Self-Consistent Field Analysis of Multireflector Optical Resonators

The self-consistent field approach is used to obtain integral equations for the modes in symmetric and nonsymmetric resonators with arbitrary numbers of mirrors. The resonator fields are considered as TEM clockwise and counterclockwise traveling waves which for passive resonators are uncoupled and which independently satisfy the necessary boundary conditions on reflection from the resonator mirrors. An arbitrarily polarized field is resolved into two linearly polarized components which can be treated separately and identically. The component perpendicular to the plane of the resonator is considered and integral equations are obtained for the spatial distribution of resonator modes just after reflection from any mirror in both the symmetric and nonsymmetric resonators. The integral equation for the symmetric N-mirror resonator is investigated in detail. Because of the astigmatic focusing of the reflectors there is no situation corresponding to the confocal resonator, however, a ``pseudoconfocal'' resonator with nonspherical mirrors is discussed. The integral equation for the resonator with arbitrary mirror spacing is solved in the limit of infinite Fresnel numbers and the resonator field is described in terms of Hermite-Gaussian functions. The mirror spacing must satisfy the condition 0≤l/bcosα≤2. A general resonance condition is obtained and the results of numerical computations of diffraction losses are presented for three- and four-mirror resonators. For minimum diffraction loss the ratio of mirror spacing to mirror curvature is not constant but varies from mode to mode and the amount of variation differs with the number of mirrors.