Laser resonators with tilted reflectors

In this paper we solve the mode problem for laser resonators having identical tilted spherical reflectors of rectangular shape in both stable and unstable configurations. Gaussian quadrature integration is employed to convert the integral equation for the modes into a matrix equation which is solved with the matrix diagonalization program ALLMAT. Plane parallel and aligned concentric resonators have identical losses; however, the latter are shown to be much less sensitive to alignment. We find that for low loss modes in the tilted stable resonator the loss can be approximated by the average loss of two aligned resonators; the region of validity for this approximation is given. Stable resonator losses increase monotonically with tilt; however, this is not always true for the unstable resonator where the loss may decrease for small tilts.