Effective thickness, group velocity, power flow, and stored energy in a multilayer dielectric planar waveguide

The concept of effective thickness of a guided mode in a multilayer dielectric planar waveguide and the total time spent by the ray in crossing the effective thickness are given. Formulas to calculate the power flow, stored energy, group velocity, and group index for the mode in a multilayer planar waveguide are derived. These formulas are applied to study the guiding properties of three-layer, four-layer, and symmetrical five-layer waveguides. Some numerical results are given.