The equivalent Fresnel numbers of two unstable resonators of current interest for application in free-electron lasers are negative. For a resonator of this class, the equivalent collimated round-trip propagation of Siegman’s canonical formulation is a time-reversed propagation, and the modes and eigenvalues are the complex conjugates of those corresponding to a resonator having a positive equivalent Fresnel number with the same magnitude.
© 1986 Optical Society of America
Original Manuscript: August 12, 1985
Manuscript Accepted: November 18, 1985
Published: February 1, 1986
A. H. Paxton, "Unstable resonators with negative equivalent Fresnel numbers," Opt. Lett. 11, 76-78 (1986)