Deflection of a reflected intense circularly polarized light beam induced by asymmetric radiation pressure

A deflection effect of an intense laser beam with spin angular momentum is revealed theoretically by an analytical modeling using radiation pressure and momentum balance of laser plasma interaction in the relativistic regime as a deviation from the law of reflection. The reflected beam deflects out of the plane of incidence with a deflection angle up to several milliradians, when a nonlinear polarized laser, with the intensity $I_0\sim {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ and duration around tens of femtoseconds, is obliquely incident and reflected by an overdense plasma target. This effect originates from the asymmetric radiation pressure caused by spin angular momentum of the laser photons. The dependence of the deflection angle of a Gaussian-type laser on the parameters of laser pulse and plasma foil is theoretically derived, which is also confirmed by three-dimensional particle-in-cell simulations of circularly polarized laser beams with the different intensity and pulse duration.

Figure 1

Schematic diagram of reflection of an intense circularly polarized laser beam at a plane surface $(\eta =0)$ of an overdense plasma foil. The coordinate frame $(x,y,z)$ is attached to the incident beam, while the frame $(\xi ,y,\eta )$ is attached to the surface of the plasma foil. The laser pulse, propagating alone $z$ axis and being focused on the surface, is obliquely incident at an angle $\theta$ and reflected by the plasma foil. The reflected light deflects out of the plane of incidence $(y=0)$ at a deflection angle $\varphi$.

Figure 2

The Poynting vectors $\mathbf{S}$ of the tightly focused Gaussian laser beams in the numerical simulation. Panels (a)–(e) correspond to the linear polarization, while (f)–(j) correspond to the circular polarization. [(a) and (f)] $S_x$ on the plane $y=0$, [(b) and (g)] $S_y$ on the plane $y=0$, [(c) and (h)] $S_x$ on the plane $x=0$, and [(d) and (i)] $S_y$ on the plane $x=0$. Panels (e) and (j) are the schematic diagrams of the distribution of the Poynting vector, where the longitudinal component $S_z$ is two orders of magnitude scaled down to show the transverse component more clearly. $I_0$ is the peak intensity (i.e., $S_z$ at the focus of the laser beam) and $\lambda$ is the wavelength of the laser.

Figure 3

(a) The temporally averaged radiation pressure difference between $(\xi ,y,0)$ and $(\xi ,-y,0)$ in theoretical model. (b) The temporally averaged pressure difference over one laser period at $t=100\mathrm{fs}$ in simulation, when the half of laser duration finishes being reflected by the surface. (c) The electron density in simulation at $\xi =0$ and $t=150\mathrm{fs}$. The black lines are the isodensity lines, while the white solid line is the relativistic surface and the green dashed line is the axisymmetric part of white solid line with respect to $y=0$ for easy comparison. (d) The contour of the relativistic surface in simulation at $t=150\mathrm{fs}$ when the reflection is finished.

Figure 4

The electric field and angular profile of the reflected laser beam at $t=150\mathrm{fs}$. Panels (a) and (c) are the result of linear polarization, while (b) and (d) are the circular polarization. $\varepsilon$ is the total laser energy and $\phi$ is the angle between the laser momentum and the plane of incidence. The red dashed lines ($\phi >0$) in (c) and (d) are the axisymmetric part of the green solid lines ($\phi <0$) with respect to $\phi =0$.

Figure 5

[(a)–(c)] The temporal evolution of linear momentum $\mathbf{P}$ and angular momentum $\mathbf{L}$ for the entire space in simulation. (a) $P_x$ (red squared line) and $P_z$ (blue circular line) of the field for the circular polarization. (b) $P_y$ of the field for p-linear polarization (blue triangular line) and right circular polarization (red circular line). (c) $L_{\eta }$ the normal component of angular momentum for the circular polarization. (d) Comparison of the deflection angles of the simulation results (the points) and the theoretical model (the lines) with different laser intensity and pulse duration.

Figure 6

The dependence of deflection angle (a) and the linear momentum (b) of the reflected laser beam on different plasma scale length $L$ at simulation time $t=150\mathrm{fs}$. $L=0$ is the case of plasma target with a cut-off density profile.