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.
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Joseph et al. (1987) studied this question.
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