Duality relation between nonspherical mirror optical cavities and its application to gravitational-wave detectors

In this paper, we analytically prove a unique duality relation between the eigenspectra of paraxial optical cavities with nonspherical mirrors: a one-to-one mapping between eigenmodes and eigenvalues of cavities deviating from flat mirrors by h((r) over right arrow) and cavities deviating from concentric mirrors by -h((r) over right arrow), where h need not be a small perturbation. We then illustrate its application to optical cavities, proposed for advanced interferometric gravitationalwave detectors, where the mirrors are designed to support beams with rather flat intensity profiles over the mirror surfaces. This unique mapping might be very useful in future studies of alternative optical designs for advanced gravitational wave interferometers or experiments employing optical cavities with nonstandard mirrors. c 2012 Optical Society of America