Modes of a tilted-mirror optical resonator for the far infrared

In an extension of the work of A. G. Fox and T. Li of Bell Telephone Laboratories, a study was made of the modes of tilted-plane mirrors having enough tilt to use the spillover radiation (at a straight edge) as output coupling. This geometry seems desirable as an oscillator to intercept a molecular beam and extract coherent power in the far infrared. Control of the tilt angle provides variable
Q
. Amplitude and phase of the output are smooth enough to use cylindrical optics for focusing or collimating the output. The three lowest-order two-dimensional modes were studied which, under reasonable conditions, are determined by a single parameter. It is
\beta = \alpha(b/\lambda)^{1/2}
, where α = mirror tilt, b = mirror separation, and λ = wavelength. The lowest mode (TEM
0
) has loss per pass that increases almost linearly from 3 percent at
\beta = 10^{-2}
to 37 percent at
\beta = 10^{-1}
. The output appears to diverge from a virtual source about 3b behind the spillover edge of the shorter mirror. The virtual source of the lowest mode is displaced (0.7 to 1.1)(
\lambda b)^{1/2}
inward from the spillover edge. The mathematical problem proved to be an interesting exercise in devising ways to isolate an eigenfunction of an integral operator when the eigenvalues are nearly equal.