Trace formulation for photonic inverse design with incoherent sources

TL;DR

This paper introduces a trace formulation for efficiently modeling incoherent light sources in inverse design, enabling large-scale topology optimization for complex emission scenarios.

Contribution

It presents a generalized trace formulation that extends reciprocity-based methods to a continuum of emission directions, improving computational efficiency in incoherent emission inverse design.

Findings

Successfully optimized fluorescent particle geometries.

Designed structures emitting into waveguide modes.

Demonstrated scalability to thousands of design parameters.

Abstract

Spatially incoherent light sources, such as spontaneously emitting atoms, naively require Maxwell's equations to be solved many times to obtain the total emission, which becomes computationally intractable in conjunction with large-scale optimization (inverse design). We present a trace formulation of incoherent emission that can be efficiently combined with inverse design, even for topology optimization over thousands of design degrees of freedom. Our formulation includes previous reciprocity-based approaches, limited to a few output channels (e.g. normal emission), as special cases, but generalizes to a continuum of emission directions by exploiting the low-rank structure of emission problems. We present several examples of incoherent-emission topology optimization, including tailoring the geometry of fluorescent particles, a periodically emitting surface, and a structure emitting into a waveguide mode, as well as discussing future applications to problems such as Raman sensing and cathodoluminescence.