A new approach to calculating Floquet spectra of multilayered periodic wave
guides is presented. The problem is formlulated as an eigenvalue problem of
the Helmholtz equation on an infinite strip with discontinuous wavenumber.
The strip is decomposed into a rectangle and two semi-infinite domains, an
d the problem is reduced to a nonlinear eigenvalue problem involving Dirich
let-to-Neumann (DtN) operators on the interfaces of the domains. A solution
scheme based on the Taylor expansion of the DtN operator with respect to t
he Floquet exponent, whose order of convergence can be made arbitrarily lar
ge, is derived. An application to a typical waveguide geometry demonstrates
the efficiency and accuracy of the approach. (C) 2000 Academic Press.