Multipole nonlinearity of metamaterials

TL;DR

This paper develops a formalism to analyze the linear and nonlinear optical responses of metamaterials, focusing on multipole contributions and second harmonic generation, with potential applications to various structures.

Contribution

It introduces a new analytical approach to describe light propagation in nonlinear metamaterials based on multipole expansions, applicable to arbitrary geometries.

Findings

Derived equations for linear and nonlinear light propagation in metamaterials

Focused analysis on second harmonic generation in split-ring resonators

Formalism applicable to a wide range of metamaterial structures

Abstract

We report on the linear and nonlinear optical response of metamaterials evoked by first and second order multipoles. The analytical ground on which our approach bases permits for new insights into the functionality of metamaterials. For the sake of clarity we focus here on a key geometry, namely the split-ring resonator, although the introduced formalism can be applied to arbitrary structures. We derive the equations that describe linear and nonlinear light propagation where special emphasis is put on second harmonic generation. This contribution basically aims at stretching versatile and existing concepts to describe light propagation in nonlinear media towards the realm of metamaterials.