Mode localization and the Q-factor of a cylindrical microresonator

As opposed to the modes in an optical spherical/spheroidal microresonator, the whispering gallery modes in a long cylindrical microresonator are delocalized. Consequently, a circulating light beam that is evanescently coupled into the cylinder and experiences total internal reflection eventually radiates out along the cylinder axis. However, the self-interference of such a beam can produce a resonant mode that is strongly localized along the axial direction. Specifically, the mode characteristic width is (alphabeta)(-1/2), where alpha and beta are the attenuation and propagation constants of the cylinder material. The Q-factor of this mode can be almost as large as the Q-factor of modes in a spheroidal microresonator with the same alpha divided by 2.542.