Abstract
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium.
Highlights
Show that sum- and difference-frequency generation of two waves propagation in a nonlinear medium is affected by a third wave
Exact solutions and explicit analytical expressions. We will use this exact solution to deal with problems of interactions between cylindrical electromagnetic waves in a nonlinear medium
Interactions between cylindrical electromagnetic waves in a nonlinear medium have been shown in Eqs. (4), it is difficult to use this exact solution to analyse nonlinear interactions and phenomena
Summary
Show that sum- and difference-frequency generation of two waves propagation in a nonlinear medium is affected by a third wave. We will use this exact solution to deal with problems of interactions between cylindrical electromagnetic waves in a nonlinear medium. Starting from the superposition principle, the exact solution of the linear problem can be extended to describe cylindrical waves in the medium: E(r, t) = ∑ζ iJ 0(kir)cos(ωit), i
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