Ray chaos and Q spoiling in lasing droplets.

The highest Q optical resonators known are dielectric microspheres in which the high Q modes are created by total internal reflection of light circulating just inside the surface of the sphere[1, 2]. These high Q modes are referred to as “whispering gallery” (WG) modes or alternatively as “morphology-dependent resonances” (MDR’s) [2]. If the dielectric is a liquid droplet containing an appropriate dye then the droplet acts as a high Q micro-resonator to support lasing action of the dye when optically pumped [3]. The resonance properties of an ideal spherical dielectric, for which the wave equation separates, are described by Mie theory where the quasi-modes are the product of spherical Bessel functions jl(nkr) (n is the index of refraction) and vector spherical harmonics [4]. The radial equation then contains a repulsive term l(l + 1)/r2 which is the analogue of the angular momentum barrier for light rays and an effectively attractive term associated with the higher index of refraction in the liquid. The combination of the attractive “well” represented by the dielectric and the repulsive angular momentum barrier gives rise to quasi-bound states of the effective potential near the rim of the droplets[4] for certain ratios of l to kR (k is the wavevector in vacuum, R the radius of the spherical droplet). In the ideal sphere these resonances are only broadened by evanescent leakage (“tunneling”), hence their enormous Q values.