Dynamics of optical spatial solitons near the interface between two quadratically nonlinear media

Analytical investigations are carried out for the soliton propagation and reflection in a magnetized positive-ion-negative-ion plasma having two types of electrons based on the reductive perturbation technique. It is found that this type of plasma does not support rarefactive solitons, which are otherwise found to propagate in negative-ion-containing plasmas with isothermal electrons. This is the consequence of the low-temperature electron component present in the plasma. Two types of compressive solitons, namely, the fast wave soliton and the slow wave soliton, are found to exist, but only the fast compressive solitons will reflect. The effect of ion temperature is to enhance the soliton reflection; the same is the case for an increased number of negative ions. However, the effect of low-temperature electrons is to weaken the soliton reflection. Interestingly, the solitons are found to downshift after their reflection, and this shift is less under the effects of stronger magnetic field, smaller wave propagation angle, and a higher concentration of low-temperature electrons. However, larger amplitude solitons are more downshifted, and the shift is more for higher ion temperature and when the wave propagates with larger phase velocity.

A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe${}_{2}$ (LGT) crystals. Once irradiated by a cw laser beam of $10 \ensuremath{\mu}$m wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.

Using the finite-difference time-domain method, we model the propagation of spatial optical solitons having two orthogonal electric field vector components, and the scattering of such solitons by compact subwavelength air holes (i.e., abrupt dielectric discontinuities in the direct paths of the solitons). Our propagation and scattering studies assume a realistic glass characterized by a three-pole Sellmeier linear dispersion, an instantaneous Kerr nonlinearity, and a dispersive Raman nonlinearity. An unexpected spatial soliton scattering phenomenon is observed: the coalescence of the scattered electromagnetic field into a propagating lower-energy spatial soliton at a point many tens of wavelengths beyond the scattering air hole. Overall, our computational technique is general, and should permit future investigations and design of devices exploiting spatial soliton interactions in background media having submicrometer air holes and dielectric and metal inclusions.

We overview theoretical and experimental results on spatial optical solitons excited in arrays of nonlinear waveguides. First, we briefly summarize the basic properties of the discrete nonlinear Schrödinger (NLS) equation frequently employed to study spa

The evolution of long nonlinear surface wave excitations in a Bénard-Marangoni shallow liquid layer is studied when the system is far from its instability threshold. For , thus for surface wave excitations with possible large amplitude, where M is the Marangoni number of the system and is its critical value bifurcating to oscillatory convecting state from a motionless one, the surface wave displacement is found to obey a dispersion-modified Burgers equation whose kink-like solutions are also studied.

Theoretical study of reorientation and torque of liquid crystal molecules under influence of external electric field and experimentally generation of spatial optical soliton beam and getting a sharp switching in chiral nematic liquid crystal

Paper present a review of theoretical study and numerical simulations of effects of nonparaxiality on spatial optical solitons in transparent media with various types of optical nonlinearity: Kerr-law and saturating self-focusing non linearities in isotropic media and second-order nonlinearity in anisotropic media. The main features of spatial solitons, including their stability, transient process, and polarization characteristics are found. Conjunctions for formation of 'optical needles' - spatial solitons with sub- wavelength width - are formulated.

We demonstrate the existence of spatial soliton solutions in photonic crystal fibers (PCF's). These guided localized nonlinear waves appear as a result of the balance between the linear and nonlinear diffraction properties of the inhomogeneous photonic crystal cladding. The spatial soliton is realized self-consistently as the fundamental mode of the effective fiber defined simultaneously by the PCF linear and the self-induced nonlinear refractive indices. It is also shown that the photonic crystal cladding is able to stabilize these solutions, which would be unstable otherwise if the medium was entirely homogeneous.

This paper investigates new optical soliton solutions to the complex Ginzburg-Landau equation in the presence of white noise, a fundamental model in nonlinear optics that describes soliton dynamics. The study focuses on nine distinct forms of self-phase modulation structures, each exhibiting unique nonlinear characteristics and dispersion properties. To derive the soliton solutions, the generalized -expansion approach is employed, which is known for its effectiveness in handling nonlinear differential equations and extracting exact solutions systematically. Through this analytical framework, a variety of soliton profiles are retrieved, demonstrating the influence of nonlinear dispersion and gain-loss terms on soliton propagation. A key observation from the analysis is that the presence of white noise primarily affects the phase component of the solitons, while their amplitude remains intact. This result suggests that the robustness of the soliton amplitude against stochastic perturbations could have significant implications for practical optical communication systems and laser pulse propagation, where maintaining stable intensity profiles is crucial. The obtained results provide valuable insights into the interplay between noise and nonlinear wave dynamics, offering potential applications in fiber-optic communication, mode-locked lasers, and other areas of photonics where controlled soliton evolution is essential.•The paper investigates optical soliton solutions of the complex Ginzburg-Landau equation with white noise, focusing on nine forms of self-phase modulation with varied nonlinear and dispersive properties.•Using the generalized -expansion method, the study derives exact soliton profiles, revealing how nonlinear dispersion and gain-loss mechanisms shape soliton dynamics.•A key finding shows that white noise affects soliton phase without disturbing amplitude, highlighting amplitude robustness with implications for optical communications and laser systems.

A great deal of interest over the years has been directed to the optical space solitons for the possibility of realizing 3D waveguides with very low propagation losses. A great limitation in their use for writing complex circuits is represented by the impossibility of making curved structures. In the past, solitons in nematic liquid crystals, called nematicons, were reflected on electrical interfaces, and more recently photorefractive spatial solitons have been, as well. In the present work, we investigate refraction and total reflection of spatial solitons with saturable electro-optic nonlinearity, such as the photorefractive ones, on an electric wall acting as a reflector. Using a custom FDTD code, the propagation of a self-confined beam was analyzed as a function of the applied electric bias. The electrical reflector was simulated by applying different biases in two adjacent volumes. We observed both smaller and larger angles of refraction, up to the critical π/2-refraction condition, and then the total reflection. The radii of curvature of the associated guides can be varied from centimeters down to hundreds of microns. The straight guides showed losses as low as 0.07 dB/cm as previously observed, while the losses associated with single curves were estimated to be as low as 0.2 dB.

Lithium Noibate (LN) nano-waveguides combine the high nonlinearity and broadband transparency of LN with the sensitive tunability of geometric group velocity dispersion (GVD) and the strong field enhancement of subwavelength waveguides [1,2]. Together these properties make the newly emerging LN nano-waveguides a compelling candidate for research into dynamics of quadratic temporal solitons, and frequency conversion processes driven by solitons interacting with dispersive waves. Emission of resonant radiation (RR) by temporal solitons due to cubic nonlinearity is known to be one of the key mechanism behind supercontinuum generation [3]. Recent research into cubic solitons interacting with quadratic nonlinearities has found new mechanisms for tunable RR [4].

Dynamics of optical solitons in the perturbed Gerdjikov–Ivanov equation

The one-particle type temporal soliton exists by maintaining a balance between dispersive linear contributions on the one hand and non-linear effects on the other. The linear contributions occur from processes such as group velocity and polarization mode dispersion. The nonlinear features occur from Kerr, or power law non-Kerr behavior. In addition, a variety of perturbations, such as damping, Brillouin scattering, and Raman effects exist to alter the simple soliton solution. In this paper, we review the propagation of temporal solitons in power law non-Kerr media. This is developed through the higher nonlinear Schroedinger's equation (HNLSE). Also, the fundamentals of multiple-scales are presented that will be used to yield quasi-stationary solitons when perturbations are present. In waveguides, the one-particle type spatial soliton exists by maintaining a balance between the linear propagational diffraction and non-linear self-focusing, while possibly being subjected to a variety of perturbations. Here, we use a spatial optical soliton solution to the nonlinear Schroedinger equation in an inhomogeneous triangular refractive index profile as a small index perturbation to illustrate the oscillation property within a two dimensional waveguide. We determine, from the motion of spatial soliton, its effective acceleration, period of oscillation, and compare results with the Gaussian refractive index profile. Such spatial solitons behave as point masses existing in a Newtonian gravitational potential hole.

This work analyzes the dynamics of two-dimensional spatial solitons in dissipative graded index Kerr media, analytically and numerically. The dynamics of two-dimensional spatial solitons has been studied in a medium with lumped amplification. The presence of lumped amplification in the medium results in the formation of soliton like waves called similaritons. The spatial soliton dynamics has been studied in a dissipative medium. In a dissipative graded index Kerr medium, the balancing between the coefficients of constant dissipation and lumped amplification results in the stabilization of the beam. The beam dynamics has also been studied by varying amplification coefficients with propagation distance. Hyperbolic, linear, and exponential amplification profiles are considered. When amplification coefficient varies with propagation distance, the beam gets compressed. The beam compression is higher in the case of exponential amplification profile than that of hyperbolic and linear amplification profiles.

Self-trapping of light beams in nonlinear self-focusing Kerr media has been explored intensively during the last three decades. The self trapped beams, often in the form of spatial solitons, evolve from nonlinear changes in the refractive index (δn) of the material proportional to the intensity distribution of the light, when the confining effect of the refractive index exactly compensates for the defocusing effect of diffraction. Motivated by experimental results of self-focusing of light beams [1] in the presence of the optical Kerr effect, a theoretical solution for the resulting spatial solitons was found [2,3]. This was followed by demonstrations of self-trapping in vapors [4], liquids [5], and finally, in the last few years, spatial solitons in solid (glass) media [6]. However, the index changes needed for optical-Kerr spatial solitons require high intensities, often exceeding 1 MWatt/cm2. Several other materials, such as slightly-absorbing liquids, exhibit Kerr-like thermal nonlinearities at much lower power densities (Watts/cm2), typically with a negative δn. These materials enabled the observations of dark spatial solitons [7] (narrow dark “notches”) and optical vortex solitons [8,9] (dark solitons were also observed using optical-Kerr nonlinearities in ZnSe [10] at GWatt/cm2 power densities). The most distinct properties of all these Kerr-like solitons are (i) a strong intensity dependence and the existence of a power threshold, and (ii) stability of bright solitons only in a single transverse dimension (consequently, bright Kerr-type solitons can be observed only in a planar waveguide, otherwise the soliton becomes unstable and cannot be observed).KeywordsDark SolitonInput BeamBright SolitonSpatial SolitonPhotorefractive CrystalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.