Approximate Methods

For dielectric waveguides, the only canonical shapes with closed surfaces in the transverse plane that possess exact analytic solutions to guided wave problems are the circular cylinder and the elliptical cylinder, as discussed in previous chapters. An exact analytic solution does not exist for the case of wave propagation along a dielectric waveguide of rectangular shape. The need for approximate techniques to solve the problem associated with rectangular or more general shaped dielectric structures is apparent. Two approximate techniques will be discussed in particular: (a) the Marcatili approach [1] and (b) the circular harmonic point matching technique [2]. Other notable approximate techniques by Schlosser and Unger [3], using rectangular harmonics, by Eyges, et al., using the extended boundary condition method [4], and by Shaw et al. [5], using a variational approach will not be discussed here due to their computational complexity. Other computational techniques are discussed in Chap. 15.