Subwavelength plasmonic lattice solitons in arrays of metallic nanowires

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings

This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

Soliton-like surface plasmon polaritons generated on the surface of a silver nanowire embedded in a Kerr nonlinear medium

The behavior of surface plasmon polaritons (SPPs) generated on the surface of a silver nanowire by coaxial Gaussian beams in Kerr nonlinear mediums is studied numerically. Enhancement of the propagation of the SPPs is realized due to the introduction of the nonlinear effect. Further adjusting the nonlinearity or the beam's intensity results in a soliton-like propagation of SPPs. This can be explained by the nonlinear self-focusing effect transferring more light into SPP modes and counteracting the attenuation caused by the absorption of metal. This result may contribute to SPP-based applications where an enhanced propagation length is needed.

Discrete optics in optomechanical waveguide arrays

The propagation properties of light in optomechanical waveguide arrays (OMWAs) are studied. Due to the strong mechanical Kerr effect, the optical self-focusing and self-defocusing phenomena can be realized in the arrays of subwavelength dielectric optomechanical waveguides with the milliwatt-level incident powers and micrometer-level lengths. Compared with the conventional nonlinear waveguide arrays, the required incident powers and lengths of the waveguides are decreased by five orders of magnitude and one order of magnitude, respectively. Furthermore, by adjusting the deformation of the nanowaveguides through a control light, the propagation path of the signal light in the OMWA can be engineered, which could be used as a splitting-ratio-tunable beam splitter. This Letter provides a new platform for discrete optics and broadens the application of integrated optomechanics.

Semidiscrete Quantum Droplets and Vortices

We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state), stable on-site- and intersite-centered semidiscrete quantum droplets (QDs) emerge in the array, as fundamental ones and self-trapped vortices, with winding numbers, at least, up to five, in both tightly bound and quasicontinuum forms. The application of a relatively strong trapping potential leads to squeezing transitions, which increase the number of sites in fundamental QDs and eventually replace vortex modes by fundamental or dipole ones. The results provide the first realization of stable semidiscrete vortex QDs, including ones with multiple vorticity.

Subwavelength topological edge states based on localized spoof surface plasmonic metaparticle arrays

Plasmonic cluster arrays have demonstrated rich physics in topological photonics, but they are seriously affected by the material loss and limited by the requirement of high-precision machining. Here, we propose a kind of ultra-thin metaparticle arrays which can mimic the coupled localized plasmonic resonances at lower frequency ranges and so that can overcome the loss and fabrication problems in real metal plasmonic systems. The metaparticle is a metallic disk with circuitous grooves that can support both spoof electric and magnetic localized resonances, and these resonances can be pushed to a subwavelength region through tuning the geometric parameters. In virtue of the highly field confinement of these localized resonances, it is thought to be an ideal experimental platform to be an analogy with various near-field interactions in topological materials. As a first proof-of-concept study to show this feasibility, the subwavelength topological edge states at the zigzag metaparticle chain boundaries are numerically and experimentally demonstrated at microwave ranges. Moreover, the subwavelength topological edge states in this zigzag chain can be excited simply by the plane wave incidence, and the edge modes at two ends can be selectively excited by controlling the polarization direction. Therefore, this kind of metaparticle array not only provides an ideal platform to experimentally study various near-filed interaction dominated topological systems but may also find massive potential applications.

Dynamics of Gaussian beam modeled by fractional Schrödinger equation with a variable coefficient

In the paper, we investigate the propagation dynamics of the Gaussian beam modeled by the fractional Schrödinger equation (FSE) with a variable coefficient. In the absence of the beam's chirp, for smaller Lévy index, the Gaussian beam firstly splits into two beams, however under the action of the longitudinal periodic modulation, they exhibit a periodically oscillating behaviour. And with the increasing of the Lévy index, the splitting behaviour gradually diminishes. Until the Lévy index equals to 2, the splitting behaviour is completely replaced by a periodic diffraction behaviour. In the presence of the beam's chirp, one of the splitting beams is gradually suppressed with the increasing of the chirp, while another beam on the opposite direction becomes stronger and exhibits a periodically oscillating behaviour. Also, the oscillating amplitude and period are investigated and the results show that the former is dependent on the modulation frequency, the Lévy index and the beam's chirp, the latter depends only on the modulation frequency. Thus, the evolution of the Gaussian beam can be well manipulated to achieve the beam management in the framework of the FSE by controlling the system parameters and the chirp parameter.

A comparative analysis of surface and bulk contributions to second-harmonic generation in centrosymmetric nanoparticles

Second-harmonic generation (SHG) from nanoparticles made of centrosymmetric materials provides an effective tool to characterize many important properties of photonic structures at the subwavelength scale. Here we study the relative contribution of surface and bulk effects to SHG for plasmonic and dielectric nanostructures made of centrosymmetric materials in both dispersive and non-dispersive regimes. Our calculations of the far-fields generated by the nonlinear surface and bulk currents reveal that the size of the nanoparticle strongly influences the amount and relative contributions of the surface and bulk SHG effects. Importantly, our study reveals that, whereas for plasmonic nanoparticles the surface contribution is always dominant, the bulk and surface SHG effects can become comparable for dielectric nanoparticles, and thus they both should be taken into account when analyzing nonlinear optical properties of all-dielectric nanostructures.

Plasmonic topological insulators for topological nanophotonics

Photonic topological insulators are optical structures supporting robust propagation of light at their edges that are topologically protected from scattering. Here we propose the concept of plasmonic topological insulators (PTI) that not only topologically protect light at the lattice edges but also enable their confinement and guidance at the deep-subwavelength scale. The suggested PTI are composed of an evanescently coupled array of metallic nanowires that are modulated periodically along the light propagation direction. The intrinsic loss associated with the PTI is found not to deteriorate their topological protection on the edge modes. The proposed PTI may find interesting applications in nanophotonics, where the tolerance to the fabrication disorders for device applications are essential.

General analytic expression and numerical approach for the Kerr nonlinear coefficient of optical waveguides

The Kerr nonlinear coefficient γ is a key parameter that quantifies the nonlinear strength of an optical waveguide. For lossy waveguides such as plasmonic waveguides, the literature is confusing because various expressions derived by different groups have generally not been validated, and the conditions when they apply are not explicitly specified. Here we derive a rigorous and full-vectorial model, leading to both a general analytic expression and a general numerical approach for finding γ, as well as to their underlying relationship. Our results, exemplified by lossless and lossy waveguides, are consistent not only with each other, but also with the results in literature under appropriate limiting conditions. This work provides a benchmarked framework to understand and engineer nonlinear nanophotonic devices.

Discrete plasmonic solitons in graphene-coated nanowire arrays

We study the discrete soliton formation in one- and two-dimensional arrays of nanowires coated with graphene monolayers. Highly confined solitons, including the fundamental and the higher-order modes, are found to be supported by the proposed structure with a low level of power flow. Numerical analysis reveals that, by tuning the input intensity and Fermi energy, the beam diffraction, soliton dimension and propagation loss can be fully controlled in a broad range, indicating potential values of the graphene-based solitons in nonlinear/active nanophotonic systems.

Tunable Anderson localization in disorder graphene sheet arrays

We study the electromagnetic wave propagating in coupled monolayer graphene waveguide arrays (CMGWAs). It is found that Anderson localization exists when the disorder in the coupling strength between adjacent waveguides is introduced. We find that changing the statistical parameters of the disorder coupling strength between waveguides can be used to tailor the properties of the Anderson localization modes in the strong coupling region which is beyond the coupled-mode theory. Benefiting from the electric tunable surface conductivity, we further demonstrate via the full vectorial simulation that the localization strength of the Anderson localized mode can be manipulated by changing the applied gate voltage on the CMGWAs. Our results might facilitate the manipulation of electromagnetic wave propagation in the coupled waveguide array system.

Plasmonic lattice solitons in nonlinear graphene sheet arrays

We investigate the plasmonic lattice solitons (PLSs) in nonlinear graphene sheet arrays (GSAs) composed of spatially separated graphene sheets embedded in dielectric. Both the nonlinearities of graphene and dielectric are considered. The self-focusing PLSs at the Brillouin zone edges can be yielded by balancing the normal diffraction of surface plasmon polaritons (SPPs) via either the nonlinear effect of graphene or self-focusing dielectric. The self-defocusing PLSs corresponding to anomalous diffraction of SPPs at the Brillouin zone center could be yielded by the nonlinearity of self-defocusing dielectric alone. The width and propagation distance of the PLSs are dependent on the period of the GSAs and the chemical potential of graphene. Thanks to the strong confinement of SPPs, the PLSs in GSAs can be squeezed into an effective width as small as λ/250. The study may find applications in optical circuits and switches on deep-subwavelength scale.

Ultrathin niobium nanofilms on fiber optical tapers--a new route towards low-loss hybrid plasmonic modes

Due to the ongoing improvement in nanostructuring technology, ultrathin metallic nanofilms have recently gained substantial attention in plasmonics, e.g. as building blocks of metasurfaces. Typically, noble metals such as silver or gold are the materials of choice, due to their excellent optical properties, however they also possess some intrinsic disadvantages. Here, we introduce niobium nanofilms (~10 nm thickness) as an alternate plasmonic platform. We demonstrate functionality by depositing a niobium nanofilm on a plasmonic fiber taper, and observe a dielectric-loaded niobium surface-plasmon excitation for the first time, with a modal attenuation of only 3-4 dB/mm in aqueous environment and a refractive index sensitivity up to 15 μm/RIU if the analyte index exceeds 1.42. We show that the niobium nanofilm possesses bulk optical properties, is continuous, homogenous, and inert against any environmental influence, thus possessing several superior properties compared to noble metal nanofilms. These results demonstrate that ultrathin niobium nanofilms can serve as a new platform for biomedical diagnostics, superconducting photonics, ultrathin metasurfaces or new types of optoelectronic devices.

Surface lattice solitons in diffusive nonlinear media with spatially modulated nonlinearity

Two families of gap and twisted surface lattice solitons in diffusive nonlinear periodic media with spatially modulated nonlinearity are reported. It is shown that the existence and stability of such solitons are extremely spatially modulated nonlinearity sensitive. For self-focusing nonlinearity, gap surface solitons belonging to the semi-infinite gap are stable in whole existence domain, twisted surface solitons are also linearly stable in low modulated strength region and a very narrow unstable region near the upper cutoff appears in high modulated strength region. In the self-defocusing case, surface gap solitons belonging to the first gap can propagate stably in whole existence domain except for an extremely narrow region close to the Bloch band, twisted solitons belonging to this gap are unstable in the entire existence domain.

Modulated coupled nanowires for ultrashort pulses

We predict analytically and confirm with numerical simulations that intermode dispersion in nanowire waveguide arrays can be tailored through periodic waveguide bending, facilitating flexible spatiotemporal reshaping without breakup of femtosecond pulses. This approach allows simultaneous and independent control of temporal dispersion and spatial diffraction that are often strongly connected in nanophotonic structures.

Self-deflecting plasmonic lattice solitons and surface modes in chirped plasmonic arrays

We show that chirped metal-dielectric waveguide arrays with focusing cubic nonlinearity can support plasmonic lattice solitons that undergo self-deflection in the transverse plane. Such lattice solitons are deeply subwavelength self-sustained excitations, although they cover several periods of the array. Upon propagation, the excitations accelerate in the transverse plane and follow trajectories curved in the direction in which the separation between neighboring metallic layers decreases, a phenomenon that yields considerable deflection angles. The deflection angle can be controlled by varying the array chirp. We also reveal the existence of surface modes at the boundary of truncated plasmonic chirped array that form even in the absence of nonlinearity.

Subwavelength binary plasmonic solitons

We study the formation of subwavelength solitons in binary metal-dielectric lattices. We show that the transverse modulation of the lattice constant breaks the fundamental plasmonic band and suppresses the discrete diffraction of surface plasmon waves. New types of plasmonic solitons are found, and their characteristics are analyzed. We also demonstrate the existence of photonic-plasmonic vector solitons and elucidate their propagation properties.

Rabi oscillations and stimulated mode conversion on the subwavelength scale

We study stimulated mode conversion and dynamics of Rabi-like oscillations of weights of guided modes in deeply subwavelength guiding structures, whose dielectric permittivity changes periodically in the direction of light propagation. We show that despite strong localization of the fields of eigenmodes on the scales below the wavelength of light, even weak longitudinal modulation couples modes of selected parity and causes periodic energy exchange between them, thereby opening the way for controllable transformation of the internal structure of subwavelength beams. The effect is reminiscent of Rabi oscillations in multilevel quantum systems subjected to the action of periodic external fields. By using rigorous numerical solution of the full set of the Maxwell's equations, we show that the effect takes place not only in purely dielectric, but also in metallic-dielectric structures, despite the energy dissipation inherent to the plasmonic waveguides. The stimulated conversion of subwavelength light modes is possible in both linear and nonlinear regimes.

Tunable subwavelength photonic lattices and solitons in periodically patterned graphene monolayer

We study linear and nonlinear mode properties in a periodically patterned graphene sheet. We demonstrate that a subwavelength one-dimensional photonic lattice can be defined across the graphene monolayer, with its modulation depth and correspondingly the associated photonic band structures being controlled rapidly, by an external gate voltage. We find the existences of graphene lattice solitons at the deep-subwavelength scales in both dimensions, thanks to the combination of graphene intrinsic self-focusing nonlinearity and the graphene plasmonic confinement effects.

Plasmonic kinks and walking solitons in nonlinear lattices of metal nanoparticles

We study nonlinear effects in one-dimensional (1D) arrays and two-dimensional (2D) lattices composed of metallic nanoparticles with the nonlinear Kerr-like response and an external driving field. We demonstrate the existence of families of moving solitons in 1D arrays and characterize their properties such as an average drifting velocity. We also analyse the impact of varying external field intensity and frequency on the structure and dynamics of kinks in 2D lattices. In particular, we identify the kinks with positive, negative and zero velocity as well as breathing kinks with a self-oscillating profile.

Tunneling inhibition for subwavelength light

We show that light tunneling inhibition may take place in suitable dynamically modulated waveguide arrays for light spots whose features are remarkably smaller than the wavelength of light. We found that tunneling between neighboring waveguides can be suppressed for specific frequencies of the out-of-phase refractive index modulation, affording undistorted propagation of the input subwavelength light spots over hundreds of Rayleigh lengths. Tunneling inhibition turns out to be effective only when the waveguide separation in the array is above a critical threshold. Inclusion of a weak focusing nonlinearity is shown to improve localization. We analyze the phenomenon in purely dielectric structures and also in arrays containing periodically spaced metallic layers.

Multiband vector plasmonic lattice solitons

We predict multiband vector plasmonic lattice solitons (PLSs) in metal-dielectric waveguide arrays, in both focusing and defocusing nonlinearities. Such vector solitons consist of two components originating from different transmission bands. By simulating the full nonlinear Maxwell's equations, we demonstrate the diffractionless propagation of vector PLSs and their discrete diffraction when only one component is present. Their subwavelength size characteristics and the influences of metallic losses are also studied.

Subwavelength plasmon solitons in a one-dimensional chain of coupled metallic nanorods

We investigate analytically the subwavelength plasmonic lattice solitons excited in an optical plasmonic waveguide consisting of a chain of nanorods embedded in a Kerr nonlinear optical medium with strong near-field interactions. A nonlinear lattice equation with onsite and intersite nonlinear terms describing the plasmon wave propagating along the chain is derived. Stability analysis predicts that modulation instability can occur and that, correspondingly, conditions for localized modes will exist. We analyze the nonlinear excitations for genuine discreteness and nonlinearity enhanced by the fields strongly confined in the nanosized dielectric gaps. Based on a quasidiscreteness approach, we obtain a nonlinear Schrödinger equation and find that the system supports bright and dark soliton solutions in different frequency bands. It is also shown that the existence of different solitons depends strongly on the type of nonlinearity of the embedded medium.

Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles

The study of metal nanoparticles plays a central role in the emerging novel technologies employing optics beyond the diffraction limit. Combining strong surface plasmon resonances, high intrinsic nonlinearities and deeply subwavelength scales, arrays of metal nanoparticles offer a unique playground to develop novel concepts for light manipulation at the nanoscale. Here we suggest a novel principle to control localized optical energy in chains of nonlinear subwavelength metal nanoparticles based on the fundamental nonlinear phenomenon of modulation instability. In particular, we demonstrate that modulation instability can lead to the formation of long-lived standing and moving nonlinear localized modes of several distinct types such as bright and dark solitons, oscillons, and domain walls. We analyze the properties of these nonlinear localized modes and reveal different scenarios of their dynamics including transformation of one type of mode to another. We believe this work paves a way towards the development of nonlinear nanophotonics circuitry.

Soliton-plasmon resonances as Maxwell nonlinear bound states

We demonstrate that soliplasmons (soliton-plasmon bound states) appear naturally as eigenmodes of nonlinear Maxwell's equations for a metal/Kerr interface. Conservative stability analysis is performed by means of finite element numerical modeling of the time-independent nonlinear Maxwell equations. Dynamical features are in agreement with the presented nonlinear oscillator model.

Surface plasmonic lattice solitons

We reveal the existence of the surface plasmonic lattice solitons (surface PLSs) at the boundary of a semi-infinite metallic-dielectric periodic nanostructure. We find that the truncation of the periodic structure imposes a threshold power for the existence of surface PLSs, and significantly enhances the modal localization. The propagation and excitation of surface PLSs as well as their potential application in the all-optical subwavelength switching are also demonstrated.

Optical spatial solitons: historical overview and recent advances

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays

We study modulational instability in nonlinear arrays of subwavelength metallic nanoparticles and analyze numerically nonlinear scenarios of the instability development. We demonstrate that modulational instability can lead to the formation of regular periodic or quasiperiodic modulations of the polarization. We reveal that such nonlinear nanoparticle arrays can support long-lived standing and moving oscillating nonlinear localized modes--plasmon oscillons.

Subwavelength plasmonic kinks in arrays of metallic nanoparticles

We analyze nonlinear effects in optically driven arrays of nonlinear metallic nanoparticles. We demonstrate that such plasmonic systems are characterized by a bistable response, and they can support the propagation of dissipative switching waves (or plasmonic kinks) connecting the states with different polarization. We study numerically the properties of such plasmonic kinks which are characterized by a subwavelength extent and a tunable velocity.

Ring-like solitons in plasmonic fiber waveguides composed of metal-dielectric multilayers

We design a plasmonic fiber waveguide (PFW) composed of coaxial cylindrical metal-dielectric multilayers in nanoscale, and constitute the corresponding dynamical equations describing the propagation modes in the PFW with the Kerr nonlinearity in the dielectric layers. The physics is connected to the discrete matrix nonlinear Schrödinger equations, from which the highly confined ring-like solitons in scale of subwavelength are found both for the visible lights and the near-infrared lights in the self-defocusing condition. Moreover, when increasing the intensity of the input light the confinement can be further improved due to the cylindrical symmetry of the PFW, which means both the width and the radius of the ring are reduced.

Subwavelength vortical plasmonic lattice solitons

We present a theoretical study of vortical plasmonic lattice solitons, which form in two-dimensional arrays of metallic nanowires embedded into nonlinear media with both focusing and defocusing Kerr nonlinearities. Their existence, stability, and subwavelength spatial confinement are investigated in detail.

Coupled-mode approach to surface plasmon polaritons in nonlinear periodic structures

We present a coupled-mode theory describing light propagation in an array of nonlinear plasmonic waveguides. Our model predicts a two-band dependence of the propagation constant versus transverse quasi-momentum and existence of discrete and gap plasmon solitons.

Nonlinear pulsed excitation of high-Q optical modes of plasmonic nanocavities

We present a comprehensive theoretical and numerical analysis of the physical mechanisms pertaining to the nonlinear pulsed excitation of optical modes in plasmonic cavities made of metallic nanowires. Our analysis is based on extensive numerical simulations carried out both in the frequency and time domains. The numerical algorithm used in our study is based on the multiple scattering method and allows us to include in our analysis the effects of both the surface and bulk nonlinear polarizations generated at the second harmonic (SH). In particular, we investigate the physical properties of plasmonic modes excited at the SH as the result of the interaction of femtosecond optical pulses with plasmonic nanocavities. We show that such cavities have two distinct types of modes, namely, plasmonic cavity modes and multipole plasmon modes generated via the hybridization of modes of single nanowires. Our analysis reveals that the properties of the latter modes depend only weakly on the cavity geometry, whereas the lifetime and quality factor of plasmonic cavity modes vary considerably with the system parameters.