Nonlinear frequency conversion of nondiffracting modes via nondegenerate four-wave mixing in atomic vapor

We investigate the nonlinear frequency conversion of nondiffracting optical modes via a nondegenerate four-wave mixing (FWM) process in rubidium vapor. In this process, two strong control fields and a weak probe field mutually interact via a four-level double-$\mathrm{\ensuremath{\Lambda}}$ type atomic system to produce a low frequency weak Stokes field which is a phase conjugate to probe. We show that any arbitrary mode such as Airy, Bessel, Mathieu, and Weber beams encoded initially in the spatial envelope of the probe field are efficiently transferred to the FWM Stokes field by satisfying the phase-matching condition. Interestingly, we found that the transmitted intensity profiles of the Stokes beam are identical to that of the probe beam, while the phase profile is complementary. The phase conjugation property of output beams is revealed by interfering them with a copropagating plane wave. We further found the fidelity in terms of structural similarity between two transmitted modes of about $99%$, which substantiates the high efficiency of the FWM process. The efficient transfer and frequency conversion of such diffraction-free beams may have potential applications in nonlinear optical and quantum technologies.