Abstract

First, the effective structure thickness is extended from a three-layer waveguide to a multilayer waveguide; this thickness depends on the choice of the reference layer. The general expression for the dispersion caused by changes in various physical parameters is then presented. The result is valid for both TE and TM modes. The expression has the form $N\frac{\partial N}{\partial \xi }={\displaystyle \sum \left[G_i\left(\begin{array}{ccc}\partial d_i& & \partial \lambda \\ & -& \\ d_i\partial \xi & & \lambda \partial \xi \end{array}\right)+Q_i{n}_i\begin{array}{c}\partial n_{}\\ \\ \partial \xi \end{array}\right]},$ where N is the effective index, d_i and n_i are, respectively, the thickness and refractive index of the layer i, λ is the wavelength of light, and ξ is any parameter on which N depends. G_i is called the geometry coefficient and Q_i the material coefficient. The geometry coefficients of the two outermost layers are zero; that of the layer i within the structure is equal to the ratio between the thickness of the layer to the effective thickness of the guide with this layer as the reference layer, multiplied by a factor. For a TE mode, the material coefficient of the layer i is exactly equal to the power fraction carried by this layer; the material coefficient for a TM mode has a more complicated expression. We apply the results to three-, four-, and symmetrical five-layer waveguides. Numerical results are presented.

© 1988 Optical Society of America