Temporal Optical Solitons Research Articles

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 Schrodinger 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.

Slow vector optical solitons in a cold five-level hyper V-type atomic system

A new scheme of five-level hyper V-type atomic system is proposed with the aim of generating slow temporal vector optical solitons. Two transitions in the five-level atomic medium independently interact with the two orthogonally polarized components of a low intensity linear-polarized pulsed probe field, while two other transitions are driven by control laser fields. We demonstrate that various distortion-free slow temporal vector optical solitons, such as bright-bright, bright-dark, dark-bright and dark-dark vector solitons, can be evolved from the probe field. Besides, we also show that the modified Hubbard model that includes the Manakov system may be realized by adjusting the corresponding self- (cross-) phase modulation and dispersion effects of this system.

Dissipative optical solitons

This paper presents a review of the general properties of dissipative spatial and temporal optical solitons and setups for shaping them. Information is presented concerning the first publications on dissipative optical solitons, and the current status of this research is analyzed.

Ultraslow temporal vector optical solitons in a cold four-level tripod atomic system

We show the possibility of generating ultraslow temporal vector optical solitons in a cold lifetime-broadened four-level tripod atomic medium under Raman excitation. We demonstrate that the two orthogonally polarized components of the low-intensity signal field can evolve into various distortion-free temporal vector optical solitons, such as bright-bright vector solitons with ultraslow group velocity. These results are produced from the balance of self- and cross-phase modulation effects and dispersion. We also show that Manakov temporal vector solitons may be realized by adjusting the corresponding self- and cross-phase modulation and dispersion effects of our system.

Binding mechanism of temporal soliton molecules

Temporal optical soliton molecules were recently demonstrated; they potentially allow a further increase of data rates in optical telecommunication. We present a theoretical study aimed at an explanation of the mechanism responsible for the binding force. To this end we use a perturbation treatment in several variants. We find that the well-known soliton interaction as mediated by the optical Kerr effect, when suitably modified for chirped pulses, captures essential features like the existence of a stable equilibrium separation and small-scale oscillations around this point. Predictions of these models are compared to numerical simulations.

Ultraslow temporal vector optical solitons in a cold five-state atomic medium under Raman excitation

We theoretically investigate the formation of ultraslow temporal vector optical solitons in a lifetime-broadened five-state atomic system under Raman excitation. By analysing the interaction between the atomic system and two strong, linear-polarized continuous wave control fields and a weak, linear-polarized pulsed signal field, having two orthogonally polarized components, we find that the Maxwell equations of describing the propagation of two orthogonal polarization components can evolve into two coupled nonlinear Schrödinger equations, which admit solutions describing vector solitons, including bright–bright, bright–dark, dark–bright and dark–dark vector solitons with ultraslow group velocity. More importantly, the Manakov temporal vector solitons can be easily realized in our system by adjusting the corresponding parameters such as the Rabi frequencies of the control fields, one- and two-photon detunings. The unique features of the two coupled nonlinear Schrödinger equations are also discussed.

Weak-light ultraslow vector solitons via electromagnetically induced transparency

We propose a scheme to generate temporal vector optical solitons in a lifetime broadened five-state atomic medium via electromagnetically induced transparency. We show that this scheme, which is fundamentally different from the passive one by using optical fibers, is capable of achieving distortion-free vector optical solitons with ultraslow propagating velocity under very weak drive conditions. We demonstrate both analytically and numerically that it is easy to realize Manakov temporal vector solitons by actively manipulating the dispersion and self- and cross-phase modulation effects of the system.

Phase structure of soliton molecules

Temporal optical soliton molecules were recently demonstrated; they potentially allow further increase of data rates in optical telecommunication. Their binding mechanism relies on the internal phases, but these have not been experimentally accessible so far. Conventional frequency-resolved optical gating techniques are not suited for measurement of their phase profile: Their algorithms fail to converge due to zeros both in their temporal and their spectral profile. We show that the VAMPIRE (very advanced method of phase and intensity retrieval of $E$-fields) method performs reliably. With VAMPIRE the phase profile of soliton molecules has been measured, and further insight into the mechanism is obtained.

Nonlinear tunneling of temporal and spatial optical solitons through organic thin films and polymeric waveguides

Nonlinear optical organic materials will be the key elements for future high-bit-rate telecommunications and ultrafast photonic technologies. We show that the process of nonlinear tunneling of optical solitons through a strong nonlinear thin film barrier, for example, a nonlinear organic thin film barrier, exhibits jump-like nonadiabatic evolution, which eventually leads to the soliton “fission reactions”. Nonlinear “fission reaction” is attended by generation of “colored” solitons with different frequencies and group velocities. It seems very attractive to use the nonlinear soliton tunneling effect through thin film of polydiacetylene para-toluene sulfonate in developing a whole class of basically novel all-optical soliton logic devices.

Temporal optical solitons via multistep χ (2) cascading

We consider a multistep χ(2) cascading for light pulses with the dispersion of the system taken into account. Using the method of multiple scales we derive a set of coupled envelope equations governing the nonlinear evolution of the fundamental, second and third harmonic waves involved simultaneously in two nonlinear optical processes, i.e. second harmonic generation and sum frequency mixing. We show that three-wave temporal optical solitons are possible in three- and four-step cascading in the presence of a group-velocity mismatch between different pulses.

Comparison between Staggered and Unstaggered Finite-Difference Time-Domain Grids for Few-Cycle Temporal Optical Soliton Propagation

The auxiliary-differential-equation formulation of the finite-difference time-domain method has become a powerful tool for modeling electromagnetic wave propagation in linear and nonlinear dispersive media. In the first part of this paper, we compare the stability and accuracy of second- and fourth-order-accurate spatial central discretizations on staggered grids with a third-order-accurate spatial discretization on an unstaggered grid, combined with a second-order leapfrog time integration scheme for modeling linear dispersive phenomena in a one-dimensional single-resonance Lorentz medium. We use on the unstaggered grid the NS2 scheme introduced by Y. Liu, which combines forward and backward differencing for the spatial derivatives. Phase and attenuation errors are determined analytically across the entire frequency band of the low-loss single-resonance Lorentz model. In the second part of the paper, we compare the use of one-dimensional staggered and unstaggered grids for modeling the transient evolution of few-cycle optical localized pulses in a dispersive Lorentz medium with a delayed third-order nonlinearity. The focus of the study is on the decay of higher-order solitons under the combined action of dispersion, self-phase modulation, self-steepening, and stimulated Raman scattering. Numerical results from the simulations on the unstaggered and staggered grids are in excellent agreement. This study demonstrates the accuracy of the unstaggered scheme augmented with a linear/nonlinear dispersive media formulation for temporal soliton propagation.

Dissipative optical solitons

This paper presents a review of the general properties of dissipative spatial and temporal optical solitons and setups for shaping them. Information is presented concerning the first publications on dissipative optical solitons, and the current status of this research is analyzed.

Cantor set fractals from solitons

We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a single input soliton.

Derivation of dimensional and material requirements for propagation and processing of temporal optical solitons in planar geometry channel waveguides: erratum

We investigate the dispersion of the group velocity of light in slab and rectangular waveguides and obtain analytic expressions for the first derivative of the propagation vector with respect to the angular frequency and numerical values for the second derivative for both geometries. The last quantity is an important parameter in the temporal soliton propagation equation, which motivates this research. Provided the dispersion within the channel can be adjusted properly, planar geometry waveguides can represent good candidates for the optical processing of temporal solitons carried by optical fibers. We discuss the manner in which the dispersion coefficient depends on waveguide dimensions and material constants, and we determine the parameters that optimize soliton processing.

Derivation of dimensional and material requirements for propagation and processing of temporal optical solitons in planar geometry channel waveguides

We investigate the dispersion of the group velocity of light in slab and rectangular waveguides and obtain analytic expressions for the first derivative of the propagation vector with respect to the angular frequency and numerical values for the second derivative for both geometries. The last quantity is an important parameter in the temporal soliton propagation equation, which motivates this research. Provided the dispersion within the channel can be adjusted properly, planar geometry waveguides can represent good candidates for the optical processing of temporal solitons carried by optical fibers. We discuss the manner in which the dispersion coefficient depends on waveguide dimensions and material constants, and we determine the parameters that optimize soliton processing.

Two-parameter family of exact solutions of the nonlinear Schrödinger equation describing optical-soliton propagation.

By using a direct method for obtaining exact solutions of the nonlinear Schr\odinger equation that describes the evolution of spatial or temporal optical solitons, a two-parameter family of solutions is given. These exact solutions describe the periodic wave patterns that are generated by the spatial or temporal modulational instability, the periodic evolution of the bright solitons superimposed onto a continuous-wave background, and the breakup of a single pulse into two dark waves which move apart with equal and opposite transverse components of the velocities.