Ultraslow bright and dark optical solitons in a cold three-state medium

We show the formation of ultraslow bright and dark optical solitons in a lifetime-broadened three-state atomic system under Raman excitation. We also discuss why such ultraslow optical solitons may not exist under the conditions of the usual electromagnetically induced transparency configuration where zero one- and two-photon detunings are required.     

Ultraslow optical solitons in a four-level tripod atomic system

We investigate possible formation and propagation of localized, shape-preserving nonlinear optical pulse in a resonant, lifetime-broadened four-level tripod atomic system via electromagnetically induced transparency (EIT). We prove both analytically and numerically that although in anomalous dispersion regimes near resonance a superluminal optical soliton may appear, such soliton suffers serious absorption. However, by choosing appropriate parameters to make the system work in normal dispersion regimes and within an EIT transparency window, ultraslow optical solitons with very low light intensity can form and propagate stably in the system.     

Ultraslow optical solitons in tunnel-coupled double semiconductor quantum well

This paper investigates the nonlinear evolution of the pulse probe field in an asymmetric coupled-quantum well driven coherently by a pulse probe field and two controlled fields. This study shows that, by choosing appropriate physical parameters, self-modulation can precisely balance group velocity dispersion in the investigated system, leading to the formation of ultraslow optical solitons of the probe field. The proposed scheme may lead to the development of the controlled technique of optical buffers and optical delay lines.     

Ultraslow optical solitons via electromagnetically induced transparency: a density-matrix approach

We study the ultraslow optical solitons in a resonant three-level atomic system via electromagnetically induced transparency under a density-matrix (DM) approach. The results of linear and nonlinear optical properties are compared with those obtained by using an amplitude variable (AV) approach. It is found that the results for both approaches are the same in the linear regime if the corresponding relations between the population-coherence decay rates in the DM approach and the energy-level decay rates in the AV approach are appropriately imposed. However, in the nonlinear regime there is a small difference for the self-phase modulation coefficient of the nonlinear Schr\"{o}dinger equation that governs the time evolution of probe pulse envelope. All analytical predicts are checked by numerical simulations.     

Two-component spatial optical solitons in a four-state ladder system via electromagnetically induced transparency

We propose a scheme to generate two-component spatial optical solitons in a lifetime broadened four state atomic system with a ladder configuration via electromagnetically induced transparency. We show that, different from the schemes using passive optical media such as photorefractives and planar waveguides, the two-component spatial optical solitons in the present coherent resonant system can be produced with very low light intensity. The stability of the two-component spatial optical solitons and their interaction are also investigated by numerical simulations.     

Unidirectional optical solitons in a two-level medium

Self-induced transparency is analyzed for optical pulses interacting with a two-level system by solving an integrable system of evolution equations without using the slowly varying envelope approximation. A suitable modification of the inverse scattering method is developed to find soliton solutions. The characteristics of linearly and circularly polarized optical solitons (including those created in a laser) are compared. To assess the scope of the two-level model, the effects due to additional levels are analyzed in the adiabatic approximation. It is shown that these effects violate the integrability of the model and lead to loss of self-induced transparency for pulses with duration comparable to oscillation period. However, self-induced transparency is recovered in the quasi-monochromatic limit. Applications of the results are discussed.     

Observation of optical spatial solitons in a highly nonlocal medium

We report on the observation and quantitative assessment of self-trapped pulsating beams in a highly nonlocal nonlinear regime. The experiments were conducted in nematic liquid crystals and allow a meaningful comparison with the prediction of a scalar theory in the perturbative limit, while addressing the need for beyond-paraxial analytical treatments.     

Slow vector optical solitons in a cold four-level inverted-Y atomic system

The authors show the formation of slow temporal vector optical solitons in a cold lifetime-broadened four-level inverted-Y atomic system. We demonstrate that Maxwell’s equations for describing two orthogonally polarised components of a low intensity signal field can evolve into two coupled nonlinear Schr?dinger equations, which results in various distortion-free temporal vector optical solitons, such as bright-bright or dark-dark vector solitons. These results are produced from the correct balance between dispersion, self- and cross-phase modulation (SPM and XPM) effects. We also show that the integrable Manakov model can be realised by adjusting the corresponding SPM, XPM and dispersion effects of this inverted-Y atomic system.     

Dynamics of coupled ultraslow optical solitons in a coherent four-state double-${\sf \Lambda}$ system

We present a systematical investigation, both analytical and numerical, on the dynamics of two nearly lossless and distortion-free weak nonlinear optical pulses in a cold, lifetime-broadened four-state double-Λ system via electromagnetically induced transparency. Starting from theequations of motion of atomic response and probe fields, we give a detail derivation of two coupled nonlinear Schrödinger equations that control the nonlinear evolution of two probe field envelopes by means of a standard method of multiple-scales. We show that stable optical solitons with very slow propagating velocity can be generated under very low input light intensity when working in the transparency window of probe absorption spectrum induced by two continuous-wave control fields. We demonstrate that coupled optical soliton pairs are possible in the system through cross-phase modulational instability and mutual trapping effect of solitons. We provide various coupled optical soliton pair solutions explicitly and analyze their stability numerically.     

Moving near-gap solitons in the nonlinear optical medium

For a one-dimensional nonlinear optical medium with a periodic refraction index, new two-parameter soliton solutions of electrodynamics equations have been found. These solutions represent two interacting waves that propagate in two opposite directions. The oscillation frequency of each wave may fall either into the forbidden gap in the linear spectrum or outside it, and the group velocity may vary from zero to a maximal value that is determined by the parameters of the medium. Algebraic soliton solutions have been found as the limit of the nonlinear solutions, when the nonlinear wave frequency tends to the frequency of one of the linear-spectrum branches.     

Stability of weakly nonparaxial spatial optical solitons in a medium with a Kerr nonlinearity

A variant of perturbation theory is developed to determine the characteristics and stability of transversely two-dimensional spatial solitons in a Kerr medium under conditions of small deviations from paraxial. Distributions of the transverse and longitudinal components of the soliton electric and magnetic fields are obtained. It is shown that the power of a nonparaxial soliton in a Kerr medium increases as the propagation constant increases. A linear analysis is made of soliton stability. In addition to confirming stability, this analysis revealed “internal modes” of nonparaxial solitons and their characteristics were determined.     

Spherical solitons in a Kerr medium

Solutions of the complete system of the Maxwell equations for a Kerr medium are found numerically in the form of spherical surface waves—spherical solitons.     

Ultraslow optical waveguiding in an atomic Bose-Einstein condensate

We investigate waveguiding of ultraslow light pulses in an atomic Bose-Einstein condensate. We show that under the conditions of off-resonant electromagnetically induced transparency, waveguiding with a few ultraslow modes can be realized. The number of modes that can be supported by the condensate can be controlled by means of experimentally accessible parameters. Propagation constants and the mode conditions are determined analytically using a Wentzel-Kramers-Brillouin analysis. Mode profiles are found numerically.     

Raman lasing with a cold atom gain medium in a high-finesse optical cavity

We demonstrate a Raman laser using cold (87)Rb atoms as the gain medium in a high-finesse optical cavity. We observe robust continuous wave lasing in the atypical regime where single atoms can considerably affect the cavity field. Consequently, we discover unusual lasing threshold behavior in the system causing jumps in lasing power, and propose a model to explain the effect. We also measure the intermode laser linewidth, and observe values as low as 80 Hz. The tunable gain properties of this laser suggest multiple directions for future research.     

Planar spatiotemporal solitons in a quadratic nonlinear medium

The averaged Lagrangian method has been used to derive an analytical solution in the form of planar light bullets for the system of equations describing the second-harmonic generation in a medium with anomalous dispersion. The stability of this solution is confirmed by the simulation for different relations between the nonlinearity, diffraction, and dispersion in the cases of input pulses at both frequencies and at only the fundamental frequency.     

Fractional optical solitons

This Letter shows that soliton propagation can be described by an extended NLS equation which incorporates fractional dispersion and a fractional nonlinearity. The fractional dispersive term is written in terms of Grünwald-Letnikov fractional derivatives (FDs). Forward and backward FDs are introduced in order to satisfy the conservation of energy. It is found that the soliton solutions of this model form a continuous family and are stable. The Vakhitov-Kolokolov criterion is used to confirm the stability of these fractional solitons.     

Nonparaxial vortex vector solitons in a nonlinear cubic medium

The propagation of narrow three-dimensional wave beams in a nonlinear cubic medium has been analyzed taking into account all vector components of the wave field, including radial, angular, and longitudinal ones. Soliton solutions to the Maxwell equations in the form of vortex solitons are found, and their properties are investigated.     

Composite spatial solitons in a saturable nonlinear bulk medium

We review the generation of the recently predicted multi-component spatial optical solitons in a saturable nonlinear bulk medium. We present numerical simulations for an effectively isotropic model and experimental results for a set of different combinations of a Gaussian beam co-propagating incoherently with a beam of a more complex internal structure, such as a higher order transverse laser mode. We discuss the different formation processes and the general properties of a variety of different dipole-mode composite solitons and expand our investigations to the generation of a quadrupole-mode composite soliton. Received: 1 December 2000 / Revised version: 12 January 2001 / Published online: 21 March 2001