Self-consistent calculation of metamaterials with gain

TL;DR

This paper introduces a computational method for self-consistently modeling dispersive metallic metamaterials with embedded gain media, accounting for nonlinear effects and loss compensation.

Contribution

It develops a novel self-consistent computational scheme for metamaterials with gain, including nonlinearities and effective parameter retrieval.

Findings

Existence of a critical pump rate for loss compensation

Nonlinear effects due to gain depletion beyond certain field strength

Transmission, reflection, and absorption characteristics analyzed

Abstract

We present a computational scheme allowing for a self-consistent treatment of a dispersive metallic photonic metamaterial coupled to a gain material incorporated into the nanostructure. The gain is described by a generic four-level system. A critical pumping rate exists for compensating the loss of the metamaterial. Nonlinearities arise due to gain depletion beyond a certain critical strength of a test field. Transmission, reflection, and absorption data as well as the retrieved effective parameters are presented for a lattice of resonant square cylinders embedded in layers of gain material and split ring resonators with gain material embedded into the gaps.