An Efficient Numerical Method for Analyzing Photonic Crystal Slab Waveguides

Computing the eigenmodes of a photonic crystal (PhC) slab waveguide is computationally expensive, since it leads to eigenvalue problems in threedimensional domains which 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. c © 2011 Optical Society of America