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

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