TABLE OF CONTENTS This appendix provides a summary of plane-wave interactions at dielectric interfaces and a summary of special cases which are of importance in laser-diode design, in particular, indicating one reason why TE modes are slightly more strongly reflected from a cleaved facet than TM modes.
Start with Maxwell's two famous equations [1 3] for the electromagnetic fields:
| (A1.1) |  |
| (A1.2) |  |
In this work, the optical waveguide is formed from uniform layered slabs of different relative permittivity ? r = n 2 = ( n r+ j n i,) 2, giving the material's complex refractive index n with n r determining the real refractive index and n i determining the optical gain (Appendix 5). Taking the notation of Figure 3.1, the normal to the optical slab guides is in the O y direction and the TE (TM) waves may be classified as those modes with the E (H) field in the plane of the slabs i.e. in the Ox direction. With a uniform permittivity within each slab, elimination of H from eqns. A1.1 and A1.2 leads to the wave equation
| (A1.3) |  |
Taking an infinite uniform isotropic slab of material where there is no variation over the xy plane ( ?/ ?x = ?/ ?y=0) but only electric fields E x with optical frequencies ?, these fields propagate in the...
