Electromagnetic modes in dielectric equilateral triangle resonators

Resonant electromagnetic modes are analyzed inside a dielectric cavity of equilateral triangular cross section and refractive index n, surrounded by a uniform medium of refractive index n'. The field confinement is determined only under the requirements needed to maintain total internal reflection of the internal electromagnetic fields, matched to external evanescent waves. Two-dimensional electromagnetics is considered, with no dependence on the coordinate perpendicular to the cross section, giving independent TE and TM polarizations. Generally, the mode spectrum becomes sparse and the minimum mode frequency increases rapidly as the index ratio N=n/n' approaches 2. For specified quantum numbers and N, the TM modes are lower in frequency than the TE modes. Quality factors are estimated by supposing that evanescent boundary waves leak cavity energy at the triangle vertices; diffractive effects are not included. At an index ratio that is large compared with a mode's cutoff ratio, this method predicts greater field confinement for TE polarization and higher quality factors than for TM polarization. (c) 2006 Optical Society of America.