Nonlocal homogenization for nonlinear metamaterials

TL;DR

This paper develops a theoretical framework for calculating the nonlinear optical properties of metamaterials, highlighting the importance of spatial dispersion effects near resonances and predicting new phenomena like simultaneous harmonic generation.

Contribution

It introduces a consistent method incorporating spatial dispersion into nonlinear susceptibility calculations for metamaterials, extending previous models.

Findings

Spatial dispersion effects are significant near permittivity resonances.

Spatial dispersion can enable simultaneous generation of two harmonic signals.

Derived formulas reduce to known forms when spatial dispersion is negligible.

Abstract

We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects of spatial dispersion become especially pronounced in the vicinity of effective permittivity resonance where nonlinear susceptibilities reach their maxima. In that case spatial dispersion may enable simultaneous generation of two harmonic signals with the same frequency and polarization but different wave vectors. We also prove that the derived expressions for nonlinear susceptibilities transform into the known form when spatial dispersion effects are negligible. In addition to revealing new physical phenomena, our results provide useful theoretical tools for analysing resonant nonlinear metamaterials.