Paraxial and nonparaxial regimes of angular momentum absorption from twisted light

TL;DR

This work derives a unified, exact framework for transferring angular momentum from twisted light to a finite absorbing disk, valid in both paraxial and nonparaxial regimes. It starts from the 4-potential of Bessel twisted beams and yields closed-form expressions for the orbital angular momentum density $\rho_z$, the Poynting flux $S_\varphi$, and the total angular momentum $M_z$, revealing how beam wavelength, polarization, and cone angle control the transfer. A key finding is a staircase-like, geometry-driven dependence of absorbed angular momentum on object size in the extreme nonparaxial regime, interpretable via Berry curvature and a geometric Hall-type response with an effective coefficient $\nu_{\text{eff}}(\theta)=l-\text{Λ}(1-\cos\theta)$. The results enable size-sensitive probing and controlled angular-momentum transfer with structured light and offer a framework that can be extended to other structured-field interactions.

Abstract

We present a unified theoretical framework for the transfer of angular momentum from a Bessel wave of twisted light to a fully absorbing disk of finite radius. Exact expressions for the orbital angular momentum density and the total angular momentum transmitted to the disk are obtained for both paraxial and nonparaxial regimes. By varying the beam wavelength, polarization, and cone angle, several experimentally relevant regimes of angular momentum transfer are identified. In the extreme nonparaxial regime, the absorbed angular momentum displays a staircase-like dependence on the object size, which can be interpreted as a geometric Hall-type response of the twisted field. The results suggest potential applications for controlled angular momentum transfer and size-sensitive probing of absorbing objects.

Figures (7)

• Figure 1: Normalized energy density $\tilde{u}$ and transverse Poynting vector $\tilde{\mathbf{S}}_{\perp}$ for twisted radiation in the paraxial regime (left) and the nonparaxial regime (right). The beam parameters $l=1$ and $\Lambda=1$ are used. Orange arrows correspond to clockwise circulation of the Poynting vector, while purple arrows correspond to counterclockwise circulation.
• Figure 2: Dependence of the dimensionless angular momentum density $\tilde{\rho}_z$ on the dimensionless parameter $\zeta = kr$ at fixed wavenumber $k$. The left panel corresponds to the paraxial regime with $\theta = 0.01$, while the right panel corresponds to the nonparaxial regime with $\theta = 1.3$. The gray lines indicate the upper and lower bounds of the angular momentum density in the asymptotic regime $\zeta \sin{\theta} \gg |l^2 - 1/4|$.
• Figure 3: $z$ projection of the total angular momentum in the paraxial regime for two beams with $l=\Lambda=1$ (orange line) and $l=\Lambda=-1$ (purple line). In both cases the object size is fixed. The gray lines indicate the asymptotic bounds of the total angular momentum, $\pm a/(\mu_0\theta)$.
• Figure 4: $z$ projection of the total angular momentum in the paraxial regime for right-circularly polarized ($\Lambda=1$, orange line) and left-circularly polarized ($\Lambda=-1$, purple line) beams with $l=1$. The radiation wavelength is fixed.
• Figure 5: $z$ projection of the total angular momentum in the strongly nonparaxial regime for a right-circularly polarized beam ($\Lambda=1$) with wavelength $\lambda=532~\mathrm{nm}$. Curves correspond to $l=1,2,3$.