Methods and systems for composite topological design

Abstract

A method for topological design optimization in which a number of objective scattering(S) parameters are initially decomposed into a product of smaller devices (primitives). Each of the primitives are optimized in parallel using inverse design; and the topologies of the smaller devices are then composited into a final device design region, in which the final device design region is an initialization of a final optimization, advantageously saving computation time. According to at least one embodiment, the herein described optimization procedure can be utilized in order to design a composite power combiner that is essentially phase-insensitive.

Description

Attorney Docket No.105018-201 METHODS AND SYSTEMS FOR COMPOSITE TOPOLOGICAL DESIGN CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. Patent Application Serial No.63 / 632,680, filed April 11, 2024, and U.S. Patent Application Serial No.63 / 632,728, filed April 11, 2024, under applicable sections of 35 U.S.C §119 and 35 U.S.C.120, the contents of which are hereby incorporated by reference as if disclosed herein in their entireties. STATEMENT REGARDING FEDERAL SPONSORED RESEARCH AND DEVELOPMENT

[0002] This invention was made with government support under grant number DE-AR0000942, awarded by the Department of Energy. The government has certain rights in the invention. BACKGROUND

[0003] Inverse design has matured as a powerful and useful tool for a number ofapplications, including, for example, the design of photonic integrated circuits (PICs), thereby enabling the creation of efficient, highly-compact, and novel devices. Recent progress in fabrication-constraint-aware optimization techniques has yielded practical demonstrations of inverse-designed devices and systems fabricated in foundry, further driving the adoption of inverse design. In this regard, a wide array of fundamental building blocks have been successfully demonstrated, such as grating couplers, waveguide bends, mode converters, polarization splitter-rotators, and wavelength multiplexors, in which these components have typically outperformed conventional and intuition-based designs in terms of both efficiency and area.

[0004] Frequently, inverse design is employed in multi-objective design problems, inwhich multiple figures-of-merit (FOMs) are either minimized or maximized simultaneously. Multi-objective optimizations may require simultaneously optimizing the performance of a device over a number of dimensions such as wavelength (i.e., bandwidth), waveguide modes, polarizations, scattering parameters, fabrication variation (i.e., under / over-etch), or other operating conditions, each represented by their own FOM. Accordingly, multiple engineering 1 31116671.1Attorney Docket No.105018-201 simulations are typically required in order to evaluate all objective functions, and therefore the computation cost of multi-objective optimization tends to scale linearly with the number of objectives.

[0005] Furthermore and as the scale of photonic devices increases, the difficulty offinding feasible and efficient solutions also increases. Conventional wisdom dictates that as the complexity of the design requirements increases or grows, the number of free parameters of the model must correspondingly increase in order to accommodate this increased level of complexity. For a topological device, increasing the number of design parameters translates directly to increasing the size of the design region, thus increasing the number of device pixels sand yielding a larger search space. This larger design space, in turn, increases the probability of the existence of a suitable solution to the number of design requirements. However, finding such a solution within a non-convex and exponentially-increasing search space increases optimization times and may lead to convergence issues. For example, an inverse-designed 10µm x10µm dual- polarization vertical coupler has been demonstrated in which the coupler was optimized over two fiber polarization states and ~ 80nm bandwidth. While the design objective of this device was successfully achieved, the model consisted of 720,000 free parameters requiring several days of computation time on a high performance computing cluster to be optimized over more than 500 iterations (>1000 simulations).

[0006] Much of the known art on inverse design of large devices aims to reduce thecomputational cost of the optimization. These known approaches may be broadly categorized as either reducing the number of iterations required to provide an optimal design solution, or reducing the computational cost of each iteration. Various approaches attempt to more efficiently traverse the feasible design space, such as hierarchical shape optimization, always-feasible design generation using conditional generators, and adaptive projection. Others have explored replacing conventional constrained optimization approaches (e.g., L-BFGS-B) with generative neural networks and reinforcement learning in order to predict the next iteration. While deep- learning-assisted optimizations have shown orders of magnitude reduction in design time for pre- trained models, these models tend to be device-specific, and collecting training data and training the model can be computationally expensive. 2 31116671.1Attorney Docket No.105018-201

[0007] Reducing the per-iteration computational cost requires reducing the cost ofengineering simulations (typically either Finite-Difference-Time-Domain (FDTD) or Finite- Difference-Frequency Domain (FDFD) and the cost of computing the objective gradient, which are by far the most expensive step of inverse design. Automatic differentiation has been widely employed to improve the memory and speed scaling of computing the objective function gradient, regardless of the number of design parameters. Hybrid time-frequency domain solvers are able to evaluate broadband min-max objectives with fewer simulations by combining the efficiency of FDFD solvers with the broadband performance of FDTD solvers. FDTD simulations may be accelerated by more than 100 times by leveraging graphics processing unit (GPU) computing techniques. Significant reduction in FDFD simulation time has also been shown by augmenting iterative solvers with data-driven convolutional neural networks. Finally, many researchers have proposed the usage of full engineering (EM) simulations through surrogate modeling, which attempts to use various machine learning models, such as deep neural networks, to predict the performance of a design, although such methods may suffer from poor generality and inaccuracy if training data is insufficient. BRIEF DESCRIPTION

[0008] Therefore and according to at least one aspect, a hierarchal inverse designmethodology is herein described for purposes of optimizing large-scale, multi-objective integrated photonic devices, this methodology being termed throughout as “composite topological optimization.” A principle of this inverse design methodology is to decompose the objective S-parameters into a product of smaller, easily-optimized devices, hereinafter referred to as “primitives.” These primitives are then optimized in parallel via inverse design and the optimized topologies are composited into a single design region, which serves as the initialization of a final optimization. In this manner, final device optimization starts from an initial point that is already near-optimal. Therefore, the difficulty of finding a suitable solution within a very large search space is avoided, as the composite topological design (that which is constructed of individual feasible and efficient devices) requires far fewer iterations (simulations) to converge. 3 31116671.1Attorney Docket No.105018-201

[0009] In accordance with at least one embodiment, there is provided a method fortopologically optimizing photonic devices, the method comprising decomposing a number of objectives into a product of smaller objectives (primitives), optimizing each of the primitives in parallel using inverse design, and compositing the topologies of the primitives into a final device design region, the final device design region being an initialization of a final optimization.

[0010] According to another aspect, there is provided a method for designing a photonicpower combiner having decreased phase sensitivity, the method comprising: combining two first order optical input modes; splitting the combined input optical modes into a fundamental and second order mode; downconverting the second order mode into the fundamental mode; and combining each of the resulting modes, wherein the combined modes are in-phase.

[0011] According to another aspect, there is provided a non-transitory machine-readablemedium containing software instructions executable by a processor for optimizing a topological device design, comprising instructions to: i) decompose a number of S-parameters of a design objective into a product of smaller devices (primitives), the number of S-parameters and primitives being determined by a designer and initially received by the medium; ii) individually optimizes each of the primitives in parallel using inverse design; and iii) composites the topologies of the smaller devices into a final device design region, wherein the final device design region is an initialization of a final optimization.

[0012] According to an embodiment, the herein described composite topologicaloptimization methodology can be demonstrated in the design of a phase-insensitive 2x1 power combiner, which minimizes insertion loss over a relative input phase difference of ∆ø = ± 180 degrees and 100nm bandwidth (1500nm – 1600nm). Broadband phase-insensitive power combining is a difficult design problem with no conventional solution. The phase dependence of directional couplers and multi-mode interference (MMI) couplers is typically a desired characteristic. That is, actively controlling the interference of two beams is fundamental to many 4 31116671.1Attorney Docket No.105018-201 applications such as coherent detection, photonic neuromorphic computing, optical switching, and optical phased arrays. However, this interference may be undesirable and detrimental in other applications. For example, when combining two optical inputs for maximum output power, a photonic power combiner requires either active phase control or optical path length matching to insure that the two optical inputs are in-phase for maximizing combining efficiency. These requirements could be alleviated if the power combiner were optimized for reduced phase- sensitivity, such that high combining efficiency is maintained regardless of the relative phase difference of the input beams. Such a device would enable the creation of efficient, compact, and entirely-passive power combining networks, potentially replacing the active phase-intensity compensation required in systems combining multiple sources with varying wavelengths, phase, and amplitudes, such as grating-array-based photonic receivers, RF over-fiber links, microwave photonic systems, and multi-dimensional optical interconnects.

[0013] These and other features and advantages will be readily apparent from thefollowing Detailed Description, which should be read in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] FIG. 1 is a high-level flowchart depicting a topological device optimizationprocedure;

[0015] FIG. 2A (a)- (d) and FIG. 2B (a) – (d) illustrate a schematic / pictorial compositetopological design procedure in accordance with an embodiment in which Sobjis expanded into a product of primitives Si. These primitives are individually optimized according to this design procedure as isolated topological devices in parallel, which are then composited and subsequently optimized in order to form a final design;

[0016] FIG. 3 depicts a flow chart representative of a composite topological deviceoptimization procedure in accordance with aspects of the present disclosure;

[0017] FIG. 4 is a schematic diagram of a phase-insensitive power combiner operatingprinciple in accordance with one or more embodiments. Per this principle and by mapping the 5 31116671.1Attorney Docket No.105018-201 relative phase difference of the optical inputs to orthogonal spatial mode amplitudes, destructive interference is avoided, and phase-dependence can be significantly reduced;

[0018] FIG. 5(a) depicts a permittivity map of a final optimized composite design of aphotonic device in accordance with an embodiment;

[0019] FIG. 5(b) depicts simulated E-fields for the optimized composite device design ofFIG.5(a) for ∆ø = 0°, 90° and 180°, respectively;

[0020] FIG. 6(a) graphically depicts simulated power combining efficiency versusrelative phase and wavelength for the composite design of FIGS.5(a) and 5(b); and

[0021] FIG. 6(b) graphically illustrates best and worse case power combining efficiencyfor the optimized composite device design of FIGS 5(a), 5(b) and 6(a). DETAILED DESCRIPTION

[0022] The following Detailed Description relates to a method for composite topologicaldesign, further including an example of a photonic component (e, g., a power combiner) that is phase-insensitive, which is optimized in accordance with aspects of the composite topological design procedure. For purposes of the following description, various terms are used in order to provide a suitable frame of reference with regard to the accompanying drawings. These terms, however, should not be interpreted as narrowing the concepts which are described herein, except where so specifically indicated. In addition, the drawings are also provided to show salient features of the herein described invention. The drawings should not be relied upon for scalar purposes.

[0023] As discussed herein, a topological optimization procedure is based on inversedesign principles. More specifically, topological photonic inverse design aims to determine the optimal permittivity distribution of a device in order to satisfy a given design objective. The general inverse design problem can be formulated as a bound-constrained minimization problem, 6 31116671.1Attorney Docket No.105018-201 min F(ρ, x) ρ s.t. A(ρ, ω)x – b = 0 (1) gi (ρ, ω) ≤ 0 for i ^ {1…Nfab }0 ≤ ρ ≤ 1

[0024] in which F(‧) is the objective function describing the design goal, which typicallydepends on the simulated fields, x, and the design parameters, ρ. A(ρ, ω) is an operator that represents the physics governing the device, to solve for the fields, x resulting from current source(s), b. For passive photonic devices, A typically represents Maxwell’s equations in 2D or 3D while b represents fields of the input waveguide mode(s), although other operators and sources may be employed depending on the physics of the design problem. Finite Difference Time Domain (FDTD) solvers (for broadband and time-domain simulations) can employ the time-dependent variant of Maxwell’s equations, while Finite Difference Frequency Domain (FDFD) solvers (for single or few-wavelength simulations) solve the steady state variant. ^^^ {^^( ^ ^^)}^^^^^^^^ = 1are the set of Nf abfabrication constraints that must be satisfied in order to ensure Some approaches instead choose to implement constraints as weightedpenalty terms in the objective function, discouraging infeasible designs rather than explicitly enforcing manufacturability. While this latter approach can avoid convergence issues related to constraint conflicts, this latter approach may produce designs that require manual post- processing for design rule compliance.

[0025] As further shown in FIG. 1, the three-field density variable approach is used forparameterizing the design region. More specifically, the three-field density parameterization defines the design region using a continuous, normalized spatial density field (ρ) 110, which isthen filtered (^^ → ^̃^) 120 to improve manufacturability and robustness, and then projected(^̃^ → ^̅^) 130 in order to produce a quasi-discrete density field. The resulting projected field 130then defines the spatial permittivity distribution of the physical device via material interpolation. Defining the permittivity via a continuous variable in this way allows for efficiently solving the optimization problem via gradient descent methods, rather than requiring expensive discrete optimization techniques. However, a continuous permittivity distribution is not manufacturable. That is, the final design must be a discrete distribution of the core and cladding materials 7 31116671.1Attorney Docket No.105018-201 obeying manufacturability constraints (e.g., minimum length scales, minimum area, etc.), thus motivating the need for the filtering and projection steps. The filtering transformation to field 120 removes small features from the design, thus implicitly enforcing manufacturability by restricting the design space. The filtering operation of the design field 120 can be performed, according to at least one embodiment, via a multi-dimensional convolution with a filter kernel w(x), ^̃^ = ^^(^^) ∗ ^^. (2)

[0026] A simple conic kernel is used^^−^^(^^) = {|^^|^^for |^^| ≤ ^^ , (3)0 otherwise

[0027] in which R is the kernel radius and c is a normalization constant such that∫ ^^(^^)^^^^ = 1. The linear filter kernel provides good convergence, albeit at the expense ofproducing large areas of intermediate permittivities. Alternative filter kernels, such as Pythagorean means and morphological transforms, have been demonstrated to improve optimization robustness, and multiple filters may also be applied successfully in order to achieve robustness to multiple manufacturing constraints. A nonlinear projection function P(‧)then maps the filtered field ^̃^ 120 to a quasi-discrete projected field ^̅^ 130. A hyperbolic tangent projection function is use ^̅^ = ^^(^̃^) =tanh^^ƞ+tanhβ(^̃^+ƞ) tanh^^ƞ+tanh^^(1−ƞ) , (4)

[0028] in which ƞ is the projection threshold (ƞ = 0.5 corresponds to symmetricprojections) and β is the projection strength (^^(^^) → ^^(^^ − ƞ) as ^^ → ∞, where H is theHeaviside step filter). The hyperbolic tangent projection is continuously differentiable, thus supporting gradient-based optimization, while still producing a near-discrete permittivity distribution for purposes of manufacturability. Still referring to FIG.1, the projected field 130 then serves as the input of the permittivity interpolation to define the structure of the physical device. A simple linear interpolation of the core and cladding material permittivities can be used ∈^^= ^̅^ ∙ ∈^^^^^^^^+ (1 − ^̅^) ∙ ∈^^^^^^^^ , (5)8 31116671.1Attorney Docket No.105018-201

[0029] which is sufficient for a broadband linear device.

[0030] Optionally, manufacturability may be explicitly enforced via geometric constraintfunctions, ^^^^(^̅^), although this approach restricts the optimization to bound-constrained methods. Constraint functions generally take the form of an indicator function, which identifies inflection regions in the filtered or projected fields 120, 130, applied over the discretized parameter set. Because manufacturability is enforced as an optimization constraint rather than as a penalty term in the objective function, the geometric constraint functions need not be differentiable and can thus evaluate the manufacturability of a truly discretized design rather than requiring a quasi- discrete field. In practice, it is difficult to exactly satisfy the geometric constraints. Therefore andinstead, the geometric constraints are evaluated within an assigned tolerance ^^^^(^^) ≤ ^^^^ , whichis reduced over the course of optimization in order to gradually impose the geometric constraints. In accordance with at least one embodiment, reliance can be made on filtering and projection to implicitly enforce manufacturability, in which employing of constraint functions can be opted out.

[0031] To solve the photonic inverse design optimization problem, there is a need toefficiently compute the gradients of the objective function (box 150) with respect to the designvariables ^^^^(^^^^)⁄ ^^^^^^ .

[0032] The objective gradient can be expanded using the chain rule as^^^^ ^^^^ ^^^^ ^^^^ ^^^̅^ ^^^ =^^ ^^̃^^^(6) ^^^^^^^^^^ ^^^^^^^^^̅^^^^^^̃^^^^^^^^^

[0033] The adjoint method enables the computation of the field gradients with respect to^^^^ the device permittivity ( ^^∈^^) using only two simulations, a forward simulation 160 and an adjoint simulation 170, regarding of the number of design parameters. This latter efficiency is crucial to the scalability of the number of design parameters, and enables realization of complex topologies from large parameter sets without paying a penalty in the computation of the gradient. The other intermediate gradients are then easily computed using automatic differentiation (AD), given that these latter gradients are defined a continuous differentiable functions (e.g., the objective 9 31116671.1Attorney Docket No.105018-201 function is defined in terms of the device fields). The field gradient component could also be computed using AD, where AD is effectively used to differentiate through the Maxwell solver, although in practice the adjoint method is typically preferred.

[0034] The objective function is the mean-squared error of the simulated forward S-parameters ^^ ^^^^, ^^^^(^^^^) = |^^ ^^^^ − ^^^^^^|2 ,in which ^^ ∈ [1, ^^] and ^^ ∈ [1, ^^] are the indices of therespectively. The core scattering matrix of the device isrepresented(^^^^^^^^ × ^^^^^^^^) × (^^^^^^^^^^ × ^^^^^^^^^^) × (^^^^^^ × ^^^^^^), where^^^^^^^^, ^^^^^^^^^^ , and ^^^^^^ are the numbers of relevant polarizations, spatial modes, and input / outputwaveguides of the device, respectively. Defining the objective function in this manner enables simultaneous optimization of all S-parameters (e.g., maximizing forward transmission while minimizing reflection losses).

[0035] With reference to FIGS. 2A, 2B and 3, the principle of composite topologicaloptimization in accordance with the present invention is to expand the m-input, n-output objective S-parameters into a left product of k primitive S-parameters. ^^^^^^^^ = ∏^^ ^^=1 ^^^^, (7)

[0036] where k and S i are determined by the designer, as shown schematically in FIG.2A and 2B. The number of inputs m and outputs n are determined by the number of respective input and output states, rather than the number of physical ports, where a state may be considered a discrete combination of the parameters over which the device is optimized (e.g. ,polarization, spatial modes, wavelengths, physical ports, etc.). Hence, each state can be considered as a virtual port of the S-parameter model. Optical paths within the composite design may therefore diverge and converge as necessary, where any ℓ parallel operations may be represented as the block diagonal of the respective S-matrices, ^^^^,1 ⋯ 031116671.1Attorney Docket No.105018-201

[0037] The composite optimization technique herein described benefits from beingagnostic to the underlying topology optimization method and a designer may therefore choose whichever method is most suitable for the specific design problem. The primitive design region dimensions should be selected together with any additional hyperparameters of the composite model (e.g., waveguide placement and width, convergence parameters, etc.). The final design region is composited using a simple nearest-neighbor placement method on a graph model node adjacency, in which the design region is defined by the bounding box of the placed primitives.

[0038] FIG. 3 illustrates a flow chart of the foregoing methodology in which the initiateddesign takes place by primitive decomposition 210, followed by parallel optimization of the various primitives 220, as done in accordance with the flowchart of FIG 1, previously discussed. A composite layout can be generated 230 from the permittivity maps of each of the various primitives, thereby resulting in a composite topological optimization 240.

[0039] In some embodiments, the foregoing methodology is embodied in software orfirmware for operation on a processor. That is, other embodiments of the present technology include non-transitory computer-readable storage media and / or devices having stored thereon instructions that when executed by one or more processors perform the methods and processes described herein. According to an embodiment, a non-transitory machine-readable medium comprising software instructions executable by a processor for optimizing a topological device design, the medium comprising instructions to receive the number of S-parameters and number of primitives, and in which the medium is configured to decompose the number of S-parameters of a design objective into a product of the smaller devices (primitives), each of the foregoing initially determined by the designer, which are received by the medium. The medium then individually optimizes each of the primitives in parallel using inverse design, as previously discussed; and then composites the topologies of the smaller devices into a final device design region, wherein the final device design region is an initialization of a final optimization.

[0040] The processor may include, for example, a processing unit and / or programmablecircuitry. The storage device may include a machine readable storage device including any type of tangible, non-transitory storage device, for example, any type of disk including floppy disks, optical disks, compact disk read-only memories (CD-ROMs), compact disk rewritables (CD- 11 31116671.1Attorney Docket No.105018-201 RWs), and magneto-optical disks, semiconductor devices such as read-only memories (ROMs), random access memories (RAMs) such as dynamic and static RAMs, erasable programmable read-only memories (EPROMs), electrically erasable programmable read-only memories (EEPROMs), flash memories, magnetic or optical cards, hard drives, solid state memory, or any type of storage devices suitable for storing electronic instructions.

[0041] The following relates to an example of a photonic device design using the hereindescribed methodology. Power combining using traditional devices (e.g., multi-mode interference couplers, Y- junctions) is a phase-sensitive transformation wherein the combining ^^ efficiency (ƞ^^^^^^^^^^= ^^^^^^ ) follows a cosine-squared behavior (^^ 2^^^^^^∞ cos (∆∅⁄ 2 ) ) due to phase-dependent Fundamentally, it is impossible to losslessly combine multiple spatially-or temporally- input modes into a single output mode. Initially, it may seem that phase-insensitive power combining violates this proof and is thus impossible, as the pairs of in-phase (∆∅ = 0deg ) and out of phase (∆∅ = 180deg ) fundamental input modes constitutetemporally-orthogonal modes. However, the afore mentioned proof only forbids perfect combining into a single output mode. Thus, while the phase-insensitive power combiner couples the fundamental mode of a single output waveguide (a single spatial mode), it will be shown with reference to FIG.4 that the output couples to two (2) temporally orthogonal output modes (the fundamental mode with zero degree absolute phase and 180 degrees absolute phase). In this way, the device serves to map the relative phase difference between the input modes to the absolute phase of the output mode, thus preserving modal orthogonality and enabling theoretically perfect, phase-insensitive combining of two beams.

[0042] As shown in FIG. 4, the phase-insensitive power combining described here isdecomposed into a series of mode conversion, splitting and combining stages to sequentially transform between spatially and temporally orthogonal intermediate modes. By intelligently selecting and composing such spatiotemporal transformations, destructive interference of orthogonal modes is avoided entirely.

[0043] The input stage first maps the relative phase of two fundamental input stages tothe relative amplitudes of the fundamental and second-order output modes 12 31116671.1Attorney Docket No.105018-201 ^^∆∅^^ ∆∅ |Ψ ^ = ^^ |Ψ ^^^I,0(^^,^^)exp (2 )^^O,0(^^,^^)cos (2 ) O1 I = ^^1 [−^^∆∅^^] = [∆∅ )sin)], (9)the input stage, and ^^I,i(^^O,j) is the wavefunction of the i-th input (j-th output) mode. Thistransformation is enabled by the a posteriori observation that two (2) in-phase (∆∅ = ±180°)modes easily combine into the anti-symmetric second-order mode. This device is referred to here as a “phase-mode combiner.” With reference to FIG.4 and after the input phase mode combiner 320, a mode splitter 330 routes the fundamental and second-order modes TM0 and TM1 to the upper and lower branches 340 and 350, respectively. In the lower branch 350, the second-order mode TM1is down-converted to the fundamental mode TM0via a mode converter 360. The upper branch 340 is a strip waveguide, which passes the fundamental mode TM0. Finally, an output Y-combiner 370 couples the two in-phase fundamental modes TM0from the upper and lower branches 340, 350 into a single fundamental output mode TM0, in which the absolute phase is proportional to the relative phase of the input modes 310. Though FIG.4 relates to transverse magnetic modes, it will be readily understood that the foregoing implementation can also readily apply to each of the fundamental and second order electrical optical modes, (e.g., TE0, TE1, etc.).

[0045] An open-source FDFD solver with adjoint method support can be used inaccordance with this embodiment to perform all simulations, allowing the computation of the objective function gradient using two (2) simulations per input state. As shown in FIGS.5(a) – 6(d), the power combiner is optimized over three (3) discrete phase conditions,∆∅^^ = {−180°, 0°, +180°}, and five (5) discrete wavelengths,^^^^ = {1.50^^^^, 1.525^^^^, 1.55^^^^, 1.575^^^^, 1.60^^^^} for TM input modes. Conic filtering andopen-close morphological transformations are applied during optimization to enforce a 75 nm minimum scale constraint, which is compatible with commercial foundry fabrication. With reference to FIGS.6(a) and (b), the optimized phase-insensitive power combiner according to this specific example demonstrates a best-caseƞ^^^^ = 92.7% (^^^^ = 0.33^^^^) for ∆∅ = −10°, λ = 1.51μm and worst-caseƞ^^^^ = 65.6% (^^^^ = 1.83dB) for ∆∅ = 80°, λ = 1.51μm. Thus, the power combiner is able toefficiently combine all TM sources across the full C-band, suitable for all-optical power 13 31116671.1Attorney Docket No.105018-201 combining without the need for active phase and intensity control in applications including, but not limited to microwave photonic systems and multi-dimensional direct-detection transmission links.

[0046] While the invention has been described in terms of particular variations andillustrative figures, those of ordinary skill in the art will recognize that the invention is not limited to the variations or figures described. In addition, where methods and steps described above indicate certain events occurring in certain order, those of ordinary skill in the art will recognize that the ordering of certain steps may be modified and that such modifications are in accordance with the variations of the invention. Additionally, certain of the steps may be performed concurrently in a parallel process when possible, as well as performed sequentially as described above. Therefore, to the extent there are variations of the invention, which are within the spirit of the disclosure or equivalent to the inventions found in the claims, it is the intent that this patent will cover those variations as well.

[0047] To the extent that the claims recite the phrase “at least one of” in reference to aplurality of elements, this is intended to mean at least one or more of the listed elements, and is not limited to at least one of each element. For example, “at least one of an element A, element B, and element C,” is intended to indicate element A alone, or element B alone, or element C alone, or any combination thereof. “At least one of element A, element B, and element C” is not intended to be limited to at least one of an element A, at least one of an element B, and at least one of an element C.

[0048] This Detailed Description uses examples to disclose the invention, including thebest mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims. 14 31116671.1Attorney Docket No.105018-201

[0049] The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprise” (and any form of comprise, such as “comprises” and “comprising”), “have” (and any form of have, such as “has” and “having”), “include” (and any form of include, such as “includes” and “including”), and “contain” (and any form of contain, such as “contains” and “containing”) are open-ended linking verbs. As a result, a method or device that “comprises,” “has,” “includes,” or “contains” one or more steps or elements possesses those one or more steps or elements, but is not limited to possessing only those one or more steps or elements. Likewise, a step of a method or an element of a device that “comprises,” “has,” “includes,” or “contains” one or more features possesses those one or more features, but is not limited to possessing only those one or more features. Furthermore, a device or structure that is configured in a certain way is configured in at least that way, but may also be configured in ways that are not listed.

[0050] The corresponding structures, materials, acts, and equivalents of all means or stepplus function elements in the claims below, if any, are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description set forth herein has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the disclosure. The embodiment was chosen and described in order to best explain the principles of one or more aspects set forth herein and the practical application, and to enable others of ordinary skill in the art to understand one or more aspects as described herein for various embodiments with various modifications as are suited to the particular use contemplated and in accordance with the following appended claims. Additional embodiments include any one of the embodiments described above and described in any and all exhibits and other materials submitted herewith, where one or more of its components, functionalities or structures is interchanged with, replaced by or augmented by one or more of the components, functionalities or structures of a different embodiment described above and as set forth in the following appended claims. 15 31116671.1Attorney Docket No.105018-201 PARTS LIST FOR FIGS.1 – 6(b) 105 box 110 density field 120 filtered field 130 projected field 150 box 160 forward simulation 170 adjoint simulation 210 box 220 box 230 box 240 box 310 input mode(s) 320 input phase mode combiner 330 mode splitter 340 upper branch 350 lower branch 360 mode converter 370 output mode power combiner 16 31116671.1

Claims

Attorney Docket No.105018-201 CLAIMS 1. A composite topological optimization method, the method comprising:decomposing a number of S-parameters of a design objective into a product of smaller devices (primitives); individually optimizing each of the primitives in parallel using inverse design; and compositing topologies of the smaller devices into a final device design region, wherein the final device design region is an initialization of a final optimization.

2. The optimization method according to claim 1, wherein the method is applicable in thedesign of photonic devices.

3. The optimization method according to claim 2, wherein the photonic device is a powercombiner.

4. The optimization method according to claim 3, wherein the power combiner made inaccordance with the method is optimized for phase insensitivity.

5. A method for designing a photonic power combiner having decreased phase sensitivity,the method comprising: combining two first order optical input modes; splitting the combined input optical modes into a fundamental and second order mode; downconverting the second order mode into the fundamental mode; and combining each of the resulting modes, wherein the combined modes are in- phase.

6. The method according to claim 5, wherein the combining of the two fundamental modesis done using an input phase-mode combiner. 17 31116671.1Attorney Docket No.105018-201 7. The method according to claim 5, wherein the splitting of the combined input opticalmodes is done using a mode splitter.

8. The method according to claim 5, wherein the splitting of the combined input opticalmodes includes transmission of one of the two modes along a first branch and transmission of the other of the two modes along a second branch.

9. The method according to claim 8, including disposing a mode converter along one of thefirst and second branches.

10. A non-transitory machine-readable medium comprising software instructions executableby a processor for optimizing a topological device design, the medium comprising instructions to: i) decompose a number of S-parameters of a design objective into a product of smaller devices (primitives), the number of S-parameters and primitives being determined by a designer and initially received by the medium; ii) individually optimizes each of the primitives in parallel using inverse design; and iii) composites the topologies of the smaller devices into a final device design region, wherein the final device design region is an initialization of a final optimization.

11. The medium according to claim 10, in which the device being optimized by the mediumis a photonic device.

12. The medium according to claim 11, wherein the photonic device is a power combiner13. The medium according to claim 12, wherein the power combiner is optimized for phaseinsensitivity. 18 31116671.1

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