Propagation Of Spatial Solitons Research Articles

Rotationally symmetric transverse magnetic vector wave propagation for nonlinear optics

In this paper the theory and simulation results are presented for 3D cylindrical rotationally symmetric spatial soliton propagation in a nonlinear medium using a modified finite-difference time-domain general vector auxiliary differential equation method for transverse magnetic polarization. The theory of 3D rotationally symmetric spatial solitons is discussed, and compared with two (1 + 1)D, termed “2D” for this paper, hyperbolic secant spatial solitons, with a phase difference of π (antiphase). The simulated behavior of the 3D rotationally symmetric soliton was compared with the interaction of the two antiphase 2D solitons for different source hyperbolic secant separation distances. Lastly, we offer some possible explanations for the simulated soliton behavior.

An energy-stable finite element method for nonlinear Maxwell's equations

In this paper, we consider the three-dimensional (3D) nonlinear Maxwell's equations in the optical media characterized by linear Lorentz dispersion, nonlinear Kerr effect and delayed Raman scattering. Using Crank-Nicolson time discretization and special treatment of the nonlinearity, we propose a second order accurate (in time) finite element method for the nonlinear problem. Fully discrete energy stability analysis is established to show that the scheme is unconditionally stable. The nonlinear system is solved by Newton-Krylov method. In order to efficiently solve the linearized algebraic system in each Newton sub-iteration, we further develop an effective preconditioner by using suitable approximations to the nonlinearity and the auxiliary space preconditioning technique. Numerical experiments are provided to examine the accuracy, the energy stability, the parallel scalability and the robustness in preconditioning of our proposed scheme. We then apply the scheme to simulate the spatial soliton propagation in 3D nonlinear glass. We also demonstrate the performance of the scheme in handling complex geometry through simulating the wave scattering by a spherical hole in the nonlinear optical glass.

Chirped spatial solitons on a continuous-wave background in weak nonlocal media with polynomial law of nonlinearity

Spatial soliton propagation in a cubic-quintic-septimal optical material with a weakly nonlocal response is examined. We demonstrate that bright and gray solitons on a continuous-wave background exist for the envelope equation describing their dynamis in the physical media. In addition, optical kink and anti-kink type solitons are also identified. We find that these waveforms exhibit a frequency chirping property which is inversely proportional to the beam intensity. A noteworthy characteristic is that the chirped soliton solutions include no free parameters and their properties such as their amplitude, spatial width and propagation constant are determined solely by the material parameters. The numerical examples are structured for illustrating the propagation dynamics of these solitons in the optical system. The role of weak nonlocality on the modulation instability gain has also been discussed.

Interplay between diffractive radiation shed and damping coefficient on nematicon propagation

This study considers the propagation of spatial soliton in nematic liquid crystals in the presence of damping in the nonlocal regime. The importance of diffractive radiation shed for an undisturbed propagation of nematicon has been analysed in this paper using variational and numerical methods. When the damping coefficient is constant, a large value of diffractive radiation height is required to counteract the effect of damping. If the damping coefficient varies with the propagation distance, the diffractive radiation has an important role in reducing the damping effect. In the case of the periodic damping profile, even larger diffractive radiation is needed to overcome the effect of damping as compared to the constant damping profiles. But a low value of diffractive radiation is enough to overcome the hyperbolic damping.

Propagation of local spatial solitons in power-law nonlinear PT-symmetric potentials based on finite difference

We consider the (2+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity under the parity-time-symmetry potential by using the Crank–Nicolson alternating direction implicit difference scheme, which can also be used to solve general boundary problems under the premise of ensuring accuracy. We use linear Fourier analysis to verify the unconditional stability of the scheme. To demonstrate the effectiveness of the scheme, we compare the numerical results with the exact soliton solutions. Moreover, by using the scheme, we test the stability of the solitons under the small environmental disturbances.

Soliton dynamics in finite nonlocal media with cylindrical symmetry

The effect of finite boundaries in the propagation of spatial nonlocal solitons in media with cylindrical symmetry is analyzed. Using Ehrenfest's theorem together with the Green's function of the nonlinear refractive index equation, we derive an analytical expression for the force exerted on the soliton by the boundaries, verifying its validity by full numerical propagation. We show that the dynamics of the soliton are determined not only by the degree of nonlocality, but also by the boundary conditions for the refractive index. In particular, we report that a supercritical pitchfork bifurcation appears when the boundary condition exceed a certain threshold value.

Electro-optic steering of random laser emission in liquid crystals

Electro-optic steering of random laser emission in liquid crystals

Thermo-optic soliton routing in nematic liquid crystals

We demonstrate thermo-optic control on the propagation of optical spatial solitons in nematic liquid crystals. By varying the sample temperature, both linear and nonlinear optical properties of the reorientational material are modulated by acting on the refractive indices, the birefringence, and the elastic response. As a result, both the trajectory and transverse confinement of spatial solitons can be adjusted, demonstrating an effective means to tune and readdress self-induced optical waveguides.

Waves in hyperbolic and double negative metamaterials including rogues and solitons

The topics here deal with some current progress in electromagnetic wave propagation in a family of substances known as metamaterials. To begin with, it is discussed how a pulse can develop a leading edge that steepens and it is emphasised that such self-steepening is an important inclusion within a metamaterial environment together with Raman scattering and third-order dispersion whenever very short pulses are being investigated. It is emphasised that the self-steepening parameter is highly metamaterial-driven compared to Raman scattering, which is associated with a coefficient of the same form whether a normal positive phase, or a metamaterial waveguide is the vehicle for any soliton propagation. It is also shown that the influence of magnetooptics provides a beautiful and important control mechanism for metamaterial devices and that, in the future, this feature will have a significant impact upon the design of data control systems for optical computing. A major objective is fulfiled by the investigations of the fascinating properties of hyperbolic media that exhibit asymmetry of supported modes due to the tilt of optical axes. This is a topic that really merits elaboration because structural and optical asymmetry in optical components that end up manipulating electromagnetic waves is now the foundation of how to operate some of the most successful devices in photonics and electronics. It is pointed out, in this context, that graphene is one of the most famous plasmonic media with very low losses. It is a two-dimensional material that makes the implementation of an effective-medium approximation more feasible. Nonlinear non-stationary diffraction in active planar anisotropic hyperbolic metamaterials is discussed in detail and two approaches are compared. One of them is based on the averaging over a unit cell, while the other one does not include sort of averaging. The formation and propagation of optical spatial solitons in hyperbolic metamaterials is also considered with a model of the response of hyperbolic metamaterials in terms of the homogenisation (‘effective medium’) approach. The model has a macroscopic dielectric tensor encompassing at least one negative eigenvalue. It is shown that light propagating in the presence of hyperbolic dispersion undergoes negative (anomalous) diffraction. The theory is ten broadened out to include the influence of the orientation of the optical axis with respect to the propagation wave vector. Optical rogue waves are discussed in terms of how they are influenced, but not suppressed, by a metamaterial background. It is strongly discussed that metamaterials and optical rogue waves have both been making headlines in recent years and that they are, separately, large areas of research to study. A brief background of the inevitable linkage of them is considered and important new possibilities are discussed. After this background is revealed some new rogue wave configurations combining the two areas are presented alongside a discussion of the way forward for the future.

Variational method to spatial soliton propagation in a waveguide with periodic parabolic index profile

In this paper, we study spatial soliton propagation in a waveguide with periodic parabolic refractive index profile. Wave equation in the present of the refractive index profile includes diffraction, self-focusing (SF) and self-defocusing (SDF). To solve the wave equation, we use variational method and finally discuss the effect of self-defocusing and maximum potential depth on soliton behaviour.

Spatial soliton propagation through waveguides: rectangular and parabolic rectangular index profile

In this study we have investigated the spatial soliton propagation in two rectangular and parabolic rectangular index profile waveguides. Effects of maximum index variation, Δn0, waveguide width, L and well numbers, N have been studied. We see that swing period is a function of the waveguide parameter Δn0. As Δn0 increases, the swing period becomes shorter. But, by increasing of waveguide width, this swing period become larger. For even well numbers except for N = 6, oscillations is not symmetric around the oscillation center. Thus, systems with well numbers N = 2 and N = 4 is not suitable for waveguide applications. By using of parabolic rectangular indices we overcome this difficulty. But, in this new system, soliton moves slower and damping of soliton oscillation occurs more rapidly.

Spatial soliton propagation through a triangular waveguide: A Runge Kutta study

In this work, we have studied a traveling soliton through a triangular refractive index waveguide. Our calculations have been performed with a 4th order Runge Kutta method which we have presented the algorithm. Then we have checked the numerical accuracy and found it desirable. In our investigations, the light beam inside a waveguide have been oscillated which perfectly agree with the so-called “swing effect”. In comparison with a soliton with amplitude Q=1, for soliton amplitude Q=2 a shorter oscillation period have been observed. In the meantime, for lower waveguide widths, soliton have had shorter oscillation period. Finally, for η≠0, the soliton oscillate with higher amplitude and it recede from center of waveguide which is not desirable.

Two dimensional spatial solitons in parity-time symmetric potential

This work analyzes the propagation of (2+1) dimensional spatial solitons in parity-time (PT) symmetric potential. The stationary solution of the system has been studied. The beam dynamics has been analyzed using variational and numerical methods. The soliton beam propagation is stable when the coefficient of imaginary potential is less than a threshold, which is called the phase transition point. Above the transition point, the imaginary component of the solution starts to evolve and the solution becomes unstable. When the coefficient of imaginary potential exceeds this critical value, the power of the beam increases and results in the unstable beam propagation. The stability of the stationary solution against small perturbation has been studied using linear stability analysis. The imaginary eigen value is zero when the coefficient of the imaginary potential is low. Above the phase transition point, the imaginary eigen value becomes comparable with the real eigen value and hence the solution becomes linearly unstable.

Phase-front curvature effects on nematicon generation

We investigate light self-trapping and nematicon generation in reorientional nematic liquid crystals, addressing the role of phase-front curvature and size of the TEM00 input beam excitation. The experimental results in planar cells are in excellent agreement with a semi-analytical model and numerical simulations. These findings can substantially aid characterization and generation of spatial solitons in liquid crystals and be readily generalized to other nonlocal nonlinear media and soft matter systems.

Sub-Wavelength Dual Capillaries-Assisted Chalcogenide Optical Fibers: Unusual Modal Properties in Mid-IR (2–5 μm) Spectral Range

In this study, we apply the concept of sub-wavelength light confinement to achieve flat effective mode area ( $A_{{\rm eff}}$ ) characteristics over a wide wavelength range of 1400 nm in nano-sized dual capillary assisted chalcogenide core optical fibers. An unusual spectral behavior of $A_{{\rm eff}}$ is observed where the effective mode area increases, remains constant for a wide bandwidth, decreases and again increases with the increase in wavelength. The spectral region, in which this behavior is observed, can be tuned by varying the structural parameters of the fiber. Additionally, we noticed that the fiber exhibits four zero dispersion wavelengths for a particular polarization which suggests that sub-wavelength light localization can be an alternative solution for the dispersion engineering in order to attain multiple zero dispersion wavelengths. The fabrication tolerance of the dispersion profile has been found to fall within the current fabrication accuracies achievable. We believe that our findings might be useful in different applications such as light-matter interaction and spatial soliton propagation.

Nonlinear competition in nematicon propagation.

We investigate the role of competing nonlinear responses in the formation and propagation of bright spatial solitons. We use nematic liquid crystals (NLCs) exhibiting both thermo-optic and reorientational nonlinearities with continuous-wave beams. In a suitably prepared dye-doped sample and dual beam collinear geometry, thermal heating in the visible affects reorientational self-focusing in the near infrared, altering light propagation and self-trapping.

Stability conditions for one-dimensional optical solitons in cubic-quintic-septimal media

Conditions for stable propagation of one-dimensional bright spatial solitons in media exhibiting optical nonlinearities up to the seventh-order are investigated. The results show well-defined stability regions even when all the nonlinear terms are focusing. Conditions for onset of the supercritical collapse of the optical beam are identified too. A variational approximation is used to predict dependence of the soliton propagation constant on the norm, and respective stability regions are identified using the Vakhitov-Kolokolov criterion. Analytical results obtained by means of the variational approximation are corroborated by numerical simulations of the cubic-quintic-septimal nonlinear Schroedinger equation.

Dynamic behavior of the incoherent optical spatial solitons in a nonlocal nonlinear medium

Dynamic behavior of the propagation of incoherent optical spatial solitons in a nonlocal nonlinear medium is investigated. By means of the Hirota method, we obtain the soliton solutions, based on which we find that is positively related to , but inversely related to and , whereas is independent of them, with as the slowly varying amplitude of the beam, as the refractive index change, , , and as the unperturbed refractive index, frequency of the propagating beam, and beam intensity distribution, respectively. Head-on and bound-state soliton interactions are both given, and one interaction period decreases with and increasing in the bound state one. With the external perturbations taken into consideration, the associated chaotic motions of the perturbed model are studied, and the corresponding power spectra and phase projections are obtained. Both the weak and developed chaotic states are investigated, and the difference between them roots in the relative magnitude of nonlinearities and perturbations. Such chaotic motions can be weakened via increasing and or decreasing . Periodic motion is obtained with the nonlinearities and perturbations balanced.

Two-dimensional solitons in a quintic-septimal medium

We report an observation of spatial solitons in a medium managed to present fifth-seventh (focusing-defocusing) refractive nonlinearities with suppressed third-order nonlinearity. Propagation of two-dimensional bright spatial solitons for \ensuremath{\sim}10 Rayleigh lengths was observed and characterized in a suspension of silver nanoparticles in acetone using the scattered light imaging method. Numerical calculations based on a nonlinear Schr\odinger-type equation, including contributions up to the seventh-order susceptibility, were performed showing good agreement with the experimental results.

Analytic Studies on the Helmholtz Spatial Solitons in Power-Law Optical Materials

In order to describe refraction phenomena, the propagation of a spatial soliton in power-law optical materials is considered. Hereby, we work on the behavior of solitons described by a generalized nonlinear Helmholtz equation in the power-law optical materials. Via the Hirota method, analytic one- and two-soliton solutions are obtained. We study the spatial solitons in two adjoining power-law materials with dissimilar medium coefficients. Based on the choice of the Heaviside function in the equation, we distinguish the two different optical materials. One-soliton dynamics with different choices of the nonlinear and linear refractive properties along the propagation direction of the carrier wave are discussed. In the first medium, with an increase of the inverse width, the soliton will be amplified. In the second medium, the soliton amplitude will increase when the linear refractive property increases, or the nonlinear refractive property decreases. Asymptotic analysis is carried out on the two-soliton solutions. Through a graphic and asymptotic analysis, we find that there exist elastic and inelastic collisions between two solitons, as well as soliton fusion.