Comparative Analysis of Some Schell-Model Beams Propagating Through Turbulent Atmosphere

In this paper, we investigate a comparative analysis of some Generalized Laguerre-Gaussian Schell-model beams through a paraxial ABCD optical system in a turbulent atmosphere. Based on the extended Huygens-Fresnel diffraction integral, analytical expressions for the spectral density in the receiver plane of the studied beams are derived in detail. By studying the effects of the source coherence parameters and the atmospheric turbulence strength, the numerical results indicate that the profile of these Schell-model beams takes different shapes during their propagation.

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

The aim of the present note is to derive an integral transform I = ∫ 0 ∞ x s + 1 e - β x 2 + γ x M k , v ( 2 ζ x 2 ) J μ ( χ x ) d x , I = \int_0^\infty {{x^{s + 1}}{e^{ - \beta x}}^{2 + \gamma x}{M_{k,v}}} \left( {2\zeta {x^2}} \right)J\mu \left( {\chi x} \right)dx, involving the product of the Whittaker function Mk, ν and the Bessel function of the first kind Jµ of order µ. As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters k and ν 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 [13], [3]).

Evolution of Spatiotemporal Intensity of Partially Coherent Pulsed Beams with Spatial Cosine-Gaussian and Temporal Laguerre–Gaussian Correlations in Still, Pure Water

A new family of partially coherent pulsed beams with spatial cosine-Gaussian and temporal Laguerre–Gaussian correlations, named spatial cosine-Gaussian and temporal Laguerre–Gaussian correlated Schell-model (SCTLGSM) pulsed beams, is introduced. An analytic propagation formula is derived for the SCTLGSM pulsed beam through the spatiotemporal ABCD optical system characterizing a continuous dispersive medium. As an example, the evolution of spatiotemporal intensity of the SCTLGSM pulsed beam in a still, pure water column is then investigated. It is found that the SCTLGSM pulsed beams simultaneously exhibit spatiotemporal self-splitting and self-focusing phenomena, which can be attributed to the special spatial/temporal coherence structures and the presence of pulse chirper in the source plane. The physical interpretation of the obtained phenomena is given. The results obtained in this paper will be of interest in underwater optical technologies, e.g., directed energy and communications.

Research on the propagation of partially coherent cosh-Gaussian beams through an ABCD optical system in non-Kolmogorov turbulence by effective tensor approach

An efficient tensor approach is used to study the propagation of partially coherent cosh-Gaussian beams through an ABCD optical system in non-Kolmogorov turbulence. Analytical expressions for the average intensity of the beam propagation are derived. The properties of the average intensity are investigated with a numerical example. One finds that the propagation of the beam with larger spatial coherence length is less affected by distance when the propagation distance is long enough, and as the Ch-parameter increases, the beam propagation is less effected by turbulent atmosphere. It is also found that the average intensity distribution of the cosh-Gaussian beams with larger spatial correlation length is more affected by the structure constant of turbulence (i.e., turbulence level). By choosing a suitable Ch-parameter and spatial coherence length, the partially coherent cosh-Gaussian beams can be better transmitted in non-Kolmogorov turbulence. Our results will be useful in free-space communication.