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.
Abstract We investigate the nonlinear frequency conversion of non-diffracting optical modes via non-degenerate four-wave mixing(FWM) process in rubidium vapor. In this process, two strong control fields and a weak probe field mutually interact via afour-level double-Λ type atomic system to produce a new 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 probe field are efficiently transferred to FWM Stokes field by satisfying the phase matching condition. Interestingly, we found that the transmitted intensity profiles of Stokes beam are identical to that of probe beam while phase profile is complimentary.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 FWM process. The efficient transfer and frequency conversion of such diffraction-free beams may have potential applications in nonlinear optical and quantum technologies.
A numerical simulation for studying the kinetics of phase-conjugate beams generated by multigrating four-wave mixing has been developed. It has been applied to investigate the four-wave mixing process in BaTiO3 by use of realistic coupling coefficients. The role of the distinct gratings has been analyzed. Depending on the experimental conditions, constructive as well as destructive interference of the different contributions was obtained. Moreover, because of grating competition effects, π-phase changes in the phase-conjugate beam can occur during the kinetics. For large values of the coupling strength and specific regions of the physical parameters, unstable four-wave mixing dynamics were obtained. The analysis of the results provides some criteria for predicting the phase conjugator’s behavior in multigrating conditions.