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

Designs from the groups PSL2(q) for certain q

Using primitive actions of the projective special linear groups PSL2(q), q = 37, 41, 43, 47 and 49 some 1-designs are constructed. The automorphism group of all the constructed designs are found. It is shown that all subgroups of the automorphism group of PSL2(q), q = 37, 41, 43, 47 and 49 appear as the automorphism group of the constructed designs.Quaestiones Mathematicae 32(2009), 297–30

A tunable flat terahertz lens using Dirac semimetals: a simulation study

Abstract We propose and design a flat and tunable terahertz lens achieved through a two-dimensional photonic crystal composed of an array of rods made of a Dirac semimetal placed in air as the background medium. The structure of interest is a graded index photonic crystal, made possible by the slight variations in the rods’ radii in a direction perpendicular to the direction of the light propagation. Dirac semimetals' ability to respond to variations in their Fermi energy level manifested as a change in the refractive index provides the tunability of our proposed lens. The interaction of electromagnetic waves with the designed structure is investigated for both transverse magnetic and transverse electric polarizations using two-dimensional finite-difference time-domain method

On the number of connected components of divisibility graph for certain simple groups

The divisibility graph D(G) D(G) for a finite group G G is a graph with vertex set cs(G)∖{1} cs(G)∖{1}‎ ‎where cs(G) cs(G) is the set of conjugacy class sizes of G G‎. ‎Two vertices a a and b b are adjacent whenever a a divides‎ ‎b b or b b divides a a‎. ‎In this paper we will find the number of connected components of D(G) D(G) where G G is a‎ ‎simple Zassenhaus group or an sporadic simple group‎