Abstract

The absorption of a mirror coating can be measured by observing the frequency shift and mode coupling In a resonator. These changes are caused by deformation of the mirror substrate as the light energy is absorbed. We model the substrate as a right circular cylinder and consider only expansion in the length of the cylinder, as expansion in the radial direction is small compared to the laser spot size. The deformations of both a uniform absorption across the surface of the mirror as well as a point absorption are computed analytically. The frequency shift and mode coupling of a cavity with one of the deformed mirrors are calculated by perturbation techniques, and the findings are compared with experimental results using high-finesse power buildup cavities. For 1 W incident on a resonator with BK7 mirror substrates, a finesse of 3000, 10-ppm absorption, and a 0.4-rhm spot size, we calculate a maximum deformation of 120 Å. For a Zerodur substrate in the same conditions, the lower thermal expansion coefficient reduces the deformation to 1.7 Å.

© 1988 Optical Society of America