Theory of Deformed Fabry Perot Resonator

Abstract

On the basis of the cavity picture of Fabry Perot resonator which we have developed previously, a theory of deformed resonator is presented, and applied to the circular Fabry Perot resonators with a tilted mirror and a curved mirror. The loss of the resonator is expressed as the imaginary part of the diagonal element of the radiative perturbation matrix, in the representation by the eigenfunctions of the closed resonator with the mirror deformed. The radiation loss per one transit is given for the tilt deformation by the concise formula: δ d = A l m N -1.5 + B l m K 2 N 0.5 , where N ≡ a 2 /µ L , a denotes the radius of disc. L the axial length, µ the wave length and K the ratio of maximum deformation to the wave length, i.e. K = D a /µ where D is the tilt angle. For the curve deformation, δ d = A l m N -1.5 ± C l m K N -0.5 , where K = a 2 /2 R µ, R denotes the radius of curvature, and ±refers to the negative or the positive curvature of the mirror. A l m , B l m and C l m are constants corresponding to the modes of resonance and numerically tabulated in the tables. It is seen that, as the tilt deformation K increases, it becomes possible for some higher modes to have the least radiation loss, and a map for the modes of the least radiation loss is drawn in a N - K diagram.