Resonant plane waves in metamaterials with dipoles and quadrupoles coupled with quantum system

TL;DR

This paper develops an analytical model combining multipole and density matrix formalisms to study gain, magnetic properties, and propagation in metamaterials with dipoles and quadrupoles, aiding design optimization.

Contribution

It introduces a natural extension of existing models to analyze plane wave propagation in gain-enabled metamaterials with multipole interactions.

Findings

Analytical insights into gain and magnetic interplay in metamaterials.

Optimization strategies for metamaterial design.

Clarification of previous discussions on metamaterial propagation.

Abstract

Here the multipole approach [13], in combination with the density matrix formalism is used for establishing of the model for MMs with gain. This approach allows us to investigate analytically or semi-analytically the interplay between gain and magnetic properties of the MMs, the influence of internally unstable operation mode for spasers (MAs coupled with emitters, which the MMs consist of) on the propagation characteristics, and finally to optimize MM design. Moreover, the presented model is in line with the previously presented approach [16] (actually is its natural extension on the problem of plane wave propagation) and from the other side pretty clear and observable. The results presented in this paper resolve the discussion excited by [12] followed by [35-38].