In this paper, we aim to establish several new closed-form evaluations of certain integral transforms involving the rational and exponential functions, which are expressed in terms of confluent hypergeometric function and related functions. Also, we consider some special cases. The presented integral formulas are useful in many fields of mathematical physics, particularly in the propagation of some waves through random turbulent media. The main result is applied to investigate the closed-form of unusual scattering parameters used in the biological tissues. It is found that there is a good agreement between the numerical and theoretical evaluations.
The current study examines the diffraction of Humbert beam of type-II by a helical axicon based on the diffraction integral formula. The considered beam is a new donut beam family which generated by converting the Bessel-Gaussian beams passing through a paraxial ABCD optical system with a SPP. For the diffracted beam produced by the stationary phase approach, we have formulated the intensity distribution. By adjusting the input beam features and the topological charge of the helical axicon, numerical simulations are carried out to examine the behavior of the diffracted beam.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.