The Fabry‐Perot Interferometer with a Large Fresnel Number

The Fabry‐Perot Interferometer is investigated on the basis of the Huygens‐Fresnel Principle. An integral equation is derived which describes its features when used as a laser resonator. An asymptotic expansion is given for a large Fresnel Number. The first‐order approximation describes the waves resonating between the mirrors. A formal solution is obtained which is consistent from the viewpoint of the diffraction theory. This solution reveals the most significant result that in the region close to the axis the observable single mode patterns are in the form of parabolic cylinder functions. Thus, apart from an immaterial phase variation, the lowest‐order eigenfunction associated with the resonating waves is a Gaussian and not a cosine function as is widely believed. The theoretical results presented are obviously in favorable agreement with the familiar experimental observations. They predict, for instance, the filamentary nature of the laser action in an imperfect ruby crystal.