Second-order theory of the aberration sensitivity of a positive-branch, confocal unstable cavity

Abstract

A second-order theory of the aberration sensitivity that is characteristic of a positive-branch, confocal unstable cavity is presented within the framework of the Fresnel–Kirchhoff diffraction integral formulation of the transverse-mode structure. The analysis includes the effects of the ray-trajectory deviation due to the intracavity aberration source and also takes into account diffraction at the cavity feedback aperture. The dependence of the aberration sensitivity on the applied aberration source strength as well as its dependence on the cavity Fresnel number is described. This new analysis shows that the zeroth-order geometric approximation that is due to Anan’ev [ Sov. J. Quantum Electron., Vol. 1, 565 ( 1972)] is obtained in the limit as the applied intracavity aberration strength goes to zero. In addition, the diffractive behavior of the aberration sensitivity is shown to increase to its geometric value as the Fresnel number of the unstable cavity is increased, this increase being more rapid for larger transverse aberration order k.