Observation of Raman self-focusing in an alkali-metal vapor cell

Over the last decade there has been a growing interest in effects that utilize atomic coherence to manipulate the propagation of light inside a medium 1 . As an example, using an appropriately phased Raman coherence, one can render a medium transparent to a resonant laser beam with the technique of electromagnetically induced transparency EIT 2–4 . For nonlinear mixing processes, the concept of maximum atomic coherence is particularly important. It is now understood that frequency conversion in the regime of maximum coherence proceeds very efficiently with phasematching playing a negligible role 5–7 . In resonant, EITlike systems, a maximally coherent state is adiabatically prepared using a counterintuitive pulse timing sequence. In far-off resonant atomic systems, which is the case in this work, preparation is achieved with two laser beams whose frequency difference is slightly detuned from the frequency of the two-photon Raman transition. When a dipole-forbidden Raman transition is driven to a maximally coherent state, the population is almost equally split between the two Raman states, and the off-diagonal density matrix element of the transition approaches its maximum value, 1 /2. In far-off resonant systems, one important consequence of maximum coherence is the modification of the refractive indices of the driving laser beams 8,9 . Noting Fig. 1, depending on the sign of the two-photon detuning, , the established atomic coherence is either inphase or out-of-phase with the strong two-photon drive. As a result, the refractive indices of the two driving lasers, Ep and Es, are either enhanced 0 or reduced 0 . The modification of the refractive indices is intensity dependent and varies across the spatial profile of the beams. As a result, the medium acts as a lens causing self-focusing or self-defocusing of the driving lasers. One important application of Raman self-focusing is to the field of spatial optical solitons. It has recently been predicted that, under appropriate conditions, diffraction may be balanced by Raman selffocusing and as a result two-frequency optical solitons are formed 10–12 . In alkali-metal vapor cells, the formation of these solitons, termed spatial Raman solitons, require low optical power 100 mW that is readily achievable with continuous-wave cw lasers. Due to operating near maximum coherence, 1 /2, these solitons are stable in full three spatial dimensions. Numerical simulations of these solitons predict well-defined soliton-soliton collision properties and reveal many rich nonlinear dynamics 12 . Spatial Raman solitons in alkali-metal vapor cells may also find possible practical applications in areas such as all-optical information processing 13,14 . In this paper, we utilize the hyperfine transition between F=1 and F=2 levels and demonstrate Raman self-focusing and self-defocusing of the two driving laser beams, Ep and Es, in a Rb vapor cell. Before proceeding with a detailed description of our experiment, we would like to cite pertinent earlier work. By using high-peak power, Q-switched pulsed lasers, Harris group at Stanford has recently demonstrated Raman self-focusing in molecular hydrogen H2 15 . Selffocusing in a resonant, three level scheme under the conditions of EIT was observed by Moseley and colleagues 16,17 . Optical wave-guiding in a V scheme by using strong optical pumping was demonstrated by Truscott et al. 18 . There has been substantial theoretical work on electromagnetically induced focusing in a variety of near-resonance, multifrequency systems 18–22 . Raman gain and slow light propagation in far-off resonant Rb alkali-metal atoms were recently demonstrated by Deng and colleagues 23 . We also