Boundary layer analysis of infrared whispering-gallery waveguides

The full vector modal solutions and losses of a biconcave infrared (IR) waveguide are determined using a boundary layer analysis of Maxwell's equations. The conditions on the surface of the guide are given by an effective impedance condition arising from an additional boundary layer analysis inside the metal in the high (but still finite) conductivity limit. This method easily gives the basic modes in terms of products of Airy and parabolic cylinder functions, and also explicitly shows the modal coupling caused by arbitrary bending and twisting of the waveguide. The results also show that while the quasi-TM (transverse magnetic) mode losses are large, the quasi-TE (transverse electric) mode losses remain small even with high second curvature. Thus, it should be possible to fabricate low-loss flexible IR waveguides that propagate energy using these quasi-TE modes.