Abstract

Computing the eigenmodes of a photonic crystal (PhC) slab waveguide is computationally expensive, since it leads to eigenvalue problems in three-dimensional domains that are large compared with the wavelength. In this paper, a procedure is developed to reduce the eigenvalue problem for PhC slab waveguides to a nonlinear problem defined on a small surface in the waveguide core. The reduction process is efficiently performed based on the so-called Dirichlet-to-Neumann maps of the unit cells. The nonlinear eigenvalue problem can be efficiently solved by standard root-finding methods, such as the secant method.

© 2011 Optical Society of America

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