Efficient diffraction control using a tunable active-Raman gain medium

We present a scheme to create an all-optical tunable and lossless waveguide using a controllable coherent Raman process in an atomic rubidium vapor in an $\mathcal{N}$-type configuration. We employ a Gaussian Raman field and a Laguerre-Gaussian control field to imprint a high-contrast tunable waveguidelike feature inside the atomic medium. We numerically demonstrate that such a waveguide is able to guide arbitrary modes of a weak probe beam to several Rayleigh lengths without diffraction and absorption. Our results on an all-optical waveguide-based scheme may have potential applications in lossless image processing, high-contrast biomedical imaging, and image metrology.

Figure 1

Displays a schematic diagram of four level $\mathcal{N}$-type atomic system. The transitions $|3\rangle \leftrightarrow |1\rangle$ is coupled by a strong Raman field with Rabi frequency ${\mathrm{\Omega }}_r$. A weak probe field with Rabi frequency ${\mathrm{\Omega }}_p$ couples the transition $|3\rangle \leftrightarrow |2\rangle$. The transition $|4\rangle \leftrightarrow |2\rangle$ is driven by a strong control field with Rabi frequency ${\mathrm{\Omega }}_c$. ${\gamma }_{ij}$ are the spontaneous decay rates from excited states $|i\rangle$ to ground states $|j\rangle$. The field detunings for Raman, probe, and control are represented as ${\mathrm{\Delta }}_r, {\mathrm{\Delta }}_p$, and ${\mathrm{\Delta }}_c$, respectively.

Figure 2

Variation of the imaginary part of susceptibility with probe detuning, in the absence of the control field (a) and in presence of the control field (b). The parameters for panel (a) are ${\mathrm{\Omega }}_r^0=2\gamma , {\mathrm{\Omega }}_c^0=0\gamma$, and ${\mathrm{\Delta }}_c=0\gamma$. The parameters for panel (b) are ${\mathrm{\Omega }}_r^0=2\gamma , {\mathrm{\Omega }}_c^0=1.5\gamma$, and ${\mathrm{\Delta }}_c=0\gamma$ (green dotted-dashed line); ${\mathrm{\Omega }}_r^0=2\gamma , {\mathrm{\Omega }}_c^0=3.0\gamma$, and ${\mathrm{\Delta }}_c=0\gamma$ (red-dashed line); ${\mathrm{\Omega }}_r^0=2\gamma , {\mathrm{\Omega }}_c^0=3.0\gamma$, and ${\mathrm{\Delta }}_c=10\gamma$ (violet double dotted-dashed line). Other parameters are ${\gamma }_{31}=0.5\gamma , {\gamma }_{32}=0.5\gamma , {\gamma }_{41}=0.5\gamma , {\gamma }_{42}=0.5\gamma , {\gamma }_c={10}^{-3}\gamma , {\mathrm{\Delta }}_r=150\gamma , \lambda =795$ nm, and $\mathcal{N}=3\times {10}^{12}$ atoms/${\mathrm{cm}}^3$.

Figure 3

Panel (a) displays the spatial variation of Raman and control beam profiles in the $x$ direction at the $y=0$ plane. Panels (b) and (c) show the variation of the imaginary and real parts of susceptibility in the $x$ direction at the $y=0$ plane, respectively, in the absence (blue solid line) and in the presence (red dashed and green dotted-dashed lines) of the control field. The parameters for the blue solid line are ${\mathrm{\Omega }}_r^0=2\gamma$ and ${\mathrm{\Omega }}_c^0=0\gamma$, for the green dotted-dashed line they are ${\mathrm{\Omega }}_r^0=2\gamma$ and ${\mathrm{\Omega }}_c^0=1.5\gamma$, and for the red-dashed line they are ${\mathrm{\Omega }}_r^0=2\gamma$ and ${\mathrm{\Omega }}_c^0=3\gamma$. In addition to $w_r=50 \mu \mathrm{m}, w_c=50 \mu \mathrm{m}$, and ${\mathrm{\Delta }}_p=150.01\gamma$, all other parameters are same as those in Fig. 2 except for ${\mathrm{\Delta }}_c=10\gamma$.

Figure 4

Panel (a) shows the normalized intensity of the input probe beam $\left(H{G}_{00}\right)$ in the transverse x-y plane. Panels (b) and (c) show the output intensity of the probe beam in the absence of the control beam and in the presence of the control beam, respectively, at a propagation distance of $z=4$ mm. Panel (d) shows the evolution of the integrated power of the probe beam in the absence of the control beam (blue solid line) and in the presence of the control beam (red dashed line), with the propagation distance $z$. The parameters are ${\mathrm{\Omega }}_p^0=0.001\gamma , w_p=10 \mu \mathrm{m}, {\mathrm{\Omega }}_r^0=2\gamma , {\mathrm{\Omega }}_c^0=3.5\gamma$, and $q_1=q_2=2$. Other parameters are the same as those in Fig. 3.

Figure 5

Panel (a) shows the normalized intensity of the input probe beam $\left(H{G}_{10}\right)$ in the transverse x-y plane. Panels (b) and (c) show the output intensity of the probe beam in the absence of the control beam and in the presence of the control beam, respectively, at a propagation distance of $z=2$ mm. Panel (d) shows the evolution of integrated power of the probe beam in the absence of the control beam (blue solid line) and in presence of the control beam (red dashed line), with the propagation distance $z$. All parameters are same as those in Fig. 4 except for ${\mathrm{\Omega }}_c^0=3\gamma , w_r=60 \mu \mathrm{m}, w_c=60 \mu \mathrm{m}$, and $\mathcal{N}=8\times {10}^{12}$ atoms/${\mathrm{cm}}^3$.

Figure 6

Panel (a) shows the normalized intensity of the input probe beam $\left(H{G}_{20}\right)$ in the transverse x-y plane. The output intensity of the probe beam, shown in the absence of the control beam (b) and in the presence of the control beam (c), at a propagation distance of $z=1$ mm. Panel (d) shows the variation of integrated power of the probe beam with the propagation distance $z$, in the absence of the control beam (blue solid line) and in the presence of the control beam (red dashed line). The parameters are ${\mathrm{\Omega }}_c^0=3\gamma , w_r=90 \mu \mathrm{m}, w_c=90 \mu \mathrm{m}, {\mathrm{\Delta }}_r=195\gamma , {\mathrm{\Delta }}_c=55\gamma , {\mathrm{\Delta }}_p=195.01\gamma$, and $\mathcal{N}=1\times {10}^{13}$ atoms/${\mathrm{cm}}^3$. Other parameters are the same as those in Fig. 4.

Figure 7

Panel (a) shows the variation of the imaginary part of susceptibility for the Raman field with Raman detuning. Panel (b) shows the intensity (normalized with initial peak value) of the Gaussian Raman beam at different propagation lengths inside the medium. In panel (b), the blue solid line represents the intensity profile for the input Raman Gaussian beam, the red dashed line represents the intensity of the output Raman beam at $z=2$ mm, and the green dotted-dashed line represenst the intensity of the output Raman beam at $z=4$ mm. The parameters considered here are the same as those in Fig. 4.