Propagation of a Bessel–Gaussian beam in a gradient-index medium

Approximate solutions for propagating light beams in a material with quadratic, exponential, and quartic transverse refractive index profiles

“…The Jacobi 'sn' function is integrable, periodic, and can be expressed as a Fourier series [39]. More specifically, for the real-valued arguments in (22), we can use the simple 1-term Fourier expansion [40]…”

“…To illustrate, figure 2 shows a comparison of (23) and the exact solution (22) for several different values of the initial condition x 0 =0.04, 0.1, 0.2. This simple 1-term model does not appear to have seen widespread use in the literature.…”

“…[17-1917-19]) or GRadient INdex (GRIN) materials [20,21], where one can tailor a particular refractive index profile to produce the desired behavior. For example Alberucci et al [11] studied periodic modulation of the refractive index in waveguide design while [20,22] used GRIN materials to modify the profiles of Gaussian and Bessel-Gaussian beams respectively. The focus on this work is on several specific types of transverse index modulations and how their influence on a propagating beam can be quickly and accurately modeled.…”

Periodic properties of partially coherent generalized Hermite cosh-Gaussian beams through a gradient-index medium

“…Thus, propagation of light beam in various optical systems has sparked significant interest among numerous researchers (Benzehoua and Belafhal, 2022, Benzehoua and Belafhal, 2023, Saad et al 2024a. Specifically, researchers have delved into the propagation characteristics within a gradient index medium for different kinds of beams, including Ince-Gaussian beams (Gutierrez-Vega and Bandres 2005), Laguerre-Gaussian beams (Newstein and Rudman 1987), Airy-Gaussian beams (Deng 2011), hypergeometric laser beams (Kotlyar et al 2013), Elegant Ince-Gaussian beams (Bai et al 2011), Airy-Gaussian vortex beams (Zhao et al, 2016) Chirped Airy beams (Feng et al 2017), hollow sinh-Gaussian beams (Zou et al 2017), Bessel beams (Cao et al 2018), Bessel-Gaussian beam (Pei et al 2019), Gaussian vortex beams (Yang et al 2020), non-diffracting Lommel beams (Hui et al 2021), Generalized Humbert-Gaussian beam (Nossir et al 2023, Hollow higher-order cosh-Gaussian beam (Saad and Belafhal 2021), Whittaker-Gaussian laser beam (Nossir et al, 2023), lorentz-gauss vortex beam (Qusailah et al, 2023), Tricomi beams (Qiu et al, 2023) and more. Meanwhile, partially coherent beams have also been studied and achieved valuable research results which have important applications in atmospheric optics, optical micromanipulation and nonlinear optics (Dan and Zhang 2009;Chen et al 2017;Wang et al 2019).…”

Asymmetries Caused by Nonparaxiality and Spin–Orbit Interaction during Light Propagation in a Graded-Index Medium

“…The paraxial approximation is usually used to study the propagation of light beams in a graded-index medium. Both ray and wave optics are applied to analyze the propagation of light in graded-index media [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In [39], the polarization-dependent Goos-Hanchen (GH) beam shift at a graded-index dielectric interface was examined.…”