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1.
Opt Lett ; 49(8): 1923-1926, 2024 Apr 15.
Article in English | MEDLINE | ID: mdl-38621040

ABSTRACT

In this paper, we investigate a two-dimensional photonic array featuring a circular shape and an alternating gain and loss pattern. Our analysis revolves around determining the presence and resilience of optical ring modes with varying vorticity values. This investigation is conducted with respect to both the array's length and the strength of the non-Hermitian parameter. For larger values of the array's length, we observe a reduction in the stability domain as the non-Hermitian parameter increases. Interestingly, upon increasing the vorticity of the optical modes, full stability windows emerge for shorter lattice size regime.

2.
Phys Rev E ; 104(2-1): 024219, 2021 Aug.
Article in English | MEDLINE | ID: mdl-34525531

ABSTRACT

We examine the linear and nonlinear modes of a one-dimensional nonlinear electrical lattice, where the usual discrete Laplacian is replaced by a fractional discrete Laplacian. This induces a long-range intersite coupling that, at long distances, decreases as a power law. In the linear regime, we compute both the spectrum of plane waves and the mean-square displacement (MSD) of an initially localized excitation, in closed form in terms of regularized hypergeometric functions and the fractional exponent. The MSD shows ballistic behavior at long times, MSD∼t^{2} for all fractional exponents. When the fractional exponent is decreased from its standard integer value, the bandwidth decreases and the density of states shows a tendency towards degeneracy. In the limit of a vanishing exponent, the system becomes completely degenerate. For the nonlinear regime, we compute numerically the low-lying nonlinear modes, as a function of the fractional exponent. A modulational stability computation shows that, as the fractional exponent decreases, the number of electrical discrete solitons generated also decreases, eventually collapsing into a single soliton.

3.
Sci Rep ; 11(1): 10044, 2021 May 11.
Article in English | MEDLINE | ID: mdl-33976370

ABSTRACT

We examine a fractional discrete nonlinear Schrodinger dimer, where the usual first-order derivative in the time evolution is replaced by a non integer-order derivative. The dimer is nonlinear (Kerr) and [Formula: see text]-symmetric, and for localized initial conditions we examine the exchange dynamics between both sites. By means of the Laplace transformation technique, the linear [Formula: see text] dimer is solved in closed form in terms of Mittag-Leffler functions, while for the nonlinear regime, we resort to numerical computations using the direct explicit Grunwald algorithm. In general, we see that the main effect of the fractional derivative is to produce a monotonically decreasing time envelope for the amplitude of the oscillatory exchange. In the presence of [Formula: see text] symmetry, the oscillations experience some amplification for gain/loss values below some threshold, while beyond threshold, the amplitudes of both sites grow unbounded. The presence of nonlinearity can arrest the unbounded growth and lead to a selftrapped state. The trapped fraction decreases as the nonlinearity is increased past a critical value, in marked contrast with the standard (non-fractional) case.

4.
Opt Lett ; 46(10): 2256-2259, 2021 May 15.
Article in English | MEDLINE | ID: mdl-33988558

ABSTRACT

We examine the existence and stability of nonlinear discrete vortex solitons in a square lattice when the standard discrete Laplacian is replaced by a fractional version. This creates a new, to the best of our knowledge, effective site-energy term, and a coupling among sites, whose range depends on the value of the fractional exponent $\alpha$, becoming effectively long range at small $\alpha$ values. At long distance, it can be shown that this coupling decreases faster than exponentially: $\sim\exp (- |{\textbf{n}}|)/\sqrt {|n|}$. In general, we observe that the stability domain of the discrete vortex solitons is extended to lower power levels, as the $\alpha$ coefficient diminishes, independently of their topological charge and/or pattern distribution.

5.
Opt Lett ; 45(13): 3569-3572, 2020 Jul 01.
Article in English | MEDLINE | ID: mdl-32630901

ABSTRACT

We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schrödinger equation. In particular, we analyze the existence and stability of vortex-type solutions finding localized patterns with symmetric and asymmetric profiles, ranging from topological charge S=1 to S=3. By taking into account the presence of anisotropy, which is inherent to experimental realization of waveguide arrays, we identify different stability behaviors according to their topological charge. Our findings might give insight into experimental feasibility to observe these kinds of vortex states.

6.
Sci Rep ; 10(1): 5229, 2020 Mar 23.
Article in English | MEDLINE | ID: mdl-32251317

ABSTRACT

We study the transport properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the bands leading to a linear form of selftrapping. In the strong nonlinearity regime, the dynamics of the excitations depends strongly on the local environment around the initial excitation site that leads to a highly fluctuating selfrapping profile. For a binary nonlinear disorder, it is shown that the spreading of the flat band fundamental mode, is completely inhibited for a finite fraction of all cases. This fraction corresponds to the fraction of times the same value of (random) nonlinearity is assigned to all sites of the fundamental mode.

7.
Phys Rev E ; 100(4-1): 042214, 2019 Oct.
Article in English | MEDLINE | ID: mdl-31770892

ABSTRACT

We examine a one-dimensional nonlinear (Kerr) waveguide array which contains a single "void" waveguide where the nonlinearity is identically zero. We uncover a family of nonlinear localized modes centered at or near the void, and their stability properties. Unlike a usual impurity problem, here the void acts like a repulsive impurity causing the center of the simplest mode to lie to the side of the void's position. We also compute the stability of extended nonlinear modes showing significant differences from the usual homogeneous nonlinear array. The transmission of a nonlinear pulse across the void shows three main regimes-transmission, reflection, and trapping at the void's position-and we identify a critical momentum for the pulse below (above) where the pulse gets reflected (transmitted), or trapped indefinitely at the void's position. For relatively wide pulses, we observe a steep increase from a regime of no transmission to a regime of high transmission, as the amplitude of the soliton increases beyond a critical wave-vector value. Finally, we consider the transmission of an extended nonlinear wave across the void impurity numerically, finding a rather complex structure of the transmission as a function of wave vector, with the creation of more and more transmission gaps as nonlinearity increases. The overall transmittance decreases and disappears eventually, where the boundaries separating passing from nonpassing regions are complex and fractal-like.

8.
Sci Rep ; 8(1): 17330, 2018 Nov 26.
Article in English | MEDLINE | ID: mdl-30478353

ABSTRACT

We propose a generalization of the Su-Schrieffer-Heeger (SSH) model of the bipartite lattice, consisting of a periodic array of domain walls. The low-energy description is governed by the superposition of localized states at each domain wall, forming an effective mono-atomic chain at a larger scale. When the domain walls are dimerized, topologically protected edge states can appear, just like in the original SSH model. These new edge states are formed exclusively by soliton-like states and therefore, the new topological states are qualitatively different from the regular SSH edge states. They posses a much longer localization length and are more resistant to on-site disorder, in marked contrast to the standard SSH case.

9.
J Phys Condens Matter ; 30(37): 375602, 2018 Sep 19.
Article in English | MEDLINE | ID: mdl-30074488

ABSTRACT

We study the electron transport in a deformable lattice modeled in the semiclassical approximation as a discrete nonlinear elastic chain where acoustic phonons are in thermal equilibrium at temperature T. We reveal that an effective dynamic disorder induced in the system due to thermalized phonons is not strong enough to produce Anderson localization. However, for weak nonlinearity we observe a transition between ballistic (low T) and diffusive (high T) regimes, while for strong nonlinearity the transition occurs between the localized soliton (low T) and diffusive (high T) regimes. Thus, the electron-phonon interaction results in weak temperature-dependent dynamic localization.

10.
Sci Rep ; 8(1): 2186, 2018 02 01.
Article in English | MEDLINE | ID: mdl-29391465

ABSTRACT

We study the bulk and surface nonlinear modes of a modified one-dimensional discrete nonlinear Schrödinger (mDNLS) equation. A linear and a modulational stability analysis of the lowest-order modes is carried out. While for the fundamental bulk mode there is no power threshold, the fundamental surface mode needs a minimum power level to exist. Examination of the time evolution of discrete solitons in the limit of strongly localized modes, suggests ways to manage the Peierls-Nabarro barrier, facilitating in this way a degree of soliton steering. The long-time propagation of an initially localized excitation shows that, at long evolution times, nonlinear effects become negligible and as a result, the propagation becomes ballistic. The qualitative similarity of the results for the mDNLS to the ones obtained for the standard DNLS, suggests that this kind of discrete soliton is an robust entity capable of transporting an excitation across a generic discrete medium that models several systems of interest.

11.
J Phys Condens Matter ; 29(47): 475801, 2017 Nov 29.
Article in English | MEDLINE | ID: mdl-28976358

ABSTRACT

In this work we study analytically and numerically the spectrum and localization properties of three quasi-one-dimensional (ribbons) split-ring resonator arrays which possess magnetic flatbands, namely, the stub, Lieb and kagome lattices, and how their spectra are affected by the presence of perturbations that break the delicate geometrical interference needed for a magnetic flatband to exist. We find that the stub and Lieb ribbons are stable against the three types of perturbations considered here, while the kagome ribbon is, in general, unstable. When losses are incorporated, all flatbands remain dispersionless but become complex, with the kagome ribbon exhibiting the highest loss rate. The stability of flatband modes of certain split-ring resonator arrays suggests that they could be used as components of future stable magnetic storage devices.

12.
Phys Rev E ; 93(3): 032205, 2016 Mar.
Article in English | MEDLINE | ID: mdl-27078342

ABSTRACT

We examine the transport of extended and localized excitations in one-dimensional linear chains populated by linear and nonlinear symmetric identical n-mers (with n=3, 4, 5, and 6), randomly distributed. First, we examine the transmission of plane waves across a single linear n-mer, paying attention to its resonances, and looking for parameters that allow resonances to merge. Within this parameter regime we examine the transmission of plane waves through a disordered and nonlinear segment composed by n-mers randomly placed inside a linear chain. It is observed that nonlinearity tends to inhibit the transmission, which decays as a power law at long segment lengths. This behavior still holds when the n-mer parameters do not obey the resonance condition. On the other hand, the mean square displacement exponent of an initially localized excitation does not depend on nonlinearity at long propagation distances z, and shows a superdiffusive behavior ∼z(1.8) for all n-mers, when parameters obey the resonance merging condition; otherwise the exponent reverts back to the random dimer model value ∼z(1.5).

13.
Phys Rev Lett ; 114(24): 245503, 2015 Jun 19.
Article in English | MEDLINE | ID: mdl-26196986

ABSTRACT

We present the first experimental demonstration of a new type of localized state in the continuum, namely, compacton-like linear states in flat-band lattices. To this end, we employ photonic Lieb lattices, which exhibit three tight-binding bands, with one being perfectly flat. Discrete predictions are confirmed by realistic continuous numerical simulations as well as by direct experiments. Our results could be of great importance for fundamental physics as well as for various applications where light needs to be conducted in a diffractionless and localized manner over long distances.

14.
Article in English | MEDLINE | ID: mdl-24730959

ABSTRACT

We examine the PT-symmetry-breaking transition for a magnetic metamaterial of a finite extent, modeled as an array of coupled split-ring resonators in the equivalent circuit model approximation. Small-size arrays are solved completely in closed form, while for arrays larger than N=5 results were computed numerically for several gain and loss spatial distributions. In all cases, it is found that the parameter stability window decreases rapidly with the size of the array, until at N=20 approximately it is not possible to support a stable PT-symmetric phase.

15.
Article in English | MEDLINE | ID: mdl-23848755

ABSTRACT

We explore the fundamental question of the critical nonlinearity value needed to dynamically localize energy in discrete nonlinear cubic (Kerr) lattices. We focus on the effective frequency and participation ratio of the profile to determine the transition into localization in one-, two-, and three-dimensional lattices. A simple and general criterion is developed, for the case of an initially localized excitation, to define the transition region in parameter space ("dynamical tongue") from a delocalized to a localized profile. We introduce a method for computing the dynamically excited frequencies, which helps us validate our stationary ansatz approach and the effective frequency concept. A general analytical estimate of the critical nonlinearity is obtained, with an extra parameter to be determined. We find this parameter to be almost constant for two-dimensional systems and prove its validity by applying it successfully to two-dimensional binary lattices.

16.
Opt Express ; 21(1): 927-34, 2013 Jan 14.
Article in English | MEDLINE | ID: mdl-23388986

ABSTRACT

We show, numerically and experimentally, that the presence of weak disorder results in an enhanced energy distribution of an initially localized wave-packet, in one- and two-dimensional finite lattices. The addition of a focusing nonlinearity facilitates the spreading effect even further by increasing the wave-packet effective size. We find a clear transition between the regions of enhanced spreading (weak disorder) and localization (strong disorder).

17.
Phys Rev Lett ; 108(7): 070401, 2012 Feb 17.
Article in English | MEDLINE | ID: mdl-22401179

ABSTRACT

We introduce a novel concept of surface bound states in the continuum, i.e., surface modes embedded into the linear spectral band of a discrete lattice. We suggest an efficient method for creating such surface modes and the local bounded potential necessary to support the embedded modes. We demonstrate that the surface embedded modes are structurally stable, and the position of their eigenvalues inside the spectral band can be tuned continuously by adding weak nonlinearity.

18.
Opt Lett ; 35(17): 2895-7, 2010 Sep 01.
Article in English | MEDLINE | ID: mdl-20808361

ABSTRACT

We analyze localization of light in honeycomb photonic lattices restricted in one dimension, which can be regarded as an optical analog of graphene nanoribbons. We discuss the effect of lattice topology on the properties of discrete solitons excited inside the lattice and at its edges. We discuss a type of soliton bistability, geometry-induced bistability, in the lattices of a finite extent.

19.
Opt Lett ; 35(16): 2738-40, 2010 Aug 15.
Article in English | MEDLINE | ID: mdl-20717441

ABSTRACT

We experimentally study light localization at phase-slip waveguides and at the intersection of phase slips in a two-dimensional (2D) square photonic lattice. Such systems allow for the observation of a variety of effects, including the existence of spatially localized modes for low powers, the generation of strongly localized states in the form of discrete bulk and surface solitons, as well as a crossover between one-dimensional and 2D localization.

20.
Opt Lett ; 34(18): 2721-3, 2009 Sep 15.
Article in English | MEDLINE | ID: mdl-19756083

ABSTRACT

We study a waveguide array with an embedded nonlinear saturable impurity. We solve the impurity problem in closed form and find the nonlinear localized modes. Next, we consider the scattering of a small-amplitude plane wave by a nonlinear impurity mode, and discover regions in parameter space where transmission is fully suppressed. We relate these findings with Fano resonances and propose this setup as a means to control the transport of light across the array.

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