The field distributions in a Fabry-Perot interferometer with a very small Fresnel number

Abstract

The Fabry-Perot interferometer approximately by a system of two infinitely long, plane parallel strip mirrors is investigated on the basis of a standing-wave type formulation. The corresponding integral equation is numerically solved for a very small value of the Fresnel number. The field distributions in the plane of symmetry are given and discussed. In this limit of a very small Fresnel number the mirrors are very far apart and the problem under investigation may be looked at from the viewpoint of antenna theory. The Bouwkamp and de Bruijn work on the optimum current distribution of a thin wire antenna is outlined, and the connection with the resonator theory is established. It is demonstrated that these two theories predict similar distributions. In a sense, the resonator formulation may be considered to be a generalization of that antenna work. Siegman has carried out experiments with a ruby laser whose end faces had been unsilvered except over a minute area of one end face. The mode patterns observed at the opposite end face are in favourable agreement with the theoretical results presented. In conclusion, it is believed that Siegman hs now verified by experiment the mathematical analysis carried out by Bouwkamp and de Bruijn two decades ago.