An instability criterion for nonlinear standing waves on nonzero backgrounds

A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a finite interval. Localized standing wave solutions on a non-zero background, e.g., dark solitons trapped by the inhomogeneity, are identified and studied. A novel instability criterion for such states is established through a topological argument. This allows instability to be determined quickly in many cases by considering simple geometric properties of the standing waves as viewed in the composite phase plane. Numerical calculations accompany the analytical results.Comment: 20 pages, 11 figure

Shape-induced force fields in optical trapping

Advances in optical tweezers, coupled with the proliferation of two-photon polymerization systems, mean that it is now becoming routine to fabricate and trap non-spherical particles. The shaping of both light beams and particles allows fine control over the flow of momentum from the optical to mechanical regimes. However, understanding and predicting the behaviour of such systems is highly complex in comparison with the traditional optically trapped microsphere. In this Article, we present a conceptually new and simple approach based on the nature of the optical force density. We illustrate the method through the design and fabrication of a shaped particle capable of acting as a passive force clamp, and we demonstrate its use as an optically trapped probe for imaging surface topography. Further applications of the design rules highlighted here may lead to new sensors for probing biomolecule mechanics, as well as to the development of optically actuated micromachines

Giant resonant light forces in microspherical photonics

Resonant light pressure effects can open new degrees of freedom in optical manipulation with microparticles, but they have been traditionally considered as relatively subtle effects. Using a simplified two-dimensional model of surface electromagnetic waves evanescently coupled to whispering gallery modes (WGMs) in transparent circular cavities, we show that under resonant conditions the peaks of the optical forces can approach theoretical limits imposed by the momentum conservation law on totally absorbing particles. Experimentally, we proved the existence of strong peaks of the optical forces by studying the optical propulsion of dielectric microspheres along tapered microfibers. We observed giant optical propelling velocities ∼0.45 mm s−1 for some of the 15-20 µm polystyrene microspheres in water for guided powers limited at ∼43 mW. Such velocities exceed previous observations by more than an order of magnitude, thereby providing evidence for the strongly enhanced resonant optical forces. We analyzed the statistical properties of the velocity distribution function measured for slightly disordered (∼1% size variations) ensembles of microspheres with mean diameters varying from 3 to 20 µm. These results demonstrate a principal possibility of optical sorting of microspheres with the positions of WGM resonances overlapped at the wavelength of the laser source. They can be used as building blocks of the lossless coupled resonator optical waveguides and various integrated optoelectronics devices