Field theory description of the non-perturbative optical nonlinearity of epsilon-near-zero media

TL;DR

This paper introduces a non-perturbative, field-theoretic approach to describe the strong optical nonlinearity in epsilon-near-zero media like ITO, capturing saturation effects and extending existing models.

Contribution

It develops a scalar field theory with a Born-Infeld Lagrangian to model non-perturbative nonlinear optical effects in ENZ media, particularly ITO.

Findings

Established a non-perturbative model for ITO nonlinearities.

Demonstrated the natural emergence of Born-Infeld dynamics in ENZ media.

Extended electrodynamics models to include saturation effects.

Abstract

In this paper we introduce a fully non-perturbative approach for the description of the optical nonlinearity of epsilon-near-zero (ENZ) media. In particular, based on the rigorous Feynman path integral method, we develop a dressed Lagrangian field theory for light-matter interactions and discuss its application to dispersive Kerr-like media with order-of-unity light-induced refractive index variations. Specifically, considering the relevant case of Indium Tin Oxide (ITO) nonlinearities, we address the novel regime of non-perturbative refractive index variations in ENZ media and establish that it follows naturally from a scalar field theory with a Born-Infeld (BI) Lagrangian. Moreover, we developed a predctive model that includes the intrinsic saturation effects originating from the light-induced modification of the Drude terms in the linear dispersion of ITO materials. Our results extend the Huttner-Barnett-Bechler electrodynamics model to the case of non-perturbative optical Kerr-like media providing an intrinsically nonlinear, field-theoretic framework for understanding the exceptional nonlinearity of ITO materials beyond traditional perturbation theory.