Experiments in quadratic spatial soliton generation and steering in a noncollinear geometry

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.

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.

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.

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.

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 present first-time calculations from the time-domain vector Maxwell's equations of spatial optical soliton propagation and mutual deflection, including carrier waves, in a 2-D homogeneous Kerr-type nonlinear dielectric. The nonlinear Schrodinger equation predicts that two co-propagating, in-phase spatial solitons remain bound to each other, executing a periodic separation. This disagrees with our new extensively tested finite-difference time-domain (FD-TD) solution of Maxwell's equations. FD-TD shows that co-propagating in-phase spatial solitons become unbound, i.e. diverge to arbitrarily large separations, if the ratio of soliton beamwidth to wavelength is order 1 or less. Not relying upon paraxial approximations or analogies to temporal soliton interactions, FD-TD appears to be a robust means of obtaining detailed models of the interaction of sub-picosecond pulsed light beams in nonlinear media directly in the space-time domain. >

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.

Computer simulation of propagation and switching of both temporal and spatial solitons is presented. The simulation is based on the solutions of a general wave equation by a newly developed beam propagation method.

Laser generated soliton waveguides in photorefractive crystals

Evolution of spatial solitons in quadratic media with fluctuating nonlinearity

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.

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.

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.

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

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.