Transverse rotation of the momentary field distribution and the orbital angular momentum of a light beam

The transverse beam pattern, usually observed in experiment, is a result of averaging the optical-frequency oscillations of the electromagnetic field distributed over the beam cross section. An analytical criterion is derived that these oscillations are coupled with a sort of rotation around the beam axis. This criterion appears to be in direct relation with the usual definition of the beam orbital angular momentum.Comment: 9 pages, 1 figure with animatio

Exact Floquet states of a driven condensate and their stabilities

We investigate the Gross-Pitaevskii equation for a classically chaotic system, which describes an atomic Bose-Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded in chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states could be prepared from the uniformly initial states by slow growth of the external potential.Comment: 14 pages, 3 eps figures, final version accepted for publication in J. Phys.

Distribution of nearest distances between nodal points for the Berry function in two dimensions

According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that both the real and imaginary parts of the wave function are random Gaussian fields we analyze the correlation function and densities of the nodal points. Using two approaches (the Poisson and Bernoulli) we derive the distribution of nearest neighbor separations. Furthermore the distribution functions for nodal points with specific chirality are found. Comparison is made with results from from numerical calculations for the Berry wave function.Comment: 11 pages, 7 figure

Polarization resolved angular patterns in nematic liquid crystal cells

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analyzing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the $4\times 4$ matrix formalism and the orthogonality relations are used to derive the analytical expressions for the transmission and reflection matrices. The polarization resolved angular patterns in the two-dimensional projection plane are characterized in terms of the polarization singularities: C points (points of circular polarization) and L lines (lines of linear polarization). In the case of linearly polarized plane waves incident on the homeotropically aligned cell, we present the results of detailed theoretical analysis describing the structure of the polarization singularities. We apply the theory to compute the polarization patterns for various orientational structures in the NLC cell and discuss the effects induced by the director orientation and biaxiality.Comment: pdflatex, rextex4, 22 pages, 7 figures (jpeg

Mutations in the latent TGF-beta binding protein 3 (LTBP3) gene cause brachyolmia with amelogenesis imperfecta

Inherited dental malformations constitute a clinically and genetically heterogeneous group of disorders. Here, we report on four families, three of them consanguineous, with an identical phenotype, characterized by significant short stature with brachyolmia and hypoplastic amelogenesis imperfecta (AI) with almost absent enamel. This phenotype was first described in 1996 by Verloes et al. as an autosomal recessive form of brachyolmia associated with AI. Whole-exome sequencing resulted in the identification of recessive hypomorphic mutations including deletion, nonsense and splice mutations, in the LTBP3 gene, which is involved in the TGF-beta signaling pathway. We further investigated gene expression during mouse development and tooth formation. Differentiated ameloblasts synthesizing enamel matrix proteins and odontoblasts expressed the gene. Study of an available knockout mouse model showed that the mutant mice displayed very thin to absent enamel in both incisors and molars, hereby recapitulating the AI phenotype in the human disorder

Internal flows and energy circulation in light beams

We review optical phenomena associated with the internal energy redistribution which accompany propagation and transformations of monochromatic light fields in homogeneous media. The total energy flow (linear-momentum density, Poynting vector) can be divided into spin part associated with the polarization and orbital part associated with the spatial inhomogeneity. We give general description of the internal flows in the coordinate and momentum (angular spectrum) representations for both nonparaxial and paraxial fields. This enables one to determine local densities and integral values of the spin and orbital angular momenta of the field. We analyse patterns of the internal flows in standard beam models (Gaussian, Laguerre-Gaussian, flat-top beam, etc.), which provide an insightful picture of the energy transport. The emphasize is made to the singular points of the flow fields. We describe the spin-orbit and orbit-orbit interactions in the processes of beam focusing and symmetry breakdown. Finally, we consider how the energy flows manifest themselves in the mechanical action on probing particles and in the transformations of a propagating beam subjected to a transverse perturbation.Comment: 50 pages, 21 figures, 173 references. This is the final version of the manuscript (v1) modified in accord to the referee's remarks and with allowance for the recent development. The main changes are: additional discussion of the energy flows in Bessel beams (section 4.1), a lot of new references are added and the Conclusion is shortened and made more accurat

Roadmap on structured light

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized

Coherence singularities in the field generated by partially coherent sources

We analyze the coherence singularities that occur in the far field that is generated by a broad class of partially coherent sources. It is shown that for rotationally symmetric planar quasihomogeneous sources the coherence singularities form a two-dimensional surface in a reduced three-dimensional space. We illustrate our results by studying the topology of the coherence singularity of a partially coherent vortex beam. We find that the geometry of the phase singularity can be associated with conic sections such as ellipses, lines, and hyperbolas.TelecommunicationsElectrical Engineering, Mathematics and Computer Scienc