Optical Resonances of a Spherical Dielectric Microcavity: Effects of Perturbations

Abstract

The resonances of a dielectric microsphere (morphology-dependent resonances (MDR's), whispering gallery modes, or quasinormal modes) have extremely large (>10 6 ) quality factors (Q's) even when the sphere is as small as a few wavelengths. Perturbations in the refractive index or the shape of a microsphere shift the resonance frequencies and change the Q's from those of the unperturbed sphere. Here we develop an effective-average model to compute the first-order perturbation-induced changes in the resonance frequencies and the Q's of the MDR's. Near or on a resonance, a modified definition of mode volume is used to approximate the microsphere as a closed cavity. Analogous to the modal gain or loss in a waveguide cavity, an effective-average modal gain or loss in an inhomogeneous microsphere is defined. Both the effective-average and a time-independent perturbation theory are used to model optical bistability in a dielectric microsphere. Dispersive and absorptive optical bistability result from intensity-dependent perturbations in the real and the imaginary part of the refractive index, respectively. The effect of perturbations (e.g., size changes, shape deformations, and temperature-dependent absorption) on the dye-lasing spectra from liquid microdroplets are discussed. We show that perturbation effects can be used to develop optical diagnostics for the determination of droplet properties such as evaporation rate, shape deformation, surface tension, and temperature.

Optimal sizes of dielectric microspheres for cavity QED with strong coupling

“…Over the wavelength range 630 − 850nm, quality factors Q ≈ 8 × 10 9 have been realized, and cavity finesse F = 2.3 × 10 6 demonstrated [2,3]. Such high quality factors make the WGMs of small dielectric spheres a natural candidate for use in cavity QED [1,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20].…”

Polarimetric response of magnetodielectric core–shell nanoparticles: an analysis of scattering directionality and sensing

“…As an alternative, high refractive index (HRI) dielectric NPs have been proposed to help to solve this problem. In addition, HRI materials at the nanometer scale show both dipole-electric and magnetic morphological resonances, which are very close in frequency, giving rise to coherent magnetodielectric effects [2]. As predicted by Kerker et al [3] for magnetodielectric point-like scatterers, under certain conditions for the values of their dielectric permittivity ò and their magnetic permeability μ, zero backward and almost-zero forward scattering intensity can be achieved.…”

“…Because of the linearity of Maxwell's equations, the spectral behaviour of the scattered radiation due to HRI dielectric NPs in the absence of absorption is scalable. This behaviour depends on the size parameter and particle geometry [2,6]. Nevertheless, absorption dramatically changes their electromagnetic response.…”

Light guiding and switching using eccentric core-shell geometries

“…In addition, they can present magnetic properties in spite of being non-magnetic materials in nature 6 . So, both electric and magnetic resonances can be observed as a consequence of the excitation of whispering gallery modes 7 . Their spectral position and intensity depend on the NP size, its refractive index and that of the surrounding medium, m med 8 , 9 .…”