Exact field decomposition for TM waves in nonlinear media

Abstract

We show that the electric field components E(x) and E(z) of a transverse magnetic (TM) wave propagating in a nonlinear medium can be formally decomposed through a conservation law, provided that partial differentialxx/ partial differentialE(z)(2) = partial differentialzz/ partial differentialE(x)(2). If this condition is satisfied, then the electromagnetic field distribution can be exactly obtained by quadrature. For the case of a guided nonlinear TM mode, our procedure can be employed to establish the eigenvalue equation directly.