Nonlinear Waveguide Arrays Research Articles

Spontaneous Parametric Down-Conversion and Quantum Walks in Arrays of Quadratic Nonlinear Waveguides

We analyze the process of photon-pair generation with simultaneous quantum walks in a quadratic nonlinear waveguide array. We demonstrate that the spontaneous parametric down-conversion in the array allows for creating quantum states with strongly pronounced spatial correlations, which are qualitatively different from those possible in bulk crystals or through quantum walks in linear waveguide arrays. Most importantly, the photon correlations can be controlled entirely classically by varying the spatial profile of the pump beam or the phase-matching conditions.

Spectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays

We study experimentally and numerically the dynamics of a recently found topological phase transition for discrete quadratic solitons with linearly coupled SH waves. We find that, although no stationary states are excited in the experimental situation, the generic feature of the phase transition of the SH is preserved. By utilizing simulations of the coupled mode equations we identify the complex processes leading to the phase transition involving spatial focusing and the generation of new frequency components. These distinct signatures of the dynamic phase transition are also demonstrated experimentally.

Surface solitons in trilete lattices

Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrödinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter—actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss.

All-optical discrete vortex switch

We introduce discrete vortex solitons and vortex breathers in circular arrays of nonlinear waveguides. The simplest vortex breather in a four-waveguide coupler is a nonlinear dynamic state changing its topological charge between $+1$ and $\ensuremath{-}1$ periodically during propagation. We find the stability domain for this solution and suggest an all-optical vortex switching scheme.

INTERFACE WAVE COMPRESSION IN NONLINEAR BI-DISPERSIVE HETERO-STRUCTURE WAVEGUIDE ARRAYS

The propagation behavior of an optical pulse is investigated at the interface of two different nonlinear bi-dispersive waveguide arrays. It is found that the peak power has a great impact on the propagation of the pulse. When the peak power is high enough, the major part of the initial pulse can be guided and confined in the interface of this waveguide array. Because of the interplay between asymmetry discrete diffraction, dispersion and Kerr nonlinearity of hetero-structure waveguide array, the output pulse develops a rectangular-like intensity profile with richer bandwidth, and its power spectrum in the frequency domain is rather uniform, i.e., less modulated. Therefore, the output pulse from the hetero-structure waveguide array can be compressed more efficiently than that of a homogeneous element.

Nonlinear beam interactions in semi-infinite waveguide arrays

The interactions between coherent beams launched near the interface of one-dimensional semi-infinite Kerr-type nonlinear waveguide arrays have been theoretically investigated. We have explored the effect of the input intensities, the relative phase of the optical beams, and the modulation of the refractive index of the optical lattices on nonlinear beam interaction dynamics. For in-phase beams with different incident intensities, the highly-localized spatial soliton was dragged in a discrete fashion by a low-intensity diffracting beam. Anomalous fusion of two out-of-phase beams, and energy exchange between the excited channels were observed at high intensities. The possibility of employing nonlinear interactions for optical signal re-addressing, all-optical switching is also discussed.

Strong asymmetry for surface modes in nonlinear lattices with long-range coupling

We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially-decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increase (decrease) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.

Coupled-mode approach to surface plasmon polaritons in nonlinear periodic structures

We present a coupled-mode theory describing light propagation in an array of nonlinear plasmonic waveguides. Our model predicts a two-band dependence of the propagation constant versus transverse quasi-momentum and existence of discrete and gap plasmon solitons.

Interface solitons in one-dimensional locally coupled lattice systems

Fundamental solitons pinned to the interface between two discrete lattices coupled at a single site are investigated. Serially and parallel-coupled identical chains (\textit{System 1} and \textit{System 2}), with the self-attractive on-site cubic nonlinearity, are considered in one dimension. In these two systems, which can be readily implemented as arrays of nonlinear optical waveguides, symmetric, antisymmetric and asymmetric solitons are investigated by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric solitons exist in the entire parameter space, while the symmetric and asymmetric modes can be found below some critical value of the coupling parameter. Numerical results confirm these predictions for the symmetric and asymmetric fundamental modes. The existence region of numerically found antisymmetric solitons is also limited by a certain value of the coupling parameter. The symmetric solitons are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric solitons, in both systems. The antisymmetric fundamental solitons, which may be stable or not, do not undergo any bifurcation. In bistability regions stable antisymmetric solitons coexist with either symmetric or asymmetric ones.

Compactons in Nonlinear Schrödinger Lattices with Strong Nonlinearity Management

The existence of compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged discrete nonlinear Schrödinger equation, the resulting effective interwell tunneling depends on the modulation parameters and on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multisite stable discrete compactons in nonlinear optical waveguide and Bose-Einstein condensate arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.

The appearance of gap solitons in a nonlinear Schrödinger lattice

We study the appearance of discrete gap solitons in a nonlinear Schrödinger model with a periodic on-site potential that possesses a gap evacuated of plane-wave solutions in the linear limit. For finite lattices supporting an anti-phase ( q = π / 2 ) gap edge phonon as an anharmonic standing wave in the nonlinear regime, gap solitons are numerically found to emerge via pitchfork bifurcations from the gap edge. Analytically, modulational instabilities between pairs of bifurcation points on this “nonlinear gap boundary” are found in terms of critical gap widths, turning to zero in the infinite-size limit, which are associated with the birth of the localized soliton as well as discrete multisolitons in the gap. Such tunable instabilities can be of relevance in exciting soliton states in modulated arrays of nonlinear optical waveguides or Bose–Einstein condensates in periodic potentials. For lattices whose gap edge phonon only asymptotically approaches the anti-phase solution, the nonlinear gap boundary splits in a bifurcation scenario leading to the birth of the discrete gap soliton as a continuable orbit to the gap edge in the linear limit. The instability-induced dynamics of the localized soliton in the gap regime is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsically localized modes (discrete breathers) from the extended out-gap soliton reveals a phase transition of the solution.

Competing nonlinearities in quadratic nonlinear waveguide arrays

We demonstrate experimentally the existence of competing focusing and defocusing nonlinearities in a double-resonant system with quadratic nonlinear response. We use an array of periodically poled coupled optical waveguides and observe inhibition of the nonlinear beam self-action independent on power. This inhibition is demonstrated in both regimes of normal and anomalous beam diffraction.

Discrete reduced-symmetry solitons and second-band vortices in two-dimensional nonlinear waveguide arrays

Considering a two-dimensional lattice of weakly coupled waveguides, where each waveguide may carry two orthogonal modes of dipolar character, we present a nonlinear discrete vector model for the study of Kerr optical solitons with profiles having a reduced symmetry relative to the underlying lattice. We describe analytically and numerically existence and stability properties of such states in square and triangular lattices and also reveal directional mobility properties of two-dimensional gap solitons which were recently observed in experiment. The model also describes one-site peaked discrete vortices corresponding to experimentally observed "second-band" vortex lattice solitons, for which oscillatory instabilities are predicted. We also introduce a concept of "rotational Peierls-Nabarro barrier" characterizing the minimum energy needed for rotation of stable dipole modes and compare numerically translational and rotational energy barriers in regimes of good mobility.

Rogue waves as spatial energy concentrators in arrays of nonlinear waveguides

In an array of nonlinear waveguides, a giant compression of the input beam can be achieved by exciting a rogue wave. Input field almost homogeneously distributed over hundreds of waveguides concentrates practically all the energy into a single waveguide at the output plane of the structure. We determine the required input profile of the electric field to achieve this. We illustrate the phenomenon by modeling the array by direct numerical simulations of the discrete nonlinear Schrödinger equation.

Beam interaction in one-dimensional inhomogeneous Kerr nonlinear arrays

The interactions between two parallel and co-polarized beams in weakly coupled cubic focusing nonlinear waveguide arrays with transverse inhomogeneous modulation of the refractive index were investigated by means of beam propagation method. Results show that the in-phase beams attract each other and coalesce when the inhomogeneous parameter is smaller than a critical value. For the out-of-phase beams, oscillations exist at low power level, and the larger inhomogeneous parameter, the larger period and amplitude of oscillation. At a high power level, solitonlike propagation of weak coupling occurs. The inhomogeneity of waveguide arrays provide a flexible way to control the interactions of beams, and may find potential applications in all-optical systems.

Gap and dark solitons in discrete photorefractive media with intensity-resonant nonlinearity

Light propagation in one-dimensional nonlinear waveguide arrays with self-defocusing intensity-resonant nonlinearity is investigated theoretically. We study thoroughly conditions for existence and stability of both gap and discrete dark solitons. According to the linear stability analysis both fundamental types (on-site and intersite) of gap solitons may be stable. Discrete dark solitons are unstable except in the low-power regime and, depending on system parameters, evolve into either gray solitons, breathers, or background radiation. Mobility of these solitons is analyzed by the free energy concept: gap solitons are immobile but dark solitons can be easily set in motion.

Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays

We study the effects associated with spatiotemporal light localization near the edge of a semi-infinite array of weakly coupled nonlinear optical waveguides. It was shown earlier that such a system can support the existence of a novel class of $(2+1)$-dimensional continuous-discrete spatiotemporal solitons, which are stable in a broad region of their parameters. We analyze the collisions between this type of spatiotemporal optical solitons and demonstrate that such collisions are strongly affected by the presence of the surface. In particular, since these solitons can be located at different distances from the edge of the waveguide array, we observe a variety of collision scenarios and different outcomes. In addition to well-known scenarios of soliton fusion and symmetric scattering, we get strongly asymmetric outcomes that can be understood as soliton switching.

Geometry and transport in a model of two coupled quadratic nonlinear waveguides

This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled chi((2)) waveguides is modeled and analyzed in terms of transport and geometry in the phase space. This gives us a transport problem in the phase space resulting from the coupling of the two Hamiltonian systems for each waveguide. In particular, the effect of the presence of partial and complete barriers in the phase space on the transfer of intensity between the waveguides is studied, given a specific input and range of material properties. We show how these barriers break down as the coupling between the waveguides is increased and what the role of resonances in the phase space has in this. We also show how an increase in the coupling can lead to chaos and global transport and what effect this has on the intensity.

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.

Dispersive Shock Waves in Nonlinear Arrays

We experimentally study dispersive shock waves in nonlinear waveguide arrays. In contrast with gap solitons, the nonlinearity here pushes the propagation constant further into the transmission bands, facilitating Bloch mode coupling and energy transport. We directly observe this coupling, both within and between bands, by recording intensity in position space and power spectra in momentum space.