Inverse Design of Multi-Input Multi-Output 2-D Metastructured Devices

Abstract

In this work, an optimization-based inverse design method is provided for multi-input multi-output (MIMO) metastructured devices. Typically, optimization-based methods use a full-wave solver in conjunction with an optimization routine to design devices. Due to the computational cost this approach is not practical for designing electrically-large aperiodic metastructured devices. To address this issue, a 2-D circuit network solver using reduced order models of the metastructure's unit cells is introduced. The circuit network solver is used in conjunction with a gradient-based optimization routine that uses the adjoint variable method to solve large-scale optimization problems like those posed by metastructured devices. To validate the inverse design method, a planar beamformer and an analog signal processor for aperture field reconstruction are designed and validated with full-wave simulations.

Design of Planar and Conformal, Passive, Lossless Metasurfaces That Beamform

“…The gradient descent optimization used to optimize the sheets is accelerated by a semi-analytic gradient calculation using the adjoint variable method. The adjoint variable method formulation was adapted from that in [7], where it was successfully applied to metasurface optimization. Specifically, in [7], the adjoint variable method was applied to the circuit-based design of multi-input multi-output metastructures.…”

“…The adjoint variable method formulation was adapted from that in [7], where it was successfully applied to metasurface optimization. Specifically, in [7], the adjoint variable method was applied to the circuit-based design of multi-input multi-output metastructures. Here, it is adapted to the design of metasurface beamformers.…”

“…where I represents the current density expansion coefficients obtained from the solution of the linear system in (7), diag( ) refers to the creation of a diagonal matrix with the elements of the argument appearing along the diagonal, and I λ is the solution to the adjoint problem…”

“…In (17), R is an M-by-N matrix formed by evaluating (15) at the M observation angles in the far-field with the currents J q on all N elements replaced by 1∠0 • when pulse basis functions are used (see (A.13)). Also, Z is the method of moments impedance matrix in (7) and E adj is the adjoint field defined in (A.17). The entire gradient is calculated by solving only 2 linear systems (( 7) and ( 17)) at each iteration independent of the number of unknown sheet reactances N. The gradient in ( 16) is used in a classical gradient descent optimization method to optimize the impedance sheets.…”

“…In [3], [4], [10], [11], [17], [21], the authors add explicitly defined surface wave fields, E sw , and optimize their amplitudes. In [5], [7], [12], [13], [15], [16], [23] and in this work, the optimization is performed directly on the sheet impedances, η. In some cases, optimization considers both the impedances and the induced surface current simultaneously as in [14].…”