Normalized parameters for the guiding properties of TM modes in a thin-film waveguide

Abstract
By redefining the normalized parameters for the TM modes of a planar optical waveguide, it is shown that expressions for the guiding properties of the waveguide for the TM modes can be considerably simplified. These new definitions yield a form for the characteristic equation of TM modes that is formally identical to the TE case. In addition, examples are given that show that expressions for guiding properties such as dispersion and effective thickness for TM modes now differ only by the addition of reduction factors from the TE case. These reduction factors are obtained in a logical manner, and the physical reasons for their existence can be clearly seen.