Bright Soliton Pairs Research Articles

The multiple bright soliton pairs of the fully PT-symmetric nonlocal Davey-Stewartson I equation

This article investigates the dynamics of multiple bright soliton pair interactions in the fully PT -symmetric nonlocal Davey–Stewartson I equation. The bright soliton pair solutions are derived by employing the bilinear KP-hierarchy reduction method, and are expressed in terms of determinants. To study the interactions of the multiple soliton pairs, the long-time asymptotic analysis for these soliton solutions is performed by using the analysis of determinants, and the asymptotic expressions of the N individual soliton pair solutions are given as the sum of expressions for the 2N single soliton solutions. The asymptotics shows that the soliton pairs only exhibit elastic collisions and the two solitons in each soliton pair share equal amplitudes

Chemical oscillation in ultracold chemistry

We demonstrate the occurrence of oscillatory reactions in the ultra-cold chemistry of atom-molecular Bose-Einstein condensate. Nonlinear oscillations in the mean-field dynamics occur for a specific range of elliptic modulus, giving rise to both in- and out-phase modulations in the atom-molecule population density. The reaction front velocity is found to be controlled by photoassociation, which also regulates the condensate density. Two distinct pairs of in-phase bright localized gap solitons are found as exact solutions, the existence of one of which necessarily requires a background. Cnoidal atomic density waves along with a plane-wave molecular motion are observed in both attractive and repulsive domains. The role of intra- and inter-species interactions on both existence and stability is explicated in the presence of photoassociation.

Oscillation properties of matter-wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter- and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton (without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.

Parameter regulation for periodic wave pair and photovoltaic soliton pair excitations in the bias photovoltaic-photorefractive crystal

In the bias photovoltaic-photorefractive crystal, the two-component nonlinear Schrödinger equation can portray the dynamics of periodic wave pair and photovoltaic soliton pair. These excitations are analytically revealed including the Jacobian sn-cn type and sn-dn type periodic wave pair and their related dark-bright soliton pair, the mixed elliptic function pair excitation and their related bi-peaked soliton and bright soliton pair. In view of these results, the formation conditions of these periodic wave and soliton pairs are related to parameters of the photovoltaic field, the space charge electric field, irradiance and nonlinearity. Moreover, the excitation regulation of soliton pairs including amplitudes, widths and the change of propagation constants based on the parameter related to the photovoltaic field and space charge electric field is investigated in the bias photovoltaic-photorefractive LiNbO3 crystal.

Investigation of the interaction of a pair of bright optical spatial pyroelectric solitons during their in-phase propagation in an undoped lithium niobate crystal at a wavelength of 532 nm

The formation of two-dimensional bright spatial solitons by in-phase laser beams with a wavelength of 532 nm propagating in the bulk of photorefractive lithium niobate crystal under the reversal of the sign of the nonlinear optical response of the material with the contribution of the pyroelectric effect has been experimentally demonstrated. It is shown that varying the distance between the beams at the input face of the crystal leads to the interaction of pyroelectric solitons, which allows the formation of non-rectilinear propagation paths of light beams.

Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystals

The evolution of spatial solitons in the photovoltaic photorefractive crystal can be governed by the specific coupled nonlinear Schrodinger equations. Under the photovoltaic field with the external bias field, the coupled cn–sn-type periodic wave solution and the corresponding photorefractive bright–dark soliton pair were constructed to describe the evolution of beam. The influence of the external bias field on solitonic dynamics is analyzed. In the photovoltaic crystal, coupled sn–cn-type, sn–dn-type periodic wave solutions, solution constructed by products of elliptic functions and the corresponding dark–bright soliton pair and coupled double-peaked soliton solutions are found to describe the evolution of a spatial-phase-modulated photovoltaic soliton and a non-phase-modulated beam.

Coupling of separate solitons in a series circuit of two photon photorefractive crystals exhibiting simultaneous quadratic and linear nonlinearities

Separately coupled optical spatial solitons are shown to exist in a biased series two-photon photorefractive(TPPR) crystal circuit consisting of two TPPR crystals which have the quadratic and linear electro-optic(EO) effect present simultaneously. The space charge field in each photorefractive(PR) crystal in the circuit has been derived. We find that the space charge field in each crystal is coupled with the space charge field in the other crystal. We consider the cases of separately coupled bright, dark and grey solitons and obtain the numerical solutions for the spatial solitons’ profile. The coupling effect due to the soliton peak intensity in each crystal and the gating beam intensity is studied in detail. The light induced current causes a change in the spatial profile of the dark or grey soliton in one of the crystal which results in a change in the spatial profile and propagation of the soliton in the other crystal. We also find that the bright soliton intensity in one crystal does not affect the soliton in the other crystal. A change in the gating beam intensity in one crystal influences the soliton in the other crystal and this is true for all the three cases of dark, grey and bright separate soliton pairs.

Gaussian soliton pairs in an unbiased photorefractive crystal due to the pyroelectric effect

The characteristics of the dynamical evolution of incoherently coupled Gaussian soliton pairs in unbiased photorefractive media forming solely due to the pyroelectric effect are studied for the first time. A parameter space spawning a large set of bright Gaussian soliton pairs in unbiased photorefractive crystals having a large pyroelectric coefficient has been found. These soliton pairs can exist if the light beams have similar polarization, equal wavelength and are mutually incoherent. A change in the temperature of the photorefractive crystal induces a temporary pyroelectric field resulting in the formation of a space-charge field. The existence curve for these soliton pairs is studied for different values of the temperature change. It is also established that both individual components of the soliton pair should have equal spatial widths for stable propagation. The whole parameter space in which these soliton pairs exist as a changeless entity has been investigated in terms of the spatial width of the soliton pair, their peak power, and the magnitude of temperature change of the crystal. The magnitude of the temperature change profoundly affects the evolution characteristics of these Gaussian soliton pairs. The stability of such soliton pairs has been demonstrated using the paraxial theory. Bistable states have been shown to exist in the system irrespective of the magnitude of the temperature change for the case when both components of the soliton pair have equal power. A lithium niobate (LN) crystal has been considered to illustrate the relevant results.

Lump and Mixed Rogue‐Soliton Solutions of the (2 + 1)‐Dimensional Mel’nikov System

Lump wave and line rogue wave of the (2 + 1)‐dimensional Mel’nikov system are derived by taking the ansatz as the rational function. By combining a rational function and different exponential functions, mixed solutions between the lump and soliton are derived. These solutions describe the interaction phenomena of the lump‐bright soliton with fission and fusion, the half‐line rogue wave with a bright soliton, and a rogue wave excited from the bright soliton pair, respectively. Some special concrete interaction solutions are depicted in both analytical and graphical ways.

Optical solitons in birefringent fibers with quadratic–cubic nonlinearity by extended G′/G-expansion scheme

The extended G′/G-expansion scheme retrieves bright, dark and singular optical soliton pairs for birefringent fibers that maintains quadratic–cubic nonlinearity. In addition, complexiton solutions are also presented which emerges from the scheme. The existence criteria for these solutions are enumerated.

Incoherently coupled Gaussian soliton pairs in biased photorefractive crystal having both the linear and quadratic electro-optic effect

Propagation characteristics of incoherently coupled Gaussian soliton pairs are studied in photorefractive media having both the linear and electro-optic effect. Applying paraxial ray approximation, a very large family of bright–bright Gaussian soliton pairs in photorefractive crystals having both the linear and quadratic electro-optic effect has been identified. These composite solitons can exist only when the carrier beams have the same polarization, wavelength and are mutually incoherent. It is shown that the incoherently coupled soliton pair cannot propagate as a stationary entity if its components have different spatial widths. A wide parameter space of spatial width of the soliton pair and its power has been found where it can exist as a stationary entity. The paraxial theory shows that the identified family of soliton pairs is stable. An interesting finding is that of bistable states in this system for the degenerate case of the power being same for both components of the soliton pair. A relevant example has been taken for illustration of our results where the crystal is PMN-0.33PT.

Spatial solitons in a nonlocal fused coupler

We study soliton-modes of optical pulses and their stabilities in a nonlocal nonlinear fused dual-core planar waveguide. Taking the different parameters, we find the symmetric, antisymmetric and asymmetric bright soliton pairs and dipole soliton pairs. During the long-distance propagation, the amplitudes of some solitons adding the white noise exhibit periodic oscillations and the solitons except asymmetric soliton can propagate steadily. We also find that the phases and profiles of solitons in the nonlocal coupler are determined by the propagation constant, the amplitude of the optical field and the region of the fused segment.

Coherently coupled screening spatial soliton pairs due to the two-photon photorefractive effect

A theoretical study of coherently coupled spatial soliton pairs propagating along the same line in biased two-photon photorefractive crystals is presented. Our results show that coherently coupled bright–bright and dark–dark soliton pairs propagating collinearly can be supported in a steady-state regime under appropriate conditions. Moreover, the effects of the intensity ratio, the initial phase difference between two incident coherent beams, and various external bias fields on the existence conditions and properties of these soliton pairs have been discussed in detail. The stability of these soliton pairs has also been discussed by means of beam propagation methods. Finally, the temperature dependence of the dark irradiance and diffusion process on the intensity profiles and self-deflection of coherently coupled bright–bright soliton pairs are also analyzed.

Vector nematicons: Coupled spatial solitons in nematic liquid crystals

Families of soliton pairs, namely vector solitons, are found within the context of a coupled nonlocal nonlinear Schr\odinger system of equations, as appropriate for modeling beam propagation in nematic liquid crystals. In the focusing case, bright soliton pairs have been found to exist provided their amplitudes satisfy a specific condition. In our analytical approach, focused on the defocusing regime, we rely on a multiscale expansion methods, which reveals the existence of dark-dark and antidark-antidark solitons, obeying an effective Korteweg-de Vries equation, as well as dark-bright solitons, obeying an effective Mel'nikov system. These pairs are discriminated by the sign of a constant that links all physical parameters of the system to the amplitude of the stable continuous wave solutions, and, much like the focusing case, the solitons' amplitudes are linked, leading to mutual guiding.

Incoherent Interaction Between Bright–Bright Photovoltaic Soliton in an Unbiased Series Two-Photon Photorefractive Crystal Circuit: Self-Deflection Investigation

We investigated the effects of self-deflection on incoherent interaction between photovoltaic bright–bright soliton pairs in photorefractive crystals under steady-state condition in an unbiased series two-photon photorefractive crystal circuit in one dimension. The numerical schemes according to the Crank–Nicholson and Runge–Kutta methods are applied to simulate the propagation of incoherent interaction for studying self-deflection by considering the diffusion process with different normalized separation distances, different amplitude and different δ. We also offer some applications about this subject.

Molecular transport network security using multi-wavelength optical spins

Multi-wavelength generation system using an optical spin within the modified add-drop optical filter known as a PANDA ring resonator for molecular transport network security is proposed. By using the dark-bright soliton pair control, the optical capsules can be constructed and applied to securely transport the trapped molecules within the network. The advantage is that the dark and bright soliton pair (components) can securely propagate for long distance without electromagnetic interference. In operation, the optical intensity from PANDA ring resonator is fed into gold nano-antenna, where the surface plasmon oscillation between soliton pair and metallic waveguide is established.

Peregrine solitons and algebraic soliton pairs in Kerr media considering space–time correction

Abstract Exact unified rational solutions describing a family of Peregrine solitons as well as related algebraic soliton pairs in either self-focusing or self-defocusing Kerr media are presented, with distinct defining regimes and an explicit relationship for those of opposite nonlinearity. The active role of the space–time correction effect that plays in these soliton species is highlighted, leading to unique dynamics such as the persistence of Peregrine solitons in a defocusing Kerr medium, the availability of giant peak amplitude for the bright–bright soliton pair, and the existence of so-called bright–dark soliton pair. The evolution dynamics of the algebraic two-soliton state toward a spliced single soliton is also discussed.

Drug Delivery System Model using Optical Tweezer Spin Control

A new concept of molecular motor using optical tweezers within a modified optical add–drop filter known as PANDA ring resonator is proposed. In simulation, dark and bright solitons are input into the system. The orthogonal tweezers can be formed within the system and detected simultaneously at the output ports. Under the resonant condition, the optical tweezers generated by dark and bright soliton pair corresponding to the left-hand and right-hand rotating solitons (tweezers) can be generated. In application, the trapped molecules can be moved and rotated to the required destinations, which can be useful for healthcare applications, especially, in drug delivery, medical diagnosis and therapy.

Optical Capsule and Tweezer Array for Molecular Motor Use

A generation of optical capsules and tweezers within a modified optical add-drop filter known as PANDA ring resonator with a new concept is proposed. By using dark and bright solitons, the orthogonal tweezers can be formed within the system and observed simultaneously at the output ports. Under the resonant condition, the optical capsules and tweezers generated by dark and bright soliton pair corresponding to the left-hand and right-hand rotating solitons (tweezers) can be generated. When a soliton is interacted by an object, an angular momentum of either bright or dark tweezers is imparted to the object, in which two possible spin states known as tweezer spins are exhibited. Furthermore, an array of molecular capsules and spins, i.e., trapped molecules can be generated and detected by using the proposed system, which can be used to form large scale tweezer or capsule spins. In application, the trapped molecules can be moved and rotated securely to the required destinations, which can be useful for many applications, especially, in medical diagnosis, therapy and surgery.

Manakov solitons in biased photorefractive crystals with both the linear and quadratic electro-optic effect

It is shown theoretically that the dark–dark, bright–bright and dark–bright Manakov soliton pairs can exist in biased photorefractive materials with both the linear and quadratic electro-optic effect under steady-state conditions. These soliton pairs can be generated provided that the total intensity of the two mutually inherent, with the same wavelength optical beams is much lower than the sum of the background intensity and the dark irradiance. It is also found that the intensity full width at half maximum of these Manakov solitons is inversely proportional to the square root of a quadratic polynomial of the external bias field. Moreover, the linear and quadratic electro-optic effects can be enhanced, decreased, even offset under appropriate conditions.