2D Periodic Arrays Research Articles

Patterning of 2D second harmonic generation active arrays in ferroelectric nematic fluids

Ferroelectric nematic liquid crystals exhibit unique non-linear optical properties, with the potential to become transformative materials for photonic applications. A promising direction relies on the fabrication of tailored polar orientational patterns via photoalignment, thus shaping the non-linear optical susceptibility through thin slabs of the ferroelectric fluid. Here, we explore the fabrication of 2D periodic SHG active arrays in ferroelectric nematic fluids, for different materials, cell thicknesses and motifs. Based on polarizing optical microscopy observations in combination with optical simulations, second harmonic generation microscopy and interferometry, the 3D structure of the motifs is revealed. Two different 2D periodic patterns are explored, showing that the balance between flexoelectric and electrostatic energy can lead to different domain structures, an effect which is rooted in the difference between the flexoelectric properties of the materials. It is shown that by combining the surface-inscribed alignment with different spontaneous degrees of twist, 2D SHG active arrays can be obtained in the micrometre scale, in which adjacent areas exhibit maximum SHG signals at opposite angles.

Use of periodic 2D pillar array for performance enhancement of AlN-based SMR BAW resonators

This paper discusses the applicability of a two-dimensional (2D) periodic pillar array as the first layer of an acoustic mirror for AlN-based solidly mounted resonators of bulk acoustic waves. It is based on the idea that the periodic pillar array behaves like a uniform layer when the period is much smaller than the wavelength and its behavior is given by the ensemble average of pillar materials. The simulation shows that the effective electromechanical coupling factor can be enhanced close to that of AlN-based film bulk acoustic resonators when the slot ratio is large. It is also shown that the use of a 2D pillar array can enhance the reflectivity of the Bragg reflector. It should be noted that the periodic 2D pillar array can also control the anisotropy of wave propagation along the surface. Owing to this, transverse mode resonances can be suppressed well by adjusting the wave dispersion curve properly.

Subdiffusion in an array of solid obstacles

More than a decade ago, Goychuk reported on a universal behavior of subdiffusive motion (as described by the generalized Langevin equation) in a one-dimensional bounded periodic potential (Goychuk 2009 Phys. Rev. E 80 046125) where the numerical findings show that the long-time behavior of the mean squared displacement is not influenced by the potential, so that the behavior in the potential, under homogenization, is the same as in its absence. This property may break down if the potential is unbounded. In the present work, we report on the results of simulations of subdiffusion in a two-dimensional (2D) periodic array of solid obstacles (i.e. in an unbounded potential) with different packing fractions. It is revealed that the universal subdiffusive behavior at long times is not influenced by the presence of solid scatterers, whose presence influences the behavior at intermediate times only. This result is discussed as having possible relations to the emerging problem of interpretation of results on trajectories of tracers spreading in the brain’s extracellular space.

Molecular-level periodic arrays of long-chain poly(3-hexylthiophene-2,5-diyl) driven by an electric field.

Two-dimensional (2D) periodic arrays of conductive polymers represent attractive platforms for wiring functional molecules into the integrated circuits of molecular electronics. However, the large-scale assembly of polymer periodic arrays at the molecular level faces challenges such as curling, twisting, and aggregation. Here, we assembled the periodic arrays of long-chain poly(3-hexylthiophene-2,5-diyl) (P3HT, Mw = 65 k) at the solid-liquid interface by applying an electric field, within which the charged chain segments were aligned. Atomic force microscopy (AFM) imaging revealed that individual P3HT chains assemble into monolayers featuring face-on orientation, extended chain conformation and isolated packing, which is thermodynamically more stable than folded chains in 2D polycrystals. The assembly process is initiated with the formation of disordered clusters and progresses through voltage-dependent nucleation and growth of extended-chain arrays, wherein continuous conformational adjustments along the nucleation pathway exhibit dependence on the cluster size.

2D compound structures with deep subwavelength period on silicon fabricated by double time delayed femtosecond laser beams

In this work, two orthogonally polarized femtosecond laser beams are employed to irradiate a p-doped silicon wafer with an electrical resistivity of 0.008 Ω·cm. It is interesting to find that 2D compound structures composed of sub-wavelength periodic ripples and deep sub-wavelength nanodot array can be produced when proper laser fluence and time delay between the dual laser beams are used. The formation of the periodic ripples can be explained by the interference between the preceding incident laser and it induced surface plasmon polaritons (SPPs). The periodic nanodot array has a period down to ∼200 nm and the radius of the nanodot is ∼30 nm, most of which appear at the boundary between the ditch and ridge of the ripple. During the ripples’ formation, the residual melting silicon is most probably located at the boundary between the ditch and ridge of the ripple. Furthermore, the period of the nanodot array is roughly equal to the perimeter of the nanodot. Therefore, it is considered that the dot array may be generated due to the Rayleigh-Taylor instability of the melting silicon. It is also noted that these nanodots are all uniformly arranged along vertical lines, indicating that the subsequent incident laser may break the stochastic characteristic of the Rayleigh-Taylor instability and produce the 2D periodic dot array. The thermo-hydrodynamical process combined with the interference effect between SPPs and the incident laser can benefit the formation of complex surface structures with versatile functions.

Vertical-cavity surface-emitting phase shifter.

This study proposes a novel technique for a 2D beam steering system using hybrid plasmonic phase shifters with a cylindrical configuration in a 2D periodic array suitable for LIDAR applications. A nanoscale VCSEP design facilitates a sub-wavelength spacing between individual phase shifters, yielding an expanded field of view and side lobes suppression. The proposed design includes a highly doped sub-micron silicon pillar covered by a thin layer of nonlinear material and an additional conductive metal layer. Characterization of a single VCSEP demonstrated a Free Spectral Range (FSR) of 53.28 ± 2.5 nm and a transmission variation of 3 dB, with VπL equal to 0.075 V-mm.

Surface lattice resonance of circular nano-array integrated on optical fiber tips

As metallic nanoparticles are arranged to form a 2D periodic nano-array, the coupling of the localized surface plasmonic resonance (LSPR) results in the well-known phenomenon of surface lattice resonances (SLRs). We theoretically investigate the SLR effect of the circular nano-array fabricated on the fiber tips. The difference between the 2D periodic and circular periodic arrays results in different resonant characteristics. For both structures, the resonant peaks due to the SLRs shift continuously as the array structures are adjusted. For some specific arrangements, the circular nano-array may generate a single sharp resonant peak with extremely high enhancement, which originates from the collective coupling of the whole array. More interestingly, the spatial pattern of the vector near-field corresponding to the sharp peak is independent of the polarization state of the incidence, facilitating its excitation and regulation. This finding may be helpful for designing multifunctional all-fiber devices.

Acousto‐Plasmo‐Magnonics: Coupling Spin Waves with Hybridized Phonon‐Plasmon Waves in a 2D Artificial Magnonic Crystal Deposited on a Plasmonic Material

AbstractCoupling between spin waves (SWs) and other waves in nanostructured media has emerged as an important topic of research because of the rich physics and the potential for disruptive technologies. Herein, a new phenomenon is reported in this family involving coupling between SWs and hybridized phonon‐plasmon waves in a 2D periodic array of magnetostrictive nanomagnets deposited on a silicon substrate with an intervening thin film of aluminium that acts as a source of surface plasmons. Hybridized phonon‐plasmon waves naturally form in this composite material when exposed to ultrashort laser pulses and they non‐linearly couple with SWs to produce a new breed of waves – acousto‐plasmo‐spin waves that can exhibit a “frequency comb” spanning more than one octave. This phenomenon, that we call acousto‐plasmo‐magnonics resulting from tripartite coupling of magnons, phonons and plasmons, is studied with time‐resolved magneto‐optical‐Kerr‐effect microscopy. The findings also reveal the presence of parametric amplification in this system; energy is transferred from the hybridized phonon‐plasmon modes to the acousto‐plasmo‐spin wave modes to amplify the latter. This opens a path to design novel active metamaterials with tailored and enhanced response. It may enable high‐efficiency magneto‐mechanical‐plasmonic frequency mixing in the GHz−THz frequency regime and provide a unique avenue to study non‐linear coupling, parametric amplification, and frequency comb physics.

All-dielectric metasurface based ultranarrow bandpass filter in optical C-band

Metasurface-based nanophotonics devices can potentially replace traditional bulky optical components such as optical filters, modulators, and switches. In this study, we report a dielectric metasurface-based ultranarrow bandpass filter operating at 1549.8 nm with the ability to tune the central wavelength within the C-band. The proposed tunable filter consists of a 2D periodic array of gallium arsenide blocks placed on top of a quartz substrate. The introduction of a symmetry-breaking defect results in an ultranarrow resonance with an FWHM of 0.31 nm at a 1549.8 nm wavelength when a TE-polarized wave is normally incident. The sharp, high Q factor resonance is understood to be governed by the symmetry-protected bound state in the continuum. The resonant response can be tuned by changing the periodicity, thickness, and asymmetry of the metasurface constituents. The multipolar analysis indicates the excitation of the electric quadrupole mode at the resonance wavelength. Our findings can be useful for the design of compact tunable ultranarrow bandpass filters for optical communications systems.

Robust and non-robust bound states in the continuum in rotationally symmetric periodic waveguides.

A fiber grating and a one-dimensional (1D) periodic array of spheres are examples of rotationally symmetric periodic (RSP) waveguides. It is well known that bound states in the continuum (BICs) may exist in lossless dielectric RSP waveguides. Any guided mode in an RSP waveguide is characterized by an azimuthal index m, the frequency ω, and Bloch wavenumber β. A BIC is a guided mode, but for the same m, ω and β, cylindrical waves can propagate to or from infinity in the surrounding homogeneous medium. In this paper, we investigate the robustness of nondegenerate BICs in lossless dielectric RSP waveguides. The question is whether a BIC in an RSP waveguide with a reflection symmetry along its axis z, can continue its existence when the waveguide is perturbed by small but arbitrary structural perturbations that preserve the periodicity and the reflection symmetry in z. It is shown that for m = 0 and m ≠ 0, generic BICs with only a single propagating diffraction order are robust and non-robust, respectively, and a non-robust BIC with m ≠ 0 can continue to exist if the perturbation contains one tunable parameter. The theory is established by proving the existence of a BIC in the perturbed structure mathematically, where the perturbation is small but arbitrary, and contains an extra tunable parameter for the case of m ≠ 0. The theory is validated by numerical examples for propagating BICs with m ≠ 0 and β ≠ 0 in fiber gratings and 1D arrays of circular disks.

Laser-driven self-organized evolution of 1D- and 2D-Nanostructures from metal thin-films on silicon: Influence of alloying and oxidation

One- and two-dimensional laser-induced periodic surface structure (LIPSS) formation of various metal (Ag, Cu, Fe, Zn, Ti) thin films on silicon wafers is achieved by irradiation with circularly polarized 532 nm nanosecond laser pulses. The occurrence and the evolution of pseudo-1D linear periodic, 2D honeycomb-like structures, and 2D periodic nanoparticle arrays were mapped for each element in dependence on the energy applied, i.e. the effective pulse number, and the metal thin film thickness. Samples series with increasing pulse counts monitor, like snapshots, the progressive pattern evolution. Because the metal thin films are of nanometer thickness only, the co-structuring of the silicon substrate must be taken into account in all cases. Even more complex are LIPSS formations on samples carrying two stacked thin films. The LIPSS formation process of thin films becomes rather complex as soon as co-structuring of the substrate, oxidation of the material, and alloy formation with substrate material or a potential second thin film layer are considered. All these effects affect the morphology of the formed LIPSS patterns.

Directional amplified spontaneous emissions from Ag nanohole array with high diffraction orders.

Surface plasmon excitations in metallic hole arrays have been extensively studied in the context of light-matter interaction, since the generated Bloch surface plasmon polariton (Bloch-SPP) exhibits unique properties of nanoscale light confinement, near-field enhancements, and long-range metal surface propagation. In this work, we experimentally demonstrate a plasmonic device that exhibits highly directional emission in visible light; using Ag film with a thickness of 100 nm deposited on a subwavelength porous alumina array as a plasmonic cavity, four-level rhodamine 6G (R6G) is selected as the gain material. It is suggested that a Bloch-SPP with high diffraction orders on a Ag nanohole array can generate a strong local electric field and a high Purcell factor at a nanohole edge. Moreover, directional five-fold enhanced amplified spontaneous emission (ASE) with polarization dependence is observed under a low threshold of 199.9 W/cm2 in the visible light region, which comes from the optical feedback provided by the 2D periodic nanohole array. This work opens up a wide range of applications for real-time tunable wavelength, controlled multimode laser, fluorescence detection, etc.

CORRELATIONS OF INTERFACIAL HEAT TRANSFER COEFFICIENT AND THERMAL DISPERSION FOR TURBULENT CONVECTIVE FLOW IN POROUS MEDIUM

Effective properties like interfacial heat transfer coefficient and longitudinal and transverse thermal dispersion play an important role in the up-scaled mathematical models of porous medium. However, most of the existing correlations are obtained by assuming that fluid flow in porous medium is laminar. Therefore, numerical simulations were conducted in the study to investigate interfacial heat transfer coefficient and longitudinal thermal dispersion for turbulent convective flow in porous medium. For the sake of simplification, a two-dimensional (2D) periodic array of square rods was chosen as physical geometry. Moreover, a low-Re turbulence model suitable for backward-facing step geometry was applied to better capture the turbulent characteristic in porous medium. By the exhausted numerical results, an interfacial heat transfer coefficient correlation was obtained. Furthermore, due to the inverse relationship between interfacial heat transfer coefficient and longitudinal thermal dispersion, the expression of longitudinal thermal dispersion was derived. By comparing with existing experimental data and correlations in the literature, the correlations of interfacial heat transfer coefficient and longitudinal and transverse thermal dispersion were validated. In light of the proposed correlations, it is feasible to establish a more reliable macroscopic mathematical model of porous medium.

Proving Surface Plasmons in Graphene Nanoribbons Organized as 2D Periodic Arrays and Potential Applications in Biosensors

Surface-plasmon-based biosensors have become excellent platforms for detecting biomolecular interactions. While there are several methods to exciting surface plasmons, the major challenge is improving their sensitivity. In relation to this, graphene-based nanomaterials have been theoretically and experimentally proven to increase the sensitivity of surface plasmons. Notably, graphene nanoribbons display more versatile electronic and optical properties due to their controllable bandgaps in comparison to those of zero-gap graphene. In this work, we use a semi-analytical approach to investigate the plasmonic character of two-dimensional graphene nanoribbon arrays, considering free-standing models, i.e., models in which contact with the supporting substrate does not affect their electronic properties. Our findings provide evidence that the plasmon frequency and plasmon dispersion are highly sensitive to geometrical factors or the experimental setup within the terahertz regime. More importantly, possible applications in the molecular detection of lactose, α-thrombin, chlorpyrifos-methyl, glucose, and malaria are discussed. These predictions can be used in future experiments, which, according to what is reported here, can be correctly fitted to the input parameters of possible biosensors based on graphene nanoribbon arrays.

Synthesis of Self-Assembled Single Atomic Layer Gold Crystals-Goldene.

We report, for the first time, a technique to synthesize free-standing, one-atom thick 2D gold crystals (namely, goldene) and self-assembled 2D periodic arrays of goldene. High-resolution transmission electron microscopy (HRTEM) imaging of goldene revealed herringbone and honeycomb lattices, which are primarily gold surface features due to its reconstruction. Imaging of these surface-only features by a nonsurface characterization technique such as HRTEM is an unequivocal proof of the absence of three-dimensionality in goldene. Atomic force microscopy confirmed 1-2 Å thickness of goldene. High-resolution X-ray photoelectron spectroscopy (HR-XPS), selective area electron diffraction, and energy-dispersive X-ray spectroscopy confirmed the chemical identity of goldene. We discovered the phenomenon of electric field-induced self-assembly of goldene supracrystals with a herringbone structure and developed an electric field printing (e-print) technique for goldene arrays. Goldene showed a semiconductor response with a knee voltage of ∼3.2 V, and I/V spectroscopy revealed periodic room temperature Coulomb blockade oscillations. These observations are consistent with the theoretical calculations reported in the literature predicting enhanced Coulombic interactions between gold valence electrons and the nucleus in stable 2D gold. Goldene exhibited multiple, intense, and well-resolved optical absorption peaks and several fine bands across the UV-vis region, and we calculated its optical band gap to be 3.59 eV. Magnetic force microscopy measurements of goldene periodic arrays showed a ∼5 mV peak amplitude confirming its ferromagnetism. Optical and magnetic properties of goldene are consistent with those reported in the literature for 2D planar gold clusters with less than 12 atoms.

Quasi‐Bound States in the Continuum Enhanced Second‐Harmonic Generation in Thin‐Film Lithium Niobate

AbstractThis work reports the second‐harmonic generation (SHG) in a z‐cut thin‐film lithium niobate (LN) under nearly normal‐incident linearly‐polarized pumping. To utilize the largest nonlinear term which is along the out‐of‐plane direction in the z‐cut LN film, the film is patterned with a 2D periodic array to support symmetry‐protected bound states in the continuum (BICs) bearing strong out‐of‐plane electric field component. Enabled by such optical resonances near the BIC condition at the pumping wavelength, significant enhancement in SHG compared to an unpatterned film is observed. This approach, combining transparent thin‐film nonlinear materials with tailored BICs, offers prospects for engineering compact coherent light sources in a broad wavelength range.

Nanometer-sensitive wideband opto-mechanical switching concept

The present paper is concerned with the mechanically extremely sensitive reflection switching concept of a free-space wave impinging on an array of dielectric or semiconductor pillars. Splitting the pillars of a 2D periodic array in its resonant reflection regime at a prescribed wavelength into two parts with a low-index gap of a few nanometers between parts cancels the reflection of a plane wave under normal incidence. The underlying principle lies in the strong and abrupt discontinuity of the electric field component parallel to the pillar axes caused by the gap. The electromagnetic field distribution is consequently deeply perturbed and no longer corresponds to that of an optical resonance of the array; this suppresses the reflection. The electromagnetic analysis of a silicon pillar array leads to the design of a gapless experimental model fabricated by microsystem technologies that exhibits a broad reflection maximum of a few tens of nm at a prescribed wavelength in the visible and near-IR range, and of a pillar structure with nanometer-thick low-index gap exhibiting no reflection peak over this wide wavelength range. A transmission ratio of 1:30 at a 1080 nm peak wavelength between a gapless and a 1.5 index, 30 nm-thick gap structures was measured.

Analysis and design of two-dimensional compound metallic metagratings using an analytical method.

The recently proposed concept of metagrating enables wavefront manipulation of electromagnetic (EM) waves with unitary efficiency and relatively simple fabrication requirements. Herein, two-dimensional (2D) metagratings composed of a 2D periodic array of rectangular holes in a metallic medium are proposed for diffraction pattern control. We first present an analytical method for diffraction analysis of 2D compound metallic metagrating (a periodic metallic structure with more than one rectangular hole in each period). Closed-form and analytical expressions are presented for the reflection coefficients of diffracted orders for the first time. Next, we verify the proposed method's results against full-wave simulations and demonstrate their excellent agreement. As a proof of principle, two applications are presented using the proposed analytical method. The first application is a perfect out-of-plane reflector that transfers a normal transverse-magnetic (TM) polarized plane wave to an oblique transverse-electric (TE) polarized plane wave in the y - z plane. The second one is a five-channel beam splitter with an arbitrary power distribution between channels. Using the proposed analytical method, we designed these metagratings without requiring even a single optimization in a full-wave solver. The performance of the designed metagratings is better than previously reported structures in terms of power efficiency and relative distribution error. Our analytical results reveal that 2D metagratings can be used for manipulating EM waves in the plane and out of the plane of incidence with very high efficiency, thereby leading to extensive applications in a wide range of frequencies from microwave to terahertz (THz) regimes.

Preparation of 2D Periodic Nanopatterned Arrays through Vertical Vibration-Assisted Convective Deposition for Application in Metal-Enhanced Fluorescence

The performance of a metal-enhanced fluorescence (MEF) substrate is fundamentally based on the orientation of the metal nanostructures on a solid substrate. In particular, two-dimensional (2D) periodic metallic nanostructures exhibit a strong confinement of the electric field between adjacent nanopatterns due to localized surface plasmon resonance (LSPR), leading to stronger fluorescence intensity enhancement. The use of vertical vibration-assisted convective deposition, a novel, simple, and highly cost-effective technique for preparing the 2D periodic nanostructure of colloidal particles with high uniformity, was therefore proposed in this work. The influences of vertical vibration amplitude and frequency on the structure of thin colloidal film, especially its uniformity, monolayer, and hexagonal close-packed (HCP) arrangement, were also investigated. It was found that the vibration amplitude affected film uniformity, whereas the vibration frequency promoted the colloidal particles to align themselves into defect-free HCP nanostructures. Furthermore, the results showed that the self-assembled 2D periodic arrays of monodisperse colloidal particles were employed as an excellent template for a Au thin-film coating in order to fabricate an efficient MEF substrate. The developed MEF substrate provided a strong plasmonic fluorescence enhancement, with a detection limit for rhodamine 6G as low as 10−9 M. This novel approach could be advantageous in further applications in the area of plasmonic sensing platforms.

In-plane directionality control of strongly localized resonant modes of light in disordered arrays of dielectric scatterers.

In this work we propose and analyze techniques of in-plane directionality control of strongly localized resonant modes of light in random arrays of dielectric scatterers. Based on reported diameters and areal densities of epitaxially grown self-organized nanowires, two-dimensional (2D) arrays of dielectric scatterers have been analyzed where randomness is gradually increased along a preferred direction of directionality enhancement. In view of the multiple-scattering mediated wave dynamics and directionality enhancement of light in such arrays, a more conveniently realizable, practical structure is proposed where a 2D periodic array is juxtaposed with a uniform, random scattering medium. Far- and near-field emission characteristics of such arrays show that in spite of the utter lack of periodicity in the disordered regime of the structure, directionality of the high-Q resonant modes is modified such that on average more than 70% of the output power is emitted along the pre-defined direction of preference. Such directionality enhancement and strong localization are nonexistent when the 2D periodic array is replaced with a one-dimensional Bragg reflector, thereby confirming the governing role of in-plane multiple scattering in the process. The techniques presented herein offer novel means of realizing not only directionality tunable edge-emitting random lasers but also numerous other disordered media based photonic structures and systems with higher degrees of control and tunability.