Periodic Holes Research Articles

Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain

Let $A$ be an annular type domain in $\mathbb{R}^2$. Let $A_\delta$ be a perforated domain obtained by punching periodic holes of size $\delta$ in $A$; here, $\delta$ is sufficiently small. Suppose that $\J$ is the class of complex-valued maps in $A_\delta$, of modulus $1$ on $\partial A_\delta$ and of degrees $1$ on the components of $\partial A$, respectively $0$ on the boundaries of the holes. <br><br> We consider the existence of a minimizer of the Ginzburg-Landau energy <br><br> $E_\lambda(u)=\frac 1\2_[\int_{A_\delta}](|\nabla u|^2+\frac\lambda 2(1-|u|^2)^2)$ <br> among all maps in $u\in\J$. <br><br> It turns out that, under appropriate assumptions on $\lambda=\lambda(\delta)$, existence is governed by the asymptotic behavior of the $H^1$-capacity of $A_\delta$. When the limit of the capacities is $>\pi$, we show that minimizers exist and that they are, when $\delta\to 0$, equivalent to minimizers of the same problem in the subclass of $\J$ formed by the $\mathbb{S}^1$-valued maps. This result parallels the one obtained, for a fixed domain, in [3], and reduces homogenization of the Ginzburg-Landau functional to the one of harmonic maps, already known from [2]. <br><br> When the limit is $<\pi$, we prove that, for small $\delta$, the minimum is not attained, and that minimizing sequences develop vortices. In the case of a fixed domain, this was proved in [1].

Periodic Nanometer-Scale Holes Fabricated by Using Plasma Ashing Technique and Selective Liquid Phase Deposition

Periodic Nanometer-Scale Holes Fabricated by Using Plasma Ashing Technique and Selective Liquid Phase Deposition

Scanning of the bands of a microstructured fiber via its bending

The propagation-constant bands responsible for the loss in a microstructured quartz fiber with a cladding in the form of a periodic hexagonal hole structure and with a core in the form of a missing hole are investigated theoretically and experimentally. The theory is based on a new model of the cladding, which is represented as a set of strongly coupled optical waveguides of a triangular cross section. The strong coupling results in splitting of the propagation constants of these optical waveguides into bands. In the experiment, a new technique for scanning these bands is proposed and realized for the case when the fiber has a bend with a variable radius. The theory provides for an adequate description of the results.

Performance evaluation and optimization of a high-efficient phonon rectifier

We report rectification enhancement of acoustic waves through a double array of periodic triangular holes embedded in an elastic medium of an acoustic phonon rectifier. We numerically investigate the transmission rates of waves and hence the efficiency of the rectifier using the Finite-Difference-Time-Domain (FDTD) method. We alter the position of the arrays and investigate the optimal position for high-efficient rectification to facilitate practical applications.

Hybrid photovoltaic cell with well-ordered nanoporous titania–P3HT by nanoimprinting lithography

We have made bulk heterojunction hybrid photovoltaic cells with highly ordered nanoporous titania (TiO 2)–poly(3-hexylthiophene) (P3HT). The nanostructured titania, which has a periodic hexagonal hole array with 80–90 nm diameter, was fabricated by the nanoimprinting technique. The nanoporous titania was synthesized by coating the sol–gel mixture of titanium ethoxide (IV), HCl, and 2-propanol on indium tin oxide (ITO) surface. The coated surface was then embossed with an array of PMMA nanopoles, which was produced using a nanoporous alumina (Al 2O 3) template. The photovoltaic cells with nanostructured titania have a higher power conversion efficiency of 0.16% compared to conventional thin-film titania, under air mass 1.5 (100 mW/cm 2) global illumination.

Radiation‐induced fabrication of polymer nanoporous materials from microphase‐separated structure of diblock copolymers as a template

AbstractPolymer nanoporous materials with periodic cylindrical holes were fabricated from microphase‐separated structure of diblock copolymers consisting of a radiation‐crosslinking polymer and a radiation‐degrading polymer through simultaneous crosslinking and degradation by γ‐irradiation. A polybutadiene‐block‐poly(methyl methacrylate) (PB‐b‐PMMA) diblock copolymer film that self‐assembles into hexagonally packed poly(methyl methacrylate) cylinders in polybutadiene matrix was irradiated with γ‐rays. Solubility test, IR spectroscopy, and TEM and SEM observations for this copolymer film in comparison with a polystyrene‐block‐poly(methyl methacrylate) diblock copolymer film revealed that poly(methyl methacrylate) domains were removed by γ‐irradiation and succeeding solvent washing to form cylindrical holes within polybutadiene matrix, which was rigidified by radiation crosslinking. Thus, it was demonstrated that nanoporous materials can be prepared by γ‐irradiation, maintaining the original structure of PB‐b‐PMMA diblock copolymer film. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5916–5922, 2007

Wavelength selective quantum dot infrared photodetector with periodic metal hole arrays

In this letter, the effect of extraordinary transmission of periodic metal hole arrays is directly integrated into the quantum dot infrared photodetector with broadband response. It is found that the detector response is strongly modulated by the extraordinary transmission from the excitation of surface plasmon.

Internal structure visualization and lithographic use of periodic toroidal holes in liquid crystals

The formation of a large-area ordered structure by organic molecular soft building blocks is one of the most exciting interdisciplinary research areas in current materials science and nanotechnology. So far, several distinct organic building blocks--including colloids, block copolymers and surfactants--have been examined as potential materials for the creation of lithographic templates. Here, we report that perfect ordered arrays of toric focal conic domains (TFCDs) covering large areas can be formed by semi-fluorinated smectic liquid crystals. Combined with controlled geometry, that is, a microchannel, our smectic liquid-crystal system exhibits a high density of TFCDs that are arranged with remarkably high regularity. Direct visualization of the internal structure of the TFCDs clearly verified that the smectic layers were aligned normal to the side walls and parallel to the top surface, and merge with the circular profile on the bottom wall surface. Moreover, we demonstrate a new concept: smectic liquid-crystal lithography. Grown in microchannels from a mixture of liquid-crystal molecules and fluorescent particles, TFCDs of the smectic liquid crystals acted as a template, trapping particles in an ordered array. Our findings pose new theoretical challenges and potentially enable lithographic applications based on smectic liquid-crystalline materials.

Properties of Electromagnetic Wave Propagation Emerging in 2-D Periodic Plasma Structures

Periodic structures in plasmas form unique dispersions of electromagnetic waves, which are examined in numerical calculation. Above electron plasma frequency, where waves equivalently propagate in dielectric media, plasma arrays with 2-D periodicity produce frequency regions of forbidden propagation, like band gaps in a photonic crystal. Below electron plasma frequency, where waves are usually forbidden to propagate due to cutoff phenomenon, bulk plasmas with periodic holes can become wave-propagating media in which localized surface modes play an important role. Such features give rise to concepts of dynamic wave controllers that change their inner electron density in time.

Tuning the extraordinary optical transmission through subwavelength hole array by applying a magnetic field

The transmission of light through a thin Ag film with a periodic subwavelength hole array can be influenced by the presence of the externally applied magnetic field H. Using a three-dimensional finite element method, we show that the spectral locations of the transmission peak resonances can be shifted by varying the magnitude and direction of the H. The transmission peaks have blueshift, and the higher the magnitude of H the larger the blueshift. The shift is due to the change of cavity resonance condition as a result of the magneto-induced anisotropy in the optical properties of the Ag film. Hence, high transmittance for any desired wavelength can be achieved by applying an appropriate H to the metallic film of optimized material and hole parameters.

High-efficient acoustic wave rectifier

We propose an acoustic wave rectifier comprising double arrays of periodic triangular holes, inspired from the ray-acoustics. We numerically investigate the transmission rates of waves using the Finite-Difference Time-Domain method, and find the optimal position of the arrays for efficient rectification. Very close arrangement of the arrays provides high efficiency and large transmission rate.

Surface-Plasmon-Polariton Assisted Diffraction in Periodic Subwavelength Holes of Metal Films with Reduced Interplane Coupling

Metal films grown on an Si wafer perforated with a periodic array of subwavelength holes have been fabricated and anomalous enhanced transmission in the midinfrared regime has been observed. High order transmission peaks up to Si(2,2) are clearly revealed due to the large dielectric constant contrast of the dielectrics at the opposite interfaces. The Si(1,1) peak splits at oblique incidence both in TE and TM polarization, which confirms that anomalous enhanced transmission is a surface-plasmon-polariton (SPP) assisted diffraction phenomenon. Theoretical transmission spectra agree excellently with the experimental results and confirm the role of SPP diffraction by the lattice.

Extraordinary transmission through a silver film perforated with cross shaped hole arrays in a square lattice

In this work, the transmission through cross shaped hole with different sizes but the same lattice constant was measured with the polarized light to investigate the variation of localized charge oscillation around the hole. The comparison between the transmission intensities through the similarly arranged periodic hole array with different hole shapes, i.e., cross, square, and rectangular, were also measured. The cross shaped hole gives rise to a larger transmission of light than those perforated with square or rectangular hole.

Selective excitation of surface-polariton Bloch waves for efficient transmission of light through a subwavelength hole array in a thin metal film

Electromagnetic (EM) field was found to be able to transmit efficiently through a subwavelength hole array in a metal thin film at specific resonant frequencies. By analyzing the near-field distributions of EM fields in the array system, as well as the corresponding Fourier spectra, we show that the surface-polariton (SP) Bloch waves focus the energy of the incident plane-wave EM field to the vicinity of the hole at resonances (through SP scattering provided by the periodic hole). Furthermore, the wave vectors of the SP waves that contribute to the focusing effect are quantized as functions of the geometric shape of the holes in such a way that the focusing effect of the EM energy into the hole is maximal. The transmission efficiency and bandwidth at resonances are found to partially depend on the number of SP modes which contribute to the focusing effect.

Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface

A perfect electric conductor surface with one-dimensional periodic rectangle holes is proposed as a surface-plasmon-like waveguide, where designed surface plasmon modes with very low group velocity are confined in a subwavelength region. It is shown that the half maximum of electric field intensity of the mode can be confined in a 0.20λ×0.10λ subwavelength region on the transversal plane and the group velocity approaches to zeros, where λ is the wavelength in vacuum.

액정을 주입한 광자결절광섬유의 온도변화에 따른 파장 스위칭

본 연구에서는 클래딩 영역에 주기적인 공기층이 있는 광자 결정 광섬유에 액정을 주입하고, 온도를 변화시켜 주면서 빛의 투과 스펙트럼의 변화를 측정하였다. 액정을 주입한 광섬유는 특정 온도에서 특정 파장에 대해 여러 가지 투과특성을 얻어 낼 수 있었다. 광섬유에 가해주는 온도에 따라서 투과하는 광 신호를 약 <TEX>$10\sim15dB$</TEX> 정도 최소화 할 수 있었는데, 이를 이용하면 특정 파장 대역에서 광 신호를 소광시킬 수 있는 광 스위칭 소자에 응용 가능할 것이다. We have measured the optical spectra while varying the temperature of photonic crystal fibers (PCFs) with periodic air holes in the cladding. These are liquid crystal infiltrated fibers. For the liquid crystal infiltrated PCFs, we obtained the transmission of several wavelengths at specific temperatures. The transmission power could be reduced by about <TEX>$10\sim15dB$</TEX> by varying the applied temperature in the liquid crystal PCF. We expect that it is applicable as a wavelength switching device in the specific wavelength band.

Resonance Absorption of Metallic Plate with Subwavelength HoleArray

The optical reflectance by a metallic plate arranged with array consistingof subwavelength periodic square hole is investigated by using thethree-dimensional finite-difference time-domain method (3D-FDTD). Thereare dips in the reflectivity spectra, which indicate the absorptionpeaks. The absorption peaks behave differently according to the ratio ofhole width and the period of the hole array. Combined with the nearfields of the absorption peaks, it is found that the surface plasmon(SP) resonance on the surface of plate and localized SP in the hole playa major role for the two absorptions.

Numerical investigation of the transmission enhancement through subwavelength hole array

The transmission characteristics of a metallic film with subwavelength periodic square hole arrays are investigated by using the three-dimensional finite-difference time-domain (3D-FDTD) method. The influences of the hole size, the refractive index of substrate, the refractive index of filled medium, the thickness of film as well as the incident angle on the characters of transmission spectra are studied. It is found that the transmission can be enhanced by filling the holes with higher refractive index medium. This enhancement can be explained by the collaboration of localized waveguide resonance with surface plasmon resonance.

Enhanced near-infrared transmission through periodic H-shaped arrays

We report experimental observation of enhanced near infrared transmission through periodic H-shaped arrays in metallic thin films. A broad transmission band centered at about 1.6 μm is found and the transmission coefficient can be as high as about 16.3% for an arm width of 120 nm for the H-pattern. The position of the transmission peak shifts to a short wavelength by about 140 nm when the arm width is increased to 200 nm. This variation feature is inverse to that found in periodic hole arrays. It indicates that the localized surface plasmon is an important parameter contributing to the enhanced transmission. The H-shaped arrays exhibit a strong polarization effect consistent with the geometry anisotropy. Numerical simulations by using a transfer matrix method reproduce quite well the obtained transmission spectrum.

Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays

Metallic plates embedded between dielectric slabs and perforated by rectangular arrays of subwavelength holes with a dense periodicity in one of the directions support extraordinary transmission (ET) phenomena, viz. strong peaks in the transmittance frequency dependence. Stacks of such perforated plates support ET phenomena with propagation along the stack axis that is characterized by the left handed behavior. The incorporation of the dielectric materials and dense periodicity allows significantly reducing the illuminated area of the perforated plate required experimentally to observe the ET phenomena as compared to the areas required in the case of free standing rectangular hole arrays. This facilitates the experimental investigation of ET under excitation in the Fresnel zone of Gaussian beams.