Conditions for Zero Reflectance of Thin Dielectric Films on Laser Materials*

Theoretical equations are developed for complete elimination of the reflection of a solid laser material by a single dielectric film and also a specific four-layer dielectric system. The index and thickness of the single layer and the layer adjacent to the substrate in the multilayer system must be increased by an amount depending on the magnitude of the gain coefficient, in order to produce perfect matching. Reflectance as a function of frequency is calculated for several specific examples of matched and unmatched systems. Ordinary dielectric-matching conditions are sufficient for the specific examples treated until the gain coefficient is about 106 m−1. Increasing the gain coefficient decreases the width of the low-reflectance region for a perfectly matched system.