Bounds on Efficiency Metrics in Photonics

TL;DR

This paper introduces a semidefinite programming approach to compute bounds on efficiency metrics in photonics, providing a practical tool for optimizing device performance.

Contribution

It presents a novel relaxation method for efficiency metrics expressed as quadratic ratios, with an open-source Julia package for simulations and bounds.

Findings

Bounded maximal mode conversion purity for specific device sizes.

Demonstrated effectiveness of the SDP relaxation in photonics efficiency metrics.

Provided a practical computational tool for photonics device optimization.

Abstract

In this paper, we present a method for computing bounds for a variety of efficiency metrics in photonics, such as the focusing efficiency or the mode purity. We focus on the special case where the objective function can be written as the ratio of two quadratic functions of the field and show that there exists a simple semidefinite programming relaxation for this problem. We provide a numerical example of bounding the maximal mode conversion purity for a device of given size. This paper is accompanied by an open source Julia package for basic simulations and bounds.