Short Solitons Research Articles

Probing the decelerating trajectory of a Raman soliton using temporal reflection.

Temporal reflection is a process where an optical pulse reflects off a moving boundary with different refractive indices across it. In a dispersive medium, this process creates a reflected pulse with a frequency shift that changes its speed. Such frequency shifts depend on the speed of the moving boundary. In this work, we propose and experimentally show that it is possible to probe the trajectory of the boundary by measuring the frequency shifts while changing the initial delay between the incident pulse and the boundary. We demonstrate this effect by reflecting a probe pulse off a short soliton, acting as a moving boundary that decelerates inside a photonic crystal fiber because of intrapulse Raman scattering. We deduce trajectory of the soliton from the measured spectral data for the reflected pulse.

Raman-induced mode coupling in temporal waveguides formed by short solitons

We study the propagation of optical pulses trapped inside a temporal waveguide formed by two solitons in a dispersive nonlinear medium such as an optical fiber. The solitons are short enough that they decelerate as their spectra shift continuously toward the red side because of intrapulse Raman scattering. We show that the shape of a probe pulse trapped between the two solitons evolves in a periodic fashion, while its spectrum shifts toward the blue side. We develop a coupled-mode theory showing that such changes occur because of mode coupling induced by the deceleration of the short solitons, resulting in a curved waveguide. A simplified two-mode model is used to introduce a single-parameter governing modal coupling and to find the condition under which coupling becomes weak enough that the probe pulse blueshifts its spectrum without changes in its pulse shape.

Single and multi-vertices solitons in lattices of active Morse - van der Pol units

The dynamical evolution of one-dimensional lattice of active units (otherwise said particles) endowed with anharmonic Morse interactions and active–dissipative van der Pol negative friction is here studied both analytically and numerically. One of the directions of this evolution is the formation and stable propagation of dissipative soliton-like perturbations (in short solitons) against the background of some stationary displacement of units (pedestal). It is shown that the evolution of units at leading-front of the soliton is determined by mutual repulsive forces, while that of units at trailing-tail of the soliton is determined by the active–dissipative forces. Approximate analytically solvable models of the leading-front and the trailing-tail are obtained, which make it possible to predict soliton parameters and admissible range of pedestal values with high accuracy. There is also a scenario of N-vertices soliton formation emerging from a single soliton and (N-1)-vertices soliton. The possibility of controlling the number of vertices of multi-vertices solitons is offered, a feature which can be used in the problems of energy accumulation and transport in periodic structures.

Temporal reflection of an optical pulse from a short soliton: impact of Raman scattering

We study temporal reflection of an optical pulse from the refractive-index barrier created by a short pump soliton inside a nonlinear dispersive medium such as an optical fiber. One feature is that the soliton’s speed changes continuously as its spectrum redshifts because of intrapulse Raman scattering. We use the generalized nonlinear Schrödinger equation to find the shape and spectrum of the reflected pulse. Both are affected considerably by the soliton’s trajectory. The reflected pulse can become considerably narrower compared to the incident pulse under conditions that involve a type of temporal focusing. This phenomenon is explained through space–time duality by showing that the temporal situation is analogous to an optical beam incident obliquely on a parabolic mirror. We obtain an approximate analytic expression for the reflected pulse’s spectrum and use it to derive the temporal version of the transformation law for the q parameter associated with a Gaussian beam.

Zig-zag, bright, short and long solitons formation in inhomogeneous ferromagnetic materials.Kraenkel-Manna-Merle equation with space dependent coefficients

The ferromagnetism induced by an external magnetic field (EMF), in (3+1) dimensions, is governed by Kraenkel–Manna–Merle equation (KMME). A (1+1) dimensionalmodel equation was derived in the literature. Here, this later model equation is considered with space-dependent coefficients, which stands to inhomogeneous ferromagnetism. Exact solutions are obtained by using the extended unified method. The numerical results of the solutions are represented in graphs. They show multiple geometric waves structures, which are zig-zag bright, short and long, solitons in ferromagnetic materials (FMMs). It is found that when the EMF exhibits short (or ultra short), the ferromagnitization exhibits long (or short) solitons. It is also observed that that the ferromagnetism exhibits highly oscillatory waves, with increasing damping parameter. The novelty of this work stems from the fact that the problem of in-homogeneous ferromagentism, studied here is completely new. Further, the zig-zag solitons structures, found here, are so.

The pure-quartic soliton laser

Ultrashort pulse generation hinges on the careful management of dispersion. Traditionally, this has exclusively involved second-order dispersion, with higher-order dispersion treated as a nuisance to be minimized. Here, we show that this higher-order dispersion can be strategically leveraged to access an uncharted regime of ultrafast laser operation. In particular, our mode-locked laser—with an intracavity spectral pulse shaper—emits pure-quartic soliton pulses that arise from the interaction of fourth-order dispersion and the Kerr nonlinearity. Phase-resolved measurements demonstrate that their pulse energy scales with the third power of the inverse pulse duration. This implies a strong increase in the energy of short pure-quartic solitons compared with conventional solitons, for which the energy scales as the inverse of the pulse duration. These results not only demonstrate a novel approach to ultrafast lasers, but more fundamentally, they clarify the use of higher-order dispersion for optical pulse control, enabling innovations in nonlinear optics and its applications. By suppressing the second- and third-order intracavity dispersion using an intracavity spectral pulse shaper, a mode-locked laser that emits pure-quartic soliton pulses that arise from the interaction of the fourth-order dispersion and the Kerr nonlinearity is demonstrated.

Nonlinear Dynamics of Extremely Short Solitons of the Generalized Reduced Maxwell–Bloch System

The effect of remote quantum states on two allocated atomic levels during the propagation of extremely short electromagnetic pulses in a medium is considered without using the slowly varying envelope approximation. A generalization of the reduced Maxwell–Bloch system is obtained that is integrable via the inverse scattering transformation method. Its soliton and breather solutions are found and studied.

Paraxial Stage of the Spatiotemporal Dynamics of Loop Solitons

Using the averaged Lagrangian method, an analytic study of the spatiotemporal dynamics of extremely short loop solitons of the generalized Vakhnenko–Schafer–Wayne equation is carried out. The conditions under which soliton propagation occurs in the modes of defocusing and self-focusing are determined. It is shown that transverse defocusing is accompanied by a temporal compression of the soliton and a decrease in its amplitude. At the same time, with transverse self-focusing, its temporal broadening and peak amplification occur.

TEMPORAL SOLITON: GENERATION AND APPLICATIONS IN OPTICAL COMMUNICATIONS

In general, the temporal and spectral shape of a short optical soliton pulse does not change during propagation in a nonlinear medium due to the Kerr effect which balances the chromatic dispersion. Microring resonators (MRRs) can be used to generate chaotic signals. The smaller MRR is used to form the stopping and filtering system. The employed optical material was InGaAsP/InP, which is suitable for use in the practical devices and systems. The tuning and manipulation of the bandwidth of the soliton signals is recommended to control the output signals. The MRRs can be applied to produce ultra-short pulses, where the medium has a nonlinear condition, thus, using of soliton laser becomes an interesting subject. Therefore, an ultra-short pulse in the scope of pico and femtoseconds soliton pulses can be utilized for many applications in engineering communications. In order to obtain smaller bandwidth of the optical soliton pulses, we propose integrating series of MRRs. In this study, 5 fs soliton pulse could be generated using a series of five MRRs. The soliton signals experience less loss during the propagation, where they are more stable compared to normal conventional laser pulses. Using the series of MRRs connected to an add/drop system, shorter soliton bandwidth and highly multi soliton pulses can be obtained. Therefore, generation of ultra-short multi picosecond (1.2 and 1.3 ps), could be performed, where the radius of the add/drop system has been selected to 50 and 300 µm respectively.

New Type of Extremely Short Vector Solitons in a Medium of Asymmetric Molecules

A new type of extremely short terahertz electromagnetic solitons, which can be formed in a system of molecules with permanent dipole moments in stationary states, has been predicted. It has been shown that such solitons can be formed when the ordinary component of the field excites quantum transitions and, in addition, the extraordinary component dynamically shifts their frequencies. The mechanism of propagation of such solitons in the presence of the nonstationary Stark inversion of quantum levels accompanied by the effective generation of a pulse of the extraordinary wave has been analyzed. The solitons under consideration have no analogs in the visible range.

Subcycle solitonic breathers

Optical breathing solitons are known to display well-resolved cycles where the phase of pulse compression is followed by pulse stretching. Here we show that, in the extreme regimes where the soliton pulse width approaches the field cycle, the field waveform dynamics can drastically differ from this textbook scenario. We demonstrate that such extremely short soliton transients can develop optical shock waves, which seed parametric amplification, facilitating, along with ionization nonlinearity, soliton compression to subcycle pulse widths. This pulse compression scenario is shown to enable the generation of sub-quarter-cycle multigigawatt optical field waveforms in the mid infrared.

Extremely short vector solitons under the conditions of conical refraction

Propagation of extremely short electromagnetic pulses in a biaxial crystal under the conditions of conical refraction has been considered. The system of wave equations taking into account the dispersion contribution of the crystal lattice ions to the polarization response of the medium and a nonlinearity of the polarization response of electrons has been derived. It has been shown that under certain conditions this system can be reduced to an equation which is integrable by means of the inverse scattering transformation method. The proper Lax pair has been found. Physical analysis of the steady-state pulse solution of the system of wave equations has been performed.

Propagation of ultra-short solitons in stochastic Maxwell's equations

We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.

On the propagation of hypersonic solitons in a strained paramagnetic crystal

Nonlinear dynamics of a subnanosecond transverse elastic pulse in a low-temperature paramagnetic crystal placed into a magnetic field and statically strained in the same direction is investigated. Paramagnetic impurities implanted into the crystal have an effective spin of 3/2, and the pulse propagates at right angles to the magnetic field. In the general case, the structure of the pulse is such that the approximation of slowly varying envelopes, which is standard for quasi-monochromatic signals, is inapplicable. Under certain conditions, the pulse propagation in the 1D case is described by the Konno-Kameyama-Sanuki integrable wave equation for strain, which is transformed into the Hirota equation for the envelope of the given strain in the quasi-monochromatic limit. The effect of transverse perturbations on extremely short and quasi-monochromatic solitons is studied in detail. The conditions and features of self-focusing and defocusing of acoustic solitons in the form of extremely short pulses and envelope solitons are revealed. The propagation of an extremely short “half-wave” hypersonic pulse in the “acoustic bullet” regime in the medium with a quasiequilibrium population of quantum sublevels of effective spins is predicted.

The short envelope soliton dynamics in inhomogeneous dispersive media with allowance for stimulated scattering by damped low-frequency waves

We consider the soliton dynamics in terms of the extended nonlinear Schrodinger equation taking into account the inhomogeneous linear second-order dispersion (SOD) and stimulated scattering by damped low-frequency waves (SSDW). It is shown that the wave number downshift due to SSDW is compensated by an upshift due to the SOD decrease on the spatial coordinate. A new class of stationary nonlinear localized solutions (solitons) arising as an equilibrium of SSDW and decreasing spatial SOD is found analytically within the framework of the extended inhomogeneous nonlinear Schrodinger equation. A regime of the dynamic equilibrium of SSDW and inhomogeneous dispersive medium with the soliton parameters periodically varied in time is found. Analytical and numerical results are in good agreement for this regime.

Ultra-short Laser Pulse Generated by a Microring Resonator System for Cancer Cell Treatment

A microring resonator (MRRs) system incorporated with a add/drop filter is proposed in which ultra-short single, multi-temporal, and spatial optical soliton pulses are simulated and used to kill abnormal cells, tumors, and cancer. Chaotic signals are generated by a bright soliton pulse within a nonlinear MRRs system. Gold nanoparticles and ultra-short femtosecond/picosecond laser pulses’ interaction holds great interest in laser nanomedicine. By using appropriate soliton input power and MRRs parameters, desired spatial and temporal signals can be generated over the spectrum. Results show that short temporal and spatial solitons pulse with FWHM = 712 fs and FWHM = 17.5 pm could be generated. The add/drop filter system is used to generate the high-capacity, ultra-short soliton pulses in the range of nanometer/second and picometer/second.

Phase interaction of short vector solitons

An interaction of vector solitons in the frame of coupled third-order nonlinear Schrödinger equations taking into account third-order linear dispersion, nonlinear dispersion, and cross-phase modulation terms is considered. Phase nature of the solitonsʼ interaction is shown. In particular, dependence of solitonsʼ trajectories on initial distance between solitons is shown. Conditions of reflection and propagation of solitons through each other are obtained.

Hybrid squeezing of solitonic resonant radiation in photonic crystal fibers

We report the existence of a kind of squeezing in photonic crystal fibers which is conceptually intermediate between four-wave-mixing-induced squeezing in which all the participant waves are monochromatic waves, and self-phase-modulation-induced squeezing for a single pulse in a coherent state. This hybrid squeezing occurs when an arbitrary short soliton emits quasimonochromatic resonant radiation near a zero-group-velocity-dispersion point of the fiber. Photons around the resonant frequency become strongly correlated due to the presence of the classical soliton, and a reduction of the quantum noise below the shot-noise level is predicted.

Extremely short dissipative solitons in an active nonlinear medium with quantum dots

A medium consisting of quartz with embedded active (amplifying) or passive (absorbing) impurities, i.e., quantum dots, is proposed for producing extremely short dissipative solitons on the basis of the effect of enhanced self-induced transparency. The calculations show that, in such a medium, the initial standard femtosecond pulses can be transformed into extremely short dissipative solitons with a peak intensity of ∼1011 W/sm2, with a duration corresponding to the inverse frequency of transitions in impurities, and with the coherent spectral supercontinuum covering almost the entire transmission region of quartz.

Minimization of self-steepening of ultra short higher-order soliton pulse at 40 Gb/s by the optimization of initial frequency chirp

In this paper, the decay of first- and second-order ultra short pulses of the order of 50 fs due to self-steepening (SS) effect has been numerically investigated for a 40 Gb/s optical soliton system including the impact of third-order dispersion (TOD). It has been observed that the prechirp (both positive and negative) in the pulse can counteract the SS effect and improve compensation performance for the distortions .The critical positive prechirp value is found to be 1.4 and the negative prechirp is 1.2, beyond which the soliton pulse is unstable.