Exact calculation of the reflection coefficient for coated optical waveguide devices

We derive an exact solution to the problem of the reflection coefficient for a coated slab waveguide. A series of computer calculations apply these results to a λ = 1.3 μm InGaAsP laser with an active area of 0.2 micron, an active area index of refraction of 3.51, and a cladding index of refraction of 3.22. Our results show that the correction due to the index step is a few percent for an uncoated laser. For antireflection coatings (reflectivity less than 1 percent), the correction due to the index step is significant. These results are important in choosing coating indices and thicknesses when minimum reflectivities are desired (e.g., for a superluminescent diode). The results, calculated over a range of indices of refraction of the coating, show that the TE and TM reflectivities are minimized at about the same value of the index, 1.84. However, the coating thicknesses at which the reflectivity is minimized are different for the TE and TM case. For example, when the TE reflectivity is minimized, the TM reflectivity exceeds the TE reflectivity by over two orders of magnitude.