Light Waves at the Boundary of Nonlinear Media

TLDR

The authors generalize reflection and refraction laws and Fresnel formulas to predict the direction, intensity, polarization, and total reflection/transmission of boundary harmonic waves, and outline an integral‑equation framework for wave propagation in nonlinear media. They solve Maxwell’s equations for a linear–nonlinear interface, showing that harmonic waves are generated at the boundary, derive an equivalent Brewster angle, present a slab solution illustrating experimental harmonic generation, and discuss practical implications for devices.

Abstract

Solutions to Maxwell's equations in nonlinear dielectrics are presented which satisfy the boundary conditions at a plane interface between a linear and nonlinear medium. Harmonic waves emanate from the boundary. Generalizations of the well-known laws of reflection and refraction give the direction of the boundary harmonic waves. Their intensity and polarization conditions are described by generalizations of the Fresnel formulas. The equivalent Brewster angle for harmonic waves is derived. The various conditions for total reflection and transmission of boundary harmonics are discussed. The solution of the nonlinear plane parallel slab is presented which describes the harmonic generation in experimental situations. An integral equation formulation for wave propagation in nonlinear media is sketched. Implications of the nonlinear boundary theory for experimental systems and devices are pointed out.