Vortex Propagation in Orbital Angular Momentum Beams and the Effects of a Limited Aperture

Abstract

When generating light with orbital angular momentum by imprinting orbital phase onto a standard Gaussian beam, it is often assumed that the propagation of the generated spatial mode is a Laguerre-Gaussian. However, the true propagation of this beam in a realistic, aperture-limited optical system is non-trivial and has not been thoroughly explored in existing literature. We explore a numerical model that shows the development of an optical vortex mode, propagating from the plane of phase modulation, and the relation of these dynamics to the orbital phase factor $\ell$ and the spatial bandwidth of the optical system. The results of this model are compared to experimental data for beams with $\ell$ values 1, 2, 5, and 10 propagating through a range of spatial filters, with the described model showing agreement in the near field regime.

Figures (7)

• Figure 1: Visual of a HyGG mode with $\ell = 1$ forming from orbital phase modulation of a 780nm wavelength Gaussian beam with a 1.52mm beam waist, produced by solving the PWE numerically with a GV mode as an initial condition at $d_1$. The primary ring radius, $r_0$, is shown as a function of the optical axis, $z$. The Rayleigh range, $z_\mathrm{R}$, defines the propagation distance where the vortex core diameter stabilizes to that of half of the beam diameter, $z_\mathrm{R}/10$birth_and_evolution_of_optical_vortex.
• Figure 2: The top row depicts intensity images captured of GV modes across several indicated $\ell$ values at the $d_1$ position on the optical axis. The bottom row depicts the corresponding phase profiles, generated through interference with a diverging Gaussian beam which adds a radial phase curvature and gives rise to the spiral phase patterns. These images were taken using the setup shown in Fig. \ref{['fig:setup']}.
• Figure 3: Diagram of the setup as described in the text, where a $\text{HyGG}^{10}_{-10}$ mode is generated as an example SPP on the SLM, and intensity image on the camera.
• Figure 4: (Left) A comparison between the data (integrated orbitally from an intensity image as shown in the insert) and numerical model for $\text{HyGG}^2_{-2}$ at 38.5cm from $d_1$ with no LPF ($D = \infty$) applied, where $r_0(D,z)$ was measured. (Right) The $r_0(D,z)$ measurement was repeated for 5 different points along the optical axis and compared to the numerical model, the parametric fit from Eq. \ref{['eq:Y2']}, and the near field ring radius approximation from Eq. 28 of Fresnel_and_Fraunhofer.
• Figure 5: Ring radii data sets and corresponding numerical model outputs for $\ell = 1$ and $10$ under $D = 0.2mm$ and when no LPF is applied, alongside a direct comparison to the numerical model for each. The shaded region for each $\ell$ contains the other 11 data sets for each LPF used, which are omitted from these plots except for the $D = 0.4mm$ case. The respective panels for the $\ell = 2$ and $\ell = 5$ datasets were excluded for readability.