Floquet multipliers of periodic waveguides via Dirichlet-to-Neumann maps (Q1976856)

The authors consider multi-layered periodic waveguides and the calculation of the associated Floquet spectra. The calculation is reduced to a nonlinear eigenvalue problem involving Dirichlet-to-Newmann (DtN) operators on domain interfaces. They suggest using a truncated Taylor expansion of the DtN operator with respect to the Floquet exponent. The convergence is discussed and the method is illustrated by a particular example for which the methods suggested prove satisfactory.