Maximum Electromagnetic Local Density of States via Material Structuring

TL;DR

This paper develops a universal framework to determine the maximum electromagnetic local density of states (LDOS) in structured media, providing analytical bounds that guide design and material choices for photonics applications.

Contribution

It introduces a geometry-independent, energy-conservation-based method to evaluate upper bounds on LDOS, including novel scaling laws and nearly tight bounds for large devices.

Findings

Bounds depend only on bandwidth, susceptibility, and device size.

Maximum LDOS saturates with increasing susceptibility.

LDOS scales as the quartic root of bandwidth for semi-infinite lossy structures.

Abstract

The electromagnetic local density of states (LDOS) is crucial to many aspects of photonics engineering, from enhancing emission of photon sources to radiative heat transfer and photovoltaics. We present a framework for evaluating upper bounds on LDOS in structured media that can handle arbitrary bandwidths and accounts for critical wave scattering effects with no heuristic approximations. The bounds are solely determined by the bandwidth, material susceptibility, and device footprint, with no assumptions on geometry. We derive an analytical expression for the maximum LDOS consistent with the conservation of energy across the entire design domain, which upon benchmarking with topology-optimized structures is shown to be nearly tight for large devices. Novel scaling laws for maximum LDOS enhancement are found: the bounds saturate to a finite value with increasing susceptibility and scale as the quartic root of the bandwidth for semi-infinite structures made of lossy materials, with direct implications on material selection and design applications.