Evolution of spatial solitons in quadratic media with fluctuating nonlinearity

Self-induced phase-matching and three-wave bright spatial solitons in quadratic media

The effect of fluctuating parameters of quadratic nonlinear media on the dynamics of spatial solitons is analytically and numerically studied. We derive a system of equations for mean fields of both frequency components and show that fluctuations of the wave vector mismatch and the nonlinear coefficient induce effective linear and nonlinear losses, respectively. We find approximate analytical expressions for the damping rate of spatial solitons for both types of the random modulation and study the impact of the correlation length of the fluctuations. We show that the predictions of the mean field theory are in a good agreement with numerical simulations of the full stochastic system.

We present experimental and numerical observations of transverse instability in quadratic media under conditions that emphasize the inherently spatiotemporal and multidimensional nature of the wave propagation. Intensity-dependent beam filamentation is shown to be closely connected to the periodic evolution of quadratic solitons, and implications for the generation of three-dimensional spatiotemporal solitons are 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.

The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.

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.

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.

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.

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.

In this paper we present the studies of the problem of slow and immobile solitons which are excited inside the stop bands of inhomogeneous media with either quadratic or cubic nonlinearity. We found an integral criterion of slow soliton formation, determined the main properties of gар solitons. The dynamics of parametric gap soliton formation and propagation in quadratic media is illustrated by means of computer simulations and compared with such solitons due to cubic nonlinearity.

Novel effects for few-cycle pulses propagation in quadratic media with dispersion management are considered. First, the process of extraordinary wave generation in uniaxial crystal is tightly related with the process of ordinary wave profile differentiation. Velocity mismatch limits interaction efficiency and leads to splitting of generated waves into two subpulses. Such effect can be suppressed in the medium with periodic modulation of quadratic nonlinearity or with velocity mismatch sign modulation. Second, highly interesting effects arise with the third-order dispersion. Dispersive spreading can be reduced in layered medium with alternating third-order dispersion coefficients. Quadratic photonic crystals with modulated dispersion coefficients or with managed dispersion are very promising for few-cycle pulse nonlinear optics. One- and two-wave soliton trapping and propagation dynamics are also studied in such crystals. The analytical theory is accompanied with the numerical simulation results.

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.

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.

It is shown that the propagation of steady-state spatial solitons in a bismuth titanium oxide (Bi12TiO20) photorefractive crystal is strongly affected by the presence of concomitant natural optical activity. We assume that the Bi12TiO20 crystal is (110) cut and that the external bias field is along the [001¯] axis. Such orientation introduces self-focusing in one polarization of an optical wave front, whereas it has no effect whatsoever on the component orthogonal to it. Under these conditions, the equations that describe the coupled evolution of the two polarizations of an optical planar beam are derived. Our numerical study of the interaction dynamics shows that, even though the optical beam experiences periodic diffraction in one of the polarization components, it can still recover significantly at particular distances within the crystal. Moreover, it is initially capable of maintaining its solitonlike form over a certain distance of propagation. Relevant examples are provided.