# Leveraging Continuous Material Averaging for Inverse Electromagnetic Design

## TL;DR

This paper introduces a novel continuous material averaging method for inverse electromagnetic design, enabling accurate gradient computation and improved device optimization, demonstrated by a low-loss waveguide taper.

## Contribution

The paper presents a new smoothing strategy for material interfaces that enhances gradient accuracy in inverse electromagnetic design, overcoming previous limitations.

## Key findings

- Achieved a waveguide taper with 0.041 dB insertion loss at 1550 nm
- Enabled efficient and accurate gradient computation regardless of simulation resolution
- Produced a non-intuitive, optimized device design

## Abstract

Inverse electromagnetic design has emerged as a way of efficiently designing active and passive electromagnetic devices. This maturing strategy involves optimizing the shape or topology of a device in order to improve a figure of merit--a process which is typically performed using some form of steepest descent algorithm. Naturally, this requires that we compute the gradient of a figure of merit which describes device performance, potentially with respect to many design variables. In this paper, we introduce a new strategy based on smoothing abrupt material interfaces which enables us to efficiently compute these gradients with high accuracy irrespective of the resolution of the underlying simulation. This has advantages over previous approaches to shape and topology optimization in nanophotonics which are either prone to gradient errors or place important constraints on the shape of the device. As a demonstration of this new strategy, we optimize a non-adiabatic waveguide taper between a narrow and wide waveguide. This optimization leads to a non-intuitive design with a very low insertion loss of only 0.041 dB at 1550 nm.