ASYMPTOTIC ANALYSIS OF LOADED, UNSTABLE, CYLINDRICAL RESONATORS

I show that the solution of the electromagnetic equations for a loaded cavity with a large Fresnel number F (F > 100) can be obtained analytically. This asymptotic solution is obtained as a perturbation of the geometrical-optics solution, with edge-diffraction effects appearing as ripples of order 1/(F)1/2. The basic technique is to obtain a series expansion of the relevant integrals in powers of 1/(F)1/2. This scheme works even better if the laser is operating in the saturated regime. This method of solution represents an extension of the method of Butts and Avizonis [J. Opt. Soc. Am. 68, 1072 (1978)], which is applicable to empty, cylindrical, unstable resonators.