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
Numerical Approximation and Analysis
Original Manuscript: March 21, 2011
Manuscript Accepted: July 15, 2011
Published: August 30, 2011
Lijun Yuan and Ya Yan Lu, "Efficient numerical method for analyzing photonic crystal slab waveguides," J. Opt. Soc. Am. B 28, 2265-2270 (2011)