An initial-value method for integral operators—IV. Complex-valued kernels of laser theory

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A new technique is presented for the calculation of the eigenvalues and eigenfunctions of complex-valued symmetric kernels which occur in laser theory. The method combines some classical results of integral equations and complex variables with a recent technique for transforming Fredholm integral equations into a Cauchy system of differential equations. The procedure is flexible and accurate, whereas many of the classical techniques, such as Rayleigh-Ritz, yield results of doubtful accuracy for the kernels of laser theory.