The Morse critical points and problems of synthesis and analysis dielectric layer

The spectral problem of a flat dielectric layer with ever varying permittivity is solved. The initial problem is equivalently reduced to the second-kind integral equation in the sought function. By applying quadrature method we arrive at the homogeneous system of the second-kind linear algebraic equations with the nonlinear entrance of spectral parameters. The resulting dispersion equations yield not only the regular spectrum points but the Morse critical points (MCP) as well, here dispersion curves can be constructed providing effective algorithms of analysis and synthesis of the dielectric layer properties