Cavity equations for a positive or negative refraction index material with electric and magnetic non-linearities

TL;DR

This paper derives and analyzes coupled nonlinear equations for electric and magnetic fields in a ring cavity filled with nonlinear refraction index materials, reducing them to a generalized Lugiato-Lefever equation and exploring their stability.

Contribution

It introduces a reduction of coupled electric and magnetic field equations to a single generalized Lugiato-Lefever equation for nonlinear refraction index materials.

Findings

Identification of three characteristic behaviors based on parameter combinations.

Reduction of complex coupled equations to a single effective equation.

Stability analysis supported by numerical simulations.

Abstract

We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative refraction index material with third order effective electric and magnetic non-linearities. Two coupled non-linear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.