Quantum Theory of Surface Lattice Resonances

TL;DR

This paper develops a quantum optical theory to describe surface lattice resonances in nanoparticle arrays, enabling analysis of interactions with quantum emitters and nonlinear effects.

Contribution

The paper introduces a quantum theory of surface lattice resonances beyond classical approximations, enabling modeling of nonlinear interactions with quantum emitters.

Findings

Quantum input-output relations for nanoparticle lattices are derived using the electric dipole approximation.

The formalism enables coupling analysis between nanoparticle arrays and external quantum emitters.

Emitter nonlinearities can switch surface lattice resonance conditions between electronic transitions.

Abstract

The collective interactions of nanoparticles arranged in periodic structures give rise to high‐Q in‐plane diffractive modes known as surface lattice resonances. Although these resonances and their broader implications have been extensively studied within the framework of classical electrodynamics and linear response theory, a quantum optical theory capable of describing the dynamics of these structures, especially in the presence of material nonlinearities beyond ad hoc few‐mode approximations, is largely missing. To this end, we consider a lattice of metallic nanoparticles coupled to the electromagnetic field and derive the quantum input–output relations within the electric dipole approximation. As applications, we analyze coupling between the nanoparticle array and external quantum emitters, and show how the formalism extends to molecular optomechanics, where the high Q‐factors of SLRs enable coupling to collective vibrational modes. We further consider arrays composed of saturable excitonic emitters, demonstrating how emitter nonlinearities can be used to switch the SLR condition between electronic transitions. Using a perturbative approach that accounts for population dynamics, we show how these effects can be probed in pump–probe experiments and give rise to nonlinear phase‐matching phenomena. Our work provides a microscopic framework for modeling SLRs interacting with quantum emitters without phenomenological descriptions of the electromagnetic environment.

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