Excitation of morphology-dependent resonances and van de Hulst’s localization principle

Liquid Droplet Microresonators

“…[33], van de Hulst’s localization principle fails in the case of a droplet with surface irregularities. Thus, weak distortions caused by thermal capillary waves induce angular-momentum coupling of partially-scattered light waves to the resonator WGMs achieving the highest excitation efficiency for a beam impact parameter slightly smaller than the drop radius [33,34], in agreement with experimental findings. If a current scan is sent to the laser, several WGM spectra can be observed in a few-ms time.…”

Supernumerary spacing of rainbows produced by an elliptical-cross-section cylinder I Theory

“…24 -27, the equations for wave scattering by a nonspherical particle were derived to first order in the particle-shape perturbation, and in Ref. 28 the form of the equations was simplified substantially. Similarly, in Ref.…”

“…Equations ͑34͒ illustrate that two different incident partial waves, lЈ ϭ l ϩ q and lЈ ϭ l Ϫ q, are coupled to each scattered partial wave l by the Fourier component q of the surface perturbation. This is a simpler situation than for scattering by a perturbed sphere 28 where all the incident partial waves lЈ in the interval l Ϫ q Յ lЈ Յ l ϩ q are coupled with various strengths to each scattered partial wave l by the Fourier component q of the surface perturbation.…”

“…The partial-wave coupling induced by the noncircular component of the surface shape is implicit in the T-matrix formalism 32,33 and provides the physical explanation for the optimal positioning of a tightly focused laser beam on a microparticle when morphology-dependent resonances are excited. 28,34,35 Equations ͑45͒ are not especially convenient for numerical computations because they contain Bessel functions of negative order. If we assume that the cylinder surface shape is given in Fourier-series form and we substitute Eqs.…”

Partial-wave expansions of angular spectra of plane waves

“…For example, for scattering of a plane wave by a spheroid or a sphere with surface roughness, each scattered partial wave is coupled to many incident beam partial waves via the Fourier decomposition of the particle's irregular shape. 17 In Eqs. (26a) and (26b) on the other hand, each scattered partial wave is coupled to many incident beam partial waves by a combination of the beam's evanescent components and by the fact that a portion of the beam amplitude is proportional to the radially incoming wave h n ͑2͒ ͑kr͒ as the beam approaches the sphere and is proportional to the radially outgoing wave h n ͑1͒ ͑kr͒ after it leaves it.…”