Bistability and stationary gap solitons in quasiperiodic photonic crystals based on Thue–Morse sequence

The nonlinear properties of quasiperiodic photonic crystals based on the Thue–Morse sequence are investigated. The intrinsic asymmetry of these one-dimensional structures for odd generation numbers results in bistability thresholds which are sensitive to propagation direction. Along with resonances of perfect transmission, this feature allows to obtain strongly nonreciprocal propagation and to create an all-optical diode. The efficiency of two schemes is compared: passive and active when an additional short pump signal is applied to the system. The existence of stationary gap solitons in quasiperiodic photonic crystals is shown numerically, and their difference from the Bragg case is emphasized.     

Disorder-induced soliton transmission in nonlinear photonic lattices

We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range in which the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.     

Higher-order surface solitons in one-dimensional Bessel optical lattices

We demonstrate the existence of higher-order solitons occurring at an interface separating two one-dimensional (1D) Bessel optical lattices with different orders or modulation depths in a defocusing medium. We show that, in contrast to homogeneous waveguides where higher-order solitons are always unstable, the Bessel lattices with an interface support branches of higher-order structures bifurcating from the corresponding linear modes. The profiles of solitons depend remarkably on the lattice parameters and the stability can be enhanced by increasing the lattice depth and selecting higher-order lattices. We also reveal that the interface model with defocusing saturable Kerr nonlinearity can support stable multi-peaked solitons. The uncovered phenomena may open a new way for soliton control and manipulation.     

Experimental evidence of guided-resonances in photonic crystals with aperiodically ordered supercells

We report on the first experimental evidence of guided resonances (GRs) in photonic crystal slabs based on aperiodically ordered supercells. Using Ammann-Beenker (quasiperiodic, eightfold symmetric) tiling geometry, we present our study on the fabrication, experimental characterization, and full-wave numerical simulation of two representative structures (with different filling parameters) operating at near-IR wavelengths (1300-1600 nm). Our results show a fairly good agreement between measurements and numerical predictions and pave the way for the development of new strategies (based on, e.g., the lattice symmetry breaking) for GR engineering.     

双原子耦合摆阵中孤子的振幅回归现象

利用带阻尼参数激励的一维双原子非线性耦合摆阵，实验上观察到局域孤子的摆幅随激励参数的变化，而呈现稳定的、准周期的、周期的或随机的现象，并在理论上用一个五次非线性Ｓｃｈｒ?ｄｉｎｇｅｒ方程来解释     

Dynamics of wave packets and soliton interaction in terms of the third-order nonlinear Schrödinger equation

We present the results of numerical study of the evolution of wave packets and envelope soliton interaction in terms of the third-order nonlinear Schrödinger equation. It is shown that an arbitrary initial pulse evolves to a few solitons and a linear quasiperiodic wave. The interaction of solitons is accompanied by the radiation of part of the wave field in the form of a linear quasiperiodic wave from the interaction region, amplification of the soliton with larger amplitude and attenuation of the soliton with smaller amplitude.     

New Rational Solutions for Relativistic Discrete Toda Lattice System

In the present work, we examine the soliton excitations in the relativistic Toda lattice model using the rotational expansion method, where the coupling between the lattice sites is varied. For specific choices of the coupling strength we proceed to analyze the nonlinear wave excitations arising in the model which are found to be dark, singular and periodic solitary wave profiles. These solitary wave profiles are admitted to show possible modulation in its amplitude.     

Photorefractive solitons embedded in gratings in centrosymmetric crystals

We investigate (1+1D) spatial optical solitons embedded in a fixed-volume grating in centrosymmetric photorefractive crystals. We numerically identify a two-parameter soliton family and deduce both its existence surface and soliton profiles. For shallow gratings, the soliton Fourier spectrum exhibits three lobes located at the reciprocal lattice points -K, 0, and K. Soliton trapping is a consequence of both the self-induced nonlinear waveguide and the grating reflectivity, which prevents the breakaway of the lateral components. To provide a preliminary evaluation of soliton stability, we also investigate the propagation of slightly perturbed soliton profiles.     

New Rational Solutions for Relativistic Discrete Toda Lattice System

In the present work, we examine the soliton excitations in the relativistic Toda lattice model using the rotational expansion method, where the coupling between the lattice sites is varied. For specific choices of the coupling strength we proceed to analyze the nonlinear wave excitations arising in the model which are found to be dark, singular and periodic solitary wave profiles. These solitary wave profiles are admitted to show possible modulation in its amplitude.     

Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices

We demonstrated that linearly and nonlinearly amplitude-modulated (chirped) harmonic lattices can support odd and even solitons in both focusing and defocusing saturable media. The modulated lattice modifies the profiles and enlarges the stability domains of solitons, comparing with the unchirped one. Twisted solitons, or “soliton trains” whose profiles exhibit multi-peak structures can also be supported by linearly and nonlinearly chirped lattices. In sharp contrast with periodic lattices, chirped lattices remarkably broaden the existence and stability domains of twisted solitons, especially for solitons with more components. While even solitons in focusing media and twisted solitons in defocusing media are unstable, odd and twisted solitons in focusing media are stable in relatively wide parameter windows. Chirped lattice can be used as a linear guidance to realize the oscillation of solitons which is impossible in unchirped lattice.     

Linear periodic and quasiperiodic anisotropic layered media with arbitrary orientation of optic axis—A numerical study

We study numerically the linear properties of periodic and quasiperiodic anisotropic layered media. Each anisotropic slab can have arbitrary orientation of optic axis. We apply the general numerical code to recover the known results for solc filters. We propose novel periodic structures where the location and width of the gaps can be controlled easily. We also study the transmission properties of a Fibonacci sequence of anisotropic layers and show the interesting features like self-similarity and scaling.     

Quasi-periodic solutions and asymptotic properties for the nonlocal Boussinesq equation

We construct the Hirota bilinear form of the nonlocal Boussinesq(nlBq) equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.     

Spatial solitons in chi(2) planar photonic crystals

We analyze light self-confinement induced by multiple nonlinear resonances in a two-dimensional chi(2) photonic crystal. With reference to second-harmonic generation in a hexagonal lattice, we show that the system can not only support two-color (1+1)D solitary waves with enhanced confinement and steering capabilities but also enable novel features such as wavelength-dependent soliton routing.     

Asymmetrical surface soliton trains

We elucidate the existence, stability and propagation dynamics of multi-spot soliton packets in focusing saturable media. Such solitons are supported by an interface beside which two harmonically photonic lattices with different modulation depths are imprinted. We show that the surface model can support stable higher-order structures in the form of asymmetrical surface soliton trains, which is in sharp contrast to homogeneous media or uniform harmonic lattice modulations where stable asymmetrical multi-peaked solitons do not exist. Surface trains can be viewed as higher-order soliton states bound together by several different lowest order solitons with appropriate relative phases. Their existence as stable objects enriches the concept of compact manipulation of several different solitons as a single entity and offers additional freedom to control the shape of solitons by adjusting the modulation depths beside the interface.     

Phase conjugation of gap solitons: A numerical study

We study the effect of a nearby phase-conjugate mirror (PCM) on the gap soliton of a Kerr non-linear periodic structure. We show that phase conjugation of the gap soliton (in the sense of replication of the amplitude profile in the reverse direction) is possible under the condition of PCM reflectivity approaching unity. This is in contrast with the results for linear structures, where the wave profiles can be conjugated for arbitrary values of the PCM reflectivity. The sensitivity of the conjugation of the gap solitons to PCM reflectivity is ascribed to the fine balance of non-linearity with dispersion, necessary for their existence.     

Resonant light scattering by optical solitons

We consider the process of light scattering by optical solitons in a planar waveguide with homogeneous and inhomogeneous refractive index cores. We observe resonant reflection (Fano resonances) as well as resonant transmission of light by optical solitons. All resonant effects can be controlled in experiment by changing the soliton intensity.     

Aperiodic crystals: A contradictio in terminis?

Although in the prevailing view a necessary condition for having a crystalline phase is lattice periodicity, it has become clear in the last decades that there are physical systems with many properties of the usual crystalline state but without three-dimensional lattice periodicity. Incommensurate modulated crystals have been known now for some time, and a couple of years ago much excitement was raised by the discovery of quasicrystals, systems with long-range order but with five-fold symmetry axes, which exclude lattice periodicity.A discussion is given of the various generalizations of the concept of lattice periodicity. In fact, these go from ordinary periodic crystal st structures to almost chaotic ones. One of these is the notion of quasiperiodicity. Section two deals with a special type of these quasiperiodic systems, tilings or space fillings with tiles or blocks of a small number of types. In section three the symmetry of quasiperiodic systems is discussed. Here the embedding into a higher-dimensional space is the key concept. Section four deals with N-dimensional crystallographic groups that occur as symmetry groups of quasiperiodic systems, so called superspace groups. In section five the diffraction from quasiperiodic systems is treated, and in section six it is shown that in some cases quasiperiodic structures may be approximated by periodic ones, and that periodic systems sometimes are more conveniently described by quasiperiodic ones. The emphasis in the symmetry discussion is on quasicrystals.This is even more so in the remaining sections. Section seven gives a brief account of the many experimental data, section eight describes what is known about the microscopic structure. Imperfections are even more important for quasiperiodic systems than for periodic ones. They are discussed in section nine.Not only microscopically do quasiperiodic systems have similarities with ordinary crystals, but also macroscopically. The morphological laws may be generalized to quasiperiodic systems, as shown in section ten. The consequences of quasiperiodicity on the physical properties is still to a large extent unclear. Mathematically they differ much from periodic systems. A discussion of a number of results is given in section eleven.     

Interaction of in-band and in-gap lattice soliton trains in optically induced two-dimensional photonic lattices

We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons (IBSs) and gap soliton trains (GSTs), in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity. It is revealed that the $\pi$-staggered phase structures of the lattice soliton trains will lead to anomalous interactions. Solely by changing their initial separations, the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained. The `negative refraction' effect of the soliton trains on the interaction is also discussed. Moreover, two interacting IBSs can merge into one GST when attraction or energy transfer happens.     

Resonant transmission of acoustic waves through an elastic plate quasiperiodically corrugated on surfaces

In this work, we study the resonant transmission of acoustic waves through a plate with quasiperiodic surface corrugations. The transmission spectrum shows peculiar transmission peaks, which cannot be simply attributed to the coherent diffraction as recognized previously in structured hard plates (without sustaining internal modes), whereas come from the resonant excitation of the coupled Stoneley surface modes in the elastic plate. The excitation frequencies can be determined by the geometrical structure factor of the quasiperiodic lattice, combining with the dispersion relation of the surface modes.     

Optical vortex solitons and soliton clusters in photonic crystal fibres

We study higher-order nonlinear modes in the form of vortex solitons and soliton clusters propagating in the waveguides created in photonic crystal fibers made of a material with the focusing Kerr nonlinearity. We find numerically different families of such nonlinear modes with a nontrivial topology and study their bifurcations. We also study the soliton stability to propagation. We demonstrate that waveguides in photonic crystal fibers may support a variety of soliton clusters with the symmetries that may differ from the lattice symmetry. We also discuss briefly the case of a dual-core coupler created by two neighboring cores in a photonic crystal fiber and find numerically the profiles of symmetric and asymmetric nonlinear modes.