Nondiffracting optical beams in a three-level Raman system

Diffractionless propagation of optical beams through atomic vapors is investigated. The atoms in the vapor are operated in a three-level Raman configuration. A suitably chosen control beam couples to one of the transitions, and thereby creates a spatially varying index of refraction modulation in the warm atomic vapor for a probe beam that couples to the other transition in the atoms. We show that a Laguerre-Gaussian control beam allows the propagation of single Gaussian probe field modes as well as multi-Gaussian modes and non-Gaussian modes over macroscopic distances without diffraction. This opens perspectives for the propagation of arbitrary images through warm atomic vapors.

Figure 1

Diffractionless beam propagation through a vapor cell. (a) shows a schematic setup to study the propagation of a probe laser field through an atomic vapor cell. The propagation dynamics is controlled using an additional control laser field with a Laguerre-Gaussian transversal profile. (b) Three-level $\Lambda$ configuration of the vapor atoms.

Figure 2

Normalized spatial intensity profile of the control laser field. The solid (dashed) line shows the profile at the entry (exit) plane of the vapor cell. $r$ is the radial distance from the beam center. The beam waist and the Rayleigh length of the Laguerre-Gaussian beam are chosen as 120 $\mu$m and 5.7 cm, respectively.

Figure 3

Real part (a) and imaginary part (b) of the averaged susceptibility $\langle \chi \rangle$ in a thermal vapor obtained from Eq. (12) in the presence of the LG control beam. The results are shown as a function of the radial position $r$ in the beam and the Raman detuning ${\delta }_R/\gamma$. The other parameters are chosen as $G^0=1\gamma$, $w_c=120\mu$m, $g^0=0.2\gamma$, ${\Delta }_p=-170\gamma$, $D=70\gamma$, $N={10}^{12}$ atoms/cm${}^3$, and $\Gamma =0.001\gamma$.

Figure 4

Normalized intensity of the transmitted probe beam plotted against the radial distance from the beam center $r$. The solid black line shows the profile at the input of the vapor cell. The other two curves show the profile at the output after a propagation length of 5 cm. The red short-dashed curve is obtained without control field, whereas the blue long-dashed line is obtained with a LG control laser field. The inset shows the variation of the unnormalized output intensity of the probe beam. The initial width and Raman detuning of the off-resonant probe field are chosen as $w_p$ = 48$\mu$m and ${\delta }_R=-0.015\gamma$, respectively. All other parameters are as in Fig. 3.

Figure 5

Normalized intensity of the transmitted probe beam. In (a), the intensity profile is shown against the transverse coordinate $x$ in the $y=0$ plane at different propagation distances $z$. (b) compares the probe beam profile with and without the LG control field at the output of the vapor cell after a propagation of 2.5 cm. The variation of the unnormalized output intensity of the probe beam is shown in the inset. The initial amplitude and width of the off-resonant control and probe fields are chosen as $G^0=0.75\gamma$, $g^0=0.2\gamma$, $w_p=48\mu$m, $w_c=100\mu$m, and $200\mu$m. All other parameters are the same as in Fig. 3.

Figure 6

Intensity of the transmitted probe beam in the $x\text{−}y$ plane transversal to the beam propagation direction at the output of the vapor cell in the absence (upper panel) and presence (lower panel) of the LG control beam, respectively. The parameters are as in Fig. 5.

Figure 7

(a) Image of a non-Gaussian multipeak beam at the output of a vapor cell with length $L=2.5$ cm. (b) shows a comparison of the cases with and without control beam at the output of the vapor cell for the non-Gaussian beam. The parameters are as in Fig. 5 except that the non-Gaussian probe beam has width 35 $\mu$m and the LG control beam has width 200 $\mu$m.