Generation of Polarization-Tunable Hybrid Cylindrical Vector gamma Rays

Abstract

Cylindrical vector (CV) gamma rays can introduce spatially structured polarization as a new degree of freedom for fundamental research and practical applications. However, their generation and control remain largely unexplored. Here, we put forward a novel method to generate CV gamma rays with tunable hybrid polarization via a rotating electron beam interacting with a solid foil. In this process, the beam generates a coherent transition radiation field and subsequently emits gamma rays through nonlinear Compton scattering. By manipulating the initial azimuthal momentum of the beam, the polarization angle of gamma rays relative to the transverse momentum can be controlled, yielding tunable hybrid CV polarization states. Three-dimensional spin-resolved particle-in-cell simulations demonstrate continuous tuning of the polarization angle across (-90°, 90°) with a high polarization degree exceeding 60%. Our work contributes to the development of structured gamma rays, potentially opening new avenues in high-energy physics, nuclear science, and laboratory astrophysics.

Figures (5)

• Figure 1: Schematic diagram for hybrid cylindrical vector (CV) $\gamma$-ray emission through the interaction of a rotating electron beam and a foil. (a) A relativistic electron beam carrying azimuthal momentum $p_{\varphi}$ propagates in the $+\hat{x}$ direction and traverses a foil, resulting in coherent transition radiation (CTR) and producing polarized $\gamma$ rays through the nonlinear Compton scattering process. The green arrows indicate the azimuthal momentum $p_{\varphi}$ of the beam. (b) Higher-order Poincaré sphere for topological charge $l=1$, where all states on the surface are CV polarized. Points on the equator represent the hybrid mode polarized $\gamma$ rays that can be generated in this scheme. Here, $\mathbf{S}_{3}^{+1} = \pm 1$ represent radial and azimuthal polarization, respectively, while $\mathbf{S}_{1}^{+1} = \pm 1$ correspond to polarization directions at $45^\circ$ and $135^\circ$ with respect to the radial direction, respectively.
• Figure 2: (a1)-(a3) Angle resolved distribution $\log_{10}\left({\rm d} N_\gamma/{\rm d}{\rm \varOmega} \right)$ (background heatmap) and average polarization $P_\gamma$ of the emitted $\gamma$ photons with respect to the polar angle $\theta$ and the azimuth angle $\varphi$. Here, ${\rm d}{\rm \varOmega} = \sin \theta {\rm d} \theta {\rm d} \varphi$, $\theta$ is the angle between the photon momentum and the $+x$-axis, and $\varphi$ is the angle between the projection of the momentum onto the $yz$-plane and the $+y$-axis. The superimposed double-headed arrows indicate the average polarization direction, while their color represents the degree of polarization $P_\gamma$. (b1)-(b3) Angle-resolved polarization degree $P_\gamma$ (blue) and distribution ${\rm d} N_\gamma/{\rm d}\theta$ (red) of all emitted $\gamma$ photons vs $\theta$. Here, panels (a1, b1), (a2, b2), (a3, b3) correspond to the case with an initial electron azimuthal momentum of $p_{\varphi}=10m_ec$, $20m_ec$, $40m_ec$, respectively. (c) The angle $\delta$ as a function of the electron initial azimuthal momentum $p_{\varphi}$. (d) Energy-resolved polarization degree $P_\gamma$ (blue) and distribution ${\rm d}N_\gamma/{\rm d}\varepsilon_\gamma$ (red) of $\gamma$ photons within $0.15^\circ<\theta<0.65^\circ$ vs the photon energy $\varepsilon_\gamma$ for $p_{\varphi}=20m_ec$. (e) The brilliance [photons$/(\mathrm{s\,mm^2mrad^2\times0.1\%bandwidth})$] of the $\gamma$ rays as a function of the the photon energy $\varepsilon_\gamma$.
• Figure 3: (a) Distribution of the effective electric field $E^{\prime}$ in the xy plane at z=0. (b) Time-dependent photon generation rate, where the blue line represents the rate for first-photon emission and the red line represents the rate for multiple-photon emission. (c) Average polarization degree $P_{\gamma}$ as a function of energy ratio $\varepsilon_{\gamma}/\varepsilon_{e}$ and QED parameter $\chi_e$. (d) Electron trajectories during interaction with the CTR field and their projections in the $yz$ and $xz$ planes. (e) Distribution of radial forces $F_r$ acting on electrons at different times, with colour representing the number of electrons. The red solid line shows the evolution of the average radial momentum $p_r$ of the beam. (f) Distribution of photon polarization directions (black double arrows) and momentum directions (red arrows) in the $yz$ plane, with the color scale representing the effective electric field $E^{\prime}$.
• Figure 4: (a) Average polarization degree $P_{\gamma}$ (green line) and polarization angle $\delta$ (blue line) as a function of azimuthal momentum $p_\varphi$. Effects of (b) charge of the electron beam $Q_b$, (c) energy of the electron beam $\varepsilon_e$, (d) beam angle spread $\varDelta\theta$, (e) thickness of the foil, and (f) density of the foil on average polarization degree $P_{\gamma}$ (green line), number of the emitted photons $N_\gamma$ (blue line), and cutoff energy $\varepsilon_{\rm{m}}$ (red line).
• Figure 5: (a)-(b) Angle-resolved distribution $\log_{10}\left({\rm d} N_\gamma/{\rm d}{\rm \varOmega} \right)$ (background heatmap) and average polarization $P_\gamma$ of the emitted $\gamma$ rays, where (a) corresponds to electrons traversing 3 foils and (b) 7 foils. (c) Angle-resolved distribution of $\gamma$-ray polarization angle $\delta$, after traversing 7 foils. (d) Evolution of the average radial momentum of electrons (blue line) and the number of radiated photons (red line).