameters is necessary for designing a high-performance and compact device capable of compensating for the bottlenecks of conventional optical modulators.

[0024] The embodiments described herein utilize a reverse design method to generate an optical modulator (e.g., for a photonic integrated circuit) that can compensate for the bottlenecks of a conventional optical modulator (e.g., non - linearities in response, size, or other aspects) or otherwise design around the bottlenecks of a conventional optical modulator. Specifically, a photonic device with a "modulation region" is designed, which has a non - uniform arrangement of two or more different materials with different refractive indices to construct the modulation region to manipulate one or more optical properties of an optical carrier in response to a modulation bias. The modulation region is coupled to two or more ports (e.g., an input port and an output port) and a modulation actuator (e.g., to apply and / or adjust a voltage, current, temperature, and / or pressure applied to the modulation region) to form an optical modulator. To generate the design of the modulation region, an iterative reverse design method is utilized, where multiple bias points applied to the optical modulator (e.g., different magnitudes of the bias applied by the modulation actuator and / or different changes in one or more of the refractive indices of the non - uniform arrangement of the modulation region caused by the bias) are simulated or otherwise considered in parallel to determine the design of the modulation region that forms an optical modulator meeting the target performance parameters. More specifically, an optimization objective (e.g., a loss function that causes the output to be minimized) considering multiple bias points is constructed. In some embodiments, the optimization objective can implement a target response curve (e.g., monotonic, linear, or non - linear) of the optical modulator, which can compensate for the bottlenecks present in optically modulators of conventional designs.

[0025] FIG. 1 shows a reverse-designed optical modulator 100 in accordance with an embodiment of the present disclosure. The illustrated embodiment of the optical modulator 100 includes a modulation region 105, an input port 110, an output port 115, an optional port 120, a modulation actuator 125, a modulation controller 140, and other circuitry 145. The illustrated embodiment of the modulation region 105 includes a non-uniform arrangement of two or more different materials (e.g., a first material 107 and a second material 108) having different refractive indices to configure the modulation region 105 to manipulate one or more optical properties (e.g., frequency, phase, polarization, power, or a combination thereof) of an optical carrier 150 in response to a modulation bias (e.g., an adjustable voltage, current, pressure, or temperature) applied to the modulation region 105. The input port 110 is optically coupled to the modulation region 105 to inject the optical carrier 150 into the modulation region 105. The modulation actuator 125 is disposed near the modulation region 105 and is adapted to apply a modulation bias to the modulation region 105 to generate a modulation wave 155 (e.g., to convey information, correct distortion, etc.). The output port 115 is optically coupled to the modulation region 105 to receive the modulation wave 155. In some embodiments, the reverse-designed optical modulator 100 has an optional port 120. It should be understood that although only one of the optional ports 120 is shown, in some embodiments, there may be more than one optional port 120. However, in other embodiments, the reverse-designed optical modulator 100 may not include an optional port 120 (e.g., there are no other ports directly coupled to the modulation region 105 other than the input port 110 and the output port 115).

[0026] The modulation region 105 may also be referred to as the "design region" or "active region" of the optical modulator 100, which is a location where a modulation bias (e.g., an applied voltage, current, temperature, pressure) can variably adjust at least one of different refractive indices included in a non-uniform arrangement of two or more different materials. For example, the two or more different materials may include a first material 107 and a second material 108, each having a respective refractive index that can change in response to a modulation bias applied to the modulation region 105. The extent to which at least one of the different refractive indices changes is at least partially based on the magnitude of the modulation bias and the material properties of at least one of the two or more different materials (e.g., the electro-optic coefficient of the first material 107 or the second material 108). In the illustrated embodiment, the modulation region 105 is configured as an optical cavity (e.g., a resonant cavity), and the non-uniform arrangement of the first material 107 and the second material 108 results in a material interface pattern that provides the desired functionality for the optical modulator 100 in response to the modulation bias. It should be understood that the response to the modulation bias may also include when the magnitude of the modulation bias is zero or a reference value (e.g., when the modulation bias corresponds to an applied voltage, a zero magnitude of the modulation bias may correspond to 0 V or ground, when the modulation bias corresponds to an applied pressure or temperature, a zero or reference value magnitude of the modulation bias may correspond to ambient pressure or temperature, etc.).

[0027] In some embodiments, the pattern of discrete regions of the first material 107 and the second material 108 is used to selectively steer (e.g., via refraction, scattering, reflection, dispersion, or other means) an inbound optical carrier 150 received via an input port 110 to an output port 115 or an alternative port 120 under the influence of a modulation actuator 125 (e.g., to implement an on-off keying modulation scheme, where optical power is predominantly directed to the output port 115 during the on or high logic state of the modulation wave 155, or to the alternative port 120 during the off or low logic state of the modulation wave 155). In other words, the modulation wave 155 includes multiple states, each state based on the magnitude of a modulation bias, and the multiple states include a high state and a low state. In some embodiments, the non-uniform arrangement of the first material 107 and the second material 108 is configured to cause a portion (e.g., in terms of optical power) of the optical carrier 150 to be steered, scattered, or reflected away from the output port 115 when the modulation wave 155 is modulated to a low state or an intermediate state between the high state and the low state. In some embodiments, the portion of the optical carrier 150 that is steered away from the output portion 115 is directed towards the alternative port 120. In other embodiments, the on-off keying modulation scheme can be implemented by modulating other aspects of one or more optical properties of the optical carrier 150 (e.g., in addition to power or amplitude, such as frequency, phase, polarization, or a combination thereof). In the same or other embodiments, the optical modulator 100 can be used to correct distortions or otherwise provide active and / or variable manipulation of one or more optical properties of the optical carrier 150 to generate the modulation wave 155. For example, distortions in the optical carrier 150 can be corrected or compensated for by adjusting the frequency, phase, polarization, or power of the optical carrier 150. In such embodiments, it becomes particularly important that the response curve of the known optical modulator provides variable control over one or more optical properties of the optical carrier 150, since the distortions are not necessarily fixed. By customizing the response curve in a particular way (e.g., linearly, non-linearly, monotonically, or otherwise), it becomes possible to tune one or more optical properties of the optical carrier 150 in a targeted and reliable manner. It should be understood that the on-off keying modulation, distortion correction, or other schemes can be implemented by adapting the modulation actuator 125 to impart a data signal 160 onto the optical carrier 150 to generate the modulation wave 155 via the modulation bias.

[0028] In some embodiments, other circuitry 145 may include an optical receiver (e.g., a photoelectric or photovoltaic device such as a photodiode, a photocell, or others) and / or a power regulator circuit (e.g., a rectifier such as a diode, a storage capacitor, and / or other conventional regulating circuits) to receive a portion of the optical carrier 150 (e.g., when the modulation wave 155 is modulated to a state other than a high or on logic state), which may be used to recover the rejected optical power and convert the recovered optical power into electrical power (e.g., to power the modulation controller 140).

[0029] Returning to the reference modulation region 105, the first material 107 and the second material 108 are discrete regions of materials having different refractive indices, the refractive indices of which change in response to a bias (e.g., an applied voltage, current, temperature, pressure). In one embodiment, the first material 107 and the second material 108 may be a waveguide core material and a waveguide cladding material, respectively. The core and cladding materials may be the same core and cladding materials used to form the waveguide portions of the input port 110, the output port 115, and / or the optional port 120. For example, the first material 107 may be a semiconductor material (e.g., silicon, a III-V semiconductor material, a II-VI semiconductor material, lithium niobate, or other semiconductor materials), while the second material 108 may be an oxide material (e.g., silicon dioxide). In other embodiments, the first material 107 and the second material 108 may be implemented as discrete regions of intrinsic silicon and doped silicon, discrete regions of differently doped silicon, or may be a combination of other types of semiconductor materials (e.g., III-V semiconductor materials, II-VI semiconductor materials, lithium niobate, combinations thereof, etc.). In one embodiment, the modulation region 105 is approximately 1.5 um × 1.2 um, and the ports 110, 115, and 120 are waveguide portions having a width of 200 nm and a length of 600 nm. The discrete regions of the first material 107 and the second material 108 may be implemented as aggregates of incremental pixels or voxels having a size of 5 nm × 5 nm for each material type. In other words, the non-uniform arrangement of the first material 107 and the second material 108 may be reproduced by a schematic diagram defined by a plurality of pixels or voxels having an area of 5 nm × 5 nm. Of course, other pixel or voxel resolutions may be implemented (e.g., an area greater than 5 nm × 5 nm or less than 5 nm × 5 nm, pixels or voxels of different sizes, uniform pixel or voxel sizes, non-uniform pixel or voxel sizes, or other configurations).

[0030] Modulation is achieved via a modulation bias that is applied to the modulation region 105 via a modulation actuator 125, which in turn is driven by a modulation controller 140 (e.g., a microcontroller, an application specific integrated circuit, a field programmable gate array, or other configurable controller coupled to or including memory) in response to a data signal 160. Thus, the modulation controller 140 may include modulation / demodulation circuitry as well as driver circuitry to drive the modulation actuator 125. The modulation actuator 125 may be implemented using a variety of techniques to apply an adjustable electric field, temperature, or pressure to the modulation region 105. In one embodiment, the modulation actuator 125 includes electrodes around the sides of the modulation region 105, and the modulation bias is an applied voltage and / or an injected current. In another embodiment, the modulation actuator 125 includes one or more heating elements around the modulation region 105, and the modulation bias is an adjustable temperature. In yet another embodiment, the modulation actuator 125 includes an electromechanical actuator (e.g., a piezoelectric crystal, a microelectromechanical system, etc.) around the modulation region 105, and the modulation bias is an adjustable pressure. Each of these modulation biases is used to adjust at least one of the different refractive indices of the non-uniform arrangement (e.g., of the first material 107 and / or the second material 108) to provide variable control of one or more optical properties of the optical carrier 150. Specifically, the change in the non-uniformly arranged refractive index changes the way the optical carrier of at least one of the first material 107 or the second material 108, which in turn affects the scattering, refraction, reflection, and / or dispersion of the optical carrier 150 within the modulation region 101 to form the modulation wave 155. It should also be understood that the modulation actuator 125 may surround the modulation region 105 in various ways. For example, if Figure 1A is a top view of the modulation region 105, the electrodes of the modulation actuator 125 may be placed along a plane common to the modulation region 105. In the same or other embodiments, the modulation region 105 may be sandwiched between two or more electrodes (see, for example, Figures 1C to 1E ).

[0031] Figure 1B Shows an embodiment in accordance with the present disclosure Figure 1ATop view of a portion of a reverse-designed optical modulator. In the illustrated embodiment, input port 110, output port 115, and optional port 120 are each adjacent to modulation region 105 and operate as optical inputs or outputs for propagating waves. Although input port 110, output port 115, and optional port 120 are referred to as "ports", these ports can include a longitudinal length in the optical propagation direction. Thus, input port 110, output port 115, and optional port 120 can be implemented as waveguide portions having a core and a cladding, where one end of the core and the cladding is physically adjacent to or otherwise optically coupled to modulation region 105. In various embodiments, input port 110, output port 115, optional port 120, and modulation region 105 are all planar waveguide portions. These planar waveguide portions can be embedded within a semiconductor material such as a silicon-on-insulator (SOI) system, a photonic integrated circuit (PIC), etc. In some embodiments, the core and cladding materials can correspond to silicon and silicon dioxide for input port 110, output port 115, and optional port 120. In the same or other embodiments, the core and cladding materials can correspond to first material 107 and second material 108 of modulation region 105. In yet other embodiments, the core and cladding materials of input port 110, output port 115, optional port 120 can be different from first material 107 and / or second material 108.

[0032] It should be understood that the design of the optical modulator 100 is non-limiting. Instead, in some embodiments, the number (or presence) of the optional ports 120 can be configured based on the intended function of the optical modulator 100. Specifically, depending on which one of one or more optical properties of the optical carrier 150 will be modulated by the modulation region 105 in response to the modulation bias, the configuration of the optical modulator 100 can be changed. For example, if the optical modulator 100 is a polarization or phase modulator of the optical carrier 150, it may not be necessary to include the optional ports 120 because it may not be necessary to divert a portion of the optical carrier 150 away from the output port 115. However, in other scenarios, it may be advantageous to configure the optical modulator 100 to include one or more optional ports 120. For example, if the optical modulator is a power or amplitude modulator of the optical carrier 150, the optional ports 120 can correspond to or otherwise include sink ports to receive a portion of the optical power of the optical carrier 150 (e.g., when the modulation wave 155 is in a state other than the high or on state such as the off or low state or an intermediate state between high and low). Of course, it should be understood that even if the optical modulator 100 is adapted to modulate the power or amplitude of the optical carrier 150, in some embodiments, the optical modulator 100 may still not include the optional ports 120 (e.g., the modulation region 105 can direct a portion of the optical carrier 150 away from the output port 115 such that when the modulation wave 155 is in a state other than high or on, a portion of the optical carrier 150 is reflected back to the input port 110, scattered outside the modulation region 105, or otherwise not included in the modulation wave 155).

[0033] In the illustrated embodiment, the modulation region 105 is a substantially planar structure, wherein the input port 110, the output port 115, and the optional port 120 are each coplanar with the modulation region 115, but adjacent to different sides of the modulation region 115. In other embodiments, each of the input port 110, the output port 115, and the optional port 120 may be adjacent to a common side of the modulation region 105. In yet another embodiment, only two selected from the group including the input port 110, the output port 115, and the optional port 120 may be adjacent to a common side of the modulation region 105, and the unselected port included in the group may be adjacent to a side of the modulation region 105 adjacent or opposite to the common side. As previously described, it should be understood that the optional port 120 is not limited to a single port, and in some embodiments, the optional port 120 may include multiple ports that may be arranged in various ways around the modulation region 120. Additionally, it should be understood that in the illustrated embodiment, the modulation region 120 is laterally surrounded by a peripheral region 109, which may have a uniform composition (e.g., corresponding to two of the different materials forming the modulation region 105, such as the first material 107, the second material 108, or any other material), which forms a material interface boundary 151 that extends continuously and laterally around the modulation region 105, but the input port 110, the output port 115, and the optional port 120 interface with or otherwise adjoin the modulation region 105. In some embodiments, the uniform composition of the peripheral region 109 corresponds to silicon dioxide. It should be understood that the material interface boundary 151 may correspond to a location where the refractive index changes due to different material interfaces connecting and jointly forming the boundary of the optical cavity (e.g., to help reduce the optical carrier 150 from leaving the modulation region 105 through regions other than the ports 110, 115, and / or 120). It should be understood that the material interface boundary (e.g., the material interface boundary 151 and / or the material interface boundary formed by discrete regions formed by the first material 107 and the second material 108) at least partially defines the function of the optical modulator 100.

[0034] Figures 1C to 1E A cross-sectional view of a portion of an Figure 1A optically modulator in reverse design according to an embodiment of the present disclosure is shown. More specifically, Figures 1C to 1E a vertical schematic or stack of various layers that may be included in the Figure 1A illustrated optical modulator 100 is shown. However, it should be understood that the illustrated embodiment is not exhaustive, and certain features or elements may be omitted to avoid obscuring certain aspects of the invention. As Figure 1CAs shown, the optical modulator 100 includes a substrate 102, a cladding layer 104, an active layer 106, a cladding layer 108, and a modulation actuator 125. In some embodiments, the optical modulator 100 can be partially or otherwise a photonic integrated circuit or a silicon photonics device compatible with conventional manufacturing techniques (e.g., lithography techniques such as photolithography, electron-beam lithography, etc., sputtering, thermal evaporation, physical and chemical vapor deposition, etc.).

[0035] In one embodiment, an SOI wafer can be initially provided, which includes a support substrate (e.g., a silicon substrate) corresponding to the substrate 102, a silicon dioxide dielectric layer corresponding to the cladding layer 104, a silicon layer (e.g., intrinsic, doped, or otherwise), and an oxide layer (e.g., intrinsic, grown, or otherwise). In one embodiment, the silicon in the active layer 106 can be selectively etched by lithography to create a pattern on the SOI wafer, and the pattern is transferred to the SOI wafer via a dry etching process (e.g., via a photoresist mask or other hard mask) to remove portions of the silicon. The silicon can be etched all the way down to the cladding layer 104 to form voids, which can then be backfilled with silicon dioxide, and the silicon dioxide is subsequently encapsulated with silicon dioxide to form the cladding layer 108. In one embodiment, there can be several etch depths including the full etch depth of the silicon to obtain the target structure. In one embodiment, the silicon can be 220 nm thick, so the full etch depth can be 220 nm. In some embodiments, this can be a two-step encapsulation process, where two silicon dioxide depositions are performed, and intermediate chemical mechanical planarization is used to produce a planar surface.

[0036] Figure 1D A partial view of the active layer 106 taken along a portion of the peripheral region 109 (relative to Figure 1C ) is shown, and the peripheral region 109 includes an input port 110, an output port 115, or an optional port 120. More specifically, Figure 1D The portion of the active layer 106 shown in can correspond to the waveguide portion of one of the input port 110, the output port 115, or the optional port 120. In the shown embodiment, the active layer 106 includes a first material 107 with a refractive index of n 1 and a second material 108 with a refractive index of n 2 , and n 2 is different from n 1 . Uniform and continuous regions of the first material 107 and the second material 108 can form corresponding to Figures 1A to 1BThe waveguide or portion of a waveguide of the illustrated input port 110, output port 115, or optional port 120. In some embodiments, the cladding layers 104 and 108 may have a uniform composition corresponding to the second material 108 (e.g., silica). Note that Figure 1D The illustrated embodiment does not show the modulation actuator 125 because the illustrated cross-section extends through one of the input port 110, output port 115, or optional port 120, and it may not be necessary to apply a modulation bias to the input port 110, output port 115, or optional port 120.

[0037] Figure 1E Shown along Figure 1A and Figure 1B A more detailed view of the active layer 106 taken along the modulation region 105 as shown in Figure 1C ). As previously described, the modulation region 105 includes a first material 107 (e.g., silicon) and a second material 108 (e.g., silica), which are discrete regions of uniform composition that are non-uniformly scattered to form a plurality of interfaces 111 that together form a material interface pattern. Each of the plurality of interfaces 111 forming the interface pattern corresponds to a change in the refractive index of the modulation region 105 to together configure the modulation region 105 (i.e., based on the shape and arrangement of the first material 107 and the second material 108) in combination with a modulation bias to at least partially provide the function of the optical modulator 100 (i.e., manipulate one or more optical properties of an optical carrier to generate a modulated wave).

[0038] As shown, the active layer 106 is disposed between the cladding layer 104 and the cladding layer 108, and the cladding layer 104 and the cladding layer 108 are in turn disposed between the substrate 102 and the modulation actuator 125. In some embodiments, the modulation actuator 125 may correspond to an electrode, while the substrate 102 may correspond to a counter electrode. In some embodiments, an adjustable bias (e.g., voltage) may be applied between the modulation actuator 125 and the substrate 102 to generate a bias across the modulation region 105. It should be understood that in other embodiments, temperature or pressure may be applied to the modulation region 105 via the modulation actuator 125. Additionally, it should be understood that in some embodiments, the cladding layer 104 and / or the cladding layer 108 may be omitted.

[0039] It should be understood that in the illustrated embodiment of the optical modulator 100 as shown in Figures 1C to 1E , the change in refractive index is shown as being vertically consistent (i.e., the first material 107 and the second material 108 form interfaces that are substantially perpendicular or normal to the lateral plane or cross-section of the optical modulator 100). However, in the same or other embodiments, a plurality of interfaces (e.g., Figure 1EThe interface 111 shown in [Fig. 0] may not be substantially perpendicular to the lateral plane or cross-section of the optical modulator 100.

[0040] Figure 1F Fig. 1 shows a more detailed view of the modulation region 105 of an inverse-designed optical modulator according to an embodiment of the present disclosure for Figure 1A As shown, the modulation region 105 includes a non-uniform arrangement of two or more different materials (e.g., a first material 107 and a second material 108) having different refractive indices to configure the modulation region 105 to manipulate one or more optical properties of an optical carrier in response to a modulation bias. In some embodiments, the first material 107 and the second material 108 correspond to silicon and silicon dioxide, respectively. However, as discussed in the embodiments of the present disclosure, the first material 107 and the second material 108 may be materials different from silicon or silicon dioxide (e.g., the first material 107 or the second material 108 may correspond to lithium niobate, III-V semiconductor materials, II-VI semiconductor materials, different doped regions of silicon, or combinations thereof). In the illustrated embodiment, discrete regions of the first material 107 and the second material 108 may form one or more islands of a given material included in the modulation region 105. For example, the non-uniform arrangement of the first material 107 and the second material 108 may include a first island 113 of the first material 107 laterally surrounded by the second material 108 and a second island 114 of the second material 108 laterally surrounded by the first material 107. It should be understood that the non-uniform arrangement of the first material 107 and the second material 108 forms a pattern determined based on the iterative minimization of a loss function (see, for example, Figure 2A the loss function 205 shown in [Fig. 2]).

[0041] Figure 2A Fig. 2 shows a loss function 205 for the inverse design of an optical modulator according to an embodiment of the present disclosure. The loss function 205 is an example loss function that may be used as an objective function for generating Figure 1A and Figure 1B the design or schematic diagram of the modulation region 105 shown in [Fig. 1]. However, it should be understood that in other embodiments, a different or more robust loss function may be utilized instead of the loss function 205.

[0042] As described above, the non-uniform arrangement includes discrete patterns of two or more different materials (e.g., a first material 107 and a second material 108), where the pattern is selected based on an iterative minimization of a loss function (or more specifically, minimization of the output of the loss function), and the iterative minimization of the loss function incorporates multiple different states of the optical modulator 100, each state associated with a different refractive index change. By incorporating multiple states, each representing a different change in refractive index (e.g., based on the magnitude of the modulation bias applied to the modulation region 105), the response curve of the optical modulator 100 can be customized to perform in a predetermined manner (e.g., monotonic, linear, or nonlinear). Advantageously, fine-tuning how the optical modulator performs can compensate for drawbacks in conventional optical modulators or otherwise enable the optical modulator to have improved control over one or more optical properties. The inverse design technique can consider the layout of the optical modulator, such as the optical modulator 100, which is constructed with an input port 110, a modulation (design) region 105, an output port 115, and an optional port 120. By constructing the device geometries or patterns of the first material 107 and the second material 108 using the same overall topology but with different perturbations to the refractive index in at least one of the first material 107 or the second material 108, multiple bias points of the optical modulator are simulated in parallel. Thus, these parallel simulations calculate the light transmission from the input port 110 to the output port 115 in the illustrated embodiment as a function of the refractive index perturbation or change (Δn) or the magnitude of the modulation bias itself. It should be understood that while transmission T is utilized in the illustrated embodiment of the loss function 205, other properties of the optical carrier (e.g., polarization phase, frequency, etc.) can be determined in addition to or instead of transmission. Figure 2A In the illustrated embodiment of the loss function 205, other properties of the optical carrier (e.g., polarization phase, frequency, etc.) can be determined in addition to or instead of transmission.

[0043] The optimization objective of the inverse design method is constructed as one or more optical properties of the optical carrier (e.g., power, polarization, phase, frequency, or a combination thereof). In the illustrated embodiment, the loss function 205 is configured for the transmission or optical power of the optical carrier function of this transmission. The loss metric (e.g., Loss(T)) corresponds to the sum of interest points x i , where each interest point corresponds to one of the multiple states of the optical modulator (e.g., different values of refractive index change up to the maximum change in refractive index produced by different magnitudes of the modulation bias). Thus, based on the common topology or non-uniform arrangement of the first material 107 and the second material 108, each interest point can correspondingly be included in the parallel calculations or simulations of the optical modulator 100. For each interest point in the summation, the loss function is represented as the sum of two squares (e.g., T ON (x i ) – f(x i ) and TOFF (x i ) - 1 + f(x i )) However, in other embodiments, different sums may be used. When optimizing the design, the function f can be utilized to customize or otherwise implement the desired response curve of the optical modulator 100. Additionally, it should be understood that in some embodiments, penalties can be utilized to enforce certain criteria (e.g., prioritizing the performance of the maximum and minimum values of the change in refractive index or modulation bias such that the on and off logic states of the optical modulator are prioritized over any intermediate logic states set between the on or off logic states).

[0044] The inverse design operates using a design simulator (e.g., a design model) configured with an initial design or pattern for the modulation region 105 to perform a forward operation simulation of the initial design (e.g., using Maxwell's equations for electromagnetics). The output of the forward operation simulation is the simulated field response at the output port 115 and (optionally) the optional port 120. Specific performance parameters of this output field response can be selected as the parameters of interest (e.g., power loss, wavelength, etc.) and are referred to as simulated performance parameters. The loss function 205 uses the simulated performance parameters to calculate a performance loss value or metric, which can be a scalar value (e.g., the mean squared error between the simulated performance value and the target performance value). The differentiable nature of the design model enables backpropagation via the adjoint simulation of the performance loss error, which is the difference between the simulated output value and the desired / target performance value. The performance loss error (e.g., the loss gradient) is backpropagated through the design model during the adjoint simulation to generate a structural design error at the input port 110. The backpropagation of the performance loss error facilitates the calculation of additional performance gradients, such as the structural gradient representing the sensitivity of the performance loss value to changes in the structural material properties of the modulation region 105 (e.g., the topology or pattern of the first material 107 and the second material 108). These gradients are output as the structural design error, and then the structural optimizer can use this structural design error to perform iterative gradient descent (e.g., stochastic gradient descent), which optimizes or refines the initial structural design to generate a modified structural design for the modulation region 105. Then, the forward and reverse simulations can be iterated until the performance loss value falls within an acceptable design criterion (referred to as saturation). The above description is merely an example of an inverse design technique that can be used to refine or optimize the features and topology of the optical modulator 100. It should be understood that other inverse design techniques can also be implemented either alone or in combination with other conventional design techniques. Thus, the above-described inverse design technique can be applied to determine a specific material combination, feature size, and feature arrangement (i.e., pattern) to achieve the desired performance at each port for a given logic state of the optical modulator 100 using the loss function 205.

[0045] Figure 2B Example chart 250 shows optical modulator response curves 210, 215, and 220 for an optical modulator for, e.g., inverse design, according to embodiments of the present disclosure. It should be understood that response curves 210, 215, or 220 may represent Figures 1A to 1F the optical modulator 100 shown in. In the illustrated embodiment, the y-axis corresponds to the transmission at output port 115 relative to a change in refractive index (e.g., Δn) or the magnitude of a modulation bias (e.g., a change in voltage, current, pressure, or temperature applied to modulation region 105). It should be understood that the function f of loss function 205 may incorporate the change in refractive index and / or modulation bias as a metric for determining or otherwise simulating the performance of optical modulator 100 at each point of interest (e.g., the transmission at output port 115 as shown in Figure 2A , or any other one or combination of one or more optical properties of optical carrier 150 as discussed in embodiments of the present disclosure). It should be understood that each point marked “+” within chart 250 corresponds to Figure 2A one of the points of interest included in the x of loss function 205 shown in i . However, it should be understood that more or fewer points of interest may be utilized depending on the desired target granularity during the design of optical modulator 100.

[0046] In the illustrated embodiment, chart 250 shows three example response curves 210, 215, and 220 representing an embodiment of optical modulator 100 shown in Figures 1A to 1E . In some embodiments, the non-uniform arrangement of first material 107 and second material 108 is configured such that the response curve of a change in one or more optical properties of the optical carrier of optical modulator 100 relative to a change in the magnitude of the modulation bias or a change in refractive index due to the modulation bias is linear, as shown by response curve 210. In other embodiments, the non-uniform arrangement of first material 107 and second material 108 is configured such that the response curve of a change in one or more optical properties of the optical carrier of optical modulator 100 relative to a change in refractive index due to the modulation bias is non-linear, as shown by response curves 215 and 220. It should be understood that response curves 210 and 220 are monotonic (e.g., non-increasing or non-decreasing response curves). Specifically, response curves 210 and 220 are non-increasing response curves when considering a change from a zero change value of the x-axis values of chart 250 to the maximum change.

[0047] Figure 3A diagram showing an iterative inverse design of a modulation region 105 using a loss function 205 in accordance with an embodiment of the present disclosure. Diagram 305 shows how the loss function 205 saturates to a minimum value after a certain number of time steps of performing iterative forward and adjoint simulations. Diagram 310 shows how the transmission power T at the output port 115 changes for the on state (e.g., logic high) and off state (e.g., logic low) of the optical modulator 100 as the iterative design of the modulation region 105 proceeds.

[0048] Figure 4 A flowchart showing an operation process 400 of an optical modulator 100 in accordance with an embodiment of the present disclosure. The order of some or all of the process blocks that appear in the process 400 should not be considered restrictive. Instead, those of ordinary skill in the art who benefit from the present disclosure will understand that some of the process blocks can be executed in various orders not shown, or even in parallel.

[0049] In process block 405, an optical carrier 150 is received by the modulation region 105 via an input port 110 that is optically coupled to the modulation region 105. The modulation region 105 includes a non-uniform arrangement of two or more different materials (e.g., a first material 107 and a second material 108) having different refractive indices to configure the modulation region 105 to manipulate one or more optical properties (e.g., phase, polarization, power, frequency, or a combination thereof) of the optical carrier 150 in response to a modulation bias. The optical carrier 150 can be a continuous wave generated by a laser source (e.g., a laser diode, etc.) and guided into the input port 110 along a single-mode waveguide (e.g., a planar waveguide, an optical fiber, etc.). The laser source can be an on-chip device integrated into a PIC having the optical modulator 100, or a different off-chip device whose output is guided to the input port 110. In other embodiments, the optical carrier 150 may already have a data signal embedded thereon (e.g., when correcting for distortion, the optical carrier 150 may already be carrying information).

[0050] In process block 410, in response to a modulation bias applied by modulation actuator 125, an optical carrier 150 is modulated within a modulation region 105. Specifically, the modulation bias is modulated to generate a modulation wave 155 that is directed towards an output port 115 that is optically coupled to the modulation region 105. The modulation bias adjusts at least one of a non-uniform arrangement of different refractive indices to provide variable control of one or more optical properties of the optical carrier 150. The modulation actuator 125 drives the modulation bias based on a data signal 160 received at a modulation controller 140. In the illustrated embodiment, the modulation region 105 includes a non-uniform arrangement of a first material 107 and a second material 108 each having a different refractive index that disperses (e.g., scatters, refracts, diffracts, or otherwise alters) the optical carrier 150 in a controlled manner to manipulate one or more optical properties (e.g., power, phase, polarization, frequency, or a combination thereof) of the optical carrier 150 to generate the modulation wave 155. In some embodiments, the modulation bias in combination with the non-uniform arrangement of the modulation region 105 can cause a portion of the optical power of the optical carrier 150 in an on or high logic state to be directed / guided to the output port 115 (process block 415), or a portion of the optical power in a second state (e.g., low, off, or other intermediate state that is not on or high) to be directed / guided away from the output port 155 (e.g., towards an optional port 120, reflected back to the input port 110, or otherwise scattered or dispersed away from the output port 115) (process block 420). Of course, the logic state is determined by the modulation bias applied across the modulation region 105 in response to the data signal 160. Additionally, it should be understood that the magnitude of the optical power directed away from the output port 115 can depend on the magnitude of the modulation bias. For example, when in a logic high or on state, most of the optical power can be directed towards the output port 115, while when in a logic low or off state, most of the optical power can be directed away from the output port 155 (e.g., towards the optional port 120).

[0051] The modulation bias affects the power guiding by causing a small change in the refractive index of the first material 107 and / or the second material 108, and thus affects the logical state encoded on the optical carrier 150 at the output port 115. Each discrete region of the first material 107 and the second material 108 that together form a pattern or non-uniform arrangement represents a binary continuous block (uniform region) of the first material 107 or the second material 108 having a uniform refractive index. Applying a modulation bias over the overall non-uniform arrangement causes a small change in the refractive index of each continuous block of the first material 107 and / or the second material 108, which depends on whether the modulation bias guides optical power to or away from the output port 115. As previously mentioned, the first material 107 and the second material 108 can be implemented as discrete regions of two different materials (such as silicon and silicon oxide), but other material combinations can also be used. The overall pattern or non-uniform arrangement of the first material 107 and the second material 108 within the modulation region 105 can be determined via inverse design using forward and adjoint simulations that seek to minimize the loss function 205 presented above. Of course, depending on the needs of a particular application of the optical modulator 100, other design techniques and loss functions can be implemented to achieve the pattern or non-uniform arrangement of the first material 107 and the second material 108. Additionally, it should be understood that although the process 400 focuses on modulating the optical power of the optical carrier 150, other optical properties of the optical carrier 150 can also be adjusted via the modulation bias, depending on the configuration of the optical modulator 100 and the loss function used to determine the design of the modulation region 105.

[0052] Figure 5 A flowchart 500 in accordance with an embodiment of the present disclosure is shown, which details an iterative process for designing the inverse-designed optical modulator 100. The order of some or all of the process blocks that appear in the process 500 should not be considered restrictive. Instead, those of ordinary skill in the art who benefit from the present disclosure will understand that some of the processing blocks can be executed in various orders not shown, or even in parallel.

[0053] Block 505 shows configuring a simulation environment to represent a photonic integrated circuit (e.g., the optical modulator 100 including the modulation region 105, the input port 110, the output port 115, and an optional port 120). The simulation environment can be configured as pixels or voxels (see, for example, Figure 6A ) where structural parameters (e.g., refractive index), optical carrier properties (e.g., power, frequency, phase, polarization, etc.), and target performance parameters are set or otherwise configured.

[0054] Block 515 shows performing an operation simulation of the photonic integrated circuit to determine a loss metric (e.g., based on a loss function such as Figure 2AThe loss function 205) shown. The loss metric can provide information on how the simulated optical modulator performs relative to a target performance metric (see, e.g., Figure 6B ).

[0055] Block 520 shows backpropagating the loss metric through the simulation environment (e.g., as an adjoint simulation) to determine the structural gradient. It should be understood that the structural gradient can identify how changing the structural parameters of each of the voxels or pixels included in the simulation environment can affect the loss metric or value. In this way, it can be determined which changes to the structural parameters of which voxels or pixels can be used to reduce (i.e., optimize) the loss metric or value. For example, it may not make sense to modify the structural parameters of voxels that have a limited impact on reducing the loss metric.

[0056] Block 525 shows modifying the design of the photonic integrated circuit by updating the structural parameters to reduce the loss metric or value. This can be achieved, for example, by flipping the structural parameters of the voxels with the largest structural gradient to the opposite material (e.g., flipping the material of a given voxel from a first material 107 to a second material 108 and vice versa). Alternatively, small changes to the structural parameters can be utilized instead of flipping. For example, a given voxel may have a material value of 0.5, which can correspond to being between the first material 107 and the second material 108. As the iteration progresses, the material value of the given voxel can gradually shift towards 0 or 1, indicating that the material should be the first material 107 or the second material 108.

[0057] Block 530 shows checking to see if the loss metric converges or otherwise saturates after the design of the photonic integrated circuit has been modified. If the loss metric does not converge, block 530 proceeds to block 515, and the iterative process continues. However, if the loss metric does converge or some other parameter indicates the end of the simulation (e.g., reaching a time or computational cost budget), then block 530 proceeds to block 535, providing an output of the optimized design of the photonic integrated circuit (e.g., as a schematic).

[0058] Figures 6A to 6C respectively show the initial setup, operational simulation, and adjoint simulation of a simulation environment 601 for optimizing the structural parameters of a physical device (e.g., optical modulator 100) according to a reverse design embodiment. The simulation environment 601 and the corresponding initial setup, operational simulation, adjoint simulation, and structural parameter optimization can be implemented via a physical simulator using Maxwell's equations. As Figures 6A to 6C shown, the simulation environment is represented in two dimensions, however, it should be understood that higher dimensions (e.g., three-dimensional space) can also be used to describe the simulation environment 601 and the physical device. In some embodiments, Figures 6A to 6COptimization of the structural parameters of the physical device shown can be achieved, in particular, via simulations (e.g., forward and backward time propagation) that model the field response (e.g., electric and magnetic) using the finite-difference time-domain (FDTD) method.

[0059] Figure 6A An example rendering of a simulation environment 601-A that describes an electromagnetic device is shown. The simulation environment 601-A represents the simulation environment 601 at an initial time step (e.g., initial setup) for optimizing the structural parameters of a physical device. The physical device described by the simulation environment 601 can correspond to an optical modulator 100 having a designable region 605 (e.g., modulation region 105), where the structural parameters of the simulation environment can be designed, modified, or otherwise changed. The simulation environment 601 includes an excitation source 615 (e.g., Gaussian pulse, wave, waveguide mode response, etc.) at the location of the input port 110. The electric and magnetic fields (e.g., field response) within the simulation environment 601 (and the physical device) can change in response to the excitation source 615. Specific settings of the initial structural parameters, excitation source, performance parameters, and other metrics of the first-principles simulation of the physical device (i.e., the initial description) are input before the start of the simulation operation.

[0060] As shown, the simulation environment 601 (and subsequently the physical device) is described by a plurality of voxels 610, which represent the individual elements of the two-dimensional (or three-dimensional) space of the simulation environment. Each voxel is shown as a two-dimensional square, although it should be understood that the voxels can be represented as cubes or other shapes in three-dimensional space. It should be understood that the specific shape and dimensions of the plurality of voxels 610 can be adjusted according to the simulation environment 601. It should also be noted that only a portion of the plurality of voxels 610 is shown to avoid obscuring other aspects of the simulation environment 601. Each of the plurality of voxels 610 is associated with one or more structural parameters, a field value for describing the field response, and a source value for describing the excitation source at a specific location within the simulation environment 601. For example, the field response can correspond to a vector that describes the electric and / or magnetic fields of each of the plurality of voxels 610 at a specific time step. More specifically, the vector can correspond to a Yee grid that discretizes Maxwell's equations to determine the field response. In some embodiments, the field response is at least partially based on the structural parameters and the excitation source 615.

[0061] Figure 6BAn exemplary operational simulation of the simulation environment 601-B at a specific time step is shown, where the excitation source 615 is active (e.g., generating waves that propagate through the simulation environment 601 from the excitation source 615). As mentioned, the physical device is an optical modulator that can operate at the frequencies of interest and has specific waveguide modes (e.g., transverse electromagnetic mode, transverse electric mode, etc.), and the excitation source is at the input port 110. The operational simulation occurs over a plurality of time steps (see Figure 3 ), including the shown time step. When the operational simulation is performed, the change in the field response (e.g., field value) of each voxel among the plurality of voxels 610 is updated in response to the excitation source 615 and at least partially based on the structural parameters of the physical device at each time step among the plurality of time steps. Similarly, in some embodiments, the source value is updated for each voxel among the plurality of voxels (e.g., in response to the propagation of electromagnetic waves from the excitation source 615 through the simulation environment). It should be understood that the operational simulation is incremental, and as time moves forward for each time step among the plurality of time steps, the field values (and source values) are updated incrementally at each time step. It should also be noted that in some embodiments, the update is an iterative process, and the update of each field and source value is at least partially based on the previous updates of each field and source value.

[0062] When the operational simulation is performed, a performance loss function (e.g., Loss(T) indicated by the loss function 205 shown in Figure 2A ) can be calculated at least partially based on a comparison (e.g., mean square error) between the field response at a specified time step (e.g., the final time step of the operational simulation) and the desired field response at the port 620 (e.g., corresponding to the output port 115) and / or other ports (e.g., ports 615 and / or 625, depending on one or more metrics being optimized). The performance loss value can be described according to a specific performance value (e.g., power). The structural parameters can be optimized for this specific performance value.

[0063] Figure 6C An example of backpropagation of the performance loss error backward within the simulation environment 601-C that describes the physical device is shown. In one embodiment, a performance loss error is injected as a kind of back excitation source at the output port 620 and optionally at the optional port 625 during the adjoint performance simulation, for stimulating the backward field response of the voxels 610 through the simulation environment 601-C. The adjoint performance simulation of the performance loss error determines the impact of the change in the structural parameters of the voxels 610 on the performance loss value (e.g., the loss function 205).

[0064] Figure 7AFIG. 700 is a flow chart showing an example time step for forward simulation 710 and backpropagation 750 within a simulation environment in accordance with an embodiment of the present disclosure. Flow chart 700 is one possible implementation that a design model can use to perform forward operation simulation 710 and backpropagation 750 of a simulation environment. In the illustrated embodiment, the forward operation simulation utilizes the FDTD method to model the field responses (both electric and magnetic) at multiple time steps in response to an excitation source. More specifically, the time-dependent Maxwell's equations (in partial differential form) are discretized to solve for the field vector components (e.g., Figures 6A to 6C the field responses for each voxel of the multiple voxels 610 of the simulation environment 601 in

[0065] As Figure 7A shown, flow chart 700 includes update operations for operating a portion of simulation 710 and adjoint simulation 750. Operation simulation 710 occurs over multiple time steps (e.g., from an initial time step to a final time step over a predetermined or conditional number of time steps having a specified time step size), and models the changes in the electric and magnetic fields of multiple voxels that collectively correspond to the simulation environment and / or physical device of the field response (e.g., from an initial field value 711). More specifically, the update operations (e.g., 712, 714, and 716) are iterative and based on the field response, structural parameters 704, and one or more physical stimulus sources 708. After each update operation is another update operation, which represents consecutive steps forward in time within the multiple time steps. For example, update operation 714 updates the field value based on the field response determined from the previous update operation 712, source 708, and structural parameters 704. Similarly, update operation 716 updates the field value based on the field response determined from update operation 714. In other words, at each time step of the operation simulation, the field value (and thus the field response) is updated based on the previous field response and structural parameters of the physical device. Once the final time step of operation simulation 710 is executed, a loss value 718 can be determined (e.g., based on a predetermined loss function 720 or loss function 205). The loss gradient determined from block 752 can be regarded as an adjoint or virtual source (e.g., a physical stimulus or excitation source originating from the output region), which backpropagates (incrementally through the multiple time steps from the final time step until reaching the initial time step) to determine the structural gradient 768.

[0066] In the illustrated embodiment, the FDTD solution (e.g., the forward-in-time simulation 710) and the backpropagation 750 problem are described diagrammatically at a high level using only the "update" and "loss" operations and their corresponding gradient operations. The simulation is initially set up where the structural parameters, excitation source, and initial field state of the simulation environment (and the electromagnetic device) are provided. As previously discussed, the field state is updated based on the structural parameters in response to the excitation source. More specifically, the update operation is given by φ, where for i = 1, … n, Here, n corresponds to the total number of time steps (e.g., a plurality of time steps) of the forward-in-time simulation, x i corresponds to the field response of the simulation environment at time step i (the field values associated with the electric and magnetic fields of each voxel in the plurality of voxels), corresponds to the excitation source of the simulation environment at time step i (the source values associated with the electric and magnetic fields of each voxel in the plurality of voxels), and z corresponds to the structural parameters that describe the topology and / or material properties of the electromagnetic device.

[0067] Note that using the FDTD method, the update operation can be specifically stated as:

[0068]

[0069] That is, the FDTD update is linear with respect to the field and source terms. Specifically, and are linear operators that depend on the structural parameter z and act on the field x i and the source Here, it is assumed that where N is the number of FDTD field components in the forward-in-time simulation. Additionally, the loss operation is given by L = (x i , …, x n ), which takes the computed fields as input and produces a single real-valued scalar (e.g., a loss value) that can be reduced and / or minimized.

[0070] In terms of modifying or otherwise optimizing the structural parameters of the electromagnetic device, the relevant quantity to be produced is which is used to describe the change of the loss value with respect to the change of the structural parameters of the electromagnetic device and is denoted as Figure 7A the "structural gradient" shown in.

[0071] Figure 7B is a diagram 780 showing the relationship between the update operation for operating the simulation and the adjoint simulation (e.g., backpropagation) according to an embodiment of the present disclosure. More specifically, Figure 7B summarizes the operations and adjoint simulation relationships involved in computing the structural gradient which includes and The update operation 714 of the operation simulation updates the field values 713x of multiple voxels at the i-th time step i to the next time step (i.e., the i+1 time step), which corresponds to the field value 715x i+1 . The gradient 755 is used to determine For backpropagation (e.g., updating operation 756 backward in time), which is at least partially combined with the gradient 769 for calculating the structural gradient is the contribution of each field to the loss value L. Note that this is a partial derivative, so the causality of x i →x i+1 is not considered. Therefore, using the loss gradient that includes the x i →x i+1 relationship loss gradient can also be used to calculate the structural gradient and corresponds to the total derivative of the domain with respect to the loss value L. The loss gradient at a specific time step i is equal to + sum. Finally, using the one corresponding to the field gradient which is the contribution from each time / update step pair . is given by:

[0072]

[0073] For completeness, the full form at the first time in the sum is expressed as:

[0074]

[0075] Based on the definition of φ as described in equation (1), it should be noted that can be substituted into equation (3) to obtain the adjoint update for backpropagation (e.g., an update operation such as update operation 756), which can be expressed as:

[0076]

[0077] or

[0078]

[0079] The adjoint update is the backpropagation of the loss gradient from a later time step to an earlier time step, and can be called the backward solution for . The sum of the structural gradients The second term in is expressed as:

[0080]

[0081] For a specific form of φ described by equation (1).

[0082] Some of the processes explained above are described in terms of computer software and hardware. The techniques described can constitute machine-executable instructions embodied within a tangible or non-transitory machine (e.g., a computer) readable storage medium, which when executed by the machine, will cause the machine to perform the described operations. Additionally, the processes can be embodied in hardware, such as an application specific integrated circuit (“ASIC”) or others.

[0083] A tangible machine readable storage medium includes any mechanism that provides (i.e., stores) information in a non-transitory form accessible by a machine (e.g., a computer, a network device, a personal digital assistant, a manufacturing tool, any device having a set of one or more processors, etc.). For example, a machine readable storage medium includes recordable / non-recordable media (e.g., read only memory (ROM), random access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, etc.).

[0084] The foregoing description of the illustrated embodiments of the invention (including what is described in the abstract) is not intended to be exhaustive or to limit the invention to the precise forms disclosed. While specific embodiments and examples of the invention are described herein for illustrative purposes, various modifications can be made within the scope of the invention as will be recognized by those skilled in the relevant art.

[0085] These modifications can be made to the invention in light of the above detailed description. The terms used in the following claims should not be construed to limit the invention to the specific embodiments disclosed in the specification. Rather, the scope of the invention will be determined entirely by the appended claims, which are to be construed in accordance with established principles of claim interpretation.

Claims

1. An optical modulator, comprising: a modulation region including a non-uniform arrangement of two or more different materials having different refractive indices to construct the modulation region to manipulate one or more optical properties of an optical carrier in response to a modulation bias; an input port optically coupled to the modulation region to inject the optical carrier into the modulation region; a modulation actuator disposed near the modulation region and adapted to apply a modulation bias to the modulation region to generate a modulation wave, wherein the modulation bias adjusts at least one of the different refractive indices of the non-uniform arrangement to provide variable control of the one or more optical properties of the optical carrier; and an output port optically coupled to the modulation region to receive the modulation wave.

2. The optical modulator according to claim 1, wherein the one or more optical properties include at least one of frequency, phase, polarization, or power of the optical carrier.

3. The optical modulator according to claim 2, wherein the modulation actuator is adapted to load a data signal onto the optical carrier to generate a modulation wave via the modulation bias.

4. The optical modulator according to claim 2, wherein the non-uniform arrangement is further configured such that a change in the one or more optical properties of the optical carrier of the optical modulator is linear with respect to a change in the amplitude of the modulation bias or a change in the different refractive indices caused by the modulation bias.

5. The optical modulator according to claim 2, wherein the non-uniform arrangement is further configured such that a change in the one or more optical properties of the optical carrier of the optical modulator is non-linear with respect to a change in the different refractive indices caused by the modulation bias.

6. The optical modulator according to claim 5, wherein the response curve is also monotonic.

7. The optical modulator according to claim 1, wherein the modulation wave includes a plurality of states based on the amplitude of the modulation bias, the plurality of states including a high state and a low state, and wherein the non-uniform arrangement is configured to direct, scatter, or reflect a portion of the optical carrier away from the output port when the modulation wave is modulated to the low state.

8. The optical modulator according to claim 1, wherein the two or more different materials include semiconductor materials and oxide materials.

9. The optical modulator according to claim 1, wherein the modulation actuator includes one of the following: an electrode adapted to apply the modulation bias as an adjustable voltage across the modulation region; a heating element adapted to apply the modulation bias as an adjustable temperature across the modulation region; or an electromechanical actuator adapted to apply the modulation bias as an adjustable pressure across the modulation region.

10. The optical modulator according to claim 1, wherein the non-uniform arrangement includes a pattern of discrete regions of the two or more different materials, and wherein the pattern is selected based on an iterative minimization of a loss function that combines a plurality of different states of the optical modulator, each state associated with a different refractive index change.

11. The optical modulator according to claim 1, wherein the input port and the output port include corresponding waveguide portions that physically abut the modulation region.

12. The optical modulator according to claim 11 further includes a peripheral region that laterally surrounds the modulation region, wherein, the peripheral region extends continuously laterally around the modulation region, except where two or more ports are adjacent to the modulation region, and wherein the two or more ports include an input port and an output port.

13. The optical modulator according to claim 12 further includes a sink port adjacent to the modulation region, and wherein, the two or more ports include the sink port.

14. The optical modulator according to claim 12, wherein, the peripheral region has a uniform composition, and wherein the peripheral region includes a first material that is included in the two or more different materials.

15. The optical modulator according to claim 1, wherein, the two or more different materials include a first material and a second material, and wherein the non-uniform arrangement includes a first island of the first material laterally surrounded by the second material and a second island of the second material laterally surrounded by the first material.

16. A method of operating an optical modulator, the method comprising: receiving an optical carrier at an input port optically coupled to the modulation region at the modulation region, wherein the modulation region includes a non-uniform arrangement of two or more different materials having different refractive indices to configure the modulation region to manipulate one or more optical properties of the optical carrier in response to a modulation bias; and modulating a modulation bias applied to the modulation region to generate a modulation wave, wherein the modulation bias adjusts at least one of the different refractive indices of the non-uniform arrangement to provide variable control of the one or more optical properties of the optical carrier, and wherein the modulation wave is directed towards an output port optically coupled to the modulation region.

17. The method according to claim 16 further comprising: loading a data signal onto the optical carrier to generate a modulation wave by modulating the modulation bias; directing a majority of the optical power of the optical carrier to the output port when the modulation wave is modulated to a high state based on a first logic state of the data signal; and transferring a second majority of the optical power of the optical carrier away from the output port when the modulation signal is modulated to a low state based on a second logic state of the data signal.

18. The method according to claim 16, wherein, the one or more optical properties include at least one of frequency, phase, polarization, or power of the optical carrier.

19. The method according to claim 16, wherein, modulating the modulation bias applied to the modulation region includes one of the following: applying an adjustable voltage across the modulation region; heating the modulation region; or applying an adjustable pressure to the modulation region.

20. The method according to claim 16, wherein, the non-uniform arrangement is further configured such that a change in the one or more optical properties of the optical carrier of the optical modulator is linear with respect to a change in the magnitude of the modulation bias or a response curve of a change in the different refractive indices caused by the modulation bias.

21. The method according to claim 16, wherein, The non-uniform arrangement is also configured such that the change in the one or more optical properties of the optical carrier of the optical modulator is monotonic with respect to the response curve of the change in the different refractive indices due to the modulation bias.

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