Elliptic Laguerre-Gaussian beams

Abstract

An analytical expression for the diffraction of an elliptic Laguerre-Gaussian (LG) beam is derived and analyzed. We show that a beam with even singularity order has nonzero axial intensity for any degree of ellipticity and at any finite distance z from the initial plane, whereas at z = 0 and z = infinity the axial intensity is zero. We show that for a beam with a small degree of ellipticity and even order of singularity, two isolated intensity zeroes appear in the Fresnel zone on a straight line at an angle of 45 deg or -45 deg, depending whether the beam's spin is right or left. The theoretical conclusions are confirmed by numerical simulation and physical experiments.

Detection of mixed OAM states via vortex breakup

“…At a certain distance from the beam waist in the presence of an astigmatic lens, a higher order OV breaks into |l| secondary first-order vortices [39,32]. In the transverse plane at this distance there will be |l|+1 intensity peaks, oriented at a ±45 • angle relative to the tilt axis [15]. The propagation dynamics of an OV in the presence of a tilted spherical lens can be simulated using a ray transfer matrix analysis and generalized Huygens-Fresnel integral, as related in detail in [20].…”

“…Methods based on the property of multi-singular optical vortices to deform in the presence of some astigmatic media are particularly relevant to experimental use because of their extreme simplicity. Astigmatic laser beam behavior, propagation, and transformation were studied theoretically and experimentally in some detail for both Bessel modes of light [14], and Laguerre-Gaussian [15,16] ones. The invention of a rather simple Hermite to Gaussian (and vice versa) mode converter exploiting a cylindrical lens to add astigmatism into the beam [17,18] evolved into several techniques which allow experimentalists to measure the topological charge of OVs very easily [19,20].…”

Gyrator transform: properties and applications

“…Figures 4 (b, c) and (e, f) are the corresponding output modes for α = π/5 and α = π/4. Therefore the GT of scaled HG mode is an alternative for generation of the elliptic LG beams [14]. When the input function is not centred at the optical axis we can apply the shifting theorem, Eq.…”

Direct Measurement of the Topological Charge in Elliptical Beams Using Diffraction by a Triangular Aperture

“…Several EVBs were investigated earlier, including Mathieu 14 , 15 , helical Ince–Gaussian (HIG) 16 , vortex Hermite–Gaussian (VHG) beams 17 , and elliptic perfect optical vortices 18 . Other works have investigated simple ways of producing EVBs 25 , 26 . However, the diffraction of these beams by apertures has not been extensively investigated, except a method for measuring the orbital angular momentum of elliptical vortex beams by using a slit hexagon aperture 27 .…”