Electromagnetic Modes of Anisotropic Dielectric Waveguides at p-n Junctions

The field distributions and propagation constants of the lowest-order modes of anisotropic dielectric waveguide models, which are relevant to electro-optic diode modulators, are derived. Smoothly varying dielectric constant models yield results that are essentially identical to discontinuous-dielectric-constant models. The relative intensities of the two modes representing the two polarizations are shown to vary greatly with position. Models where the dielectric constant is asymmetric about the junction plane yield similar results for the propagation constants provided the asymmetry is small. The field distributions, however, can be markedly affected by even small asymmetries. For larger asymmetries no discrete modes can propagate for parameter values typical of GaP electro-optic diode modulators. Absorption differences inside and outside of the waveguide are shown to play a minor role in determining the mode characteristics, at least for GaP diodes. The variation with voltage of the various mode parameters depends on whether the dielectric discontinuities which produce the mode confinement are fixed or move with the junction boundaries. The crystalline orientation dependence is explored by considering individually the junction field in the 111, 100, and 110 directions with the light beam traveling in specific perpendicular directions. The wavefronts of the two lowest-order modes do not coincide when anisotropic absorption or arbitrarily oriented strains are present; the phase difference between the modes will then depend upon the lateral position of measurement.