An integral transform and its application in the propagation of Lorentz-Gaussian beams

summary:The aim of the present note is to derive an integral transform $$I=\int _{0}^{\infty } x^{s+1} e^{-\beta x^{2}+\gamma x} M_{k, \nu }\left (2 \zeta x^{2}\right )J_{\mu }(\chi x) dx,$$ involving the product of the Whittaker function $M_{k, \nu }$ and the Bessel function of the first kind $J_{\mu }$ of order $\mu$. As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters $k$ and $\nu$ of the Whittaker function. Eventually, we show the application of the integral in the propagation of hollow higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system (see, for details \cite {Xu2019}, \cite {Collins1970})

PROPAGATION OF BESSEL-MODULATED GAUSSIAN BEAMS THROUGH A MISALIGNED FIRST-ORDER OPTICAL SYSTEM

Abstract Based on the extended Collins formula, an analytical expression, for Bessel-modulated Gaussian (QBG) beams passing through a misaligned first-order optical system, is derived. Results show that the beam shape of the output beam remains unchanged and similar to that of the input even in the considered misaligned system. It is also indicated that the beam centre is related to the misaligned parameters and is derived from the optical axis. As an example, the propagation of zeroth-order QBG beams propagating through a misaligned thin lens is investigated numerically. Results in this paper may provide potential applications in combination technology of laser beams

KURTOSIS FACTOR OF SOME TRUNCATED AND NON-TRUNCATED LASER BEAMS

Abstract Based on the intensity moments formalism, the closed-form expressions of the kurtosis factor of some truncated and non-truncated laser beams with rectangular symmetry, as Hermite-cosh-Gaussian and super-Gaussian beams, are derived and illustrated numerically. Some particular cases are also deduced. Our results are consistent with previous works and constitute a more generalized study of kurtosis factor of laser beams

SPECTRAL SHIFTS IN THE NEAR ZONE OF A PARTIALLY COHERENT FIELD AFTER PASSING THROUGH A CIRCULAR APERTURE

Abstract In this paper, we investigate theoretically the spectral shifts in the near zone of a partially coherent field after passing through a circular aperture. The numerical results are presented for Lorentzian and Gaussian profiles of the original spectrum of the source. Various factors which have influenced on the spectral characteristics are also analyzed

Blue-detuned optical ring trap for Bose-Einstein condensates based on conical refraction

We present a novel approach for the optical manipulation of neutral atoms in annular light structures produced by the phenomenon of conical refraction occurring in biaxial optical crystals. For a beam focused to a plane behind the crystal, the focal plane exhibits two concentric bright rings enclosing a ring of null intensity called the Poggendorff ring. We demonstrate both theoretically and experimentally that the Poggendorff dark ring of conical refraction is confined in three dimensions by regions of higher intensity. We derive the positions of the confining intensity maxima and minima and discuss the application of the Poggendorff ring for trapping ultra-cold atoms using the repulsive dipole force of blue-detuned light. We give analytical expressions for the trapping frequencies and potential depths along both the radial and the axial directions. Finally, we present realistic numerical simulations of the dynamics of a 87Rb Bose-Einstein condensate trapped inside the Poggendorff ring which are in good agreement with corresponding experimental results

On the beam shape coefficients of fundamental nondiffracting beams

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N-body Quantum-mechanical Hamiltonians - Extrapotential Terms

After a brief review of the basic algebraic ingredients needed to express the quantum-mechanical Hamiltonian of an /b N/-body system in terms of curvilinear coordinates and quasi-momentum operators, the effect of changing the normalization convention is thoroughly investigated, with special emphasis on the occurrence of a nondifferential term in the expression of the kinetic energy operator, the so-called `extrapotential' term. Four examples are presented, concerning various parametrizations and various referentials, for acetylene-like molecules.Anglai

IMAGE PRODUCED BY BESSEL-MODULATED GAUSSIAN BEAMS PROPAGATING THROUGH A FRACTIONAL FOURIER TRANSFORM SYSTEM WITH TWO HARD-EDGED APERTURES

Abstract Based on the Fresnel diffraction theory, we investigate a detailed study of image produced by a Besselmodulated Gaussian (QBG) beams propagating through a Fractional Fourier Transform system with two circular apertures. By the use of cylindrical coordinate system and expansion of the hard-edged circular aperture function, an approximate analytical solution of the intensity distribution on the considered fractional Fourier system is given

Fourier-transform Spectroscopy of Carbonyl Sulfide From 1800 To 3120 Cm(-1) - the Normal Species

We have measured the FT spectrum of OCS from 1800 to 3120 cm(-1) with a resolution of 0.007 cm(-1). The spectra have been recalibrated to yield absolute uncertainties of 3 X 10(-5) cm(-1) throughout the whole range. For the normal isotopic species a total of 117 different vibrational transitions have been identified and analyzed, both for the frequencies and for the intensities. A new global rovibrational analysis of (OCS)-O-16-C-12-S-32 has been performed. Important effective Herman-Wallis terms are explained on the basis of eigenvectors. (C) 1995 Academic Press Inc