An efficient method is presented for rigorous description of three-dimensional electromagnetic diffraction fields in slot systems containing several parallel plane interfaces between dielectrics and conductors. For such structures, the method employs the representation of spatial field components in terms of two complex scalar functions. They specify two field polarizations, which reflect and refract on all parallel dielectric interfaces independently, one from the other, which essentially simplify the total solution of diffraction problem. As an example, the application of eigen-function expansions and mode-matching technique solves the specific problem of three-dimensional diffraction of a plane electromagnetic wave by a slot in a thin conducting screen located ahead of a half-infinite dielectric.
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