Quantization of fields in a Fabry-Perot cavity

A Fabry-Perot cavity, which consists of two highly reflective but slightly transmissive mirrors facing each other, is used as an interferometer in the gravitational wave detectors now being developed in Tokyo and elsewhere. The sensitive mirrors are suspended freely in order to respond to the weak incoming waves; the quantum fluctuations of the radiation pressure can he a source of noise to the mirrors. This paper examines the orthogonality and the completeness of the eigenmodes of the radiation field in the cavity as constructed by Ley and Loudon for the purpose of field quantization.