Solitons in optical lattices with nonlocal nonlinearity

Nonlocal spatial solitons are the optical spatial solitons in nonlocal nonlinear media. In this invited paper, a review is given about the progress on this subject. The nonlocal spatial solitons are phenomenologically modeled by the nonlocal nonlinear Schrodinger equation, which can be simplified to a linear model for a strong nonlocality. An exact analytical Gaussian-shaped solution to the linear model is obtained, and a spatial soliton called an accessible soliton is found to exist. A phase shift of such an accessible soliton can be very large comparable to its local counterpart, and this finding might be applied in integrated all-optical devices. More intriguing is the collision between two nonlocal spatial solitons. The interaction of two coherent accessible solitons is always attractive, independent of their relative phase, unlike in a local nonlinearity. Such an interaction behavior is experimentally observed in nematic liquid crystals, and a power-dependent X junction, AND, NOR, and XNOR gates are also experimentally demonstrated. This collisional characteristics has implications to all-optical switching and all-optical logic.

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.

In this paper, we mainly simulate the characteristics of the ground state dark soliton and the multipole dark soliton in the nonlocal and cubic-quintic nonlinear medium. Firstly, the influences of the degree of nonlocality on the amplitude and the width of the dark soliton in the self-defocusing cubic-and self-focusing quantic-nonlinear medium are studied. Secondly, we find the nonlinear parameters affecting the amplitude values of solitons, but the refractive index induced by the light beam is always a fixed value. The numerical results show that the ground state dark soliton can be propagated stably alone the z axis, and the stable states of the dipole soliton and the dark tri-pole and quadru-pole solitons are stable. However, some quadru-pole dark soliton is unstable after propagating the remote distance. Furthermore, we also discuss the characteristics of the ground state dark soliton and the dark dipole soliton in the local cubic-nonlinear and nonlocal quantic nonlinear media. Both the amplitude and the beam width of the dark ground state soliton and dark dipole soliton are also affected by the degree of nonlocality and nonlinearity. Two boundary values of the induced refractive index change with the variations of the three nonlinear parameters. The dark soliton and the dipole dark soliton are more stable in the self-focusing cubic nonlinear and the nonlocal self-defocusing quantic nonlinear medium than those in the self defocusing cubic nonlinear and nonlocal self-focusing quantic nonlinear medium. The powers of single dark soliton and dark tri-pole soliton decrease monotonically with the increase of propagation constant when the cubic-quintic nonlinearities are certain values and these degrees of nonlocalities are taken different values. Furthermore, we also analyze linear stabilities of various nonlocal spatial dark solitons. And we find that the dipole dark soliton is unstable when the propagation constant is in the region[-0.9,-1.0]. These properties of linear stabilities of other multi-pole dark solitons are the same as their propagation properties.

We address the formation and propagation of vector solitons in optical lattices in the presence of anisotropy-induced walk-off between ordinary and extraordinary polarized field components. Stable vector solitons trapped by the lattice form above a threshold power, while decreasing the lattice depth below a critical value results in the abrupt release of the caged solitons that then move across the lattice and may get trapped in a desired lattice channel.

We report a family of solitons generated by Hermite-Gaussian beams that are supported in optical lattices, also described by Hermite-Gaussian functions in combination with a harmonic potential that is modelled by a (1+1)D nonlinear Schrödinger equation. We find that this kind of solitons is stable during propagation, provided they remain below a level of the power threshold. The pure local nonlinear system studied here can mimic, up to a certain extent, a strongly nonlocal medium, thus allowing generation of accessible solitons. These Hermite-Gaussian profiles constitute a kind of uncommon analytical solitons that allow the study of nonlinear wave behavior phenomena in a more tractable and closed form.

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.

We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.

Spatial solitons were investigated in periodically poled KTiOPO4 under conditions of second harmonic generation and many new features associated with soliton generation in quasi-phase-matched samples were observed .The effects on the second harmonic generation tuning curves of the beam narrowing mechanisms responsible for soliton generation were found to be dramatic. It was demonstrated experimentally that the mutual collapse of the fundamental and harmonic beams is a complex phenomenon.

Although tightly focused input beams for efficient second harmonic (SH) generation (SHG) are usually avoided because of material damage, this is exactly the condition needed for the generation of spatial solitons (QSS) based on quadratic (χ(2)) nonlinearities.[1,2] These QSS’es are mutually self-trapped fundamental (FW) and harmonic (SH) optical beams in which the mutual beam narrowing due to photon exchange incipient in up and down conversion balances diffraction. The generation of quadratic solitons significantly affects the SHG process, for example by placing an upper limit on the amount of fundamental that can be converted to SH, by increasing the bandwidth of the process etc.[3] Of particular interest are periodically poled ferroelectric media which are an important limit of non-critical phase-matching. In fact, periodically poled LiNbO3 (PPLN) has been shown to have the lowest soliton threshold of 1.5 GW/cm2 reported to date [4]. That pioneering work established the existence of quadratic solitons in periodically poled media but neither this work, or any other work on QSSes has addressed the impact of QSS on the SHG tuning curves.

Coupled matter–wave solitons in optical lattices

An efficient technique to compensate the effects of absorption losses in the propagation of spatial solitons is analytically and numerically validated. This technique is based on the amplifying properties of certain kinds of tapered nonlinear Kerr coefficients. The analytical demonstration of its applicability is presented here for the first time.

We propose a physical setup to realize parity-time (PT) symmetric moiré optical lattices (ML) and nonlocal optical solitons in a cold Rydberg atomic system with electromagnetically induced transparency (EIT). We also show that based on the PT symmetry lattice strength and giant nonlocal Kerr nonlinearity originated from the strong, long-range atom–atom interaction, the system supports two-dimension (2D) nonlocal solitons with very low light intensity. By using numerical simulation method, we uncover the formation, properties, and dynamics of higher-order solitons and vortical ones. Our study opens a route for developing non-Hermitian nonlinear optics, especially for realizing and controlling high-dimensional weak-light optical solitons through adjustable PT-symmetric moiré lattice parameters and giant nonlocal optical nonlinearity.

Generation of spatial solitons with noncollinear excitation beams was experimentally investigated for type II second-harmonic generation in KTP. Spatial switching at a distance of 220microm and steering in a 330-microm range were demonstrated. Changes in soliton behavior induced by modification of the phase-matching condition (and) or by an imbalance of the inputs at the fundamental frequency have been characterized.

We investigate propagation and control of weak-light spatial solitons in a resonant three-level atomic system with a periodic modulated control field. It is shown that the periodic modulation acts like periodic potential which resists the propagation of the soliton in transverse direction. The soliton could be trapped by the periodic potential in the input channel. When the modulation is canceled, the soliton propagates in its initial incident direction. The periodic modulation of control field could be used to control the propagation of the weak-light probe soliton. Due to the good localization efficiency of the periodic potential, an excellent switching is realized for the probe soliton. These properties may have potential applications in all-optical switching, optical information processing and other fields.

We report on the existence and stability of mixed-gap vector surface solitons at the interface between a uniform medium and an optical lattice with fractional-order diffraction. Two components of these vector surface solitons arise from the semi-infinite and the first finite gaps of the optical lattices, respectively. It is found that the mixed-gap vector surface solitons can be stable in the nonlinear fractional Schrödinger equations. For some propagation constants of the first component, the stability domain of these vector surface solitons can also be widened by decreasing the Lévy index. Moreover, we also perform stability analysis on the vector surface solitons, and it is corroborated by the propagations of the perturbed vector surface solitons.