We propose a scheme to transfer the spatial intensity as well as phase information encoded initially in the spatial profile of a weak probe field onto a newly generated Stokes field in a nonlinear process of four-wave mixing (FWM). The FWM process is explored in a gaseous medium consisting of atoms modeled as a three-level system in the $\mathrm{\ensuremath{\Lambda}}$ configuration. We found that different orders of Hermite-Gaussian and Laguerre-Gaussian modes carried by a probe beam are effectively transferred to a Stokes beam. Interestingly, the transferred intensity of the Stokes beam is a clone of the probe beam, whereas the phase profile is conjugate to the probe. The phase distribution of the transmitted modes at the exit of the medium is explored by superimposing them on a copropagating plane wave. Moreover, the parametric amplification due to the nonlinear process of FWM prevents any information loss due to linear absorption and permits us to work at high optical depths. We found a structural similarity between transferred images of about $99%$, which provides clear evidence for the successful transfer of information in the FWM process.
We propose a scheme to transfer the spatial intensity as well as phase information encoded initially in the spatial profile of a weak probe field onto a newly generated Stokes field in a nonlinear process of four-wave mixing (FWM). The FWM process is explored in a gaseous medium consisting of atoms modeled as a three-level system in the \ensuremathΛ configuration. We found that different orders of Hermite-Gaussian and Laguerre-Gaussian modes carried by a probe beam are effectively transferred to a Stokes beam. Interestingly, the transferred intensity of the Stokes beam is a clone of the probe beam, whereas the phase profile is conjugate to the probe. The phase distribution of the transmitted modes at the exit of the medium is explored by superimposing them on a copropagating plane wave. Moreover, the parametric amplification due to the nonlinear process of FWM prevents any information loss due to linear absorption and permits us to work at high optical depths. We found a structural similarity between transferred images of about 99, which provides clear evidence for the successful transfer of information in the FWM process.
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.
In this work, we present an experimental study on the spatial profile of coherent light generated in a forward four-wave mixing (FWM) process. We are interested in investigating how the transverse structure of the incident beams, more specifically of the Hermite-Gauss (HG) modes, is transferred to the generated signal in this nonlinear process. For the experiment, we used a continuous wave diode laser to excite a sample of Rubidium atoms, on the ⁸⁵Rb D2 line, tuned to the frequency of the 5²S_(1/2) ( = 3) → 5²P_(3/2) transition. With a Spatial Light Modulator, we were able to split the laser beam in two and structure them in the desired modes. These two beams, A and B, with wave vectors kA and kB, and linear orthogonal polarizations, with quasi-copropagated configuration, were used to induce two FWM signals in the directions 2kA-kB and 2kB-kA. The spatial profile of incident beams and the two nonlinear signals were captured by a CMOS camera, and the regimes of a thin or extensive medium were investigated. We were able to obtain results for a combination of gaussian-HG beams, as well as HG-HG beams. The profiles obtained by computer simulation were compared with the experimental measurements. Our theoretical model relies on solving the paraxial equation of the generated field. It leads to the overlap integrals of the incident beams, which unfold into some interesting selection rules in the transversal plane, for the thin and extensive medium regimes, and in the longitudinal axis, only for the long medium regime. Although the extensive medium regime presents some additional selection rules, the experimental requirements are difficult to achieve in our system, among them, we highlight the Gouy phase matching. On the other hand, a good agreement between theory and experiment was observed in the thin medium regime.
In this work we present a series of results on four-wave mixing (FWM) processes induced by structured light in atomic media. We start with a theoretical study focusing on a cascade FWM process in rubidium vapor, generating a blue light field at 420 nm. In this setting, we show that in the extended-medium regime the Hermite-Gaussian basis presents a unique property of optical structure transfer. We then exploit this result to show that, by carefully tailoring the structure of the pump beams, one can obtain desired spatial modes with cylindrical and elliptical symmetries with high fidelity at the blue light output. Following that, we consider an experimental configuration where two degenerate FWM signals are generated in different directions of space by the same pump fields. In this setup, we present results in heated rubidium vapor evidencing the simultaneous conservation of orbital angular momentum (OAM) in the two FWM processes. We show that the two-channel setting allows to encode the OAM content of the input beams onto the OAM carried by the two FWM signals. Next, we explore the transverse mode dynamics in the context of optical modes contained in the so-called orbital angular momentum Poincaré sphere (PS). Defined in analogy with a general polarization state, this family of modes is parametrized in terms of polar and azimuthal angles. We show that the two FWM signals can also be described as belonging to Poincaré spheres, and that the angles on the output PS are related to those on the input PS by well-defined symmetries. The predicted FWM intensity profiles, as well as the consequences of the symmetry properties, are in good agreement with our experimental results. We also explore interesting scenarios, such as combinations of different PS modes and the fulfillment of one of the symmetry relations in each sphere independently, and restrictions that arise in the extended-medium regime. In the last part, we study the correlations between the light fields participating in the two-channel FWM configuration. Following our recent work on cold atoms, we investigate the correlations originating from the conversion of phase-noise to amplitude-noise as a result of the light-atom interaction, and discuss our attempts to discriminate transverse spatial dependencies on these correlations. Finally, we outline the quantum theory of FWM, exploring the multi-spatial-mode nature of the generated light state and the associated spatial correlations.
We explore the conservation of orbital angular momentum (OAM) in the four-wave mixing (FWM) process in hot rubidium vapor. Since most modern communication systems send data in pulses corresponding to bits, we can use OAM to encode more information in each pulse by assigning structure to each signal. Furthermore, because FWM can be used to generate entangled photon pairs, we can use this process to bring enhanced signal security. We experimentally studied FWM with a wide range of Laguerre-Gaussian modes and their superpositions and observed OAM transfer from the probe field to a generated Stokes field. By studying the output Stokes intensity and phase distributions, we confirm l mode (OAM) conservation for pure l and p modes, as well as for the superpositions of l and -l for the mode numbers up to l = 4, p = 4. We also found that p index is generally not conserved and its conservation is highly dependent on the relative sizes of the probe and pump beams in the Rb cell. We also identify parameters to improve FWM gain with OAM transfer and propose an analytical method for determining OAM p number.
Abstract We have proposed a double scheme for the efficient generation and control of spatial four-wave mixing (FWM)-induced ultraviolet light via optical angular momentum transfer from a vortex-field (Laguerre–Gaussian (LG) beam) applied once to the excited transition of the first two-photon ladder and then in the uppermost transition of the three-photon ladder in the FWM-loop configuration of a five-level atomic excitation mechanism. In both the LG-cases, at the conditions of resonant and off-resonant detunings of the two coherent fields with high Rabi frequencies guiding the multi-photon excitation route in the system, it has been shown that the vortex FWM light can propagate either in the superluminal or in the subluminal regime depending upon ‘turned-off’ and ‘turned-on’ conditions of a Raman field outside the FWM-loop, respectively. Such switching phenomenon is the most interesting outcome of the present study along with the significant phase-twisting effects as manifested in the helical phase patterns in both the LG-cases. Thus, the practical implementation of the present model under a cold atomic environment paves up a novel way of obtaining structured high-dimensional light transfer process based on the mechanism of nonlinear photonics, which might have potential applications in quantum information processing and technology in the near future.