Polarization Shaping for Control of Nonlinear Propagation

We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization—radially symmetric vector beams and Poincaré beams with lemon and star topologies—in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.

Figure 1

(a) Radial and (b) azimuthal vector beams. (c) Lemon and (d) star Poincaré beams. Red (blue) ellipses correspond to left (right) circular polarization.

Figure 2

Experimental setup. A cw wavelength-tunable (760–790 nm) Toptica diode laser is coupled to a polarization-maintaining single-mode optical fiber. The power of the laser beam is adjusted by means of a half-wave ($\lambda /2$) plate followed by a polarizing beam splitter (PBS) in order to reach the saturation threshold ($I_{\text{sat}}=5\mathrm{W}{\mathrm{cm}}^{-2}$) for the $D_2$ resonance line of Rb. A combination of a $\lambda /2$ and a $\lambda /4$ plate is used to generate an arbitrary polarization state, which is then sent to a $q$ plate (QP), with a topical charge of $q=\pm 1/2$, to generate vector vortex and Poincaré beams. This is then focused ($w_0=60\mu \mathrm{m}$) into a thermally controlled Rb atomic vapor cell by means of a lens ($f=150\mathrm{mm}$). The transmitted beam is analyzed with a combination of a $\lambda /4$ plate, a $\lambda /2$ plate, and a PBS and attenuated using neutral density filters before being recorded by a CCD camera.

Figure 3

Simulated (upper row) and experimentally reconstructed (lower row) intensity and polarization distributions of scalar and vector superposition beams after propagating through the Rb cell. The incident beams are $\cos (\gamma ){\mathrm{LG}}_{0,-1}(r,\phi ,z){\mathbf{e}}_L+\sin (\gamma )\exp (i\beta ){\mathrm{LG}}_{0,1}(r,\phi ,z){\mathbf{e}}_R$, with $\beta =-\pi /2$ and $\gamma$ specified at the top. Red (blue) ellipses correspond to left (right) circular polarization. Note that for the cases of uniformly polarized input beams ($\gamma =0$ and $\pi /2$) the beam shows a significant distortion at the output of the medium. The spiral vector beam ($\gamma =\pi /4$) shows essentially no distortion in the intensity distribution or polarization. The elliptically polarized input beams ($\gamma =\pi /8$ and $3\pi /8$) show some polarization distortion but no distortion of the intensity distribution. Minor differences in polarization rotations are mainly due to experimental imperfections.

Figure 4

Intensity and polarization distributions of lemon and star topologies after propagating through the Rb cell, numerical (upper row) and experimental (lower row). Red (blue) ellipses correspond to left (right) circular polarization. Note that these beams are far more stable than the uniformly polarized beams of the left- and rightmost columns in Fig. 3. Minor differences in polarization rotations are mainly due to experimental imperfections.