Linear and nonlinear processes of transferring optical singularities from anisotropic crystals onto the wavefront of Bessel light beams (BLBs) are investigated. The generation of high-order vortices at the propagation of BLBs along the optical axes of crystals was studied. Particularly, a nonlinear frequency doubling of Bessel vortices in the conditions of new type synchronism (full conical pha...

Bessel beams are widely used in optical metrology mainly because of their large Rayleigh range (focal length). Radial/azimuthal polarization of such beams is of interest in the fields of material processing, plasma absorption or communication. In this paper an experimental set-up is presented, which generates a Bessel-type vector beam with a spatial polarization, oscillating along the optical a...

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factoriz...

We study the distribution, in the space of Satake parameters, of local components of Siegel cusp forms of genus 2 and growing weight k, subject to a specific weighting which allows us to apply results concerning Bessel models and a variant of Petersson’s formula. We obtain for this family a quantitative local equidistribution result, and derive a number of consequences. In particular, we show t...

Generalizing the notion of placing rooks on a Ferrers board leads to a new class of combinatorial models and a new class of rook polynomials. Connections are established with absolute Stirling numbers and permutations, Bessel polynomials, matchings, multiset permutations, hypergeometric functions, Abel polynomials and forests, and polynomial sequences of binomial type. Factorization and recipro...

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

In this paper, we study Bessel processes of dimension δ ≡ 2(1 − μ), with 0 < δ < 2, and some related martingales and random times. Our approach is based on martingale techniques and the general theory of stochastic processes (unlike the usual approach based on excursion theory), although for 0 < δ < 1, these processes are even not semimartingales. The last time before 1 when a Bessel process hi...

Title of dissertation: HOLLOW BESSEL TUNNEL GUIDE: THEORY AND EXPERIMENT Narupon Chattrapiban Doctor of Philosophy, 2012 Dissertation directed by: Professor Wendell T. Hill, III Department of Physics The main objectives of this thesis were to create and investigate properties and applications of all-optical atomic guides, which are potential building blocks for atom optics experiments. Specific...