Polarization beam splitter using asymmetric power splitting and multipath interferometry

Abstract

A polarization beam splitter includes an input port, a first output port and a second output port, and a polarization beam splitting region coupled between the input port and the first and second output ports. The input port is adapted to receive a polarization multiplexed guided wave optical signal comprising a transverse electric (TE) optical signal and a transverse magnetic (TM) optical signal. The polarizing beam splitting region includes a pattern of at least two materials having different refractive indices. This pattern is shaped to direct a TE optical signal and a TM optical signal by directing a majority of a first power of a TE optical signal received at an input port to a second output port via asymmetric power splitting while directing a majority of a second power of a TM optical signal received at an input port to a first output port via multipath interferometry and demultiplexing.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to U.S. Application No. 18 / 375,717, filed October 2, 2023, the contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure relates generally to photonic devices, and specifically, but not limited to, polarization beam splitters. Background Technology

[0004] Artificial intelligence (AI) and machine learning (ML) applications are expected to place high demands on the data bandwidth of future XPUs (e.g., central processing units, graphics processing units, tensor processing units, etc.). In fact, data bandwidth is expected to become a bottleneck for the future development of XPUs. Specifically, board-to-board interconnects and chip-to-chip interconnects will need to support ever-increasing bandwidth. Optical interconnect technology holds promise for meeting this growing bandwidth demand. However, despite the high bandwidth offered by optical interconnects, conventional designs suffer from low data bandwidth density (i.e., data bandwidth per unit area). To improve the data bandwidth density of optical interconnects, the physical size of photonic integrated circuits needs to be reduced.

[0005] Polarization beam splitters (PBSs) are fundamental building blocks of high-speed optical interconnects because they enable polarization multiplexing. A PBS is an optical filter that splits an incident light beam into two separate beams with different polarizations. Ideally, these separate beams are fully polarized and orthogonal. In the context of guided light (e.g., optical fiber), the incident light may include transverse electric (TE) and transverse magnetic (TM) polarizations, while in the context of single-mode waveguides (e.g., single-mode optical fiber), the light may only include the basic spatial modes TE0 and TM0 for the corresponding polarizations. The bandwidth of the guided light can be increased by encoding different data channels on the orthogonal polarization modes TE0 and TM0.

[0006] The physical size of a standard PBS is approximately 100 μm x 8 μm. PBSs that can significantly reduce these physical sizes while maintaining desired functional characteristics (e.g., polarization crosstalk and isolation, insertion / transmission loss, back reflection, etc.) will help meet the higher data bandwidth density requirements anticipated in future XPU development. Summary of the Invention Attached Figure Description

[0008] Non-limiting and non-exhaustive embodiments of the invention are described with reference to the following figures, wherein, unless otherwise stated, the same reference numerals refer to the same parts in the various views. Not all instances of elements need to be labeled so as not to interfere with the figures where appropriate. The figures are not necessarily drawn to scale, but rather to emphasize the principles described.

[0009] Figure 1 This is a functional block diagram illustrating a polarization beam splitter (PBS) according to an embodiment of the present disclosure.

[0010] Figure 2 Details of a PBS with a reverse-designed polarization beam splitter region according to an embodiment of the present disclosure are shown.

[0011] Figure 3A and Figure 3B A transverse electric (TE) path through a polarization beam splitting region according to an embodiment of the present disclosure is shown, which directs most of the power of the TE optical signal to the output port 2 of the PBS via asymmetric power beam splitting.

[0012] Figure 4A and Figure 4B A transverse magnetic (TM) path through a polarization beam splitting region according to an embodiment of the present disclosure is shown, which directs most of the power of the TM optical signal to output port 1 via multipath interferometry.

[0013] Figure 5A This is a graph illustrating the transmission loss of a PBS according to an embodiment of the present disclosure.

[0014] Figure 5B This is a graph showing the back reflection loss of a PBS according to an embodiment of the present disclosure.

[0015] Figure 5C This is a graph illustrating the crosstalk loss of a PBS according to an embodiment of the present disclosure.

[0016] Figure 6 This is a flowchart illustrating the operation of PBS demultiplexing TE and TM optical signals according to an embodiment of the present disclosure.

[0017] Figure 7A An exemplary simulation environment for simulating the operation of a PBS under design, according to an embodiment of the present disclosure, is shown.

[0018] Figure 7B An operational simulation of a PBS according to an embodiment of the present disclosure is shown.

[0019] Figure 7C The accompanying simulation (backpropagation) of performance loss error in a simulated environment including PBS is shown according to an embodiment of the present disclosure.

[0020] Figure 8A This is a flowchart illustrating an example time step of the operation and accompanying simulation for reverse engineering a PBS according to an embodiment of the present disclosure.

[0021] Figure 8B This is a flowchart illustrating the relationship between operational simulation and accompanying simulation (backpropagation) according to embodiments of the present disclosure. Detailed Implementation

[0022] This document describes embodiments of systems, apparatus, and methods of operation for polarization beam splitters (PBS). Numerous specific details are set forth in the following description to provide a thorough understanding of the embodiments. However, those skilled in the art will recognize that the techniques described herein can be implemented or practiced without one or more of the specific details stated herein, using 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.

[0023] Throughout this specification, references to "an embodiment" or "an embodiment" mean that a particular feature, structure, or characteristic described in connection with an embodiment is included in at least one embodiment of the invention. Therefore, the phrases "in one embodiment" or "in an embodiment" appearing in various places throughout this specification do not necessarily refer to the same embodiment. Furthermore, particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0024] The PBS embodiments described herein are inspired by reverse engineering to achieve a PBS that achieves similar performance (referred to as the target performance target) in terms of transmission loss, back reflection, and crosstalk isolation, but with a significantly smaller package size than conventional designs. For example, in various embodiments, the polarization beam splitting region of the PBS described herein can be achieved within a 7 μm x 8 μm coverage area while achieving the following target performance targets: transmission loss <-1 dB, back reflection loss <-30 dB, and polarization crosstalk loss <-20 dB. Furthermore, the PBS can be integrated with other optoelectronic circuits as part of a photonic integrated circuit (PIC) fabricated using mature semiconductor lithography techniques with silicon and silicon dioxide. Of course, other materials and fabrication techniques can also be used.

[0025] Figure 1 This is a functional block diagram illustrating a PBS 100 according to an embodiment of the present disclosure. The illustrated embodiment of the PBS 100 includes a polarization beam splitting region 105, an input port 110, and output ports 1115A and 2115B (collectively referred to as "output port 115").

[0026] Although the PBS 100 is described in conjunction with its polarization beam splitting function (polarization demultiplexing), it should be understood that light propagating in the reverse direction along the output port 115 to the input port 110 will be combined (polarization multiplexed). Therefore, due to optical reciprocity, the PBS 105 can also be referred to as a polarization beam combiner or polarization multiplexer when operating in the reverse direction. Thus, a polarization beam splitter (PBS) and a polarization beam combiner (PBC) can be the same physical photonic device, but simply refer to the direction of light flow through the photonic device. Similarly, designating a given port as an "input" port and an "output" port simply refers to the directional flow of the optical signal through the PBS; however, these designations can be reversed when referring to a PBC.

[0027] Return to Figure 1 Input port 110 acts as an interface between polarization beam splitting region 105 and waveguide 120, while output port 115 acts as an interface between polarization beam splitting region 105 and waveguides 125A and 125B. The guided wave optical signal received from waveguide 120 is demultiplexed into different optical signals output from output port 115 to waveguides 125A and 125B. The guided wave optical signal is a polarization-multiplexed signal, while the demultiplexed signal output from output port 115 is a single-polarization optical signal. In the illustrated embodiment, waveguide 120 (e.g., single-mode fiber) carries transverse electric (TE) and transverse magnetic (TM) optical signals. These TE and TM optical signals can be encoded on a common carrier wavelength (e.g., 1280 nm to 1350 nm), or in some embodiments, on different carrier wavelengths. In the illustrated embodiment, the TE and TM optical signals are the basic spatial modes of single-mode fiber (e.g., TE0 and TM0). Each signal TE0 and TM0 can be encoded for a different communication channel, thereby increasing the bandwidth of waveguide 120. The PBS 100 operates by demultiplexing these different communication channels by physically separating the TM optical signal and the TE optical signal onto output ports 115A and 115B, respectively.

[0028] Figure 2 A PBS 200 with a reverse-design-inspired polarization beam splitting region is shown according to an embodiment of the present disclosure. The PBS 200 is... Figure 1 This illustrates one possible implementation of the PBS 100. Specifically, Figure 2Details of the polarization beam splitting region 205 are shown. The illustrated embodiment of the polarization beam splitting region 205 includes a pattern of at least two materials (e.g., silicon and silicon dioxide) with different refractive indices. This pattern is shaped to demultiplex the TE optical signal (e.g., TE0) and TM optical signal (e.g., TM0) received at input port 110. The pattern within the polarization beam splitting region 205 is shaped to direct most of the power of the TE optical signal received at input port 110 to output port 2115B. Sending most of the TE power to output port 2115B via asymmetric power beam splitting achieves selective guidance of the TE optical signal to output port 2115B. Correspondingly, this pattern of the polarization beam splitting region 205 is also shaped to direct most of the power of the TM optical signal received at input port 110 to output port 1115A. Sending most of the TM power to output port 1115A via multipath interferometry achieves selective guidance of the TM optical signal to output port 1115A.

[0029] In one embodiment, the polarization beam splitting region 205 is a planar waveguide in which the pattern shown is disposed, which is a two-dimensional (2D) pattern. Of course, in other embodiments, a three-dimensional (3D) pattern can also be implemented. In the illustrated embodiment, the 2D pattern is defined using two materials (e.g., silicon and silicon dioxide) with different refractive indices. The pattern is an irregular pattern. For example, from a macroscopic perspective, the irregular pattern is not formed by regular geometric shapes such as triangles, rectangles, pentagons, hexagons, octagons, etc. Instead, the pattern is an organic pattern resembling natural coastlines, channels, bays, and islands. Of course, from a microscopic perspective, the pattern can be formed by pixelated deposits of two or more materials, and each pixel can include a certain geometry. The feature size and shape of the individual material pixels depend on the manufacturing process, but the overall pattern does not resemble simple regular geometric shapes such as triangles, rectangles, or other low-order polygons (e.g., 10 sides or less).

[0030] In the illustrated embodiment, the irregular shape pattern includes a number of pattern features (i.e., features of irregular shapes) that facilitate asymmetric power beam splitting of the TE optical signal along with synchronous multipath interferometry of the TM optical signal. Figure 3A , Figure 3B , Figure 4A and Figure 4B These pattern features are shown. Specifically, Figure 3A and Figure 3B The TE path 305, passing through the polarization beam splitting region 205, is shown. This TE path directs most of the power of the TE optical signal to the output port 2115B via asymmetric power beam splitting. Accordingly, Figure 4A and Figure 4BThe TM path 405A-C, which passes through the polarization beam splitting region 205, is shown. This TM path directs most of the power of the TM optical signal to the output port 1115A via multipath interferometry.

[0031] refer to Figure 3B The TE path 305 extends from the input port 110 to the output port 2115B along an irregularly shaped channel 310. The irregularly shaped channel 310 is formed by surrounding a low-refractive-index material (such as silicon (shown in white)) with a high-refractive-index material (such as silicon dioxide (shown in black)). In the illustrated embodiment, the irregularly shaped channel 310 includes an S-shaped bend that is not obstructed by the low-refractive-index material between the input port 110 and the output port 2115B. In other words, the irregularly shaped channel 310 forms a continuous, unobstructed path with a slight, meandering S-shaped bend between the ports. The irregularly shaped channel 310 facilitates asymmetric power splitting, thereby directing most of the optical power in the TE optical signal from the input port 110 to the output port 2115B. Figure 3A This is a power density heatmap, showing the power density of the TE optical signal (in-plane electric field) passing through the polarization beam splitting region 205. As shown, most of the optical power in the TE optical signal propagates along the TE path 305 through the irregularly shaped channel 310 and reaches the output port 2115B.

[0032] refer to Figure 4A and Figure 4B TM paths 405A-C (collectively referred to as TM paths 405) extend from input port 110 to output port 1115A along multiple interferometric paths. TM paths 405A-C are also defined by a high-refractive-index material (such as silicon (shown in white)) surrounded by a low-refractive-index material (such as silicon dioxide (shown in black)). The main TM path 405A consists of two sub-paths that meander through multiple scattering locations. In other words, the main TM path 405A includes multiple scattering locations 407 formed by islands of low-refractive-index material disposed within the high-refractive-index material. The secondary TM path 405B takes an unobstructed, meandering path through the high-refractive-index material. The tertiary TM path 405C takes a less direct path (partially along the irregularly shaped channel 310) through the high-refractive-index material and is blocked by the low-refractive-index material at location 410. It is believed that the brief coupling and / or near-perpendicular incident incidence of the third-order TM path 405C onto a low-refractive-index material barrier allows a component of the TM optical signal to pass through the low-refractive-index material barrier at position 410. In any case, multiple TM paths established by the pattern between input port 110 and output port 1115A guide the majority of the optical power of the TM optical signal from input port 110 to output port 1115A via multipath interferometry. Figure 4A The power density thermal map shows the strong coupling between the TM optical signal (out-of-plane electric field) and the output port 1115A.

[0033] Figures 5A-5C The high efficiency and low crosstalk characteristics of PBS 100 (or 200) are demonstrated. Figure 5A The transmission loss curves for PBS 100 / 200 are shown within the wavelength range of interest (e.g., 1280 nm to 1350 nm). Transmission loss is characterized by s-parameters S31 and S62. Reference Figure 1 The S31 s parameter refers to the transmission / insertion loss of optical power between virtual ports VP1 and VP3. Virtual ports VP1 and VP3 correspond to the TE0 optical signals at physical ports 110 and 115B. Correspondingly, the S62 s parameter refers to the optical power loss between virtual ports VP2 and VP6. Virtual ports VP2 and VP6 correspond to the TM0 optical signals at physical ports 110 and 115A. As shown in the figure, the transmission loss (also known as insertion loss) remains below approximately -1 dB within the indicated wavelength range.

[0034] Figure 5B The back reflection loss curves of PBS 100 / 200 within the wavelength range of interest are shown. The back reflection loss is characterized by s-parameters S11 and S22. (Reference) Figure 1 The S11 and S22 parameters refer to the back reflection loss of the optical power at virtual ports VP1 and VP2. Virtual ports VP1 and VP2 correspond to the TE0 and TM optical signals at physical input port 110, respectively. As shown in the figure, within the wavelength range shown, the back reflection loss reflected from physical input port 110 remains below approximately -30 dB for both TM and TE optical signals.

[0035] Figure 5C The crosstalk (isolation) loss between the TE optical signal and the TM optical signal is shown. Crosstalk is characterized by the s-parameters S32, S412, and S42 of polarization crosstalk at physical output port 2115B (shown). Crosstalk can also be characterized by the s-parameters S51, S61, and S52 of polarization crosstalk at physical output port 115A (not shown). In the illustrated embodiment, polarization crosstalk is maintained below approximately -20 dB within the wavelength range of interest. The s-parameter values ​​listed above can be considered as target values ​​for declaring the loss function for iterative reverse design of the pattern within polarization beam splitting region 205.

[0036] Figure 6This is a flowchart illustrating an operation process 600 of a PBS 100 / 200 according to an embodiment of the present disclosure to demultiplex TE and TM optical signals received at input port 110. The order of some or all of the process blocks appearing in process 600 should not be considered limiting. Rather, those skilled in the art who benefit from this disclosure will understand that some process blocks may be performed in various orders not shown, or even in parallel.

[0037] In process block 605, polarization-multiplexed optical signals are received from waveguide 120 at input port 110. These TE and TM optical signals can be the basic optical signals TE0 and TM0. The polarization-multiplexed signals can be received simultaneously or at different times. In process block 610, most of the optical power (also known as the first power majority) of the TE optical signal is directed from input port 110 to output port 1115B via asymmetric power beam splitting. In process block 615, most of the optical power (also known as the second power majority) of the TM optical signal is directed from input port 110 to output port 1115A via multipath interferometry. In process block 620, the demultiplexed TE and TM optical signals are output from output port 115 to waveguides 125B and 125A, respectively.

[0038] As mentioned above, PBS 100 / 200 is inspired by reverse engineering. Specifically, a pattern of at least two materials with different refractive indices can be defined by iteratively minimizing a loss function that sums transmission loss, reflection loss, and crosstalk loss. The optimization objective of the reverse engineering approach can be constructed as a function of the following loss function, Loss(x).

[0039] (Formula 1) in Transmission loss(x,λ) = Transmission(x,λ) – target value 1 Reflection loss(x,λ) = Reflection(x,λ) – target value2 Crosstalk loss(x,λ) = Crosstalk(x,λ) – target value 3.

[0040] The objective is designed such that the generated structure / pattern of the polarization beam splitter region 205 is encouraged to guide the TM optical signal to output port 1 114A and the TE optical signal to output port 2 115B.

[0041] Reverse design is performed using a design simulator (also known as a design model) configured with an initial design or pattern of polarization beam splitting region 205 to perform a forward operational simulation of the initial design (e.g., using Maxwell's equations of electromagnetism). For example, the initial design could be a random pattern of silicon and silicon dioxide. The output of the forward operational simulation is a simulated field response at output port 115 in response to a stimulus at input port 110. Specific performance parameters of this output field response can be selected as parameters of interest (e.g., power loss, wavelength, crosstalk, etc.) and are referred to as simulated performance parameters. A loss function is calculated using the simulated performance parameters, which can be a scalar value (e.g., the root mean square error between the simulated performance value and the target performance value). The differentiable nature of the design model allows for backpropagation via an accompanying simulation of the performance loss error, which is the difference between the simulated output value and the desired / target performance value. During the accompanying simulation, performance loss errors are backpropagated through the design model to generate structural gradients, which represent, for example, the sensitivity of the performance loss values ​​to variations in the structural material properties (e.g., the topology or patterning of the material) of the polarization beam splitter region 205. These gradients can be computed using procedures such as TensorFlow, published by Google. A structure optimizer can then use these gradients to optimize or improve the initial structural design to generate a revised structural design for the polarization beam splitter region 205. Forward and backward simulations, along with structural optimization (e.g., iterative gradient descent, stochastic gradient descent, etc.), can then be iterated until the performance loss values ​​reach an acceptable design criterion (referred to as saturation) and / or a predetermined number of iterations are reached. The above description is merely an example of a reverse design technique that can be used to improve or optimize the characteristics and topology of the pattern within the polarization beam splitter region 205. It should be understood that other reverse design techniques can also be implemented independently or in combination with other conventional design techniques.

[0042] The aforementioned reverse engineering technique can be applied to determine specific material combinations, feature sizes, and feature arrangements (i.e., patterns) to achieve the desired polarization demultiplexing using the aforementioned loss function. Loss(x) is a function of x, where x is a vector representing the structural pattern of materials with different refractive indices within the polarization beam splitting region 205. In one embodiment, target values ​​1, 2, and 3 correspond to the combinations described above. Figures 5A-5C Listed dB values.

[0043] Figures 7A to 7CThe initial setup, operational simulation, and adjoint simulation of a simulation environment 701 for optimizing the structural parameters of a physical device (e.g., PBS 100 or 200) using a design model, according to a reverse design embodiment, are illustrated respectively. The simulation environment 701 and its corresponding initial setup, operational simulation, adjoint simulation, and structural parameter optimization can be achieved via a physics simulator using Maxwell's equations. Figures 7A to 7C As shown, the simulation environment is represented in two dimensions; however, it should be understood that higher dimensions (e.g., 3D space) can also be used to describe the simulation environment 701 and the physical apparatus. In some embodiments, particularly via simulations (e.g., time forward and backward propagation) that model the field responses (e.g., electric and magnetic fields) using finite-difference time-domain (FDTD) methods, it is possible to achieve... Figures 7A to 7C The optimization of the structural parameters of the physical device shown.

[0044] Figure 7A An example rendering of simulation environment 701-A describing an electromagnetic device is shown. Simulation environment 701-A represents simulation environment 701 at an initial time step (e.g., initial setup) for optimizing the structural parameters of the physical device. The physical device described by simulation environment 701 may correspond to a PBS 100 or 200 having a designable region 705 (e.g., polarization beam splitting region 205) in which the structural parameters of the simulation environment can be designed, modified, or otherwise changed. Simulation environment 701 includes an excitation source 715 (e.g., Gaussian pulse, wave, waveguide mode response, etc.) located at input port 110. Electric and magnetic fields (e.g., field responses) within simulation environment 701 can vary in response to changes in excitation source 715. The specific settings of the initial structural parameters, excitation source, performance parameters, and other metrics (i.e., initial description) of the input physical device for a first-principle simulation are defined before the simulation begins.

[0045] As shown in the figure, the simulation environment 701 (and the designed physical apparatus) is described by a plurality of voxels 710, which represent individual elements of the two-dimensional (or three-dimensional) space of the simulation environment. Each of the voxels is shown as a two-dimensional square; however, it should be understood that a voxel can be represented as a cube or other shape in three-dimensional space. It should be understood that the specific shape and dimensions of the plurality of voxels 710 can be adjusted according to the simulation environment 701. It should be further noted that only a portion of the plurality of voxels 710 is shown to avoid obscuring other aspects of the simulation environment 701. Each of the plurality of voxels 710 is associated with one or more structural parameters, field values ​​for describing the field response, and source values ​​for describing the excitation source at a specific location within the simulation environment 701. For example, the field response may correspond to a vector describing the electric and / or magnetic fields of each of the plurality of voxels 710 at a specific time step. More specifically, this vector may correspond to a Yee lattice that discretizes Maxwell's equations to determine the field response. In some embodiments, the field response is based at least in part on the structural parameters and the excitation source 715.

[0046] Figure 7B An example operational simulation of simulation environment 701-B at a specific time step is shown, in which excitation source 715 is active (e.g., generating a wave originating from excitation source 715 and propagating through simulation environment 701). As mentioned, the physical device is an optical modulator operating at the frequency of interest and having a specific waveguide mode (e.g., transverse electromagnetic mode, transverse electric mode, etc.), and the excitation source is located at input port 110. The operational simulation is performed over multiple time steps. During the operational simulation, the field response (e.g., field value) of each of the plurality of voxels 710 changes in response to excitation source 715 and is updated at least in part based on the structural parameters of the physical device at each of the plurality of time steps. Similarly, in some embodiments, the source value is updated for each of the plurality of voxels (e.g., in response to the propagation of electromagnetic waves from excitation source 715 through the simulation environment). It should be understood that the operational simulation is stepwise, and for each of the plurality of time steps, the field value (and source value) is updated stepwise over time within each time step. It should be further noted that in some embodiments, the update is an iterative process, and the update for each field and source value is based at least in part on the previous update for each field and source value.

[0047] During operational simulation, the performance loss function Loss(x) at each output port 720 and 725 can be calculated, at least in part, based on a comparison (e.g., mean squared error) between the field response at a specified time step (e.g., the last time step of the operational simulation) and the desired field response. The performance loss value can be described by a specific performance value (e.g., power). The structural parameters can be optimized for that specific performance value.

[0048] Figure 7C An example backpropagation of performance loss error within a simulation environment 701-C describing a physical device is illustrated. In one embodiment, the performance loss error is injected at output ports 720 and 725 during the performance simulation as a reverse excitation source for exciting a reverse field response through voxel 710 in the simulation environment 701-C. The accompanying performance simulation of the performance loss error determines the effect of variations in the structural parameters of voxel 710 on the performance loss value.

[0049] Figure 8A This is a flowchart solution 800 illustrating an example time step of a time-progressive simulation 810 and a backpropagation 850 within a simulation environment according to an embodiment of the present disclosure. Flowchart 800 is one possible implementation of a design model that can be used to perform the forward operational simulation 810 and the backpropagation 850 of the simulation environment. In the illustrated embodiment, the forward operational simulation utilizes the FDTD method to model the field response (both electric and magnetic fields) to the excitation source at multiple time steps. More specifically, the time-dependent Maxwell's equations (partial differential form) are discretized to solve for the field vector components (e.g., ...) within multiple time steps. Figures 7A to 7C The field response of each of the multiple voxels 710 in the simulation environment 701.

[0050] like Figure 8A As shown, flowchart 800 includes update operations for a portion of operational simulation 810 and accompanying simulation 850. Operational simulation 810 is performed over multiple time steps (e.g., from an initial time step through a predetermined or conditional number of time steps of a specified time step size to the last time step) and models changes in electric and magnetic fields (e.g., starting from an initial field value 811) of multiple voxels describing the simulation environment and / or physical setup, which collectively correspond to the field response. More specifically, update operations (e.g., 812, 814, and 816) are iterative and based on the field response, structural parameter 804, and one or more physical stimulus sources 808. Each update operation is immediately followed by another update operation, representing a time-sequential progression step within multiple time steps. For example, update operation 814 updates field value 813 based on the field response, source 808, and structural parameter 804 determined from the previous update operation 812 (e.g., see [link to previous update operation]). Figure 7B Similarly, update operation 816 updates the field value based on the field response determined from update operation 814 (see, for example, see...). Figure 8BIn other words, at each time step of the operational simulation, the field value (and therefore the field response) is updated based on the previous field response and the structural parameters of the physical device. Once the last time step of the operational simulation 810 has been performed, the loss value 818 can be determined (e.g., based on a predetermined loss function 820). The loss gradient determined from block 852 can be considered as an adjoint source or dummy source (e.g., a physical stimulus or excitation source originating from the output region), which backpropagates (stepwise through multiple time steps from the last time step until reaching the initial time step) to determine the structural gradient 868.

[0051] In the illustrated embodiment, from a high-level perspective, the FDTD solution (e.g., time-forward simulation 810) and backpropagation 850 problems are described graphically using only "update" and "loss" operations and their corresponding gradient operations. First, the simulation is set up, providing the structural parameters of the simulation environment (and electromagnetic devices), the excitation source, and the initial field state. 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 performed by… Given, among which, for .here, This corresponds to the total number of time steps in the forward time simulation (e.g., multiple time steps). Corresponding to the simulation environment at time step The field response at a given location (the field values ​​associated with the electric and magnetic fields of each of the multiple voxels). Corresponding to the simulation environment at time step The excitation source at that location (the source value associated with the electric and magnetic fields of each of the multiple voxels), while These correspond to structural parameters that describe the topology and / or material properties of an electromagnetic device.

[0052] It should be noted that, using the FDTD method, the update operation can be specifically described as follows:

[0053] (1)

[0054] That is, FDTD updates are linear for both field and source terms. Specifically, and These are linear operators, and they depend on the structure parameters. And act on the field respectively Heyuan Here, let's assume, Where N is the number of FDTD field components in the time-forward simulation. Additionally, the loss calculation is performed by... It is given, which takes the calculated field as input and produces a single real-valued scalar (e.g., loss value) that can be reduced and / or minimized.

[0055] The relevant quantities to be generated in revising or otherwise optimizing the structural parameters of the electromagnetic device are: It is used to describe the change in loss value relative to the structural parameters of the electromagnetic device, and is expressed as... Figure 8A The “structural gradient” shown.

[0056] Figure 8B This is a diagram 880 illustrating the relationship between operational simulation and update operations of accompanying simulation (e.g., backpropagation) according to embodiments of the present disclosure. More specifically, Figure 8B This paper summarizes the calculation of structure gradient. The operational simulations and their associated simulations are involved, and the structural gradient includes... , , and The simulation update operation 814 updates the field values ​​of multiple voxels at time step t. 813 Update to the next time step (i.e., the 1st time step) (One time step), the next time step corresponds to a field value of 815. Gradient 855 is used to determine the backpropagation (e.g., the time-reverse update operation 856). It is used in conjunction with gradient 869 to at least partially compute the structural gradient. . This represents the contribution of each field to the loss value L. Note that this is a partial derivative, therefore it does not account for... The causal relationship. Therefore, using It contains Relationship. Loss gradient It can also be used to calculate structural gradients. And it corresponds to the total derivative of the field-pair loss value L. Specific time step loss gradient at point equal The sum. Finally, using the field gradient... It starts from each time / update step. . contributions. It is given by the following formula:

[0057] (2)

[0058] For completeness, summation The complete form of the first moment is expressed as:

[0059] (3)

[0060] Based on the equation (1) The definition should be noted. It can be substituted into equation (3) to obtain the accompanying update of backpropagation (e.g., update operations such as update operation 856), which can be expressed as:

[0061] (4)

[0062] or

[0063] (5)

[0064] The accompanying update is the backpropagation of the loss gradient from a later time step to an earlier time step, and can be called the backpropagation of the loss gradient. The inverse solution. Structural gradient. The second term in the sum is represented as:

[0065] (6)

[0066] This is for the equation (1) described A specific form of.

[0067] The process described above is illustrated using computer software and hardware. The described techniques can be embodied in machine-executable instructions stored in a tangible or non-transitory machine-readable storage medium, which, when executed by a machine, will cause the machine to perform the described operations. Alternatively, the process can be embodied in hardware such as an application-specific integrated circuit (“ASIC”) or other hardware.

[0068] Tangible machine-readable storage media include any mechanism that provides (i.e., stores) information in a non-transitory form, accessible by a machine (e.g., a computer, network device, personal digital assistant, manufacturing tool, any device having a collection of one or more processors, etc.). For example, machine-readable storage media include recordable / non-recordable media (e.g., read-only memory (ROM), random access memory (RAM), disk storage media, optical storage media, flash memory devices, etc.).

[0069] The above description of the illustrative embodiments of the invention (including those described in the summary) is not intended to be exhaustive or to limit the invention to the precise forms disclosed. As those skilled in the art will recognize, while specific embodiments and examples of the invention have been described herein for illustrative purposes, various modifications are possible within the scope of the invention.

[0070] These modifications can be made to the invention within the context of the detailed description above. The terminology used in the appended claims should not be construed as limiting the invention to the specific examples disclosed in the specification. Rather, the scope of the invention will be determined entirely by the appended claims as interpreted according to the established principles of the claims.

Claims

1. A polarization beam splitter, comprising: An input port is provided, which is adapted to receive polarization-multiplexed guided wavelight signals, including transverse electric (TE) optical signals and transverse magnetic (TM) optical signals. First output port and second output port; and A polarization beam-splitting region coupled between the input port and the first and second output ports, wherein the polarization beam-splitting region comprises a pattern of at least two materials with different refractive indices, wherein the pattern is shaped to demultiplex the TE optical signal and the TM optical signal by directing a majority of the first power of the TE optical signal received at the input port to the second output port via asymmetric power beam splitting, and simultaneously directing a majority of the second power of the TM optical signal received at the input port to the first output port via multipath interferometry.

2. The polarization beam splitter of claim 1, wherein the at least two materials comprise silicon and silicon dioxide.

3. The polarization beam splitter of claim 1, wherein the input port includes an interface between the single-mode waveguide and the polarization beam splitting region, and wherein the TE optical signal and the TM optical signal are the basic polarization modes TE0 and TM0 of the single-mode waveguide, respectively.

4. The polarization beam splitter of claim 1, wherein the polarization beam splitting region includes a planar waveguide having a pattern disposed within the planar waveguide as a two-dimensional pattern of the at least two materials.

5. The polarization beam splitter of claim 1, wherein the pattern comprises: A first irregularly shaped channel, formed by a high-refractive-index material surrounding a low-refractive-index material, extends between the input port and the second output port.

6. The polarization beam splitter of claim 5, wherein the first irregular shape channel comprises an S-shaped bend that is not blocked by the low refractive index material.

7. The polarization beam splitter of claim 5, wherein the first irregularly shaped channel forms a TE path from the input port to the second output port, the TE path being shaped to selectively direct the majority of the first power of the TE optical signal to the second output port.

8. The polarization beam splitter of claim 1, wherein the pattern is shaped to selectively direct a majority of the second power of the TM optical signal to the first output port via a plurality of TM paths extending from the input port to the first output port, the TM paths being defined by a high-refractive-index material surrounded by a low-refractive-index material.

9. The polarization beam splitter of claim 8, wherein the plurality of TM paths comprises: The main TM path includes multiple scattering locations formed by islands of low-refractive-index material dispersed within the high-refractive-index material; Sub-TM path, the sub-TM path passing through the high refractive index material; as well as The tertiary TM path traverses the high-refractive-index material, and the tertiary TM path is blocked by the low-refractive-index material at at least one location. The primary TM path, the secondary TM path, and the tertiary TM path guide most of the second power of the TM optical signal received at the input port to the first output port via the multipath interferometry.

10. The polarization beam splitter of claim 1, wherein the pattern comprises an inverse design pattern defined by an iterative minimization of a loss function that sums transmission loss, reflection loss, and crosstalk loss.

11. A method for demultiplexing polarization-dependent optical signals, the method comprising: At the input port of the polarization beam splitting region, transverse electric (TE) optical signals and transverse magnetic (TM) optical signals multiplexed on a common waveguide are received, wherein the polarization beam splitting region comprises a pattern of at least two materials with different refractive indices; Multipath interferometry is used to direct most of the first power of the TM optical signal received at the input port to a first output port coupled to the polarization beam splitting region; as well as Asymmetric power beam splitting is used to direct most of the second power of the TE optical signal received at the input port to a second output port coupled to the polarization beam splitting region. When the input port is simultaneously excited by the TM optical signal and the TE optical signal, the pattern simultaneously induces the multipath interferometry and the asymmetric power beam splitting on the TM optical signal and the TE optical signal, respectively.

12. The method of claim 11, wherein the input port is disposed on a first side of the polarization beam splitting region, wherein the first output port and the second output port are disposed on a second side of the polarization beam splitting region opposite to the first side, and wherein the first output port and the second output port are physically offset from each other along the second side.

13. The method of claim 11, wherein the pattern comprises an irregular pattern of the at least two materials.

14. The method of claim 13, wherein the polarization beam splitting region comprises a planar waveguide having a pattern disposed within the planar waveguide as a two-dimensional pattern of the at least two materials.

15. The method of claim 13, wherein the irregular pattern comprises: A first irregularly shaped channel, formed by a high-refractive-index material surrounding a low-refractive-index material, extends between the input port and the second output port.

16. The method of claim 15, wherein the first irregularly shaped channel comprises an S-shaped bend that is not blocked by the low-refractive-index material.

17. The method of claim 15, wherein the first irregularly shaped channel forms a TE path from the input port to the second output port, the TE path selectively directing the majority of the first power of the TE optical signal to the second output port.

18. The method of claim 11, wherein the pattern selectively directs the majority of the second power of the TM optical signal to the first output port via a plurality of TM paths extending from the input port to the first output port, the TM paths being defined by a high-refractive-index material surrounded by a low-refractive-index material.

19. The method of claim 18, wherein the plurality of TM paths comprises: The main TM path includes multiple scattering locations formed by islands of low-refractive-index material dispersed within the high-refractive-index material; Sub-TM path, the sub-TM path passing through the high refractive index material; as well as The tertiary TM path traverses the high-refractive-index material, and the tertiary TM path is blocked by the low-refractive-index material at at least one location. The primary TM path, the secondary TM path, and the tertiary TM path guide most of the second power of the TM optical signal received at the input port to the first output port via the multipath interferometry.

20. The method of claim 11, wherein the pattern comprises an inverse design pattern defined by iterative minimization of a loss function that sums transmission loss, reflection loss, and crosstalk loss.

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