We study the four-wave mixing (FWM) in a double-Λ atomic system where two strong continuous-wave pump lasers and a weak pulsed probe laser produce an FWM generated pulse. We show that both the probe and FWM generated fields may evolve into bright and dark solitons with the same shape and the same ultraslow group velocity.
We analyze a lifetime-broadened four-state, ladder-type four-wave mixing (FWM) scheme in the context of optical soliton formation. We show that a pulsed probe field and a pulsed FWM field of considerably different frequency can evolve into a pair of matched solitons with the same temporal shape and ultraslow group velocity $({V}_{g}∕c\ensuremath{\sim}{10}^{\ensuremath{-}3})$, i.e., two-color ultraslow optical solitons. In addition, we show regimes where two-color superluminal (Vg∕c<0) optical soliton propagation may occur.
The authors theoretically investigate the formation of ultraslow dark and bright solitons via four-wave mixing (FWM) in a crystal of molecular magnets in the presence of a uniform d.c. magnetic field, where two strong continuous wave pump electromagnetic fields and a weak-pulsed probe electromagnetic field produce a pulsed FWM electromagnetic field. By solving the Maxwell–Schrödinger equations under the slowly varying envelope approximation and rotating-wave approximations, we demonstrate that both the weak-pulsed probe and FWM electromagnetic fields can evolve into dark and bright solitons with the same shape and the same ultraslow group velocity.
We investigate the simultaneous formation and propagation of coupled ultraslow optical soliton pairs in a cold, lifetime-broadened three-state double-Lambda atomic system. Starting from the equations of motion of atomic response and two-mode probe-control electromagnetic fields, we derive coupled nonlinear Schrödinger equations that govern the nonlinear evolution of the envelopes of the probe fields in this four-wave mixing scheme by means of the standard method of multiple scales. We demonstrate that for weak probe fields and with suitable operation conditions, a pair of coupled optical solitons moving with remarkably slow propagating velocity can be established in such a highly resonant atomic medium. The key elements to such a shape preserving, well matched yet interacting soliton pair is the balance between dispersion effect and self- and cross-phase modulation effects of the system.
We investigate the simultaneous formation and stable propagation of ultraslow optical soliton pairs in a lifetime broadened four-state atomic system under double-Lambda excitation with large one- and two-photon detunings. We show that detrimental probe field distortions due to strong dispersion effects under weak driving conditions can be well balanced by self- and cross-phase modulation effects, leading to a pair of temporal, group velocity, and amplitude matched ultraslow optical solitons of different frequencies.
We perform a time-dependent analysis of four-wave mixing (FWM) in a double-$\ensuremath{\Lambda}$ system in an ultraslow-propagation regime and obtain the analytical expressions of pulsed probe laser, FWM-generated pulse, phase shifts and absorption coefficients, group velocities, and FWM efficiency. With these analytical expressions, we show that an efficiently generated FWM field can acquire the same ultraslow group velocity $({V}_{g}∕c\ensuremath{\sim}{10}^{\ensuremath{-}4}--{10}^{\ensuremath{-}5})$ and pulse shape of a probe pump and that the maximum FWM efficiency is greater than 25%, which is orders of magnitude larger than previous FWM schemes in the ultraslow-propagation regime.