The Excitation of Planar Dielectric Waveguides at p-n Junctions, I

The fields excited within a planar dielectric waveguide by an externally incident electromagnetic field are studied in this paper. The dielectric waveguide fills the half space z > 0, while the half space z < 0 is air. The waveguide is formed by a nonuniform, anisotropic, nonabsorbing, dielectric medium. Different choices of the dielectric tensor for this medium yield different waveguides. Certain models which are particularly relevant to electro-optic diode waveguides and laser diode amplifiers are studied in some detail. An arbitary incident field will, in general, excite not only a finite number of propagating modes, but also a background of continuum modes. Integral representations of the total transmitted field within the waveguide as well as of the reflected field are obtained. The representation of the total transmitted field can be decomposed into a finite sum of discrete propagating modes, a continuum propagating field, and an evanescent field. Explicit evaluation of the fields depends on the solution of a pair of integral equations. In practice, the dielectric tensor of the waveguide differs but little from the dielectric constant of the surrounding material. An approximate solution is found for this case, and numerical results will appear in a following paper.