Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity

Controlled Transport Based on Multiorbital Aharonov-Bohm Photonic Caging

The induction of synthetic magnetic fields on lattice structures allows an effective control of their localization and transport properties. In this Letter, we generate effective π magnetic fluxes on a multiorbital diamond lattice, where first-order (S) and second-order (P) modes effectively interact. We implement a z-scan method on femtosecond-laser-written photonic lattices and experimentally observe Aharonov-Bohm caging for S and P modes, as a consequence of a band transformation and the emergence of a spectrum composed of three degenerated flat bands. As an application, we demonstrate a perfect control of the dynamics, where we translate an input excitation across the lattice in a completely linear and controlled way. Our model, based on a flat band spectrum, allows us to choose the direction of transport depending on the excitation site or input phase.

Dissipative switching waves and solitons in the systems with spontaneously broken symmetry

The paper addresses the bistability caused by spontaneous symmetry breaking bifurcation in a one-dimensional periodically corrugated nonlinear waveguide pumped by coherent light at normal incidence. The formation and the stability of the switching waves connecting the states of different symmetries are studied numerically. It is shown that the switching waves can form stable resting and moving bound states (dissipative solitons). The protocols of the creation of the discussed nonlinear localized waves are suggested and verified by numerical simulations.

Jackiw-Rebbi states and trivial states in interfaced binary waveguide arrays with cubic-quintic nonlinearity

We systematically investigate two types of localized states-one is the optical analog of the quantum relativistic Jackiw-Rebbi states and the other is the trivial localized state-in interfaced binary waveguide arrays in the presence of cubic-quintic nonlinearity. By using the shooting method, we can exactly calculate the profiles of these nonlinear localized states. Like in the case with Kerr nonlinearity, we demonstrate that these localized states with cubic-quintic nonlinearity also have an extraordinary property, which completely differs from many well-known nonlinear localized structures in other media. Specifically, both the peak amplitude and transverse dimension of these nonlinear localized states can increase at the same time. Apart from that, we show that high values of the saturation nonlinearity parameter can help to generate and stabilize the intense localized states during propagation, especially in the case with a negative coefficient for the cubic nonlinearity term.

Asymmetric wave transmission through one dimensional lattices with cubic-quintic nonlinearity

One dimensional lattice with an on-site cubic-quintic nonlinear response described by a cubic-quintic discrete nonlinear Schrödinger equation is tested for asymmetric wave propagation. The lattice is connected to linear side chains. Asymmetry is introduced by breaking the mirror symmetry of the lattice with respect to the center of the nonlinear region. Three cases corresponding to dimer, trimer and quadrimer are discussed with focus on the corresponding diode-like effect. Transmission coefficients are analytically calculated for left and right moving waves via backward transfer map. The different transmission coefficients for the left and right moving waves impinging the lattice give rise to a diode-like effect which is tested for different variations in asymmetry and site dependent coefficients. We show that there is a higher transmission for incoming waves with lower wavenumbers as compared to the waves with comparatively larger wavenumbers and a diode-like effect improves by increasing the nonlinear layers. We also show that in the context of transport through such lattices, the cooperation between cubic and quintic nonlinear response is not “additive”. Finally, we numerically analyse Gaussian wave packet dynamics impinging on the CQDNLS lattice for all three cases.

Asymmetric soliton mobility in competing linear-nonlinear parity-time-symmetric lattices

We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such a range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. For a given initial phase tilt, the velocity of soliton motion grows with an increase of the balanced gain/losses. In this regime of enhanced mobility, tilted solitons can efficiently drag other solitons that were initially at rest to form moving soliton pairs.

Interaction potential between discrete solitons in waveguide arrays

Using a variational approach, we obtained the interaction potential between two discrete solitons in optical waveguide arrays. The resulting potential bears the two features of soliton-soliton and soliton-waveguide interaction potentials where the former is similar to that of the continuum case and the latter is similar to the effective Pierls-Nabarro potential. The interplay between the two interaction potentials is investigated by studying its effect on the soliton molecule formation. It is found that the two solitons bind if their initial separation equals an odd number of waveguides, while they do not bind if their separation is an even number, which is a consequence of the two solitons being both either at the intersites (unstable) or being onsite (stable). We derived the equations of motion for the solitons' centre of mass and relative separation and provided analytic solutions for some specific cases. Favourable agreement between the analytical and numerical interaction potentials is obtained. Possible applications of our results to all-optical logic gates are pointed out.

All-optical switches, unidirectional flow, and logic gates with discrete solitons in waveguide arrays

We propose a mechanism by which a number of useful all-optical operations, such as switches, diodes, and logic gates, can be performed with a single device. An effective potential well is obtained by modulating the coupling between the waveguides through their separations. Depending on the power of a control soliton injected through the potential well, an incoming soliton will either completely transmit or reflect forming a controllable switch. We show that two such switches can work as AND, OR, NAND, and NOR logic gates. Furthermore, the same device may also function as a perfect soliton diode with adjustable polarity. We discuss the feasibility of realising such devices with current experimental setups.

Stability of optical solitons in parity-time-symmetric optical lattices with competing cubic and quintic nonlinearities

The existence and stability of optical solitons in the semi-infinite gap of parity-time (PT)-symmetric optical lattices with competing cubic and quintic nonlinearities are investigated numerically. The fundamental and dipole solitons can exist only with focusing quintic nonlinearity; however, they are always linearly unstable. With the competing effect between cubic and quintic nonlinearities, the strength of the quintic nonlinearity should be larger than a threshold for the solitons' existence when the strength of the focusing cubic nonlinearity is fixed. The stability of both fundamental and dipole solitons is studied in detail. When the strength of the focusing quintic nonlinearity is fixed, solitons can exist at the whole interval of the strength of the cubic nonlinearity, but only a small part of the fundamental solitons are stable. We also study numerically nonlinear evolution of stable and unstable PT solitons under perturbation.

Mobility of discrete multibreathers in the exciton dynamics of the Davydov model with saturable nonlinearities

We show that the state of amide-I excitations in proteins is modeled by the discrete nonlinear Schrödinger equation with saturable nonlinearities. This is done by extending the Davydov model to take into account the competition between local compression and local dilatation of the lattice, thus leading to the interplay between self-focusing and defocusing saturable nonlinearities. Site-centered (sc) mode and/or bond-centered mode like discrete multihump soliton (DMHS) solutions are found numerically and their stability is analyzed. As a result, we obtained the existence and stability diagrams for all observed types of sc DMHS solutions. We also note that the stability of sc DMHS solutions depends not only on the value of the interpeak separation but also on the number of peaks, while their counterpart having at least one intersite soliton is instable. A study of mobility is achieved and it appears that, depending on the higher-order saturable nonlinearity, DMHS-like mechanism for vibrational energy transport along the protein chain is possible.