Synthesis of mode converters in waveguides and gratings based on spectral theory

The paper demonstrates, relying on spectral theory, how the problem of converter synthesis may be reduced to the search of real eigen-frequencies located in the higher sheets of Riemann's surface for the corresponding eigen boundary value problems (spectral problems). Numerically this problem is solved efficiently by incorporating algorithms, which have been developed for the solution of spectral problems, into the synthesis problem.