Types Of Periodic Structures Research Articles

High period frequency LIPSS emerging on 304 stainless steel under the irradiation of femtosecond laser double-pulse trains

In this work, we used femtosecond laser double-pulse trains to produce laser-induced periodic surface structures (LIPSS) on 304 stainless steel. Surprisingly, a novel type of periodic structure was discovered, which, to the best of our knowledge, is the first in literature. We surmised that the cause for this novel LIPSS was related to the weak energy coupling of subpulses when the intrapulse delay was longer than the thermal relaxation time of stainless steel. Furthermore, we found that the fluence combination and arrival sequence of subpulses in a double-pulse train also influenced LIPSS morphology.

Self-assembled three-dimensional periodic micro-nano structures in bulk quartz crystal induced by femtosecond laser pulses.

In-volume, self-assembled, three-dimensional, periodic micro-nano structures are induced in quartz crystal by tightly focused, 500-kHz femtosecond laser pulses. With suitable pulse energy, three different types of periodic structures can be observed in modified regions using scanning electron microscopy. The first one with period (ΛE) of ~400 nm in the direction of the laser polarization, i.e. nanograting, shows indicative features similar to that in fused silica. The second one with period (ΛS) in the scan direction and the third one with period (Λk) in the laser propagation direction are both equally spaced by ~1 μm, which is close to the laser wavelength. Moreover, the structure with period (Λk) covers almost the whole cross-section of modified regions, which is distinctive to that observed in fused silica. Through the comparison of the structures induced by 1-kHz pluses and those by 500-kHz pluses, we deduce that the heat accumulation effect may have a positive influence on the formation of nanogratings in quartz crystal.

Broadband magnetoelastic coupling in magnonic-phononic crystals for high-frequency nanoscale spin-wave generation

Spin waves are promising candidates for information carriers in advanced technology. The interactions between spin waves and acoustic waves in magnetic nanostructures are of much interest because of their potential application for spin wave generation, amplification and transduction. We investigate numerically the dynamics of magnetoelastic excitations in a one-dimensional magphonic crystal consisting of alternating layers of permalloy and cobalt. We use the plane wave method and the finite element method for frequency- and time-domain simulations, respectively. The studied structure is optimized for hybridization of specific spin-wave and acoustic dispersion branches in the entire Brillouin zone in a broad frequency range. We show that this type of periodic structure can be used for efficient generation of high-frequency spin waves.

Vibration isolation characteristics of finite periodic tetra-chiral lattice coating filled with internal resonators

Owing to their locally resonant mechanism, internal resonators are usually used to provide band gaps in low-frequency region for many types of periodic structures. In this study, internal resonators are used to improve the vibration attenuation ability of finite periodic tetra-chiral coating, enabling high reduction of the radiated sound power by a vibrating stiffened plate. Based on the Bloch theorem and finite element method, the band gap characteristics of tetra-chiral unit cells filled with and without internal resonators are analysed and compared to reveal the relationship between band gaps and vibration modes of such tetra-chiral unit cells. The rotational vibration of internal resonators can effectively strengthen the vibration attenuation ability of tetra-chiral lattice and extend the effective frequency range of vibration attenuation. Two tetra-chiral lattices with and without internal resonators are respectively designed and their vibration transmissibilities are measured using the hammering method. The experimental results confirm the vibration isolation effect of the internal resonators on the finite periodic tetra-chiral lattice. The tetra-chiral lattice as an acoustic coating is applied to a stiffened plate, and analysis results indicate that the internal resonators can obviously enhance the vibration attenuation ability of tetra-chiral lattice coating in the frequency range of the band gap corresponding to the rotating vibration mode of internal resonators. When the soft rubber with the internal resonators in tetra-chiral layers has gradient elastic modulus, the vibration attenuation ability and noise reduction of the tetra-chiral lattice coating are basically enhanced in the frequency range of the corresponding band gaps of tetra-chiral unit cells.

Phase diagram for the transition from photonic crystals to dielectric metamaterials.

Photonic crystals and dielectric metamaterials represent two different classes of artificial media but are often composed of similar structural elements. The question is how to distinguish these two types of periodic structures when their parameters, such as permittivity and lattice constant, vary continuously. Here we discuss transition between photonic crystals and dielectric metamaterials and introduce the concept of a phase diagram, based on the physics of Mie and Bragg resonances. We show that a periodic photonic structure transforms into a metamaterial when the Mie gap opens up below the lowest Bragg bandgap where the homogenization approach can be justified and the effective permeability becomes negative. Our theoretical approach is confirmed by microwave experiments for a metacrystal composed of tubes filled with heated water. This analysis yields deep insight into the properties of periodic structures, and provides a useful tool for designing different classes of electromagnetic materials with variable parameters.

Strong Optomechanical Coupling in Nanobeam Cavities based on Hetero Optomechanical Crystals.

Nanobeam cavities based on hetero optomechanical crystals are proposed. With optical and mechanical modes separately confined by two types of periodic structures, the mechanical frequency is designed as high as 5.88 GHz. Due to the optical field and the strain field concentrated in the optomechanical cavity and resembling each other with an enhanced overlap, a high optomechanical coupling rate of 1.31 MHz is predicted.

Collisionless electron heating in periodic arrays of inductively coupled plasmas

A novel mechanism of collisionless heating in large planar arrays of small inductive coils operated at radio frequencies is presented. In contrast to the well-known case of non-local heating related to the transversal conductivity, when the electrons move perpendicular to the planar coil, we investigate the problem of electrons moving in a plane parallel to the coils. Two types of periodic structures are studied. Resonance velocities where heating is efficient are calculated analytically by solving the Vlasov equation. Certain scaling parameters are identified. The concept is further investigated by a single particle simulation based on the ergodic principle and combined with a Monte Carlo code allowing for collisions with Argon atoms. Resonances, energy exchange, and distribution functions are obtained. The analytical results are confirmed by the numerical simulation. Pressure and electric field dependences are studied. Stochastic heating is found to be most efficient when the electron mean free path exceeds the size of a single coil cell. Then the mean energy increases approximately exponentially with the electric field amplitude.

Temporal femtosecond pulse shaping dependence of laser-induced periodic surface structures in fused silica

The dependence of periodic structures and ablated areas on temporal pulse shaping is studied upon irradiation of fused silica by femtosecond laser triple-pulse trains. Three types of periodic structures can be obtained by using pulse trains with designed pulse delays, in which the three-dimensional nanopillar arrays with ∼100–150 nm diameters and ∼200 nm heights are first fabricated in one step. These nanopillars arise from the break of the ridges of ripples in the upper portion, which is caused by the split of orthogonal ripples in the bottom part. The localized transient electron dynamics and corresponding material properties are considered for the morphological observations.

Analysis on band gap properties of periodic structures of bar system using the spectral element method

In this paper, the band gap properties of the periodic structures of bar system, which include the rod-joint, truss, and frame structures, are studied using spectral element method (SEM). The spectral equations of the rod, beam, and joint elements are established and the spectral equations of the whole structures are further assembled. The frequency responses of the whole structures are calculated and the results are compared with those calculated by the finite element method (FEM). It can be observed that the SEM is more accurate in high frequency ranges. The band gap properties of the three types of periodic structures are studied, respectively. Furthermore, the effects of structural length, unit cell number, structural configurations, load conditions, and structural damping on the band gap properties are investigated.

BACK RADIATION REDUCTION IN PATCH ANTENNAS USING PLANAR SOFT SURFACES

In this work, we propose to use a type of periodic structures, the soft surfaces in their planar version, to reduce the back radiation of patch antennas. A key aspect of these surfaces when compared to other periodic structures is their anisotropy which provides different behaviour for different field polarization (horizontal or vertical). This make them especially convenient for this application, as the soft surfaces force the field intensity for any polarization to be zero on the surface for waves propagating along the surface. In this paper, a design example is presented and the back radiation reduction by using planar soft surfaces is demonstrated.

Periodic Structures for Improved Light Management in Thin-film Silicon Solar Cells

AbstractAdvanced light management in thin-film solar cells is important in order to improve the photo-current and, thus, to raise up the conversion efficiencies of the solar cells. In this article two types of periodic structures ¡V one-dimensional diffraction gratings and photonic crystals,are analyzed in the direction of showing their potential for improved light trapping in thin-film silicon solar cells. The anti-reflective effects and enhanced scattering at the gratings with the triangular and rectangular features are studied by means of two-dimensional optical simulations. Simulations of the complete microcrystalline solar cell incorporating the gratings at all interfaces are presented. Critical optical issues to be overcome for achieving the performances of the cells with the optimized randomly textured interfaces are pointed out. Reflectance measurements for the designed 12 layer photonic crystal stack consisting of amorphous silicon nitride and amorphous silicon layers are presented and compared with the simulations. High reflectance (up to 99 %) of the stack is measured for a broad wavelength spectrum. By means of optical simulations the potential for using a simple photonic crystal structure as a back reflector in an amorphous silicon solar cell is demonstrated.

Self-assembled periodic sub-wavelength structures by femtosecond laser direct writing

Self-assembled, sub-wavelength periodic structures are induced in fused silica by a tightly focused, linearly polarized, femtosecond laser beam. Two different types of periodic structures, the main one with period (Lambda(E)) in the direction of the laser beam polarization and the second with period (Lambda(k)) in the direction of the light propagation, are identified from the cross-sectional images of the modified regions using scanning electron microscopy. We demonstrate the spatial coherence of these nanogratings in the plane perpendicular to the beam propagation direction. The range of effective pulse energy which could produce nanogratings narrows when the pulse repetition rate of writing laser increases. The period Lambda(E) is proportional to the wavelength of the writing laser and period Lambda(k) in the head of the modified region remains approximately the wavelength of light in fused silica.

Fabrication of two- and three-dimensional periodic structures by multi-exposure of two-beam interference technique

A simple and efficient optical interference method for fabricating high quality two- and three-dimensional (2D and 3D) periodic structures is demonstrated. Employing multi-exposure of two-beam interference technique, different types of periodic structures are created depending on the number of exposure and the rotation angle of the sample for each exposure. Square and hexagonal 2D structures are fabricated by a multi-exposure of two-beam interference pattern with a rotation angle of 90 masculine and 60 masculine between two different exposures, respectively. Three-exposure, in particular, results in different kinds of 3D structures, with close lattice constants in transverse and longitudinal directions, which is difficult to be obtained by the commonly used multi-beam interference technique. The experimental results obtained with SU-8 photoresist are well in agreement with the theoretical predictions. Multi-exposure of two-beam interference technique should be very useful for fabrication of photonic crystals.

Wavelet-based multi-scale projection method in homogenization of heterogeneous media

Standard homogenization of highly heterogeneous media often filters out the fine scale information, and as a consequence, it produces acceptable results only for certain type of periodic structures. In this work, a wavelet-based multi-scale homogenization is introduced for highly heterogeneous materials where the standard asymptotic technique cannot be effectively applied. A set of scaling and wavelet functions based on the linear hat function and its corresponding wavelet transformation matrix are constructed. The advantages of this wavelet transformation constructed by hat function compared to that formulated using Haar function are identified. The mirror image technique has been employed to preserve the accurate representation of boundary conditions and to avoid numerical oscillation near the boundaries. This wavelet-based multi-scale transformation hierarchically filters out the high-scale components of the solution, and thus provides an effective framework for the multi-scale selection of the most essential scales of the solution.

Experimental study of the director pattern dynamics in the vicinity of the Fréedericksz twist geometry

We present an experimental study of the transient periodic structures appearing in the nematic director field in the magnetically induced reorientation of the director in the vicinity of the twist Fréedericksz geometry. Thin nematic samples (50 µm thick) were exposed to magnetic fields of variable intensity and orientation relative to the surface aligning direction of the sample. The director reorientation was induced by a rapid rotation of the sample in the static magnetic field producing a misalignment between the director and the magnetic field. The director field was optically monitored during the reorientation process and the transient periodic structures were characterized. Two types of periodic structures could be identified, namely bands and walls. Walls grow from bands close to the twist Fréedericksz geometry. The time dependence of the wave length and inclination of the periodic structures was obtained as a function of the magnetic field intensity and orientation relative to the surface aligning direction of the sample. The results for the bands are compared with the predictions of a model that we specifically developed to account for the non-orthogonal field orientations. It is seen that our model can account rather well for the experimental results considering that it uses only the field rotation time as adjustable parameter. All other model parameters are known.

Phononic band gaps and vibrations in one- and two-dimensional mass–spring structures

The vibrational response of finite periodic lattice structures subjected to periodic loading is investigated. Special attention is devoted to the response in frequency ranges with gaps in the band structure for the corresponding infinite periodic lattice. The effects of boundaries, viscous damping, and imperfections are studied by analyzing two examples; a 1-D filter and a 2-D wave guide. In 1-D the structural response in the band gap is shown to be insensitive to damping and small imperfections. In 2-D the similar effect of damping is noted for one type of periodic structure, whereas for another type the band gap effect is nearly eliminated by damping. In both 1-D and 2-D it is demonstrated how the free structural boundaries affect the response in the band gap due to local resonances. Finally, 2-D wave guides are considered by replacing the periodic structure with a homogeneous structure in a straight and a 90° bent path, and it is shown how the vibrational response is confined to the paths in the band gap frequency ranges.

Instabilities, Elasticity, and Wetting Effect in Multilayer Heteroepitaxial Growth

ABSTRACTFor multilayer semiconductor films comprising various material layers, the coupling of elastic states in different layers as well as the nonequilibrium nature of the growing process are essential in understanding the surface and interface morphological instability and hence the growth mechanisms of nanostructures in the overall film. We present the theoretical work on the stress-driven instabilities during the heteroepitaxial growth of multilayers, based on the elastic analysis and the continuous nonequilibrium model. We develop a general theory which determines the morphological evolution of surface profile of the multilayer system, and then apply the results to two types of periodic structures that are being actively investigated: alternating tensile/compressive and strained/spacer multilayers. The wetting effect, which arises from the material properties changing across layer-layer interfaces, is incorporated. It exhibits a significant influence of stabilization on film morphology, particularly for the short-period superlattices. Our results are consistent with the experimental observations in AlAs/InAs/InP(001) and Ge/Si(001) multilayer structures.

Some experiences from fdtd analysis of infinite and finite multi-octave phased arrays

Some experiences from finite-differences time-domain (FDTD) analysis of infinite and finite multi-octave phased arrays are presented. First, a more unified derivation of equations suitable for unit-cell analysis of phased arrays or other types of periodic structures using FDTD is presented. Second, results from FDTD calculations of small to very large multi-octave finite arrays are summarized in order to answer the question of how large an array model must be in order to capture the characteristics of both the interior and the edge elements of a large multi-octave phased array. It is found that a considerably larger number of elements is required in the broad-band case than in the normal narrow-band case, and it is also found that FDTD is well suited for such calculations. Third, simple methods to save computer memory using locally fine grids in an otherwise coarse FDTD grid to model finite-phased arrays are explored. The two local grid methods tested were found in our application to suffer from numerical instabilities.

Optical modes conversion in magneto-photonic crystal waveguides

We study the propagation of optical radiation in magnetic waveguides with the periodic domain structures (magneto-photonic crystals). Two types of periodic structures are studied––one- and two-dimensional (1D and 2D). Optical modes conversion is possessed by both the first- and second-order magneto-optic effects and scattering by the domains. In the 2D periodic structures conversion becomes anisotropic and strongly depends on the parameters of the structure. The parameters of the domain structures depend on the external magnetic field, therefore the conversion efficiency can be modulated by the variation of this field. A numerical analysis is provided of the dispersion of the interacting modes as well as of the dependence of the intensity of the converted radiation on the parameters of the domain structure.

Photonic band gaps from metallo-dielectric spheres

Joint theoretical and experimental efforts are launched to study the optical properties of photonic band-gap systems constructed with spheres containing a metal core or metallic coating. Using a multiple scattering method, we show that there can be photonic band gaps in different types of periodic structures as long as the sphere filling ratio exceeds a certain minimum. We have experimentally realized photonic crystals in the microwave regime, with the measured results in excellent agreement with the theoretical predictions.