A numerical method for the determination of the bound modes of multilayer planar dielectric waveguides is presented. It is based on the idea of tracing the evolutions of the eigenvalues (effective indices) of the waveguide as the physical parameters of the waveguide change. The eigenvalues are obtained by numerical integration of an initial-value problem. A mathematical proof is given that shows that the method guarantees that all bound modes of a lossless multilayer waveguide will be found. For a lossy waveguide, a similar mathematical proof is not available; however, numerical evidence shows that the method is still capable of finding all bound modes whose real parts of the effective indices are greater than those of the substrate and cover. The method is conceptually and computationally simple, but it is limited to searching for bound modes only.
© 1994 Optical Society of America
Lifeng Li, "Determination of bound modes of multilayer planar waveguides by integration of an initial-value problem," J. Opt. Soc. Am. A 11, 984-991 (1994)