Dynamic Control of the Polarization of Intense Laser Beams via Optical Wave Mixing in Plasmas

When intense laser beams overlap in plasmas, the refractive index modulation created by the beat wave via the ponderomotive force can lead to optical wave mixing phenomena similar to those used in crystals and photorefractive materials. A new comprehensive analytical description of the modification of the polarization state of laser beams crossing at arbitrary angles in a plasma is presented. It is shown that a laser-plasma system can be used to provide full control of the polarization state of a separate “probe” laser beam; simple analytical estimates and practical considerations are provided for the design of novel photonics devices such as laser-plasma polarizers and wave plates.

Figure 1

Interaction geometry between two laser beams (a “pump” and a “probe” with electric fields ${\mathit{a}}_0$ and ${\mathit{a}}_1$, respectively) in a plasma. (a) The beams cross at an angle $\psi$, forming a plasma grating via the ponderomotive force of the beat wave. (b) ${\mathit{\pi }}_0$ is the projection of ${\mathit{a}}_0$ in the plane of polarization of the probe beam. In the undepleted pump limit, the ${\mathit{a}}_{1\perp }$ component of the probe perpendicular to ${\mathit{\pi }}_0$ is unaffected by the coupling whereas the parallel component ${\mathit{a}}_{1\parallel }$ has its amplitude or phase (or both) modified, depending on the phase velocity of the plasma grating (cf. Fig. 2).

Figure 2

Plasma coupling coefficient $K$ (defined in text) as a function of the phase velocity of the grating $v_b$ normalized to the plasma sound speed $c_s$ (lower $x$ axis), or, equivalently, vs the frequency shift between the two laser beams (upper $x$ axis), for the following parameters: $T_e=3\mathrm{keV}$, $T_i=1\mathrm{keV}$, $Z=2$ (helium), $n_0=0.1n_c$, and ${\lambda }_0=351\mathrm{nm}$. The phase of $a_{1\parallel }$ [cf. Fig. 1] is retarded if $\mathrm{Re}(K)>0$ [or accelerated if $\mathrm{Re}(K)<0$], and its amplitude exponentially grows if $\mathrm{Im}(K)>0$ [or decays if $\mathrm{Im}(K)<0$].

Figure 3

Conceptual design for: (a) a laser-plasma polarizer and (b) a laser-plasma wave plate.