Multipole analysis of substrate-supported dielectric nanoresonator arrays with T-matrix method

TL;DR

This paper introduces a generalized T-matrix framework to analyze substrate-supported dielectric nanoresonator arrays, revealing how substrates influence optical interactions and sensing capabilities in complex nanophotonic systems.

Contribution

It develops a versatile multipole-based T-matrix method for high-order multipole interactions in substrate-supported arrays, enabling detailed analysis of optical responses and sensing performance.

Findings

Substrate presence alters multipole coupling rules in arrays.

Array density and substrate refractive index significantly affect optical response.

Substrate-supported arrays can enhance refractometric sensing sensitivity.

Abstract

Substrates, and layered media in general, are ubiquitous, affect the properties of whatever is in their vicinity, and their influence is, in an arbitrary framework, challenging to quantify analytically, especially for large arrays which escape explicit numerical treatment due to the computational burden. In this work, we develop a versatile T-matrix based framework in which we generalize the coupled multipole model towards arbitrarily high multipole orders and substrate-supported arrays. It allows us to study substrate-supported random/amorphous arrays of high index dielectric nanoparticles which are of wide interest due to relatively low losses and a highly tunable optical response, making them promising elements for nanophotonic devices. We discuss how multipole coupling rules evolve in the presence of a substrate in amorphous arrays for three interaction mechanisms: direct coupling between particles, substrate-mediated interparticle coupling and substrate-mediated self-coupling. We show the interplay between array density, distance from the substrate and its refractive in determining the optical response of an array. As an example, we use this framework to analyze refractometric sensing with substrate-supported arrays and demonstrate that the substrate plays a crucial role in determining the array sensitivity.