Transformation Inverse Design

TL;DR

This paper introduces a computationally efficient large-scale optimization method for designing transformation-optics devices, enabling the creation of reflectionless multimode waveguide components with improved boundary condition handling.

Contribution

It presents a novel optimization approach that simplifies the design of transformation-optics devices by avoiding Maxwell's equations at each step and clarifies boundary condition requirements for reflectionless interfaces.

Findings

Successfully designed multimode waveguide bends and mode squeezers

Achieved reflectionless coupling with optimized boundary conditions

Demonstrated computational efficiency over traditional methods

Abstract

We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap because transformation optics circumvents the need to solve Maxwell's equations at each step. We apply this technique to the design of multimode waveguide bends (realized experimentally in a previous paper) and mode squeezers, in which all modes are transported equally without scattering. In addition to the optimization, a key point is the identification of the correct boundary conditions to ensure reflectionless coupling to untransformed regions while allowing maximum flexibility in the optimization. Many previous authors in transformation optics used a certain kind of quasiconformal map which overconstrained the problem by requiring that the entire boundary shape be specified a priori while at the same time underconstraining the problem by employing "slipping" boundary conditions that permit unwanted interface reflections.