In this study, a new hybrid method for solving a wide range of internal and external problems of diffraction theory is proposed and substantiated on the basis of concepts described in [1-5]. It is well known that the generalized eigenmode method is based on solving a certain auxiliary eigenvalue problem in a complex region by expanding the solution in the basis functions and then finding the coefficients of this series by one of the variational methods. The basis functions must satisfy certain requirements, in particular, boundary conditions. For a region of an arbitrary shape, the choice of the basis can be a complicated task. However, this task is efficiently solved by the method based on the theory of R functions [1-4].
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