Localized Gap Modes Research Articles

Fundamental and dipole gap solitons and their dynamics in the cubic–quintic fractional nonlinear Schrödinger model with a [formula omitted]-symmetric lattice

The interplay of two linear controlled terms – fractional diffraction and parity-time (PT) symmetric lattice – gives rise to unique and interesting linear Bloch gap structures within where the nonlinear localized gap modes may exist. In this study, we explore the formation and dynamics of one-dimensional gap solitons in the cubic–quintic physical model combining the fractional diffraction and PT symmetric lattice. Two classes of gap solitons, which we name the fundamental gap solitons and dipole ones, are constructed and their stability regions within the first finite gap of the associated linear Bloch spectrum are identified by means of linear-stability analysis and direct perturbed numerical simulations. We stress that the gap solitons are always unstable under the condition of PT symmetry breaking (the imaginary part of which is above 0.5). The excitations of the stable two classes of gap solitons are also investigated by using the adiabatic variation of the system’s parameters. The results predicted here shed some light on soliton physics in physical systems with combined fractional diffraction and PT symmetric lattice and the competing nonlinearities.

One-Dimensional Gap Soliton Molecules and Clusters in Optical Lattice-Trapped Coherently Atomic Ensembles via Electromagnetically Induced Transparency

In past years, optical lattices have been demonstrated as an excellent platform for making, understanding, and controlling quantum matters at nonlinear and fundamental quantum levels. Shrinking experimental observations include matter-wave gap solitons created in ultracold quantum degenerate gases, such as Bose–Einstein condensates with repulsive interaction. In this paper, we theoretically and numerically study the formation of one-dimensional gap soliton molecules and clusters in ultracold coherent atom ensembles under electromagnetically induced transparency conditions and trapped by an optical lattice. In numerics, both linear stability analysis and direct perturbed simulations are combined to identify the stability and instability of the localized gap modes, stressing the wide stability region within the first finite gap. The results predicted here may be confirmed in ultracold atom experiments, providing detailed insight into the higher-order localized gap modes of ultracold bosonic atoms under the quantum coherent effect called electromagnetically induced transparency.

Gap solitons in parity–time symmetric moiré optical lattices

Parity–time ( PT ) symmetric lattices have been widely studied in controlling the flow of waves, and recently, moiré superlattices, connecting the periodic and non-periodic potentials, have been introduced for exploring unconventional physical properties in physics, while the combination of both and nonlinear waves therein remains unclear. Here, we report a theoretical survey of nonlinear wave localizations in PT symmetric moiré optical lattices, with the aim of revealing localized gap modes of different types and their stabilization mechanism. We uncover the formation, properties, and dynamics of fundamental and higher-order gap solitons as well as vortical ones with topological charge, all residing in the finite bandgaps of the underlying linear-Bloch wave spectrum. The stability regions of localized gap modes are inspected in two numerical ways: linear-stability analysis and direct perturbance simulations. Our results provide an insightful understanding of soliton physics in combined versatile platforms of PT symmetric systems and moiré patterns.

Nonlinear localized gap modes in width-modulated Fibonacci lattices

We address the properties of nonlinear localized gap modes supported by the width-modulated Fibonacci lattices, including their existence and stability. Linear system with the width-modulated Fibonacci lattices has multiple gaps. We find the existence of different families of nonlinear localized modes in two relatively large gaps. One of the nonlinear localized gap modes originates from the upper band-edge linear mode. Such gap modes are mostly stable in their entire existence domain, except for a small region in the middle of their existence. The other two families of nonlinear modes localized in the relatively large gap are pure nonlinear modes, and they have a narrow stable region near their upper cutoff. The results of the linear stability analysis are in good agreement with that of the propagation simulations.

Nonlinear localized modes in one-dimensional nanoscale dark-state optical lattices

Abstract Optical lattices (OLs) with conventional spatial periodic λ/2, formed by interfering the counterpropagating laser beams with wavelength λ, are versatile tools to study the dynamical and static properties of ultracold atoms. OLs with subwavelength spatial structure have been realized in recent quantum-gas experiment, offering new possibility for nonlinear and quantum control of ultracold atoms at the nano scale. Herein, we study theoretically and numerically the formation, property, and dynamics of matter-wave localized gap modes of Bose–Einstein condensates loaded in a one-dimensional nanoscale dark-state OL consisted of an array of optical subwavelength barriers. The nonlinear localized modes, in the forms of on- and off-site fundamental gap solitons, and dipole ones, are demonstrated; and we uncover that, counterintuitively, these modes exhibit always a cusplike (side peaks) mode even for a deeply subwavelength adiabatic lattice, contrary to the previously reported results in conventional deep OLs where the localized gap modes are highly confined in a single lattice cell. The (in)stability features of all the predicted localized modes are verified through the linear-stability analysis and direct perturbed simulations. Our predicted results are attainable in current ultracold atoms experiments with the cutting-edge technique, pushing the nonlinear control of ultracold atoms with short-period OLs as an enabling technology into subwavelength structures.

Assessing thermodynamical properties of Al1−xGaxSb alloys and optical modes for Al1−xGaxSb/GaAs epifilms and (AlSb)m/(GaSb)n superlattices

A generalized Green's function (GF) theory is adopted in the framework of a realistic rigid-ion-model (RIM) to assess the composition, x-dependent lattice dynamics, and thermodynamical characteristics of ideal random Al1−xGaxSb alloys. For simulating phonons, the alloy parameters are achieved by interpolating the values of the RIM force constants between AlSb and GaSb without requiring any additional interactions. The outcomes of phonon dispersions ωj(q→), Debye temperature ΘD(T), and specific heat Cv(T) compare favorably well with the existing experimental and theoretical data. An established methodology of multilayer optics is also employed for modeling the far-infrared reflectance and transmission spectra of ultrathin GaSb/GaAs, AlSb/GaAs, Al1−xGaxSb/GaAs epilayers, and (AlSb)m/(GaSb)n/GaAs superlattices at near normal (θi = 0) incidence and oblique (θi ≠ 0) incidence. An accurate appraisal of the x-dependent longitudinal-optical [ωLO(Γ)] and transverse-optical [ωTO(Γ)] phonon splitting by Berreman's effect, along with the calculated GF results of localized vibrational mode (GaSb:Al) and gap mode (AlSb:Ga), is carefully integrated into the modified-random-iso-displacement model to validate the two-phonon mode behavior in Al1−xGaxSb ternary alloys.

Matter-wave gap solitons and vortices in three-dimensional parity-time-symmetric optical lattices

SummaryPast decades have witnessed the emergence and increasing expansion of parity-time ()-symmetric systems in diverse physical fields and beyond as they manifest entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional -symmetric non-Hermitian systems have recently been explored broadly; however, understanding these systems in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional optical lattices with emphasis on multidimensional gap solitons and vortices. Utilizing direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linear band gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by optical lattices in multidimensional space, thus opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems

3D Nonlinear Localized Gap Modes in Bose‐Einstein Condensates Trapped by Optical Lattices and Space‐Periodic Nonlinear Potentials

Optical lattices and Feshbach resonance management are two mighty and widely used techniques for studying, both experimentally and theoretically, various physical issues and the underlying nonlinear dynamics of Bose−Einstein condensates. Both techniques show great power for studying solitons of different types, and particularly, the former technique realizes the creation of 1D bright matter‐wave gap solitons, whose formation and properties in multidimensional systems, however, are much less known. Herein, both techniques and study are combined, theoretically and numerically, the formation and dynamics of 3D nonlinear localized gap modes, including fundamental gap solitons and their higher‐order ones as soliton clusters, as well as gap vortices with topological charge s = 1. The stability regions of all the localized gap modes are identified by means of direct perturbed numerical simulations, revealing important insights into soliton physics in multidimensional space.

Matter-Wave Gap Solitons and Vortices in Three-Dimensional Parity-Time-Symmetric Optical Lattices

Past decades have witnessed the emergence and increasing expansion of parity-time (PT )-symmetric systems in diverse physical fields and beyond as they license entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT -symmetric non-Hermitian systems have recently been explored broadly, whose understanding in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Relying on direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linearband gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems.

Two-dimensional optical gap solitons and vortices in a coherent atomic ensemble loaded on optical lattices

Coherent atomic systems, e.g., resonantly cold atomic gases within which electromagnetically induced transparency (EIT) operates, have recently received great attention, because of their remarkable scientific properties and pivotal implications. Light behavior in such systems governed by various potentials is a new and interesting research focus, but missing literally report on two-dimensional (2D) localized gap modes in coherent atomic systems loaded on optical lattices. We survey such issue in a coherent atomic gas inside where the EIT turns on, trapped by 2D optical lattices—constituted by counter-propagating far-detuned Stark laser fields, in the framework of nonlinear Schrödinger equation derived from Maxwell-Bloch equations. Using the linear stability analysis and direct perturbed evolution we address the formation, property, and stability of 2D localized gap modes of two types, gap solitons and gap vortices, in forbidden band gaps of the underlying linear Bloch-wave spectrum. The former mode is fundamental gap solitons, and the latter belongs to higher-order gap solitons with embedded topological charge. Our results are helpful not only for in-depth understanding of soliton dynamics in coherent atomic ensemble loaded on periodic potentials, but also for laying the groundwork for forthcoming applications in optical communications and quantum information processing.

Localized gap modes of coherently trapped atoms in an optical lattice.

We theoretically investigate one-dimensional localized gap modes in a coherent atomic gas where an optical lattice is formed by a pair of counterpropagating far-detuned Stark laser fields. The atomic ensembles under study emerge as Λ-type three-level configuration accompanying the effect of electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations and the multiple scales method, we derive a nonlinear equation governing the spatial-temporal evolution of the probe-field envelope. We then uncover the formation and properties of optical localized gap modes of two kinds, such as the fundamental gap solitons and dipole gap modes. Furthermore, we confirm the (in)stability regions of both localized gap modes in the respective band-gap spectrum with systematic numerical simulations relying on linear-stability analysis and direct perturbed propagation. The predicted results may enrich the nonlinear horizon to the realm of coherent atomic gases and open up a new door for optical communication and information processing.

Self-trapped spatially localized states in combined linear-nonlinear periodic potentials

We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes, gap solitons and truncated nonlinear Bloch waves, in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity, supported by a combination of linear and nonlinear periodic lattice potentials. The former is found to be stable once placed inside a single well of the nonlinear lattice, it is unstable otherwise. Contrary to the case with constant self-focusing nonlinearity, where the latter solution is always unstable, here, we demonstrate that it nevertheless can be stabilized by the nonlinear lattice since the model under consideration combines the unique properties of both the linear and nonlinear lattices. The practical possibilities for experimental realization of the predicted solutions are also discussed.

One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential

Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic–quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrödinger equation. We incorporate an external periodic potential (linear lattice) into this model and extend it to the space-fractional scenario that begins to surface in very recent years—the nonlinear fractional Schrödinger equation (NLFSE), therefore obtaining the cubic–quintic or the purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein. Two types of one-dimensional localized gap modes are found, including the fundamental and dipole-mode gap solitons. Employing the techniques based on the linear-stability analysis and direct numerical simulations, we get the stability regions of all the localized modes; and particularly, the anti-Vakhitov–Kolokolov criterion applies for the stable portions of soliton families generated in the frameworks of quintic-only nonlinearity and competing cubic–quintic nonlinear terms.

Localized gap modes in nonlinear dimerized Lieb lattices

Compact localized modes of ring type exist in many two-dimensional lattices with a flat linear band, such as the Lieb lattice. The uniform Lieb lattice is gapless, but gaps surrounding the flat band can be induced by various types of bond alternations (dimerizations) without destroying the compact linear eigenmodes. Here, we investigate the conditions under which such diffractionless modes can be formed and propagated also in the presence of a cubic on-site (Kerr) nonlinearity. For the simplest type of dimerization with a three-site unit cell, nonlinearity destroys the exact compactness, but strongly localized modes with frequencies inside the gap are still found to propagate stably for certain regimes of system parameters. By contrast, introducing a dimerization with a 12-site unit cell, compact (diffractionless) gap modes are found to exist as exact nonlinear solutions in continuation of flat band linear eigenmodes. These modes appear to be generally weakly unstable, but dynamical simulations show parameter regimes where localization would persist for propagation lengths much larger than the size of typical experimental waveguide array configurations. Our findings represent an attempt to realize conditions for full control of light propagation in photonic environments.

Nonlocal Plasmonic Response and Fano Resonances at Visible Frequencies in Sub-Nanometer Gap Coupling Regime

Plasmonic nanoassemblies endowed with ultrasmall interparticle gaps display a rich and unusual electromagnetic response both in near- and far-field readout. The properties of such systems can be mainly ascribed to the hybridization of localized surface plasmon modes, which in turn enables a higher degree of field confinement with respect to single particles. Pushing these plasmonic resonances toward stronger coupling regimes (i.e., smaller gaps) requires particular attention to the microscopic description of the system. In this article, we theoretically show that the appearing of nonlocal effects in the electromagnetic response of a plasmonic dimer in a strong coupling regime unveils a natural extension of its hybridization scheme. We demonstrate the arising of a Fano resonant interference in the visible range, resulting from the interaction of a hybrid quadrupolar mode and a highly localized gap mode.

Inverted Ultrathin Organic Solar Cells with a Quasi-Grating Structure for Efficient Carrier Collection and Dip-less Visible Optical Absorption

We propose a metallic-particle-based two-dimensional quasi-grating structure for application to an organic solar cell. With the use of oblate spheroidal nanoparticles in contact with an anode of inverted, ultrathin organic solar cells (OSCs), the quasi-grating structure offers strong hybridization between localized surface plasmons and plasmonic gap modes leading to broadband (300~800 nm) and uniform (average ~90%) optical absorption spectra. Both strong optical enhancement in extreme confinement within the active layer (90 nm) and improved hole collection are thus realized. A coupled optical-electrical multi-physics optimization shows a large (~33%) enhancement in the optical absorption (corresponding to an absorption efficiency of ~47%, AM1.5G weighted, visible) when compared to a control OSC without the quasi-grating structure. That translates into a significant electrical performance gain of ~22% in short circuit current and ~15% in the power conversion efficiency (PCE), leading to an energy conversion efficiency (~6%) which is comparable to that of optically-thick inverted OSCs (3–7%). Detailed analysis on the influences of mode hybridization to optical field distributions, exciton generation rate, charge carrier collection efficiency and electrical conversion efficiency is provided, to offer an integrated understanding on the coupled optical-electrical optimization of ultrathin OSCs.

Excitations and management of the nonlinear localized gap modes

We discuss about the theory of nonlinear localized excitations, such as soliton and compactons in the gap of the linear spectrum of the nonlinear systems. We show how the gap originates in the linear spectrum using examples of a few systems, such as nonlinear lattices, Bose–Einstein condensates in optical lattice and systems represented by coupled nonlinear evolution equations. We then analytically show the excitation of solitons and compacton-like solutions in the gap of the linear spectrum of a system of coupled Korteweg–de Vries (KdV) equations with linear and nonlinear dispersions. Finally, we discuss about the theory of Feshbach resonance management and dispersion management of the soliton solutions.

Nonlinear guided waves and spatial solitons in a periodic layered medium

We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response (a nonlinear waveguide) embedded into a periodic layered linear medium, and describe nonlinear localized modes (guided waves and Bragg-like localized gap modes) and their stability. Then, we study modulational instability as well as the existence and stability of discrete spatial solitons in a periodic array of identical nonlinear layers, a one-dimensional nonlinear photonic crystal. Both similarities and differences with the models described by the discrete nonlinear Schrodinger equation (derived in the tight-binding approximation) and coupled-mode theory (valid for the shallow periodic modulations) are emphasized.

Quantum properties of intrinsic localized modes

The quantum properties of intrinsic localized modes in perfect anharmonic lattices are considered. A method is developed which allows one to calculate the quantum levels of these modes. Calculations are presented for the lifetime of intrinsic localized gap modes in NaI and KI due to their two-phonon quantum decay.

Nonlinear Gap Modes in a 1D Alternating Bond Monatomic Lattice with Anharmonicity

We analytically study the nonlinear localized gap modes in a one-dimensional atomic chain with uniform atomic mass but two periodically alternating force constants between the nearest neighbors by means of a quasi-continuum approximation. This model simulates a row of atoms in the direction of a diamond-structure type of crystals or molecular crystals with alternating double and single bonds. For this lattice system, we find that the harmonic plus quartic anharmonic terms of inter-site potential produce a new type of nonlinear localized gap modes with a slightly asymmetry distribution of atomic displacements. These localized gap modes are somewhat different from widely studied localized gap modes with a symmetry atomic displacement distribution in diatomic ion lattices.