We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials(MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single- and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective "management" scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.
We study the influence of higher-order effects such as third order dispersion (TOD), fourth order dispersion (FOD), quintic nonlinearity (QN), self steepening (SS) and second order nonlinear dispersion (SOND) on the dynamics of dissipative soliton (DS) in metamaterials. Considering each higher-order effect as a perturbation to the system and following Lagrangian variational method, we demonstrate stable dynamics of DS as a result of the interplay between different higher-order effects. We also perform numerical analysis to confirm the analytical results.
We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform d…
In this work, we report observations of phase transitions in 2D multistable mechanical metamaterials that are initiated by collisions of soliton-like pulses in the metamaterial. Analogous to first-order phase transitions in crystalline solids, we experimentally and numerically observe that the multistable metamaterials support phase transitions if the new phase meets or exceeds a critical nucleus size. If this criterion is met, the new phase subsequently propagates in the form of transition waves, converting the rest of the metamaterial to the new phase. More interestingly, we observe that the…
We present an analysis of modulational instability of diffractionless waves in a face-centered square lattice of waveguides featuring non-Kerr nonlinearity, which are constituted by a combination of positive and negative refractive indices. The unit cell of the lattice consists of three different waveguides with different optical properties. The dispersion curve of the lattice supports flat bands and thereby the base equations describing the model have particular solutions that correspond to the diffractionless waves propagating along the waveguides. We also observe a unique ramification of no…
We introduce a scheme of a photonic coupler built of two parallel topological-insulator slab waveguides with the intrinsic Kerr nonlinearity, separated by a gap. Josephson oscillations (JO) of a single edge soliton created in one slab, and of a pair of solitons created in two slabs, are considered. The single soliton jumping between the slabs is subject to quick radiative decay. On the other hand, the JO of the copropagating soliton pair may be essentially more robust, as one soliton can absorb dispersive waves emitted by the other. The most robust JO regime is featured by the pair of solitons…
Gas-filled hollow-core photonic crystal fibers offer unprecedented opportunities to observe novel nonlinear phenomena. The various properties of gases that can be used to fill these fibers give additional degrees of freedom for investigating nonlinear pulse propagation in a wide range of different media. In this review, we will consider some of the the new nonlinear interactions that have been discovered in recent years, in particular those which are based on soliton dynamics.
Nonlinearities in lattices with topological band structures can induce topological interfaces in the bulk of structures and give rise to bulk solitons in the topological bandgaps. Here we study a photonic Chern insulator with saturable nonlinearity and show the existence of topological bulk solitons. The fundamental bulk solitons exhibit as semi-vortex solitons, where only one pseudospin component has a nonzero vorticity. The bulk solitons have equal angular momentum at different valleys. This phenomenon is a direct outcome of the topology of the linear host lattice and the angular momentum ca…
In the present work, we explore soliton and rogue-like wave solutions in the transmission line analogue of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltagedependent and symmetric capacitance motivated by the recently developed ferroelectric barium strontium titanate (BST) thin film capacitor designs. We develop both the corresponding nonlinear dynamical lattice, as well as its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocus…
We predict that photonic moiré patterns created by two mutually twisted periodic sublattices in quadratic nonlinear media allow the formation of parametric solitons under conditions that are strongly impacted by the geometry of the pattern. The question addressed here is how the geometry affects the joint trapping of multiple parametrically-coupled waves into a single soliton state. We show that above the localization-delocalization transition the threshold power for soliton excitation is drastically reduced relative to uniform media. Also, the geometry of the moiré pattern shifts the conditio…
