Gain in Optical Coatings

The introduction of gain into an optical medium is most easily accomplished by reversing the sign of the extinction coefficient. The theoretical expression for reflectance at a simple boundary between a dielectric, lossless incident medium and a medium with a finite extinction coefficient, however, takes no account of the sign of the extinction coefficient In such an arrangement, therefore, can the presence of gain possibly result in an enhanced reflectance? Opinions in the literature differ but tend to find enhancement beyond the critical angle and none below. This study examines both cases and shows that all results are in fact correct but they are not necessarily stable and it is their stability, or lack of it, that leads to the different results.