Optical Mode Properties of 2-D Deformed Microcavities

Stand-Off Biodetection with Free-Space Coupled Asymmetric Microsphere Cavities

“…An ensemble of rays seeded into a microcavity with a given boundary and followed for a large number of internal reflections can be plotted in phase space, where each point identifies a reflection at the cavity boundary. The resulting map is known as a Poincare Surface of Section (PSOS) [ 21 , 32 , 33 ]. These plots are the stroboscopic view of a chaotic billiard system, where sinχ, the sine of the incident angle of any given reflected ray is plotted versus Φ, the polar angle at which the ray is reflected at the cavity boundary.…”

“…These ray tracing simulations, have been studied extensively in the literature, and the directional emission behavior suggested by the theory has been measured experimentally in quadrupole and half-quadrupole-half-circular (HQHC) shaped boundaries [ 21 , 23 , 32 , 34 , 35 ]. By iteratively following the points in PSOS plots, indicating the successive reflection of rays, it can be shown that chaotic ray trajectories evolve in phase space along well defined paths called “unstable manifolds” [ 32 , 33 , 36 , 37 ]. Each point along the unstable manifold is defined by the coordinates (Φ, sinχ), and can represent the point of refractive escape if sinχ equals sinχ c , the critical angle for internal reflection in a specific ARC.…”

“…The ray-optics model can be used to explain the directional emission of an ARC, however, it forbids propagating rays to jump between regions bound by the Kolmogorov-Arnold-Moser (KAM) invariant curves [ 21 , 25 , 32 , 33 ]. These KAM curves separate regions of phase space, classically forbidding chaotic trajectories of rays to diffuse into other, higher regions of phase space where more WGM-like ray trajectories occur.…”