Abstract

A diffractive formulation of the aberration sensitivity of a positive branch, confocal unstable resonator is presented. The kth-order aberration sensitivity coefficient is found to be given by ${\overline{\alpha }}_k\cong {\overline{\alpha }}_k^{(0)}\cdot {\Gamma }_{k\cdot }$The factor ${\overline{\alpha }}_k^{(0)}={\psi }_k/(M^k-1)$describes the aberration sensitivity behavior in the absence of any change in the cavity mode eigenvalue. The associated eigenvalue change due to the intracavity aberration source is accounted for by the factor Γ_k. The geometric factor ψ_kaccounts for the double interaction of the cavity field with the aberration source in a single round-trip propagation through the cavity. Within Ananev's geometric approximation, ψ_kis readily obtained from the unperturbed ray geometry of the geometric cavity mode structure. The analysis presented here includes the deviation of the ray trajectory due to the aberration source. This new analysis then yields the dependence of the aberration sensitivity coefficient on the applied aberration source strength. The diffractive expression for the aberration sensitivity is shown to increase to its geometric value as the Fresnel number of the unstable cavity is increased, this increse being more rapid for larger transverse aberration order k.

© 1985 Optical Society of America