Showing papers on "Bessel function published in 1996"

Generalized Bessel-Gauss beams

Abstract: In this paper we describe a superposition model for Bessel-Gauss beams, in which higher orders are included. An analogous model leads to a different class of beams, namely the modified Bessel-Gauss beams. Then a generalized set of beams, containing the previous beams as particular cases, is introduced. The behaviour of these beams upon propagation is investigated, both analytically and numerically.

Simulation models of a dissipative transmission line above a lossy ground for a wide-frequency range. I. Single conductor configuration

Abstract: For pt. I see ibid., vol.38, no.2, p.127, 1996. The simulation model of a multiconductor dissipative line above a lossy ground, based on the exact formulation of the Maxwell equations, is proposed for a wide frequency range. The procedure is an extension of the analysis of single conductor configurations. The exact expression of the matrix modal equation of the line is first proposed, assuming that in the system there are as many dominant discrete modes of propagation as there are conductors. New expressions of the distributed series-impedance and shunt-admittance matrices are proposed, with reference to the definition of the wire-to-ground voltage. Moreover, an easy-to-implement simulation model is proposed for use in computer codes, based on the logarithmic approximation of the Sommerfeld integrals and Bessel functions. Applications are carried out in order to compare the results of the proposed procedure and of the Carson (1926) theory, with reference to a three-conductor line above a lossy ground.

Wave propagation with rotating intensity distributions.

Abstract: Wave fields containing invariant features have recently stimulated the interest of the scientific community. Typical examples of such fields are Gaussian modes, Bessel beams @1#, and wave fronts containing phase dislocations @2#. Bessel beams are solutions of the wave equation that propagate with invariant intensity. Phase dislocations are discontinuities of the phase in a wave front such that the circulation of the phase around its axis is an integral multiple of 2p. Thus, they determine lines of zero intensity in space. Experimental evidences of optical dislocations can be found, for example, in Refs. @3‐5#. It was noted in Refs. @4,6# that, under certain circumstances, an array of dislocations nested in a Gaussian beam rotates by p/2 rad from the waist to the far field, expanding with the host beam. The objective of this paper is to investigate general solutions having rotating intensity distributions around and along the propagation axis. We start by demonstrating that these solutions are easily obtained in terms of the superposition of Gauss-Laguerre ~GL! modes. The rotation rate along the propagation is then derived and the set of all possible solutions presenting a specific total rotation angle is characterized. Finally, we analyze the limit of the rotation rate and present experimental results for optical beams. Let a scalar wave be represented by the function

Lang and Kobayashi phase equation

Abstract: Lang and Kobayashi equations for a semiconductor laser subject to optical feedback are investigated by using asymptotic methods. Our analysis is based on the values of two key parameters, namely, the small ratio of the photon and carrier lifetimes and the relatively large value of the linewidth enhancement factor. For low feedback levels, we derive a third-order delay-differential equation for the phase of the laser field. We then show analytically and numerically that this equation admits coexisting branches of stable periodic solutions that appear at different and almost constant amplitudes. These amplitudes are proportional to the roots of the Bessel function ${\mathit{J}}_{1}$(x). The bifurcation diagram of the phase equation is in good agreement with the numerical bifurcation diagram of the original Lang and Kobayashi equations. We interpret the onset of the periodic solutions as the emergence of a new set of external cavity modes with a more complicated time dependence. \textcopyright{} 1996 The American Physical Society.

Karhunen-Loeve expansion of a fast Rayleigh fading process

Abstract: An approximate Karhunen-Loeve expansion is given for a random fading process characterised by an autocorrelation function Rḡ(τ) = J0(2πfdτ), J0(x) is the zeroth order Bessel function and fd is the process fading rate.

Diffraction characteristics of the azimuthal Bessel–Gauss beam

Abstract: We examine the free-space propagation characteristics of an azimuthally polarized, circularly symmetric beam, such as that emitted by a concentric-circle-grating surface-emitting laser. We begin with the appropriate scalar wave equation and then find the azimuthal Bessel–Gauss beam solution, using both a Cartesian decomposition method and an angular spectrum representation. We find a general azimuthal diffraction integral for circularly symmetric disturbances and examine two special cases, a thin lens and a circular aperture; the azimuthally polarized beam remains well behaved in both cases. Plots of radial field profiles and longitudinal beam-waist evolution are presented.

Tunable stimulated Raman scattering by pumping with Bessel beams.

Abstract: We report on a novel pumping scheme for stimulated Raman scattering (SRS) that uses a Bessel beam. We have used this scheme for SRS from molecular vibrations in acetone and from a polariton mode in a LiIO3 crystal. A nearly diffraction-limited Stokes beam was observed along the cone axis of the Bessel beam. The generation mechanism of the Stokes beam is identified as being due to noncollinear scattering of the component plane waves that constitute the Bessel beam. Frequency tuning of SRS from polaritons in LiIO3 by variation of the Bessel beam cone angle is demonstrated.

Propagation-invariant electromagnetic fields: theory and experiment

Abstract: The vector concept of the propagation invariance is formulated to be applied to the stationary electromagnetic fields. The analysed exact solutions of the Maxwell equations are obtained on the basis of general propagation-invariant solutions of the scalar Helmholtz equation. A possible classification of the propagation-invariant fields based on quantities which appear in the complex Poynting theorem is proposed. The longitudinal periodicity of the electromagnetic field obtained due to the superposition of two Bessel beams is verified by a simple experiment.

Lines and electromagnetic fields for engineers

Abstract: 0. Preliminaries 1. Transmission Lines: Parameters, Performance, Characteristics, and Applications to Distributed Systems 2. Graphical Solutions of Transmission Line and Transmission Line-like Systems: The Smith Chart 3. Transients on Transmission Lines 4. Scalars, Vectors, Coordinate Systems, Vector Operations, and Functions 5. Theory, Physical Description, and Basic Equations of Electric Fields 6. Theory, Physical Description, and Basic Equations of Magnetic Fields 7. Theory, Physical Description, and Basic Equations of Time Varying Electromagnetic Fields Maxwell's Equations and Field Properties of Waves 8. Propagation of Plane Waves 9. Waveguides and Cavities Appendices A. Sinusoidal Steady State Formation B. Coaxial Cable Data C. Selected Laplace Formulation D. Expansions of Vector Operators in Rectangular, Spherical, and Cylindrical Coordinates E. Unit Vector Relationships and Partial Derivatives in Rectangular, Spherical, and Cylindrical Coordinates F. Vector Helmholtz Theorem G. The Unit Dyad H. Derivation of the Energy in a Magnetic Field I. Alternate Solutions Forms of the Wave Equation K. Solution of Partial Differential Equations by the Method of Separation of Variables L. Series Solutions of Ordinary Differential Equations and Solution Functions Defined by them: Trigonometric, Bessel, and Legendre Functions M. Identities, Recursion Formulas, Differential and Integral Formulas for Bessel Function and Legendre Functions N. Orthogonal Functions and Orthogonal Function Series O. Definite Integrals Which Yield Bessel Functions

Theory of third-harmonic generation using Bessel beams, and self-phase-matching

Abstract: Taking Bessel beams ({ital J}{sub 0} beam) as a representation of a conical beam, and a slowly varying envelope approximation (SVEA) we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phase-matching integral of the theory. A method to calculate the transverse-phase-matching integral containing four Bessel functions is described which avoids the computer calculations of the Bessel functions. In order to consolidate the SVEA result an alternate method is used to obtain the exact result for the third-harmonic generation. The conditions are identified in which the exact result goes over to the result of the SVEA. The theory for multiple Bessel beams is also discussed which has been shown to be the source of the wide width of the efficiency curve of the third-harmonic generation observed in experiments. {copyright} {ital 1996 The American Physical Society.}

Double bessel beam producing method and apparatus

Abstract: A double Bessel beam is produced such that two Bessel beams are superimposed on each other with respect to amplitude so as to interfere with each other. Each of the Bessel beams has a shape of the zero-order bessel function of the first kind and a light amplitude distribution different in diameter from that of the other. An apparatus for producing a double Bessel beam includes a device for producing two Bessel beams each having a shape of the zero-order Bessel function of the first kind and a light amplitude distribution different in diameter from the other, and a device for superimposing the two Bessel beams on each other with respect to amplitude so as to interfere with each other.

Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system

Abstract: We investigate the classical and non-classical reductions of the (2 + 1)-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a strong generalization of the sine-Gordon equation. A family of solutions obtained as a non-classical reduction involves a decoupled sum of solutions of a generalized, real, pumped Maxwell-Bloch system. This implies the existence of families of solutions, all occurring as a decoupled sum, expressible in terms of the second, third and fifth Painleve transcendents, and the sine-Gordon equation. Indeed, hierarchies of such solutions are found, and explicit transformations connecting members of each hierarchy are given. By applying a known Backlund transformation for the system to the new solutions found, we obtain further families of exact solutions, including some which are expressed as the argument and modulus of sums of products of Bessel functions with arbitrary coefficients. Finally, we show that the sine-Gordon system satisfies the necessary conditions of the Painleve PDE test due to Weiss et al which requires the usual test to be modified, and derive a non-isospectral Lax pair for the generalized, real, pumped Maxwell-Bloch system.

Hyperspherical theory of three-particle fragmentation and Wannier's threshold law.

Abstract: A representation of three particle wave functions well adapted to computations of low-energy fragmentation states of systems interacting electrostatically is derived. A basis called an angle-Sturmian basis, is introduced. Exact wave functions are represented by sums over the angle-Sturmian functions and integrals over the index of Bessel functions. Equations for the coefficients of the Sturmian functions are derived. Solutions of these equations are given in the approximation that one Sturmian is employed. Integral representations of the approximate three-particle wave functions are obtained. Evaluation of the integral for large hyper-radius {ital R} gives the hidden-crossing theory, familiar from representations of ion-atom interactions at low energy. It is shown that ionization components emerge simply only for complex values of {ital R}. Such components conform to Wannier{close_quote}s threshold law. {copyright} {ital 1996 The American Physical Society.}

An accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space (TE case)

Abstract: We develop a method for the analytical evaluation of the inverse Laplace transform representations for transient transverse magnetic (TM) plane wave obliquely incident on a conductive half-space. We assume that the permittivity and conductivity of the dispersive half-space are independent of frequency. The time-domain expressions for the reflected and transmitted waves are first represented as inverse Laplace transforms. The transient fields are then shown to consist of two canonical integrals. The canonical integrals, in turn, are solved analytically, thereby yielding close-form solutions involving incomplete Lipschitz-Hankel integrals (ILHIs). The ILHIs are computed numerically using efficient convergent and asymptotic series expansions, thus enabling the efficient computation of the transient fields. The exact, closed-form expressions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast Fourier transform (FFT) algorithms. An asymptotic series representation for the ILHIs is also employed to obtain a relatively simple late-time approximation for the transient fields. This approximate late-time expression is shown to accurately model the fields over a large portion of its time history.

Representation of exact and semiclassical eigenfunctions via coherent states. Hydrogen atom in a magnetic field

Abstract: Global formulas for eigenfunctions and solutions to the Cauchy problem, including the path integral representation, are obtained using the coherent states technique. The reduction of coherent states via symmetry groups is studied for a transformation from “Bessel” to “hypergeometric” states. The eigenfunctions of the Hamiltonian for the hydrogen atom in a homogeneous magnetic field are expressed in terms of Bessel coherent states. For a small field, after quantum averaging, the Hamiltonian is represented in terms of generators with quadratic commutation relations. The irreducible representations of this quadratic algebra are realized on hypergeometric states. The notion of deformed hypergeometric states is also introduced for this quadratic algebra as an analog of squeezed Gaussian packets of the Heisenberg algebra. The asymptotic equations of eigenfunctions with respect to a small field and a large leading quantum number are derived using these states and their “deaveraging.” Some explicit formulas for the Zeeman splitting of the spectrum are obtained up to the fourth order with respect to the field, as well as for lower and upper levels in the cluster, including the case of “incidence on the center.”

Dynamic Electrophoretic Mobility of a Cylindrical Colloidal Particle

Abstract: Accurate approximate formulas are obtained for the dynamic electrophoretic mobility of a cylindrical hard colloidal particle in an oscillating electric field for two cases where the cylinder is in a transverse field or in a tangential field These formulas, expressed in terms of Hankel functions and modified Bessel functions, are suitable for numerical calculation for all κa(κ is the Debye–Huckel parameter andais the particle radius) at zero particle permittivity and low zeta potentials The dynamic mobility in a tangential field is shown to depend on κain contrast to the static case, where it is independent of κa The dynamic mobility of a cylinder averaged over a random distribution of orientation of the cylinder axis is roughly equal to the mobility of a sphere with a radius of 15 times the cylinder radius

Imaging of generalized Bessel-Gauss beams

Abstract: Different kinds of Bessel-Gauss beam have been recently introduced. By considering the effect of a lens on the field, we analyse how these different sets of fields transform into one another and illustrate how a superposition model of Gaussian beams allows this transformation to be clearly interpreted.