Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of ground penetrating radar systems has been considered. Therefore, an analysis of the propagation of Bessel beams in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect diele...

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A Bessel generator multiplier for a unitary system is a bounded linear operator that sends Bessel generator vectors to Bessel generator vectors. We characterize some special (but useful) Bessel generator multipliers for the unitary systems that are ordered products of two unitary groups. These include the wavelet and the Gabor unitary systems. We also provide a detailed exposition of some of th...

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

Optical beam wander is one of the most important issues for free-space optical (FSO) communication. We theoretically derive a beam wander model for Bessel beams propagating in turbulent atmosphere. The calculated beam wander of high order Bessel beams with different turbulence strengths are consistent with experimental measurements. Both theoretical and experimental results reveal that high ord...

We experimentally measured the “self-healing” of the spatially inhomogeneous states of polarization of radial and azimuthal polarized vector Bessel beams. Radial and azimuthal polarized vector Bessel beams were generated via a digital version of Durnin’s method, using a spatial light modulator in concert with a liquid crystal q-plate. As a proof of principle, their intensities and spatially inh...

Integrated optical phased arrays for generating quasi-Bessel beams are proposed and experimentally demonstrated in a CMOS-compatible platform. Owing to their elongated central beams, Bessel beams have applications in a range of fields, including multiparticle trapping and laser lithography. In this Letter, continuous Bessel theory is manipulated to formulate the phase and amplitude conditions n...

In this paper, we study a family of analytical probability models for images within the spectral representation framework. First the input image is decomposed using a bank of filters, and probability models are imposed on the filter outputs (or spectral components). A two-parameter analytical form, called a Bessel K form, derived based on a generator model, is used to model the marginal probabi...

Basic math constants Derived from the basic ones ... from 0 and 1 ... from i ... from 1 and i ... from π ... from e ... from e and π ... from γ ... from Φ Named real math constants Other notable real constants Notable integer numbers Named/notable functions on N Named/notable integer sequences Related to Factorials Related to Hamming weight Related to Powers Related to Divisors Related to Aliqu...

In this paper, we define fractal bases and frames of L2(I×J), where I J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification L2(I×J) with tensor product space L2(I)⨂L2(J). First, recall procedure constructing perturbation continuous or integrable function. Then, composed such functions. We also obtain we...