Periodic Array Of Cylinders Research Articles

Broadband and highly efficient asymmetric optical transmission through periodic Si cylinder arrays on the dielectric substrates

Asymmetric optical transmission is widely used in various fields due to the manipulation of light direction. This work theoretically investigates highly efficient and polarization-independent asymmetric optical transmission in the broadband wavelength through the periodic Si cylinder arrays on the dielectric substrates. The simulated results show that the maximum asymmetric optical transmission can reach 0.894, with high forward transmission of 0.898 and nearly zero backward transmission of 0.004 at the wavelength of 540 nm. The structure also exhibits excellent light-trapping characteristics with low energy loss and anti-reflection. The formation of asymmetric optical transmission comes from the diffraction which contributes differently to the transmission under forward and backward illuminations. Furthermore, asymmetric optical transmission in the structure is insensitive to the refractive index of the dielectric substrate and the height of the Si cylinder, and the wavelength position of the maximum asymmetric optical transmission is only sensitive to the height of the Si cylinder. This work proposes a multifunctional nanostructure and provides guidelines for designing practical devices that utilize asymmetric optical transmission.

Estimating the interfacial permeability for flow into a poroelastic medium.

Boundary conditions between a porous solid and a fluid has been a long-standing problem in modeling porous media. For deformable poroelastic materials such as hydrogels, the question is further complicated by the elastic stress from the solid network. Recently, an interfacial permeability condition has been developed from the principle of positive energy dissipation on the hydrogel-fluid interface. Although this boundary condition has been used in flow computations and yielded reasonable predictions, it contains an interfacial permeability η as a phenomenological parameter. In this work, we use pore-scale models of flow into a periodic array of solid cylinders or parallel holes to determine η as a function of the pore size and porosity. This provides a means to evaluate the interfacial permeability for a wide range of poroelastic materials, including hydrogels, foams and biological tissues, to enable realistic flow simulations.

Achieving Complete Band Gaps of Water Waves with Shallow-Draft Cylinder Arrays

Conventionally, band gaps of water waves can be obtained with periodic arrays of bottom-mounted obstacles or vertical cylinders. However, such structures need to possess a large ratio of volume in water, and may not be easy to build and move in practical ocean engineering. Here, we theoretically propose and experimentally demonstrate that when the water surface is pierced by a fixed, rigid cylinder array, a complete band gap of water waves can be achieved, in which the propagation of water waves is forbidden in all the directions. Such a band gap can exist even when the cylinders have a draft much smaller than the water depth ($d\ensuremath{\ll}h$). Based on the complete band gap, a semicircular shape of the fixed-surface disk array is further constructed, which can block omnidirectional water waves generated by a point source.

Applicable Investigation of SPH in Characterization of Fluid Flow in Uniform and Non-Uniform Periodic Porous Media

Today, the use of numerical modeling for characterizing properties of porous media and related concepts has been widely extended, especially in subsurface flow issues such as geological CO2 storage and petroleum recovery. Therefore, in this study, the fundamental problem of laminar fluid flow through uniform or non-uniform and periodic array of cylinders was functionally investigated using the smoothed particle hydrodynamics (SPH) method as a modern and applied method of modeling in order to develop the past studies and introduce a complementary numerical tool alongside laboratory methods. All modeling processes were performed in the form of dimensionless processes for generalization and applicability at different scales. The results were used to characterize properties of porous media and to investigate basic properties such as fluid velocity, permeability, streamlines, and hydraulic tortuosity. Accuracy of modeling was shown in comparison with the results obtained in the literature. In this study, the potential of the method has been investigated in order to show the ability in modeling characteristic laboratory experiments of porous media and the possibility of using it instead of them. For this purpose, three periodic models of uniform and randomly distributed non-uniform porous media with arrays of circular, square, and diamond-shaped cylinders in a porosity range of 30–95%, with different types of cylinder distribution at the pore scale, were investigated. New equations were proposed for permeability as a function of porosity. Moreover, the method of tortuosity calculation was investigated directly through the time history of properties in the SPH method, and shape factors were obtained for the studied porous media models. The results showed that the geometry of a square cylinder with distribution in a square grid led to a higher permeability than circular and diamond-shaped grids. In contrast, diamond-shaped geometry with distribution in a hexagonal grid led to higher permeability than the other two models. Furthermore, diamond-shaped geometry had higher tortuosity, and circular and square geometries had almost identical tortuosity. Increasing the size of the modeling domain and decreasing the size of cylinders (i.e., decreasing resolution) reduces effects of the shape and the geometry of cylinders and achieves the same results. Random and non-uniform distribution of cylinders within porous media reduces fluid velocity, permeability, tortuosity, and shape factor (p) compared to the uniform models.

Computing diffraction anomalies as nonlinear eigenvalue problems.

When a plane electromagnetic wave impinges on a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the outgoing waves in one or more radiation channels vanish. Zero reflection, zero transmission, and perfect absorption are important examples of diffraction anomalies, and they are useful for manipulating electromagnetic waves and light. Since diffraction anomalies appear only at specific frequencies and/or wave vectors, and may require the tuning of structural or material parameters, they are relatively difficult to find by standard numerical methods. Iterative methods may be used, but good initial guesses are required. To determine all diffraction anomalies in a given frequency interval, it is necessary to repeatedly solve the diffraction problem for many frequencies. In this paper, an efficient numerical method is developed for computing diffraction anomalies. The method relies on nonlinear eigenvalue formulations for scattering anomalies and solves the nonlinear eigenvalue problems by a contour-integral method. Numerical examples involving periodic arrays of cylinders are presented to illustrate the new method.

Mesoscopic simulations of inertial drag enhancement and polymer migration in viscoelastic solutions flowing around a confined array of cylinders

We study the flow around a periodic array of cylinders using a mesoscopic viscoelastic fluid that mimics polymeric solutions. We model our fluid employing a novel mesoscopic method based on Smoothed Dissipative Particle Dynamics and FENE springs. We characterize the static and dynamic properties of our model solutions and compare the results with theoretical predictions based on the Zimm model. After rheological characterization of the modeled solutions, we simulate the flow around a confined array of cylinders. The balance between inertia and elasticity in our simulations is studied using a wide range of Reynolds (Re) and Weissenberg (Wi) numbers. We find that increasing the flow rate reduces the drag coefficient on the cylinder up to a critical Re corresponding to a minimum. Thereafter, inertia becomes dominant and we encounter drag enhancement for all the solutions studied, including the Newtonian solvent. With the use of simple model for the viscous and inertial contributions to drag, we conclude that inertial effects are driving the increase in the drag experienced by the cylinder. In our simulations, we also observe migration of polymer chains away from the channel walls and in the wake of the cylinder. We conclude that stress gradients induced by the curvature of streamlines and convection of the depleted layers at the walls as the principal mechanisms driving the migration of chains. We find the extent of the migration correlates well with the viscoelastic Mach number (Ma = Re Wi ) suggesting that both elastic and inertial effects play a role in this phenomenon. • A mesoscopic model fluid with viscoelastic behavior is presented. • The drag on a confined array of periodically spaced cylinders is investigated. • Drag enhancement is explained with a simple model combining inertial and viscous drag. • Polymeric migration at the walls and the wake of the cylinders is investigated.

Design of multi-material sound transmission blocker using additive manufacturing

Additive manufacturing is most commonly done through 3D printing, which can print in multiple materials. This enables the design and construction of new structures that can block sound transmission, such as a periodic array of TPU plastic cylinders embedded in a matrix of PLA plastic. The difference in wave speed between the plastics can cause reflections and interference inside the material. However, printing in multimaterials provides distinct challenges for the current 3D printing technology. When printing with multiple nozzles, the inactive nozzle can clog, and getting the two materials to fuse can yield warping and separation. We addressed these problems to fabricate a sample of TPU cylinders (1.8 cm diameter, 8.6 cm height) embedded in PLA (20 cm × 10 cm × 2 cm) and measured the change in STL relative to a block of PLA. We discovered an improved attenuation of about 5.5 dB at 6300 Hz.

The Coupled Volume of Fluid and Brinkman Penalization Methods for Simulation of Incompressible Multiphase Flows

In this work, we contribute to the development of numerical algorithms for the direct simulation of three-dimensional incompressible multiphase flows in the presence of multiple fluids and solids. The volume of fluid method is used for interface tracking, and the Brinkman penalization method is used to treat solids; the latter is assumed to be perfectly superhydrophobic or perfectly superhydrophilic, to have an arbitrary shape, and to move with a prescribed velocity. The proposed algorithm is implemented in the open-source software Basilisk and is validated on a number of test cases, such as the Stokes flow between a periodic array of cylinders, vortex decay problem, and multiphase flow around moving solids.

High-efficiency all-silicon metasurfaces with 2π phase control based on multiple resonators

Flat all-silicon metasurfaces have significant potential as ultrathin optical devices and systems that offer the advantages of mature fabrication technology and complementary metal–oxidesemiconductor compatibility. However, previously reported all-silicon metasurfaces suffered from the drawback of low transmission owing to the large intrinsic reflection loss induced by high-index silicon substrates. To achieve high transmission, silicon-based metasurfaces are usually composed of low-index dielectric substrates and silicon pillars. It is still a substantial challenge for an all-silicon metasurface to realize high transmission. In this paper, we present a design to overcome this drawback by integrating two-dimensional periodic arrays of subwavelength silicon cylinders as perfect antireflection resonators on the bottom and top surfaces of the silicon substrate. Using this design, a uniform array of all-silicon unit cells comprising a metasurface can exhibit high transmission, up to 99.5%, at the target wavelength of 10.6 µm, which indicates a significant improvement over the design without the antireflection scheme. Furthermore, as an example of a metasurface application, an all-silicon polarization-insensitive metalens is built based on a series of all-silicon unit cells with high transmission and 2π phase control, which indicates subwavelength-focusing capability. The transmission of the entire metalens reached 81.9%, and the focusing efficiency was 71%. This study not only recommends a means to develop ultrathin all-silicon optical devices with high efficiency but also proposes a general approach to achieve high-quality metasurfaces based on a single high-index dielectric.

Parametric dependence of bound states in the continuum in periodic structures: Vectorial cases

A periodic structure sandwiched between two homogeneous media can support bound states in the continuum (BICs) that are valuable for many applications. It is known that generic BICs in periodic structures with an up-down mirror symmetry and an in-plane inversion symmetry are robust with respect to structural perturbations that preserve these two symmetries. For two-dimensional (2D) structures with one periodic direction and the up-down mirror symmetry (without the in-plane inversion symmetry), it was recently established that some scalar BICs can be found by tuning a single structural parameter. In this paper, we analyze vectorial BICs in such 2D structures, and show that a typical vectorial BIC with nonzero wave numbers in both the translationally invariant and the periodic directions can only be found by tuning two structural parameters. Using an all-order perturbation method, we prove that such a vectorial BIC exists as a curve in the 3D space of three generic parameters. Our theory is validated by numerical examples involving periodic arrays of dielectric cylinders. The numerical results also illustrate the conservation of topological charge when structural parameters are varied, if both BICs and circularly polarized states are included. Our study reveals a fundamental property of BICs in periodic structure and provides a systematical approach for finding BICs in structures with less symmetry.

High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation

Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of exponential gradients in polymeric stress fields, which can lead to catastrophic instabilities if not carefully handled. A key development to overcome this issue is the log-conformation formulation, which has been applied to a range of numerical methods, but not previously applied to Smoothed Particle Hydrodynamics (SPH). Here we present a 2D incompressible SPH algorithm for viscoelastic flows which, for the first time, incorporates a log-conformation formulation with an elasto-viscous stress splitting (EVSS) technique. The resulting scheme enables simulations of flows at high Weissenberg numbers (accurate up to Wi=85 for Poiseuille flow). The method is robust, and able to handle both internal and free-surface flows, and a range of linear and non-linear constitutive models. Several test cases are considerd included flow past a periodic array of cylinders and jet buckling. This presents a significant step change in capabilties compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.

Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders

Bound states in the continuum (BICs) in a periodic structure sandwiched between two homogeneous media have interesting properties and useful applications in photonics. The topological nature of BICs was previously revealed based on a topological charge related to the far-field polarization vector of the surrounding resonant states. Recently, it was established that when symmetry-protected BICs (with a nonzero topological charge) are destroyed by generic symmetry-breaking perturbations, pairs of circularly polarized resonant states (CPSs) emerge and the net topological charge is conserved. A periodic structure can also support propagating BICs with a nonzero wave vector. These BICs are not protected by symmetry in the sense of symmetry mismatch, but they need symmetry for their robust existence. Based on a highly accurate computational method for a periodic array of slightly noncircular cylinders, we show that a propagating BIC is typically destroyed by a structural perturbation that breaks only the in-plane inversion symmetry, and when this happens, a pair of CPSs of opposite handedness emerge so that the net topological charge is conserved. We also study the generation and annihilation of CPSs when a structural parameter is varied. It is shown that two CPSs with opposite topological charge and the same handedness, connected to two BICs or in a continuous branch from one BIC, may collapse and become a CPS with a zero charge. Our study clarifies the important connection between symmetry and topological charge conservation.

Analysis of a 2D Periodic Array of Metal Cylinders with Lumped Elements in Passband

Eigenwaves of a homogeneous electromagnetic crystal (EMC) that represents a 2D array of metal cylinders with gaps containing lumped elements (LEs) forming a parallel LC circuit are studied. The array of cylinders with LEs is installed inside a planar waveguide (PW). Variations in the parameters of the EMC eigenwaves due to variations in the capacitance are analyzed. The problem of eigenwaves is solved with the aid of numerical electrodynamic simulation in the HFSS system using periodic boundary conditions. Dependences of the main technical parameters, in particular, passband on the geometrical parameters of the structure and circuit parameters are considered. It is shown that a decrease in the height of the PW filled with a dielectric material can be used to improve the EMC quality parameters. Excitation of a finite-width EMC layer is considered. It is shown that the main results obtained for the regime of eigenwaves are proven by the solution to the problem of the EMC excitation.

Regimes of flow through cylinder arrays subject to steady pressure gradients

Flows through periodic cylinder arrays have been studied extensively for applications to heat exchangers, porous media, chemical reactors, and computational fluid mechanics. Nevertheless, the variation of the pore and macro-scale flow-regimes with porosity, driving pressure gradient, and cylinder arrangement remains not fully explored. We consequently perform a thorough parametric study of such regimes for both inline and staggered arrays of circular cylinders. The Navier–Stokes and continuity equations are solved using finite-volume and immersed boundary methods. We vary the porosity from minimum values for which cylinders nearly touch, to values approaching unity. We vary the Reynolds number from values producing Stokes flow to those producing pore-scale vortex shedding. Using the results of over 1000 simulations, we explore how competition between viscous and inertial effects produces five macroscopic flow regimes. We document the validity limits of each regime, and explore how they impact the modelling of non-Darcy flow regimes. We find the practice of fitting Forchheimer-type equations to data from a wide range of Reynolds numbers produces conflicting results in the literature. For inline arrays, the Forchheimer regime is not always present, and has a smaller validity regime than alternative models. For staggered arrays, the Forchheimer regime has a strong presence, but care must be taken to account for the presence of two different Forchheimer-type regimes. We also show that transition to vortex shedding is sensitive to the numerical domain size, because the mode of instability need not be periodic over the same unit cell as the steady flow. This significantly complicates the study of vortex shedding.

Influence of the Plasmonic Nanodisk Positions Inside a Magnetic Medium on the Faraday Effect Enhancement

Light localization by metal particles of nanometer size allows to not only control the propagation of light, but also enhance magneto‐optical effects. The influence of the immersion of gold nanodisks inside a transparent magnetic medium, namely, Bi‐substituted iron garnet, is investigated, and the optimal position of the nanoparticles within the magnetic material for a strong enhancement of the effect is unraveled. Three samples with periodic arrays of Au cylinders are studied: disks on the surface of the magnetic dielectric film, inside the magnetic film, and directly under the magnetic film. The largest enhancement of the Faraday effect mediated by a localized surface plasmon resonance takes place when nanodisks are submerged inside the magnetic film at a few nanometers below its upper surface. It is shown that the most prominent influence on the Faraday effect enhancement is provided by the magnetic medium between the nanodisks. The experimental results are in good agreement with the numerical analysis.

Shape analysis of the longitudinal flow along a periodic array of cylinders

We study the behavior of the longitudinal flow along a periodic array of cylinders upon perturbations of the shape of the cross section of the cylinders and the periodicity structure, when a Newtonian fluid is flowing at low Reynolds numbers around the cylinders. The periodicity cell is a rectangle of sides of length l and 1/l, where l is a positive parameter, and the shape of the cross section of the cylinders is determined by the image of a fixed domain through a diffeomorphism ϕ. We also assume that the pressure gradient is parallel to the cylinders. Under such assumptions, for each pair (l,ϕ), one defines the average of the longitudinal component of the flow velocity Σ[l,ϕ]. Here, we prove that the quantity Σ[l,ϕ] depends analytically on the pair (l,ϕ), which we consider as a point in a suitable Banach space.

Enhancement of Sea Wave Potential Energy with Under-Sea Periodic Structures: A Simulation and Laboratory Study

This paper is devoted to a theoretical investigation on the wave amplitude enhancement of surface sea water waves with under-sea periodic arrays of cylinders. A two-dimensional shallow water wave equation is derived and solved by using the plane-wave expansion method. The lattice types studied here include triangular, square and hexagonal lattices. These under-sea structures alter the sea bottom topography and induce constructive interference on the surface water waves. Given that the wave potential energy is dependent on the square of the wave amplitude, this mechanism can thus be used to increase the potential energy. It is shown that the enhancement factor depends on two geometric parameters and the maximum wave amplitude can be found by adjusting the two geometric parameters. Among the lattice types, the triangular and square lattice structures can induce more wave amplitude enhancement (and thus potential energy) than the hexagonal structures. Guided by numerical simulations, we have performed a reduced-scale water tank experiment to demonstrate the feasibility of the proposed idea. Preliminary experimental results show promising evidence of the predicted wave amplitude enhancement, suggesting perspective real-scale nearshore deployment and test.

Nonlocal dynamics of dissipative phononic fluids

We describe the nonlocal effective properties of a two-dimensional dissipative phononic crystal made by periodic arrays of rigid and motionless cylinders embedded in a viscothermal fluid such as air. The description is based on a nonlocal theory of sound propagation in stationary random fluid/rigid media that was proposed by Lafarge and Nemati [Wave Motion 50, 1016 (2013)]. This scheme arises from a deep analogy with electromagnetism and a set of physics-based postulates including, particularly, the action-response procedures, whereby the effective density and bulk modulus are determined. Here, we revisit this approach, and clarify further its founding physical principles through presenting it in a unified formulation together with the two-scale asymptotic homogenization theory that is interpreted as the local limit. Strong evidence is provided to show that the validity of the principles and postulates within the nonlocal theory extends to high-frequency bands, well beyond the long-wavelength regime. In particular, we demonstrate that up to the third Brillouin zone including the Bragg scattering, the complex and dispersive phase velocity of the least-attenuated wave in the phononic crystal which is generated by our nonlocal scheme agrees exactly with that reproduced by a direct approach based on the Bloch theorem and multiple scattering method. In high frequencies, the effective wave and its associated parameters are analyzed by treating the phononic crystal as a random medium.

Rapidly convergent quasi-periodic Green functions for scattering by arrays of cylinders-including Wood anomalies.

This paper presents a full-spectrum Green-function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section-with application to wire gratings, particle arrays and reflectarrays and, indeed, general arrays of conducting or dielectric bounded obstacles under both transverse electric and transverse magnetic polarized illumination. The proposed method, which, for definiteness, is demonstrated here for arrays of perfectly conducting particles under transverse electric polarization, is based on the use of the shifted Green-function method introduced in a recent contribution (Bruno & Delourme 2014 J. Computat. Phys.262, 262-290 (doi:10.1016/j.jcp.2013.12.047)). A certain infinite term arises at Wood anomalies for the cylinder-array problems considered here that is not present in the previous rough-surface case. As shown in this paper, these infinite terms can be treated via an application of ideas related to the Woodbury-Sherman-Morrison formulae. The resulting approach, which is applicable to general arrays of obstacles even at and around Wood-anomaly frequencies, exhibits fast convergence and high accuracies. For example, a few hundreds of milliseconds suffice for the proposed approach to evaluate solutions throughout the resonance region (wavelengths comparable to the period and cylinder sizes) with full single-precision accuracy.

Strong resonances on periodic arrays of cylinders and optical bistability with weak incident waves

A one-dimensional periodic array of circular dielectric cylinders surrounded by air is a simple structure on which guided modes above the light line, also called bound states in the continuum (BICs), may exist. Recent studies reveal that such an array supports not only antisymmetric standing waves which are symmetry-protected BICs, but also propagating Bloch BICs and symmetric standing waves. Near a BIC, there is a family of resonant modes (depending on the Bloch wave number $\ensuremath{\beta}$) with arbitrarily large quality factors. Using a perturbation method, we show that the quality factor of the resonant mode typically depends on $\ensuremath{\beta}$ like $1/{(\ensuremath{\beta}\ensuremath{-}{\ensuremath{\beta}}_{*})}^{2}$, where ${\ensuremath{\beta}}_{*}$ is the Bloch wave number of the BIC, but near a symmetric standing wave $({\ensuremath{\beta}}_{*}=0)$, the quality factor blows up like $1/{\ensuremath{\beta}}^{4}$. This indicates that strong resonances can be more easily induced near a symmetric standing wave. As an application, we numerically study optical bistability for the periodic array assuming the cylinders have a Kerr nonlinearity. With the nonlinear effects enhanced by the resonances, it is possible to have optical bistability for weak incident waves. The numerical results confirm that the weakest incident wave for optical bistability is realized through the resonances near the symmetric standing waves.