Spin-orbit coupling of optical vector vortices in coherently prepared media

TL;DR

The paper addresses how optical vector vortices, composed of opposite-circular-polarized components carrying opposite OAM $\pm l$, propagate through coherently prepared phaseonium in a Λ configuration. Using a linear Maxwell–Bloch analysis, it shows that the OAM topology is imprinted onto the medium as spatial atomic coherence, producing $2|l|$ azimuthal transparency windows that reshape the beam intensity into petal patterns while preserving topological symmetry. The coherence-induced anisotropy drives an optical spin–orbit coupling, enabling SAM exchange and polarization rotation between left- and right-circular components, with the evolution controllable via the initial ground-state populations and relative amplitudes ($c_1$, $c_2$, $\theta$, $\psi$). This magnetic-field-free mechanism offers a clean interface for transferring vector topology from light to matter and manipulating SAM–OAM dynamics, with potential realizations in $^{87}$Rb using STIRAP to prepare the phaseonium state.

Abstract

We investigate the propagation of an optical vector vortex weakly interacting with a coherently prepared atomic medium (phaseonium) in a three-level $Λ$ configuration. The vector beam consists of vortex pulse pairs with right- and left-circular polarizations, corresponding to opposite spin angular momentum (SAM), and carrying opposite orbital angular momentum (OAM) charges $\pm l$. We show that during the propagation of the vortex pairs, analytically obtained in the linear regime, the medium inherits the topology of the vortex pair, mapping the OAM onto a spatially structured atomic coherence. This mapping produces $2|l|-$fold azimuthal transparency structures that reshape the beam intensity from a ring into a petal-like pattern. The OAM-structured atomic coherence induces a corresponding optical anisotropy within the medium, which feeds back into the propagating vector beam, resulting in optical spin-orbit coupling manifested as SAM exchange, rotation, and evolution of polarization textures. Depending on the initial ground-state population of the phaseonium, the polarization state evolves between left-circular, linear, and right-circular polarizations.

Figures (7)

• Figure 1: Schematic of the three-level atomic system forming a $\Lambda$-type configuration. The excited state $\ket{e}$ is coupled to the ground states $\ket{g_1}$ and $\ket{g_2}$ by right- and left-circularly polarized light fields with Rabi frequencies $\Omega_R$ and $\Omega_L$, respectively.
• Figure 2: Characteristic distance $z_c$ as a function of detuning $\Delta$. The curve exhibits a parabolic dependence on $\Delta$. The detuning is normalized to the decay rate $\gamma$, and the characteristic distance is normalized to the absorption length $L_{abs}$ such that, at resonance, $z_c = L_{abs}$.
• Figure 3: Absorption pattern of the right-handed beam on resonance $\Delta=0$ for different topological charge $|l|$ at $z/L_{abs}=0$: (a) $|l|=1$, (b) $|l|=2$, (c) $|l|=3$, and (d) $|l|=4$. Other parameters are $\alpha=20$, $c_1=c_2=\frac{1}{\sqrt{2}}$
• Figure 4: Intensity distributions (a)–(d) and absorption patterns (e)–(h) of the right-handed beam with $|l|=2$ at different propagation distances: (a),(e) $z/L_{abs}=0$; (b),(f) $z/L_{abs}=0.5$; (c),(g) $z/L_{abs}=1$; and (d),(h) $z/L_{abs}=20$. The other parameters are the same as those used in Fig.\ref{['Absorption Different L']}.
• Figure 5: Intensity and polarization state distributions in the transverse plane of a vector vortex beam carrying topological charge $|l|=1$ and relative amplitude $\theta=\pi/4$, corresponding to equal left- and right-handed field strengths ($|E_L|=|E_R|$ since $\cos{\theta}=\sin{\theta}$). The transverse coordinates $(x, y)$ are normalized to the beam waist $w$, and the propagation distance $z$ is normalized to the absorption length $L_{abs}$. The medium parameters are $c_1=c_2=1/\sqrt{2}$ and $\alpha=20$. Two detuning cases are shown: (a) resonant ($\Delta=0$) and (b) off-resonant ($\Delta=2\gamma$). The first, second, and third rows correspond to relative phases $\psi=0$, $\pi/2$, and $\pi$, respectively. Darker rings or lobes indicate higher intensity regions. The yellow lines denote linearly polarized states, while red and blue ellipses represent left- and right-handed circular polarizations, respectively.