Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function

Abstract

The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices are stable during the propagation through the set of lenses described in paraxial approximation, which is untypical behavior. The vortex trajectory registered at image plane due to spiral phase plate shift behaves like a rigid body. We have introduced a new factor which in our beam plays the same role as Gouy phase in pure Gaussian beam.

Introduction of Bessel higher-order cosh-Gaussian beam and its propagation through a paraxial ABCD optical system

“…As an example, free-space optical communication systems which have increased their level of competition in broadband access networks. So fundamental research area is interested in studying the propagation of laser beams through paraxial optical systems as thin lens and FRFT system (Nossir 2020, Belafhal and Dalil-Essakali 2000, Monin and Ustinov 2018, Augustyniak et al 2020, Benzehoua et Belafhal 2023, Chib et al 2022, Boufalah, Essakali 2019). This later system was initially developed by Namias (Namias 1980) as a mathematical tool to address issues in quantum mechanics and later applied to the optics field by several researchers (Zhou 2009, Chen 2009, Mendlovic and Ozaktas 1993, Ozaktas and Mendlovic 1993.…”

Propagation analysis of Whittaker–Gaussian laser beam in a gradient-index medium

“…So the study of the propagation of laser beams through optical systems has received considerable interest from many reseachers (Chib et al 2020, Ebrahim et al 2022, Belafhal and Dalil-Essakali 2000, Boufalah et al 2019, El Halba et al 2017, Benzehoua and Belafhal 2023, Monin and Ustinov 2018, Augustyniak et al 2020, Dickson 1970, Mei et al 2005, Tovar 2000, Deng 2006, Gu et al 2013, Yangjian and Sailing 2006, Gao et al 2009. Particularly in a GIM, the propagation properties for several types of beams have been investigated such as Laguerre-Gaussian beams (Newstein and Rudman 1987), Ince-Gaussian beams (Gutierrez-Vega and Bandres 2005), Elegant Ince-Gaussian beams (Bai et al 2011), Airy-Gaussian beams (Deng 2011), hollow sinh-Gaussian beams (Zou et al 2017), Gaussian vortex beams (Yang et al 2020), vortex Hermite-cosh-Gaussian beams (Lazrek et al 2022), Generalized Humbert-Gaussian beam (Nossir et al 2020), Hollow higher-order cosh-Gaussian beam (Saad and Belafhal 2021), Chirped Airy beams (Feng et al 2017), hypergeometric laser beams (Kotlyar et al 2013), Bessel beams (Cao et al 2018), and so on.…”

Calculation of a Class of Confluent Hypergeometric Equation and Analysis of its Roles in Option Pricing Models

“…The confluent hypergeometric equation is an important differential equation that arises in optics [1,2], general relativity [3,4], finance and many other areas. Its solution depends in an essential way on whether or not 𝛼, 𝛼 + 2 and 𝛼 − ሺ𝛼 + 2ሻ are integers.…”