P T-symmetry breaking in dual-core phosphate-glass photonic crystal fibers.

We investigate the properties of a soft glass dual-core photonic crystal fiber for application in multicore waveguiding with balanced gain and loss. Its base material is a phosphate glass in a P2O5-Al2O3-Yb2O3-BaO-ZnO-MgO-Na2O oxide system. The separated gain and loss cores are realized with two cores with ytterbium and copper doping of the base phosphate glass. The ytterbium-doped core supports a laser (gain) activity under excitation with a pump at 1000 nm wavelength, while the CuO-doped is responsible for strong attenuation at the same wavelength. We establish conditions for an exact balance between gain and loss and investigate pulse propagation by solving a system of coupled generalized nonlinear Schrödinger equations. We predict two states of light under excitation with hyperbolic secant pulses centered at 1000 nm: 1) linear oscillation of the pulse energy between gain and loss core (P T-symmetry state), with strong power attenuation; 2) retention of the pulse in the excited gain core (broken P T-symmetry), with very modest attenuation. The optimal pulse energy levels were identified to be 100 pJ (first state) and 430 pJ (second state).

Analysis of high-contrast all-optical dual-wavelength switching in asymmetric dual-core fibers.

We systematically present experimental and theoretical results for the dual-wavelength switching of 1560 nm, 75 fs signal pulses (SPs) driven by 1030 nm, and 270 fs control pulses (CPs) in a dual-core fiber (DCF). We demonstrate a switching contrast of 31.9 dB, corresponding to a propagation distance of 14 mm, achieved by launching temporally synchronized SP-CP pairs into the fast core of the DCF with moderate inter-core asymmetry. Our analysis employs a system of three coupled propagation equations to identify the compensation of the asymmetry by nonlinearity as the physical mechanism behind the efficient switching performance.

Scalar and vector supermode solitons owing to competing nonlocal nonlinearities.

We investigate scalar and vector multi-hump spatial solitons resulting from competing Kerr-like nonlinear responses excited in a nonlocal medium by either one or two (mutually incoherent) light beams. Two-color vector supermode solitons are more amenable to control but exhibit an intriguing form of spontaneous symmetry breaking in propagation.

Reversible ultrafast soliton switching in dual-core highly nonlinear optical fibers.

We experimentally investigate a nonlinear switching mechanism in a dual-core highly nonlinear optical fiber. We focus the input stream of femtosecond pulses on one core only, to identify transitions between inter-core oscillations, self-trapping in the cross core, and self-trapping of the pulse in the straight core. A model based on the system of coupled nonlinear Schrödinger equations provides surprisingly good agreement with the experimental findings.

Femtosecond supercontinuum generation around 1560 nm in hollow-core photonic crystal fibers filled with carbon tetrachloride.

We investigated experimentally supercontinuum generation in hollow-core photonic crystal fibers with cores infiltrated with carbon tetrachloride. As a pump source, we used a standard fiber-based femtosecond laser with a central wavelength at 1560 nm and a pulse duration of 90 fs. The first investigated fiber has a zero-dispersion wavelength at 1740 nm and generates a supercontinuum in the wavelength range from 1350 to 1900 nm. The second fiber has a zero-dispersion wavelength at 1440 nm, and the observed supercontinuum spectrum ranges from 1000 to 1900 nm. We numerically analyzed coherence of simulated supercontinuum pulses and noted that the observed supercontinuum spectra had a potential for high coherence. While the dynamics of supercontinuum generation in each of the investigated cases was revealed to be in agreement with the established state of the art in nonlinear fiber optics, our results are the first demonstration of such dynamics, to the best of our knowledge, leading up to octave spanning supercontinuum spectra in liquid-filled hollow-core silica fibers under pumping with a small-footprint femtosecond laser.

Semi-analytical approach to supermode spatial solitons formation in nematic liquid crystals.

We study light propagation in nematic liquid crystals in the context of spatial optical solitons formation. We propose a simple analytical model with multiplicative nonlinearity, which represents (qualitatively) the liquid crystal response by comprising the competition between focusing (reorientational) and defocusing (thermal) nonlocal nonlinearities. We show that at sufficiently high input power the interplay between both nonlinearities leads to the formations of two-peak solitons, which represent supermodes of the self-induced extended waveguide structure. We explain the beam splitting mechanism, discuss threshold effects and conclude that similar phenomena might be present in other media with competing nonlocal nonlinearities.

Modulational instability of coupled ring waveguides with linear gain and nonlinear loss.

We consider a nanostructure of two coupled ring waveguides with constant linear gain and nonlinear absorption - the system that can be implemented in various settings including polariton condensates, optical waveguides or atomic Bose-Einstein condensates. It is found that, depending on the parameters, this simple configuration allows for observing several complex nonlinear phenomena, which include spontaneous symmetry breaking, modulational instability leading to generation of stable circular flows with various vorticities, stable inhomogeneous states with interesting structure of currents flowing between rings, as well as dynamical regimes having signatures of chaotic behavior.

Dispersion characteristics of a suspended-core optical fiber infiltrated with water.

In this paper we present a study on the dispersion characteristics in the suspended-core optical fibers made of borosilicate of NC21A glass infiltrated with water. Replacement of air with water results in dramatic improvement of the dispersion characteristics in the fibers, valuable in the process of supercontinuum generation. A near-zero flat dispersion can be achieved in the anomalous or normal dispersion range for various diameters of the core.

Single and double linear and nonlinear flatband chains: Spectra and modes.

We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site mixing between the two lattice fields. In the single-chain system, a full analysis is presented, first, for the single nonlinear cell, making it possible to find all stationary states, viz., antisymmetric, symmetric, and asymmetric ones, including an exactly investigated symmetry-breaking bifurcation of the subcritical type. In the nonlinear infinite single-component chain, compact localized states (CLSs) are found in an exact form too, as an extension of known compact eigenstates of the linear diamond chain. Their stability is studied by means of analytical and numerical methods, revealing a nontrivial stability boundary. In addition to the CLSs, various species of extended states and exponentially localized lattice solitons of symmetric and asymmetric types are also studied, by means of numerical calculations and variational approximation. As a result, existence and stability areas are identified for these modes. Finally, the linear version of the double diamond chain is solved in an exact form, producing two split flatbands in the system's spectrum.

Dispersion engineering in nonlinear soft glass photonic crystal fibers infiltrated with liquids.

We present a numerical study of the dispersion characteristic modification of nonlinear photonic crystal fibers infiltrated with liquids. A photonic crystal fiber based on the soft glass PBG-08, infiltrated with 17 different organic solvents, is proposed. The glass has a light transmission window in the visible-mid-IR range of 0.4-5 µm and has a higher refractive index than fused silica, which provides high contrast between the fiber structure and the liquids. A fiber with air holes is designed and then developed in the stack-and-draw process. Analyzing SEM images of the real fiber, we calculate numerically the refractive index, effective mode area, and dispersion of the fundamental mode for the case when the air holes are filled with liquids. The influence of the liquids on the fiber properties is discussed. Numerical simulations of supercontinuum generation for the fiber with air holes only and infiltrated with toluene are presented.

Stabilization of solitons under competing nonlinearities by external potentials.

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

Oscillating solitons in a three-component Bose-Einstein condensate.

We investigate the properties of three-component Bose-Einstein condensate systems with spin exchange interactions. We consider different coupling constants from those very special ones leading to exact solutions known in the literature. When two solitons collide, a spin component oscillation of the two emerging entities is observed. This behavior seems to be generic. A mathematical model is derived for the emerging solitons. It describes the new oscillatory phenomenon extremely well. Surprisingly, the model is in fact an exact solution to the initial equations. This comes as a bonus.

Two-dimensional solitons in media with stripe-shaped nonlinearity modulation.

We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. It is known from recent works that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result crucially depends on the transverse shape of the stripe: while the rectangular profile supports stable 2D solitons, its smooth Gaussian-shaped counterpart makes all the solitons unstable. This difference is explained, in particular, by the VA. The double stripe with the rectangular profile admits stable solitons of three distinct types: symmetric and asymmetric ones with a single-peak, and double-peak symmetric solitons. The shape and stability of the single-peak solitons of either type are accurately predicted by the VA. Collisions between identical stable solitons are briefly considered too, by means of direct simulations. Depending on the collision velocity, we observe excitation of intrinsic oscillations of the solitons, or their decay, or the collapse (catastrophic self-focusing).

Simulation of a single collision of two bose-einstein condensates.

We propose a method for simulating a single realization of a collision of two Bose-Einstein condensates. Recently [Phys. Rev. Lett. 94, 200401 (2005)], we introduced a quantum model of incoherent elastic scattering in a collision of two counterpropagating atomic Gaussian wave packets. Here we show that this model is capable of generating data that can be interpreted as results of a single collisional event. We find a range of parameters, including relative velocity, population, and the size of colliding condensates, where the structure of the halo of scattered atoms in a single realization strongly differs from that averaged over many realizations.

Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays.

We predict a sharp crossover from nonlinear self-defocusing to discrete self-trapping of a narrow Gaussian beam with the increase of the refractive index contrast in a periodic photonic lattice. We demonstrate experimentally nonlinear discrete localization of light with defocusing nonlinearity by single site excitation in LiNbO(3) waveguide arrays.