Plasma-based polarizer and waveplate at large laser intensity

A plasma photonic crystal consists of a plasma density grating which is created in underdense plasma by counterpropagating laser beams. When a high-power laser pulse impinges the crystal, it might be reflected or transmitted. So far only one type of pulse polarization, namely the so-called $s$ wave (or TE mode) was investigated (when the electric field vector is perpendicular to the plane of incidence). Here, when investigating also so-called $p$ waves (or TM modes, where the magnetic field vector is perpendicular to the plane of incidence), it is detected that the transmission and reflection properties of the plasma photonic crystal depend on polarization. A simple analytic model of the crystal allows one to make precise predictions. The first conclusion is that in some operational regime the crystal can act as a plasma polarizer for high-intensity laser pulses. Also, differences in phase velocities for grazing incidence between $s$ and $p$ polarization are found. Thus, secondly, the crystal can be utilized as a waveplate, e.g., transforming linearly polarized laser light into circular polarization. All these processes extend to laser intensities beyond the damage intensities of so far used solid state devices.

Figure 1

Outline of a simple model for the density distribution in a crystal which is approximated by a stepwise density variation along the $x$ axis. The broken line shows the original density.

Figure 2

Outline of a simple model for a TPPC. (a) Stepwise density variation along $x$ axis; (b) top view of the TPPC with unit cell length $\mathrm{\Lambda }$ and variations of the dielectric constant $\epsilon$; (c) geometry of laser light propagation with respect to the arrangement of the crystal (defining the angle of incidence $\theta$).

Figure 3

Model calculation based on the dispersion relations (11) and (13) for propagation with $k_y=0$. TE and TM modes lead to the same result. It exactly agrees with Fig. 6(a) of Ref. [38].

Figure 4

Band structure for oblique propagation ($k_y\ne 0$) of TE modes, as calculated from the dispersion relation (11). For the TE modes we obtain exact agreement with the previous result of Fig. 8 in Ref. [38].

Figure 5

Band structure for oblique propagation ($k_y\ne 0$) of TM modes, as obtained from the dispersion relation (13).

Figure 6

Electric field $E_x$ corresponding to the TM component of a 50 fs, 800 nm laser pulse that probes a one-dimensional plasma crystal in $y$ direction ($\theta =\pi /2$). The plasma structure is located between $y=0$ and $y=45\mu \mathrm{m}$ and is outlined by the box. The fields are shown at times $t=0.77$ ps (left) and $t=1$ ps (right), respectively. The grating is opaque for the TM mode.

Figure 7

Electric field $E_z$ corresponding to the TE component of a 50 fs, 800 nm laser pulse that probes a one-dimensional plasma crystal in $y$ direction ($\theta =\pi /2$). Otherwise, the configuration is the same as in Fig. 6. The grating is transparent for the TE mode.

Figure 8

Phase velocities of waves with TE (black solid) and TM (red dashed) polarization for $k_x=0$ and the parameters (15).

Figure 9

On the left hand side, the electric field magnitude $\left|E\right|$ of an initially linear polarized laser pulse (color) is depicted before and after passing through a plasma grating (gray) with parameters (15). We have $k_x=0$. On the right we show the transverse electric field amplitude of the laser pulse before (bottom) and after (top) passing through the plasma grating. The amplitude is shown over one wavelength along the $y$ direction, close to the respective pulse maximum.