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A reconfigurable metasurface constitutes an important block of future adaptive and smart nanophotonic applications, such as adaptive cooling in spacecraft. In this paper, we introduce a new modeling approach for the fast design of tunable and reconfigurable metasurface structures using a convolutional deep learning network. The metasurface structure is modeled as a multilayer image tensor to model material properties as image maps. We avoid the dimensionality mismatch problem using the operating wavelength as an input to the network. As a case study, we model the response of a reconfigurable absorber that employs the phase transition of vanadium dioxide in the mid-infrared spectrum. The feed-forward model is used as a surrogate model and is subsequently employed within a pattern search optimization process to design a passive adaptive cooling surface leveraging the phase transition of vanadium dioxide. The results indicate that our model delivers an accurate prediction of the metasurface response using a relatively small training dataset. The proposed patterned vanadium dioxide metasurface achieved a 28% saving in coating thickness compared to the literature while maintaining reasonable emissivity contrast at 0.43. Moreover, our design approach was able to overcome the non-uniqueness problem by generating multiple patterns that satisfy the design objectives. The proposed adaptive metasurface can potentially serve as a core block for passive spacecraft cooling applications. We also believe that our design approach can be extended to cover a wider range of applications. [ABSTRACT FROM AUTHOR]

We present a novel algorithm for adjoint sensitivity analysis of time-varying responses that is based on the transmission line modeling (TLM) method. We show that by using at most one extra electromagnetic (EM) simulation, the sensitivities of the complete time domain EM response can be obtained with respect to all designable parameters regardless of their number and regardless of the number of time steps. The complete time domain signature of a certain structure can thus be efficiently and accurately predicted for perturbed structures. Our sensitivities match those obtained using the accurate and time intensive central finite differences (CFD). The adjoint sensitivities are used in the solution of inverse problems through a number of approaches exploiting surrogate model optimization and direct optimization. Our technique enables efficient identification of object position, dimensions and material properties. Index Terms--Inverse problems, optimization, sensitivity analysis, transmission line modeling (TLM) method.

We propose a sensitivity analysis method that computes the S-parameter Jacobian from the volume E-field solutions in the frequency domain. The field solutions may be provided by any valid electromagnetic analysis. The computation is a post-process, which is independent from the simulator's grid, system equations, and discretization method. The sensitivity solver uses its own finite-difference grid and a sensitivity formula based on the finite-difference frequency-domain vector Helmholtz equation for the electric field. Its computational overhead is negligible in comparison with the simulation. We use the sensitivity solver in the gradient-based optimization of microwave structures. Significant reduction of the time required by the overall optimization process is achieved. In all design examples, the sensitivities are computed from the field solutions provided by a commercial finite-element simulator. Index Terms--Computer-aided design (CAD), finite-difference method, finite-element method (FEM), gradient-based optimization, response Jacobians, sensitivity analysis.

We introduce a tuning space-mapping technology for microwave design optimization. The general tuning space-mapping algorithm is formulated, which is based on a so-called tuning model, as well as on a calibration process that translates the adjustment of the tuning model parameters into relevant updates of the design variables. The tuning model is developed in a fast circuit-theory based simulator and typically includes the fine model data at the current design in the form of the properly formatted scattering parameter values. It also contains a set of tuning parameters, which are used to optimize the model so that it satisfies the design specification. The calibration process may involve analytical formulas that establish the dependence of the design variables on the tuning parameters. If the formulas are not known, the calibration process can be performed using an auxiliary space-mapping surrogate model. Although the tuning space mapping can be considered to be a specialized case of the standard space-mapping approach, it can offer even better performance because it enables engineers to exploit their experience within the context of efficient space mapping. Our approach is demonstrated using several microwave design optimization problems. Index Terms--Computer-aided design (CAD), engineering optimization, space mapping, surrogate models, tuning.

For what is believed to be the first time, the central adjoint variable method (CAVM) is applied to the sensitivity analysis of photonic devices using the finite-difference time-domain (FDTD) technique. The FDTD-CAVM technique obtains accurate sensitivities of any desired response with respect to the different design parameters. Our technique requires only one extra FDTD simulation to extract the sensitivities with respect to all the design parameters regardless of their number. Cost-free sensitivities of the power reflectivity are also derived without any additional simulation. The results show a very good agreement between the CAVM sensitivities and those obtained using the expensive central finite difference approximation. OCIS codes: 000.4430, 130.3120, 140.4480.

For the first time, full-wave optimization exploiting adjoint Hessian matrices is applied to the design of microwave filters and transitions. The first- and second-order sensitivities of the scattering parameters are computed analytically using the adjoint network method (ANM). The mode-matching-based ANM is applied to the generalized scattering matrices of the different filter/transition components. Analytical gradient and Hessian matrices of differentiable objective functions are expressed in terms of the first- and second-order response adjoint sensitivities. Optimization techniques exploiting second-order information such as the Levenberg-Marquardt method are applied using the adjoint first- and second-order information. Significant acceleration is achieved using these techniques over gradient-based optimization techniques such as the Broyden-Fletcher-Goldfarb-Shanno method. The adjoint-based sensitivities are also exploited in efficient tolerance analysis of microwave filters. Index Terms--Adjoint networks, computer-aided design (CAD), mode-matching (MM) methods, optimization methods, sensitivity analysis.

We propose an adjoint-variable method for design sensitivity analysis of printed circuits and antennas where allowable perturbations in the design parameters are of a discrete type. We extend previous work […]

In this paper, we study the use of space-mapping (SM) techniques within the transmission-line matrix (TLM) method environment. Previous work on SM relies on an 'idealized' coarse model in the design process of a computationally expensive fine model. For the first time, we examine the case when the coarse model is not capable of providing an ideal optimal response. We exploit a coarse-grid TLM solver with relaxed boundary conditions. Such a coarse model may be incapable of satisfying design specifications and traditional SM may fail. Our approach, which exploits implicit SM (ISM) and the novel output SM (OSM), overcomes this failure. Dielectric constant, an expedient preassigned parameter, is first calibrated to roughly align the coarse and fine TLM models. Our OSM scheme absorbs the remaining deviation between the 'implicitly' mapped coarse-grid and fine-grid TLM responses. Because the TLM simulations are on a fixed grid, response interpolation is crucial. We also create a database system to avoid repeating simulations unnecessarily. Our optimization routine employs a trust region methodology. The TLM-based design of an inductive post, a single-resonator filter, and a six-section H-plane waveguide filter illustrate our approach. In a few iterations, our coarse-grid TLM surrogate, with approximate boundary conditions, achieves a good design of the fine-grid TLM model in spite of poor initial responses. Our results are verified with MEFiSTo simulations. Index Terms--Computer-aided design (CAD), electromagnetic (EM) optimization, EM simulation, filter design, space mapping (SM), transmission-line matrix (TLM) method.

We demonstrate, for the first time, the integration of adjoint variable method (AVM) sensitivities and the method of moments (MoM) within an optimization framework, where the S-parameters are used to define the cost function. The AVM efficiently estimates the sensitivities of the S-parameters using only one MoM simulation with some additional overhead. Two possible approaches are used: the adjoint finite-difference approach and the adjoint Broyden-update approach. The AVM S-parameter sensitivities are successfully utilized to optimize a band-stop filter, a band-pass filter, and an electromagnetically coupled microstrip Yagi antenna. The results show that the optimizers supported by AVM sensitivities are capable of reaching feasible designs satisfying the specifications. Index Terms--Adjoint variable method (AVM), method of moments (MoM), microstrip structures, minimax optimization, sensitivities.

An electromagnetic feasible adjoint sensitivity technique (EM-FAST) has been proposed recently for use with frequency-domain solvers. It makes the implementation of the adjoint variable approach to design sensitivity analysis straightforward while preserving the accuracy at a level comparable to that of the exact sensitivities. The overhead computations associated with the estimation of the sensitivities in addition to the system analysis are due largely to the calculation of the derivatives of the system matrix. Here, we describe the integration of the EM-FAST with two methods for accelerated estimation of these derivatives: the boundary-layer concept and the Broyden update. We show that the Broyden update approach (Broyden-FAST) leads to an algorithm whose efficiency is problem independent and allows the computation of the response and its gradient through a single system analysis with practically no overhead. Both approaches are illustrated through the design of simple antennas using method of moments solvers. Index Terms--Adjoint sensitivities, antenna design, Broyden update, design methodology, method of moments (MoM), optimization, sensitivity.

In this paper, novel radial basis function-neural network (RBF-NN) models are presented for the efficient filling of the coupling matrix of the method of moments (MoM). Two RBF-NNs are trained to calculate the majority of elements in the coupling matrix. The rest of elements are calculated using the conventional MoM, hence the technique is referred to as neural network-method of moments (NN-MoM). The proposed NN-MoM is applied to the analysis of a number of microstrip patch antenna arrays. The results show that NN-MoM is both accurate and fast. The proposed technique is general and it is convenient to integrate with MoM planar solvers. Index Terms--Method of moments (MoM), neural networks (NNs), patch antenna arrays, radial basis functions (RBFs).

Recently, we proposed a novel technique for design sensitivity analysis of high-frequency structures with respect to localized perturbations in conductive parameters. Here, we generalize the technique to include shape and material variations and utilize the response sensitivities in gradient-based optimization. Our technique belongs to the class of adjoint-variable methods. Thus, it computes the response and its gradient with only two electromagnetic (EM) simulations--of the original and the adjoint problems--regardless of the number of design parameters. For the first time, adjoint sensitivities with respect to conductive, dielectric-magnetic material and shape perturbations are computed via EM solvers on structured grids. Our approximate sensitivity analysis does not require analytical derivatives of the system matrix. This makes the technique versatile and easy to implement. The technique defaults to exact sensitivities with analytical system matrix derivatives when global design parameters are being perturbed. We discuss the accuracy of the approximate sensitivities, as well as the practicality of the exact sensitivities in specific design problems. We also discuss implementations in gradient-based optimization and illustrate them through simulation and design with the frequency domain transmission line method (FD-TLM). Index Terms--Design methodology, frequency domain TLM, sensitivity.

We propose an adjoint-variable approach to design-sensitivity analysis with time-domain methods based on structured grids. Unlike conventional adjoint-based methods, it does not require analytical derivatives of the system matrices. It is simple to implement with existing computational algorithms such as the finite-difference time-domain (FDTD) technique. The resulting FDTD algorithm produces the response and its gradient in the design parameter space with two simulations regardless of the number of design parameters. The proposed method is validated by the adjoint-based FDTD analysis of waveguide structures with metallic boundaries. Index Terms--Adjoint variable methods, design-sensitivity analysis, finite-difference time-domain (FDTD) methods.

We present a novel algorithm for efficient estimation of objective function sensitivities for time-domain transmission-line modeling (TLM) with dispersive Johns matrix boundaries. The original electromagnetic structure is simulated using TLM. An adjoint TLM simulation that runs backward in time is derived and solved. The sensitivities of the objective function with respect to all designable parameters are estimated using only the original and adjoint simulations. We show that the Johns matrix of the adjoint problem at each time step is the transpose of the corresponding matrix for the original structure. Our approach is illustrated through the estimation of the sensitivities of objective functions with respect to the dimensions of waveguide discontinuities. A very good match is obtained between our sensitivity estimates and those obtained using central difference approximation. Index Terms--Computer-aided design (CAD), electromagnetic (EM) modeling, field-based synthesis, sensitivity analysis, transmission-fine modeling (TLM) method.

Recently, an adjoint variable method (AVM) for sensitivity calculations has been proposed for use with the method of moments solvers. In this paper, we extend this method to be suitable for application to multiport devices. The target objective function is usually represented in terms of the device's S-parameters. Our AVM obtains the sensitivities of the S-parameters with respect to all design variables using only one full simulation with additional overhead. This overhead is usually less than the computation time of a full simulation. An analytical expression for the adjoint excitation is derived, leading to stable sensitivities. The potential of the proposed technique is demonstrated by analyzing low-pass and bandpass filters. The results show very good agreement between the proposed AVM and the conventional finite-difference approach (FDA). Moreover, the AVM is always faster than the FDA. The speed-up factor increases as the size of the problem increases. Index Terms--Adjoint techniques, deembedding, method of moments (MoM), microstrip filters, sensitivity.

We present a novel algorithm for efficient estimation of objective function sensitivities for time-domain transmission-line modeling (TLM) with nondispersive boundaries. The original electromagnetic structure is simulated using TLM. An adjoint TLM simulation that runs backward in time is derived and solved. The sensitivities of the objective function with respect to all designable parameters are estimated using only the original and adjoint simulations. Our approach is illustrated through the estimation of the sensitivities of objective functions with respect to the dimensions of waveguide discontinuities. A very good match is obtained between our sensitivity estimates and those obtained through the accurate and time-intensive central difference approximation. Index Terms--Computer-aided design (CAD), electromagnetic modeling, field-based synthesis, transmission-line modeling (TLM) method.

We review the space-mapping (SM) technique and the SM-based surrogate (modeling) concept and their applications in engineering design optimization. For the first time, we present a mathematical motivation and place SM into the context of classical optimization. The aim of SM is to achieve a satisfactory solution with a minimal number of computationally expensive 'fine' model evaluations. SM procedures iteratively update and optimize surrogates based on a fast physically based 'coarse' model. Proposed approaches to SM-based optimization include the original algorithm, the Broyden-based aggressive SM algorithm, various trust-region approaches, neural SM, and implicit SM. Parameter extraction is an essential SM subproblem. It is used to align the surrogate (enhanced coarse model) with the fine model. Different approaches to enhance uniqueness are suggested, including the recent gradient parameter-extraction approach. Novel physical illustrations are presented, including the cheese-cutting and wedge-cutting problems. Significant practical applications are reviewed. Index Terms--Computer-aided design (CAD), design automation, electromagnetic (EM) simulation, EM optimization, filter design, microwave filters, optimization algorithms, optimization methods, parameter extraction (PE), space mapping (SM), surrogate models.

There is a revival of the interest in adjoint sensitivity analysis techniques. This is partly because current computer-aided-design software based on full-wave electromagnetic (EM) solvers remains too slow for the purposes of practical high-frequency structure design despite the increasing capacity of computers. The adjoint-variable methods for design sensitivity analysis offer computational speed and accuracy. They can be used for efficient gradient-based optimization, in tolerance and yield analysis. Adjoint-based sensitivity analysis for circuits has been well studied and extensively covered in the microwave literature. In comparison, sensitivities with full-wave analysis techniques have attracted little attention, and there have been few applications into feasible and versatile algorithms. We review adjoint-variable methods used in high-frequency structure design with both circuit analysis techniques and full-wave EM analysis techniques. A brief discussion on adjoint-based sensitivity analysis for nonlinear dynamic systems is also included. Index Terms--Adjoint networks, computer-aided design (CAD), electromagnetic (EM) modeling, microwave circuits, optimization, sensitivity analysis.

An adjoint-variable approach to frequency-domain design sensitivity analysis is proposed for the optimization of high-frequency structures with full-wave electromagnetic solvers. We investigate sensitivity estimations based on a feasible perturbation technique which is versatile and requires only minor modifications of existing analysis algorithms. It extends the feasible ad joint-sensitivity technique previously applied in nonlinear microwave circuits to full-wave electromagnetic analysis. The solution to the adjoint problem is obtained with very little overhead once the original problem is solved. The gradient of the objective function is consequently computed through a single analysis regardless of the number of the design parameters. The concept is illustrated through the sensitivity analysis and the design of a Yagi--Uda array and a rectangular patch antenna using suitable method of moments simulators. Index Terms--Adjoint techniques, antenna design, computer-aided design, design automation, frequency-domain analysis, optimization, sensitivity.

We present a family of robust techniques for exploiting sensitivities in electromagnetic (EM)-based circuit optimization through space mapping (SM) technology. We utilize derivative information for parameter extractions and mapping updates. We exploit a partial SM (PSM) concept, where a reduced set of parameters is sufficient for parameter extraction optimization. It reflects the idea of tuning and execution time is reduced. Upfront gradients of both EM (fine) model and coarse surrogates can initialize possible mapping approximations. We introduce several effective approaches for updating the mapping during the optimization iterations. Examples include the classical Rosenbrock function, modified to illustrate the approach, a two-section transmission-line 10:1 impedance transformer and a microstrip bandstop filter with open stubs. Index Terms--CAD, design automation, electromagnetic (EM) simulation, EM optimization, microwave filters, optimization methods, space mapping.

We present a novel approach to the design of microwave structures using time-domain field synthesis. A standard transmission-line matrix (TLM) electromagnetic analysis of the starting geometry yields the structure response and the field distribution on the optimizable boundary parts. A number of characteristic frequencies equal to the number of designable parameters of the structure are determined first. For narrow-band structures, these frequencies may be natural resonance frequencies. For wide-band structures, we create appropriate resonance conditions. The target response of the structure allows us to identify the desirable values of these frequencies. For each parameter, a synthesis phase is then performed. In this phase, the optimizable boundary parts are replaced by matched TLM sources that inject sampled sinusoidal streams at the desired characteristic frequency. The TLM field model generates an electromagnetic field pattern. The synthesized geometry is obtained by examining the envelope of that field pattern. Our approach is illustrated by means of several examples. Index Terms--Computer-aided design (CAD), electromagnetic modeling, field-based synthesis, transmission-line matrix (TLM) method.

Recently, approximate adjoint sensitivity techniques with structured-grid electromagnetic solvers have been proposed. In this letter, we propose a central adjoint sensitivity formula for response sensitivity with structured-grid solvers, whose accuracy is an order higher than that of the preceding techniques. The formula is derived from a backward problem, which is considered here for the first time, and the forward problem utilized in the previous techniques. Our technique maintains the computational efficiency typical for adjoint-based methods. We illustrate it through applications with a frequency-domain transmission line method solver. Index Terms--Adjoint variable methods, frequency-domain analysis, sensitivity.