2D Periodic Structures Research Articles

Fabrication of complex periodic micro/nanopatterns by multiple interfered femtosecond laser pulses on thin solid films

Complex periodic micro/nanopatterns have been fabricated on zinc acetate thin films by the irradiation of three or two interfered 800 nm femtosecond laser beams. Three interfered laser beams produce 2D periodic microflower structures with petal sizes as small as 100 nm, which is much smaller than the laser wavelength and its diffraction-limited scale. While two interfered femtosecond laser beams lead to 2D arrayed grating-like patterns with a long period of ∼3.0 µm and a short period of ∼150 nm in two orthogonal directions, respectively. Theoretical calculation indicated that the long periodicities of flower/grating-like patterns were attributed to the interferential intensity distribution, whereas petal structures of microflowers or short periodicities of grating-like patterns were determined by the interferential polarisation distribution.

EFFICIENT SIMULATIONS OF PERIODIC STRUCTURES WITH OBLIQUE INCIDENCE USING DIRECT SPECTRAL FDTD METHOD

A simple and e-cient joint algorithm of flnite difierence time domain (FDTD) and periodic boundary condition (PBC), called as the direct spectral FDTD method, has been investigated to study three-dimensional (3D) periodic structures with oblique incidence, where both the azimuth angleand the elevation angle µ are varying. The number of sampling points for the horizontal wave number can be determined by using an adaptive approach. As numerical results, the transmission and re∞ection coe-cients from split-ring resonators (SRRs) and a dielectric grating slab are computed to validate the accuracy and e-ciency of the direct spectral FDTD method. The computed results are in good agreement to the published ones obtained by other methods.

Photocatalytic metamaterials: TiO2 inverse opals

The study of the photocatalytic activity of TiO(2) inverse opals showed that these structures behave as metamaterials: their properties arise principally from the 3D periodic structure of the material and marginally from porosity, reflectivity and scattering.

Self-Organization of Liquid-Crystal and Reactive-Mesogen into 2D Surface-Stabilized Structures

We report the experimental observation of light induced self-organization of 2D periodic structures at the liquid interface of thick nematic liquid crystal and thin reactive mesogen layers. We believe that the long scale thermal fluctuations initiate interpenetration of those two molecular species, and the geometrical asymmetry and matrix-imposed anisotropy result in very specific symmetry properties of the final blend. The photo-polymerization of the reactive mesogen is further amplifying its spatial redistribution and is fixing (stabilizing) the obtained liquid-crystal/surface-attached polymer network. The application of a strong electric field is definitely adjusting that network in terms of morphology and electro-optical response. The origin of the formation of regular and oriented periodic structures remains unclear.

PROFILES OPTIMIZATION AND CHARACTERIZATIONS OF 1D AND 2D PLASMONIC CRYSTALS

Surface plasmon polariton is surface electromagnetic waves that propagate parallel along a metal/dielectric interface through a 1D or 2D periodic structures. Since the polaritons wave is confined at interface, the surface plasma polariton (SPP) is very sensitive to any changes on this boundary that directly change the effective refractive index of the system. This enables us to do some variations to control the SPP, i.e., modifying the metallic nanostructure of the plasmonic crystal (PCL) to vary the effective refractive index. Interference lithography has been widely used to produce different orders of periodic/array of nanostructures. It also has been used as the most economist and efficient way to provide 1D and 2D plasmonic crystals over large area. However, this method suffers from nonlinear processes involved in the manufacture of nominally sinusoidal surface relief diffraction gratings that can introduce distortions. Such distortions may dramatically affect both the specular reflectivity and diffracted efficiencies from plasmonic crystals. Therefore, the quality of surface profile and some geometrical parameters need to be controlled in order to optimize the coupling condition. This will lead us to the understanding of the fundamental geometrical contribution to obtain the field enhancement and variety of profile qualities.

Plasma Amino Acid Coatings for a Conformal Growth of Titania Nanoparticles

We report on the conformal synthesis of ultrathin films from the amino acid histidine on flat silicon substrates and 3D periodic polymer structures via plasma enhanced chemical vapor deposition. We demonstrate the efficient utilization of this functional amino acid nanocoating for the formation of individual titania nanoparticles with dimensions from 2 to 15 nm depending upon reduction conditions. The titania nanoparticles were grown directly on histidine-functionalized planar and 3D polymer substrates by a wet-chemistry method that showed uniform surface coverage that reached approximately 75%. This approach demonstrates the potential for modifying the optical properties of periodic porous polymeric structures via direct conformal growth of titania nanoparticles.

Analysis and optimization of heterogeneous materials using the variational asymptotic method for unit cell homogenization

The variational asymptotic method for unit cell homogenization is used to find the sensitivity of the effective properties of periodically heterogeneous materials, within a periodic base-cell. The sensitivities are found by the direct differentiation of the variational asymptotic method for unit cell homogenization (VAMUCH) and by the method of adjoint variables. This sensitivity theory is implemented using the finite element method and the engineering program VAMUCH. The methodology is used to design the periodic microstructure of a material that allows obtaining prescribed constitutive properties. The microstructure is modeled as a 2D periodic structure, but a complete set of 3D material properties are obtained. Furthermore, the present methodology can be used to perform the micromechanical analysis and related sensitivity analysis of heterogeneous materials that have 3D periodic structures. The effective material properties of the artificially mixed materials of the microstructure are obtained by the density approach, in which the solid material and void are mixed artificially.

Fabrication of desired three-dimensional structures by holographic assembly technique

We demonstrate a novel technique to fabricate desired three-dimensional (3D) periodic structures by holographically assembling multiple one-dimensional (1D) or multiple two-dimensional (2D) structures. Thanks to the high-absorption effect of the used material, we fabricated for each time, by employing a two-beam interference technique, a 1D or a 2D structure with very limited film thickness. By using the same sample and repeating the same fabrication process, i.e., (i) spin coating, (ii) exposure, and (iii) post-exposure bake, we created, layer-by-layer, a 3D structure as desired, without the limitation of the number of layers. This technique allows rapid fabrication of very large and thick 3D photonic crystal template with variable period, flexible design, low cost, and possible introduction of arbitrary defects inside a 3D structure.

Grating-assisted generation of 2D surface plasmon interference patterns for nanoscale photolithography

Generation of 2D surface plasmon interference patterns using a 3D metal-dielectric diffraction structure is studied. The potential application field is surface plasmon interference nanolithography aimed at fabrication of 3D periodic structures. The considered structure consists of a 3D dielectric diffraction grating with a metal film applied in the substrate region. The diffraction grating is designed to transform the incident wave into a set of surface plasmons that generate 2D interference pattern underneath the metal film. The configuration of the interference patterns is analyzed theoretically. It is shown by simulations within the rigorous electromagnetic theory that high-contrast interference patterns with the period 2.5–3.5 times smaller than the incident wave length can be produced. The configuration of the calculated patterns coincides with theoretically estimated ones. At the interference maxima electric field intensity exceeds incident wave intensity by an order of magnitude. The ways to control the form and period of the interference pattern by changing polarization and length of the incident wave are presented.

含各向异性无磁左手介质周期结构中的光子带隙研究

We demonstrate a photonic band gap (PBG) from one-dimensional (1D) periodic structures created by a double-layer unit cell with an air layer and an anisotropic nonmagnetic left-handed metamaterial (LHM) layer whose permittivity elements are partially negative. The requirements imposed on the materials and structures to realize a PBG are derived when the frequency is above or below the cutoff frequency, and the transmission properties of the PBG are discussed by utilizing 4x4 transfer-matrix method with dispersive semiconductor metamaterial.

Fabrication of two- and three-dimensional periodic submicron structures by holographic lithography with a 635 nm laser and matched photopolymer

2D and 3D submicron periodic structures are first fabricated by red-induced photopolymerization using a common 635 nm semiconductor laser and specially developed red-sensitive polymer material. The principle of this new photopolymer material fabrication is explained and the absorption spectra of the material are measured. This fabrication technique allows a deeper penetration into volume and larger interference irradiation area which is more than 1 cm2. The optical design, theoretical calculations and experimental results including diffraction patterns verifying the formation of periodic structures are presented. Compared with other fabrication technologies using high-power lasers, this approach has greatly reduced the demand for laser apparatus. Therefore, it is much more accessible to most laboratories and potentially usable in holographic fabrication of photonic crystals and devices in micro electro-mechanical systems (MEMS).

Multiobjective topology optimization for finite periodic structures

Many engineering structures consist of specially-fabricated identical components, thus their topology optimizations with multiobjectives are of particular importance. This paper presents a unified optimization algorithm for multifunctional 3D finite periodic structures, in which the topological sensitivities at the corresponding locations of different components are regulated to maintain the structural periodicity. To simultaneously address the stiffness and conductivity criteria, a weighted average method is employed to derive Pareto front. The examples show that the optimal objective functions could be compromised when the total number of periodic components increases. The influence of thermoelastic coupling on optimal topologies and objectives is also investigated.

Floquet's Unit Cell Design for Periodic Structures at Optical Frequencies

We present a new theoretical approach regarding the design of 2D periodic structure at optical frequencies. The model is based on Floquet's theory and on the variational equivalent circuit. The distributed circuit model is developed through the use of the microwave network theory and the optical theory of the step discontinuities. This approach analyzes 2D dielectric periodic structures with high dielectric contrast by the transmission line model including variational equivalent circuits. The 3D Finite Element Method (FEM) model validates Floquet's design theory of the grating resonance and provides the design optimization of an optical GaAs periodic waveguide.

Phononic crystals and manipulation of sound

AbstractThe acoustic properties of phononic crystals are presented, using numerical simulations. In a first part we study some possible applications of these composite materials. In particular, we show that defect modes (cavities, wave guides, stubs...) inserted inside the 2D periodic structure may lead to the possibility of manipulating the propagation of sound and realizing selective frequency filters and efficient devices for wavelength demultiplexing. We also report on the vibration modes of a 2D plate, i.e. a phononic crystal of finite thickness along the axis of the inclusions. We investigate the existence of absolute band gaps in the band structure of the plate, either free or deposited on a substrate. This should open new perspectives in the field of high‐frequency radiofrequency devices. Finally, we present the possibility of devicing sonic insulators for frequencies of the order of kHz with relatively small thicknesses of the phononic crystal sample as compared to the wavelength. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The vibrational properties of a periodic composite pipe in 3D space

Piping system vibrations exist in many fields. Vibration control is very important because it can limit possible damage to pipe systems caused by vibrations. Applying the idea of the Bragg scattering mechanism of phononic crystals (PCs), a pipe is designed as a periodic composite material structure. Using the transfer matrix method, the band structure of an infinite periodic straight pipe structure is calculated. With knowledge of the vibration band gaps, a 3D space pipe system is designed with a composite material periodic structure, and its various vibration modes’ frequency response functions are calculated. The accuracy of the transfer matrix method is verified with the commercial software MSC.Actran. The results show that the Bragg band gaps still exist in the 3D periodic pipe structure, and vibrations are strongly attenuated within the frequency ranges of the band gaps. Using the idea of PCs in piping systems provides a novel way to reduce pipe vibration.

Optical induction of three-dimensional photonic lattices and enhancement of discrete diffraction

We demonstrate experimentally the formation of three-dimensional (3D) reconfigurable photonic lattices in a bulk nonlinear crystal by employing the optical induction technique. Such 3D lattices are established by inducing 2D square lattices in two orthogonal directions. The induced 3D periodic index structures are monitored by plane-wave guidance and Brillouin zone spectroscopy. Enhanced discrete diffraction due to the waveguide modulation and coupling in 3D lattices is also observed.

One‐ and two‐dimensional porous silicon photonic crystals: momentum dispersion relations and stopbands analysis

AbstractWe report on a novel approach to analyze and measure the optical properties of one‐ and two ‐dimensional photonic crystals (PCs) in all spatial directions inlcluding the symmetry axis of the PCs. The analysis is based on calculating momentum dispersion relations between the ordinary and the Bloch components of the wavevector and finding momentum stop‐bands of the PC. This method provides a direct way to analyze the angular dependence of the reflection and the diffraction pattern of a monochromatic optical beam approaching the PC. Measurements have been performed on 1D PCs, e.g., 1D periodic structures of micro‐porous silicon and 2D periodic arrays of macro‐porous silicon. The periodicity of these PCs is about 2.5 to 4 μm so that their momentum stop‐bands fall in the mid‐infrared (IR) wavelengths. We analyze several geometries, including slabs and prisms, to map the momentum dispersion relations and stopbands associated with guided and radiation modes. Angular reflection and diffraction measurements using a tunable CO2 laser showed a good agreement with the calculated momentum dispersion relations. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Microwave waveguides in EBG structures formed from coaxial cylinders

Infinite 2D periodic EBG structures from coaxial metal cylinders placed in a planar waveguide are investigated. Short-circuited and open-circuited metal cylinders forming, respectively, short-circuited and open-circuited sections of coaxial transmission lines are considered. It is shown that, by varying the lengths of these coaxial lines, it is possible to create defects in EBG structures that form regular waveguides. The eigenmodes of such waveguides are studied. It is shown that the EBG structures formed from coaxial metal cylinders can be used as the base for the development of multifunction microwave devices.

Layer‐by‐Layer Interference Lithography of Three‐dimensional Microstructures in SU‐8

We report on rapid fabrication of two-, two and a half-, and 3D planar periodic structures using layer-by-layer deposition and interference patterning of SU-8 photoresist. Complex structures with non-periodic vertical symmetry were fabricated controlling the cure depth by addition of a UV absorber. The fabrication method reported here can be applied for the high-volume manufacturing of solid structures for microelectromechanical systems and microfluidic devices.

Synthesis of bandpass filters designed on the basis of 1D PBG structures

A technique for the synthesis of bandpass filters designed on the basis of 1D periodic structures with resonant defects is proposed. Conditions under which the filter’s frequency characteristic approaches a Chebyshev characteristic or a maximally flat characteristic are formulated. The synthesis problem is reduced to solution of a system of nonlinear equations. Numerical results are obtained for the particular case of a periodic structure composed of dielectric layers.