Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity

TL;DR

This paper demonstrates that a nonlinear metamaterial slab with very small negative permittivity exhibits angular multi-stability and directional hysteresis in transmissivity due to the interplay of linear and nonlinear dielectric responses.

Contribution

It provides a theoretical analysis showing how a specific nonlinear metamaterial can produce multi-valued transmissivity and hysteresis effects based on incidence angle and input intensity.

Findings

Transmissivity shows angular multi-stability.

Directional hysteresis depends on input intensity.

Multiple field configurations are possible within the slab.

Abstract

We investigate propagation of a transverse magnetic field through a nonlinear metamaterial slab of sub-wavelength thickness and with a very small and negative linear dielectric permittivity. We prove that, for a given input intensity, the output intensity is a multi-valued function of the field incidence angle so that the transmissivity exhibits angular multi-stability and a pronounced directional hysteresis behavior. The predicted directional hysteresis is a consequence of the fact that the linear and nonlinear contributions to the overall dielectric response can be comparable so that the electromagnetic matching conditions at the output slab boundary allow more than one field configurations within the slab to be compatible with the transmitted field.