Nonlinear coupled-mode theory for periodic plasmonic waveguides and metamaterials with loss and gain

TL;DR

This paper develops a rigorous nonlinear coupled-mode theory for plasmonic waveguides and metamaterials with loss and gain, enabling analysis of complex electromagnetic interactions in advanced photonic structures.

Contribution

It introduces a general coupled-mode framework based on Lorentz reciprocity, applicable to a wide range of metal-dielectric structures with nonlinear effects.

Findings

Agreement with previous specific case analyses

Prediction of novel self- and cross-phase modulation effects

Applicability to diverse plasmonic and metamaterial configurations

Abstract

We derive general coupled-mode equations describing the nonlinear interaction of electromagnetic modes in media with loss and gain. Our approach is rigorously based on the Lorentz reciprocity theorem, and it can be applied to a broad range of metal-dielectric photonic structures, including plasmonic waveguides and metamaterials. We verify that our general results agree with the previous analysis of particular cases, and predict novel effects on self- and cross-phase modulation in multi-layer nonlinear fishnet metamaterials.