Classical theory of second-harmonic generation from magnetic metamaterials

TL;DR

This paper presents a classical microscopic model to explain the physical mechanisms behind strong second-harmonic generation observed in magnetic metamaterials with split ring resonators, supported by numerical simulations.

Contribution

It introduces a classical Coulomb-interacting electron gas model to analyze second-harmonic generation in magnetic metamaterials, providing both qualitative and quantitative insights.

Findings

The microscopic model captures the dominant physical mechanisms.

Numerical simulations align with experimental observations.

The approach offers a detailed understanding of second-harmonic generation.

Abstract

Strong second-harmonic generation has recently been experimentally observed from metamaterials consisting of periodic arrays of metal split ring resonators with an effective negative magnetic permeability [Science, 313, 502 (2006)]. To explore the underlying physical mechanism, a classical model derived from microscopic theory is employed here. The quasi-free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the cold-plasma wave equations. Through numerical simulations, it is demonstrated that the microscopic theory includes the dominant physical mechanisms bothqualitatively and quantitatively.