Rayleigh scattering of twisted light by hydrogenlike ions

The elastic Rayleigh scattering of twisted light and, in particular, the polarization (transfer) of the scattered photons have been analyzed within the framework of second-order perturbation theory and Dirac's relativistic equation. Special attention was paid hereby to the scattering on three different atomic targets: single atoms, a mesoscopic (small) target, and a macroscopic (large) target, which are all centered with regard to the beam axis. Detailed calculations of the polarization Stokes parameters were performed for ${\mathrm{C}}^{5+}$ ions and for twisted Bessel beams. It is shown that the polarization of scattered photons is sensitive to the size of an atomic target and to the helicity, the opening angle, and the projection of the total angular momentum of the incident Bessel beam. These computations indicate more that the Stokes parameters of the (Rayleigh) scattered twisted light may significantly differ from their behavior for an incident plane-wave radiation.

Figure 1

Geometry of the Rayleigh scattering of twisted light by a mesoscopic atomic target of size $\sigma$. While the quantization $\left(z\right)$ axis is taken along the propagation direction of the incident beam, the center of atomic target is placed on the beam axis. The emission direction of the outgoing photons is characterized by the angle ${\theta }_{k_2}$, and their polarization vector ${\mathit{e}}_{{\mathit{k}}_2}$ is described by the angle $\chi$.

Figure 2

Stokes parameters $P_1$ of Rayleigh scattered light on hydrogenlike ${\mathrm{C}}^{5+}$ ions in their ground state as a function of the emission angle ${\theta }_{k_2}$. Results for incident plane waves (black solid lines) are compared with those for Bessel beams with TAM $m=+1$ (red dashed lines) and $m=-1$ (blue dash-dotted lines), respectively. Relativistic calculations were performed for a single atom (top row) and for mesoscopic atomic targets of size $\sigma =10$ nm (middle row) and $\sigma =20$ nm (bottom row), which are centered on the beam axis. Results are shown for different helicities ${\lambda }_1$ of the incident light: ${\lambda }_1=+1$ (left column), ${\lambda }_1=-1$ (central column), and for the unpolarized light (right column). Both the opening angle ${\theta }_{k_1}={30}^{\circ }$ of Bessel beams and the photon energy $\hslash \omega =100$ eV are kept fixed.

Figure 3

Same as Fig. 2, but for the Stokes parameters $P_3$ of elastically scattered photons.

Figure 4

Stokes parameters $P_1$ (top row) and $P_3$ (bottom row) of elastically scattered photons on hydrogenlike ${\mathrm{C}}^{5+}$ ions in their ground state for a macroscopic target. Plane-wave results (black solid lines) are compared with those for Bessel beams with opening angles ${\theta }_{k_1}=1^{\circ }$ (red dashed lines), ${\theta }_{k_1}={30}^{\circ }$ (blue dash-dotted lines), and ${\theta }_{k_1}={60}^{\circ }$ (magenta dash-dot-dotted lines). Calculations were performed for different helicities ${\lambda }_1$ of the incident light: ${\lambda }_1=+1$ (left column), ${\lambda }_1=-1$ (central column), and for the unpolarized light (right column), when the photon energy $\hslash \omega =100$ eV is fixed.