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A general description of cylindrical electromagnetic waves propagating in nonlinear and inhomogeneous media is given by deducing cylindrical coupled-wave equations. Based on the cylindrical coupled-wave equations, we analyze second-harmonic generation (SHG) of some special cases of inhomogeneity, and find that the inhomogeneity of the first- and second-order polarization can influence the amplitude of the SHG. From a different point of view, exact solutions of cylindrical electromagnetic waves propagating in a nonlinear medium with a special case of inhomogeneity have been obtained previously. We show that cylindrical SHG in an inhomogeneous and nonlinear medium can also be deduced from exact solutions. As verification, we compare the results obtained from the two different methods and find that descriptions of SHG by the coupled-wave equations are in good agreement with the exact solutions.

Second-harmonic generation of cylindrical electromagnetic waves propagating in an inhomogeneous and nonlinear medium