Ab initio computational analysis of spectral properties of dielectric spheroidal resonators interacting with a subwavelength nanoparticle.

An efficient numerical method for determining the spectral characteristics and spatial distribution of the field of a spheroidal whispering-gallery-mode (WGM) resonator interacting with a dielectric nanoparticle is presented. The developed approach is based on a combination of T-matrix formalism applied to a single resonator with a dipole approximation for the field of the nanoparticle. The method is illustrated by computation of the scattered field of the resonator-particle system illuminated by an incident field in the form of a single WGM mode of TE or TM polarization mimicking the excitation of the resonances by a tapered fiber.

Level-crossing and modal structure in microdroplet resonators.

We fabricate a liquid-core liquid-clad microcavity that is coupled to a standard tapered fiber, and then experimentally map the whispering-gallery modes of this droplet resonator. The shape of our resonator is similar to a thin prolate spheroid, which makes space for many high-order transverse modes, suggesting that some of them will share the same resonance frequency. Indeed, we experimentally observe that more than half of the droplet's modes have a sibling having the same frequency (to within linewidth) and therefore exhibiting a standing interference-pattern.

Spectral modification of whispering-gallery-mode resonances in spheroidal resonators due to interaction with ultra-small particles.

The recently developed general ab initio theory of nanoparticle-induced modifications of the spectrum of whispering gallery modes of optical spheroidal resonators is applied to the case in which distinct particle-induced resonances overlap and cannot be resolved. This situation occurs in the case of resonances with low Q-factors and/or ultra-small particles. The position of the single resonance observed in these situations depends on the strengths and widths of the overlapping resonances.

Statistical properties of one-dimensional random lasers.

Statistical properties of a laser based on a one-dimensional disordered superlattice open at one side are studied numerically. The passive normal modes of the system are determined using the Feshbach projection technique. It is found that the mode competition due to the spacial hole burning leads to a saturation of the number of lasing modes with increasing pump rate.