arXiv subjects

Mario I. Molina

Publications and source records attributed to Mario I. Molina.

At least 55 records · Page 3Linked to original sources

arXiv2011

Diffusion in infinite and semi-infinite lattices with long-range coupling

We prove that for a one-dimensional infinite lattice, with long-range coupling among sites, the diffusion of an initial delta-like pulse in the bulk, is ballistic at all times. We obtain a closed-form expression for the mean square displacement (MSD) as a function of time, and show some cases including finite range coupling, exponentially decreasing coupling and power-law decreasing coupling. For the case of an initial excitation at the edge of the lattice, we find an approximate expression for the MSD that predicts ballistic behavior at long times, in agreement with numerical results.

cond-mat.dis-nn↗

arXiv2011

Surface solitons in quasiperiodic nonlinear photonic lattices

We study discrete surface solitons in semi-infinite, one-dimensional, nonlinear (Kerr), quasiperiodic waveguide arrays of the Fibonacci and Aubry-André types, and explore different families of localized surface modes, as a function of optical power content (`nonlinearity') and quasiperiodic strength (`disorder'). We find a strong asymmetry in the power content of the mode as a function of the propagation constant, between the cases of focussing and defocussing nonlinearity, in both models. We also examine the dynamical evolution of a completely-localized initial excitation at the array surface. We find that in general, for a given optical power, a smaller quasiperiodic strength is required to effect localization at the surface than in the bulk. Also, for fixed quasiperiodic strength, a smaller optical power is needed to localize the excitation at the edge than inside the bulk.

nlin.PS↗

arXiv2011

Multiplicity of vortex soliton families in the discrete Ginzburg-Landau equation, their interactions and the formation of bound states

By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions have a symmetric amplitude profile and two different topological charges. We also discover the dynamical formation of a variety of 'bound-state' solutions, composed of two or more of these vortex solitons. All of these stable composite structures persist in the conservative cubic limit, for high values of their power content.

physics.optics↗

arXiv2011

Surface bound states in the continuum

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 such embedded modes. We demonstrate that the embedded modes are structural stable, and the position of their eigenvalues inside the spectral band can be tuned continuously by adding weak nonlinearity.

nlin.PS↗

arXiv2011

Fano resonances in magnetic metamaterials

We study the scattering of magnetoinductive plane waves by internal (external) capacitive (inductive) defects coupled to a one-dimensional split-ring resonator array. We examine a number of simple defect configurations where Fano resonances occur and study the behavior of the transmission coefficient as a function of the controllable external parameters. We find that for embedded capacitive defects, the addition of a small amount of coupling to second neighbors is necessary for the occurrence of Fano resonance. For external inductive defects, Fano resonances are commonplace, and they can be tuned by changing the relative orientation or distance between the defect and the SSR array.

physics.optics↗

arXiv2011

Nonlinear light localization around the core of a `holey' fiber

We examine localized surface modes in the core of a photonic crystal fiber composed of a finite nonlinear (Kerr) hexagonal waveguide array with a central defect. Using a discrete approach, we find the fundamental surface mode and its stability window. We also examine an unstaggered, ring-shaped surface mode and find that it is always unstable, decaying to the single-site fundamental surface mode. A continuous model computation reveals that an initial vortex excitation (S=1) of small amplitude around the central hole can survive for a relatively long evolution distance. At high amplitudes, however, it decays to a ring configuration with no well-defined phase structure.

nlin.PS↗

arXiv2011

Vortex solitons of the discrete Ginzburg-Landau Equation

We have found several families of vortex soliton solutions in two-dimensional discrete dissipative systems governed by the cubic-quintic complex Ginzburg-Landau equation. There are symmetric and asymmetric solutions, and some of them have simultaneously two different topological charges. Their regions of existence and stability are determined. Additionally, we have analyzed the relation- ship between dissipation and stability for a number of solutions. We have obtained that dissipation favours the stability of the solutions.

physics.optics↗

arXiv2010

Boundary-induced Anderson localization in photonic lattices

We analyze numerically localization of light in linear square waveguide arrays restricted in one dimension (``ribbons''), whose boundaries are disordered in propagation constant and/or coupling. We find that the disordered boundary induces a localization tendency in the bulk even for relatively wide ribbons.

physics.optics↗

arXiv2010

Dissipative vortex solitons in 2D-lattices

We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a topological charge S = 1. Surprisingly, the dynamical evolution of unstable solutions of this family does not alter significantly their profile, instead their phase distribution completely changes. They transform into two-charges swirl-vortex solitons. We dynamically excite this novel structure showing its experimental feasibility.

physics.optics↗

arXiv2010

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.

nlin.PS↗

arXiv2010

Discrete and surface solitons in photonic graphene nanoribbons

We analyze localization of light in honeycomb photonic lattices restricted in one dimension which can be regarded as an optical analog of (``armchair'' and ``zigzag'') graphene nanoribbons. We find the conditions for the existence of spatially localized states and discuss the effect of lattice topology on the properties of discrete solitons excited inside the lattice and at its edges. In particular, we discover a novel type of soliton bistability, the so-called geometry-induced bistability, in the lattices of a finite extent.

nlin.PS↗

arXiv2010

Observation of localized modes at phase slips in two-dimensional photonic lattices

We study experimentally light localization at phase-slip waveguides and at the intersection of phase-slips in a two-dimensional (2D) square photonic lattice. Such system allows to observe 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 (1D) and 2D localization.

nlin.PS↗

arXiv2009

Multistability and localization in coupled nonlinear split-ring resonators

We study the dynamics of a pair of nonlinear split-ring resonators (a `metadimer') excited by an alternating magnetic field and coupled magnetically. Linear metadimers of this kind have been recently used as the elementary components for three-dimensional metamaterials or 'stereometamaterials' [N. Liu {\em et al}, Nature Photon. {\bf 3}, 157 (2009)]. We demonstrate that nonlinearity offers more possibilities with respect to real-time tunability and a multiplicity of states which can be reached by varying the external field. Moreover, we demonstrate almost total localization of the energy in one of the resonators in a broad range of parameters.

physics.optics↗

arXiv2009

Interface solitons in quadratically nonlinear photonic lattices

We study the properties of two-color nonlinear localized modes which may exist at the interfaces separating two different periodic photonic lattices in quadratic media, focussing on the impact of phase mismatch of the photonic lattices on the properties, stability, and threshold power requirements for the generation of interface localized modes. We employ both an effective discrete model and continuum model with periodic potential and find good qualitative agreement between both models. Dynamics excitation of interface modes shows that, a two-color interface twisted mode splits into two beams with different escaping angles and carrying different energies when entering a uniform medium from the quadratic photonic lattice. The output position and energy contents of each two-color interface solitons can be controlled by judicious tuning of

nlin.PS↗

arXiv2009

Fano resonances in saturable waveguide arrays

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 mean to control the transport of light across the array.

nlin.PS↗

arXiv2009

Surface solitons in two-dimensional quadratic photonic lattices

We study two-color surface solitons in two-dimensional photonic lattices with quadratic nonlinear response. We demonstrate that such parametrically coupled optical localized modes can exist in the corners or at the edges of a square photonic lattice, and we analyze the impact of the phase mismatch on their properties, stability, and the threshold power for their generation.

nlin.PS↗

arXiv2008

Bulk and surface localized states on a magnetic nonlinear impurity

We study localized modes on a single magnetic impurity positioned in the bulk or at the surface of a one-dimensional chain, in the presence of a magnetic field $B$ acting at the impurity site. The strong on-site nonlinear interaction $U$ between two electrons of opposite spin at the impurity site, modelled here as a nonlinear local term, and the presence of the external field induce a strong correlation between parallel and anti-parallel spin bound states. We find that, for an impurity in the bulk, a localized vector mode (with up and down spin components) is always possible for any given value of $U$ and $B$, while for a surface impurity, a minimum value of both, $U$ and $B$ is needed to create a vector mode. In this case, up to two localized modes are possible, but only one of them is stable. The presence of the surface seems to destabilize the bulk mode in the parameter region U~B, creating a "forbidden strip" region in parameter space, bounded by U=B+V and U=B-V, approximately.

nlin.PS↗

arXiv2008

Interface solitons in two-dimensional photonic lattices

We analyze localization of light at the interface separating square and hexagonal photonic lattices, as recently realized experimentally in two-dimensional laser-written waveguide arrays in silica glass with self-focusing nonlinearity [A. Szameit {\em et al.}, Opt. Lett. {\bf 33}, 663 (2008)]. We reveal the conditions for the existence of {\em linear} and {\em nonlinear} surface states substantially influenced by the lattice topology, and study the effect of the different symmetries and couplings on the stability of two-dimensional interface solitons.

nlin.PS↗