Regularization of jump points in applying the adaptive spatial resolution technique

The performance of the adaptive spatial resolution technique is improved by making the resolution function of the coordinate transformation as smooth as possible. To this end, the smoothness of the resolution function is probed and a quantitative criterion is proposed to make the jump points; which were conventionally equidistant from each other, regularized. The here-proposed regularization is applied to two different recent formulations and its effects on the overall convergence rate and on the presence of numerical artifacts in analysis of highly conducting gratings are studied. Dielectric and metallic gratings at optical and microwave frequencies are considered and the helpfulness of the proposed technique is discussed.     

超表面上表面等离激元波的光栅衍射行为研究

本文利用严格数值仿真研究了550~700 nm波段的可见光通过金属光栅耦合方式激发的表面等离激元(SPP)波在金属表面的光栅衍射行为与现象。研究结果表明:SPP波在金属表面的衍射行为与自由空间光相比有极大不同,由于SPP波的近场属性,经金属光栅衍射后在近场可表现出明显的光栅分光现象,但经过一段传输距离后则分光现象消失而表现为不同级次的光合为同一束光;在近场衍射情况下,其情况与自由空间光衍射行为类似,对SPP亚波长金属光栅来说同样只有零级透射光;而当金属光栅周期大于SPP波长时,高级衍射级次则开始出现。研究结果对下一步在金属表面上实现微米级片光谱仪器具有重要借鉴意义。     

两种亚波长金属波片的透射特性对比

综合等效介质理论和表面等离子激元(SPP)Bloch模型,对比分析了两种新的亚波长光栅结构:二维矩形金属光栅和二维椭圆柱金属光栅。利用时域有限差分(FDTD)算法,对比分析了两种结构的透射率及其相位延迟与入射光波长及偏振角变化的关系,尤其两种结构实现λ/4波片功能所对应的透射特性。仿真结果表明,当入射光偏振角为75°时,两种结构均可实现λ/4波片功能,此时二维矩形和椭圆柱金属光栅的透射率分别为0.77和0.67,表明二维矩形金属光栅比椭圆柱光栅具有更好的透射效果。对应550～800nm的入射波长,两种光栅在各自允许的入射偏振角范围内均表现了较为平坦的宽带透射特性。     

Crossed gratings: A theory and its applications

We introduce a rigorous formulation for the problem of the diffraction by a finitely-conducting, bi-periodic surface. The formationon is based on a coordinate transformation which maps the grating surface onto a plane. The transformed Maxwell equations are resolved using an iterative technique. The numerical implementation is tested against a number of criteria, including a comparison with two recently developed formalisms. As well, it is shown to give results in agreement with the Reciprocity Theorem, which is derived for efficiencies of crossed gratings in unpolarized light. The method has been shown to work throughout the whole range of values of surface conductivity. We investigate the effect of a surface-corrugation on the solar absorptance of a metallic mirror. We discuss a useful equivalence property linking the behaviour of crossed gratings with that of classical gratings. We exhibit for the first time a grating in a highly-reflecting metal capable of totally absorbing unpolarized incident light. On leave from the Department of Theoretical Physics, School of Physics, University of Sydney, Sydney, N.S.W., 2006, Australia     

亚波长金属光栅的表面等离子体激元共振特性

亚波长金属光栅在共振波长处有光场局域增强、异常透射等现象,为深入认识其共振机制,本文研究了亚波长金属光栅的表面等离子体激元（SPP）共振特性。通过研究不同金属光栅的几何结构以及金属介电常数对SPP共振波长的影响,获得了3种共振波长的基本物理机制。采用周期边界元法进行数值模拟,在边界积分方程的基础上结合平面波展开方法来处理任意形状的周期性结构。模拟结果表明,3种共振波长可以分别由金属的材料、金属光栅周期和金属光栅厚度所调谐。该研究为微纳米光学器件的设计提供了依据。     

Brewster incidence for metallic gratings

This paper is a first report on a theoretical and numerical study undertaken in order to understand the grating anomalies linked with an important absorption of energy. It is shown that metallic gratings can exhibit anomalies which consists of total absorption of a plane wave.     

Band gaps in the spectra of terahertz surface plasmons on metallic diffraction gratings

The effect of the appearance of band gaps in the energy spectra of terahertz surface plasmons has been experimentally observed and investigated. The band gaps are formed due to the interference interaction of the surface plasmons excited by pulsed terahertz radiation on metallic diffraction gratings. It has been shown that the experimental dispersion curves of terahertz plasmons are in good agreement with the dispersion curves obtained in the numerical simulation.     

Microstructured design of metallic diffraction gratings for light trapping in thin-film silicon solar cells

In thin-film silicon solar cells, a flexible optical design for light collection is developed that can enhance the optical path length in absorber layer. In this paper, we demonstrate the rectangular, trapezoidal and triangular metallic diffraction gratings as back reflectors. The potential of the structures in the solar cells is investigated by means of numerical simulations, i.e., the Rigorous Coupled Wave Analysis enhanced by the Modal Transmission Line theory. The results show that the 0-order reflection can be suppressed and the energy can be transferred to high diffraction orders by metallic diffraction gratings, especially the triangular metallic diffraction gratings.     

Calculation and optimization of parameters of deep groove gratings with multilayer dielectric coating for compression of high-power laser pulses

The method of calculating the electromagnetic wave field diffracted by a holographic grating with a multilayer dielectric coating is developed. The method consists of the representation of the field inside dielectric layers in the form of a plane-wave expansion for weakly damped harmonics and an expansion over functions of the concomitant coordinate system for strongly damped orders. This modification of the method allows calculation of the diffraction efficiency and the electric field strength for the deep groove gratings. It is shown that a diffraction element that possess high efficiency and radiation strength can be obtained even when the profile of the dielectric layers flattens with an increase in the distance from the grating’s metallic layer.     

Calculation of the band diagrams of metallic wire photonic crystals

The band structures of three-dimensional metallic photonic crystals in the form of thin wires are calculated using integral equations and periodic Green??s functions with allowance for several tens of current harmonics and several thousands of space harmonics. The convergence of the algorithm, the accuracy of the results, and the dependence of the bandgap width are studied.     

A new theory for multiprofile,buried gratings

A new theory for dielectric coated metallic gratings is presented. The formalism is well adapted to the case for which the dielectric overcoatings are separated by plane interfaces or for which the modulated interfaces do not interpenetrate. We show that the numerical program is well suited to the theoretical study of the use of gratings as beam sampling mirrors in the infrared region.     

Higher order harmonics suppression in extreme ultraviolet and soft x-ray

The extreme ultraviolet and soft x-ray sources are widely used in various domains. Suppressing higher order harmonics and improving spectral purity are significant. This paper describes a novel method of higher order harmonics suppression with single order diffraction gratings in extreme ultraviolet and soft x-ray. The principle of harmonic suppression with single order diffraction grating is described, and an extreme ultraviolet and soft x-ray non-harmonics grating monochromator is designed based on the single order diffraction grating. The performance is simulated by an optical design software. The emergent beams of a monochromator with different gratings are measured by a transmission grating spectrometer. The results show that the single order diffraction grating can suppress higher order harmonics effectively, and it is expected to be widely used in synchrotron radiation, diagnostics of laser induced plasma, and astrophysics.     

亚波长金属光栅的表面等离子体激元共振特性

亚波长金属光栅在共振波长处有光场局域增强、异常透射等现象,为深入认识其共振机制,本文研究了亚波长金属光栅的表面等离子体激元(SPP)共振特性。通过研究不同金属光栅的几何结构以及金属介电常数对SPP共振波长的影响,获得了3种共振波长的基本物理机制。采用周期边界元法进行数值模拟,在边界积分方程的基础上结合平面波展开方法来处理任意形状的周期性结构。模拟结果表明,3种共振波长可以分别由金属的材料、金属光栅周期和金属光栅厚度所调谐。该研究为微纳米光学器件的设计提供了依据。     

Broadband Terahertz Polarization Converter and Asymmetric Transmission Based on Coupled Dielectric‐Metal Grating

Coupled dielectric‐metal gratings are investigated for broadband terahertz (THz) wave polarization conversion and asymmetric transmission by the experiments and numerical simulations, which are composed of the subwavelength Si grating and metallic wire grating layers. The dielectric grating layer with a large artificial birefringence and low dispersion is employed as a phase engineered waveplate, and the metal wire grating arranged with a 45° angle to the dielectric grating is utilized as a high‐efficiency polarizer. Due to the subwavelength integration, this coupled grating presents a local resonance coupling mechanism between dielectric and metal gratings, which greatly enhances the polarization rotation and expands the bandwidth, not a simple combination with dielectric and metallic gratings. The results demonstrate that a broadband asymmetric transmission with an extinction ratio of 30dB from 0.2 to 1.2 THz is achieved and the highest transmission of 90% can be obtained. It provides a simple way towards practical applications for THz artificial dispersion materials, polarization control and asymmetric transmission.     

An adaptive harmonic balance method for predicting the nonlinear dynamic responses of mechanical systems—Application to bolted structures

Aeronautical structures are commonly assembled with bolted joints in which friction phenomena, in combination with slapping in the joint, provide damping on the dynamic behavior. Some models, mostly nonlinear, have consequently been developed and the harmonic balance method (HBM) is adapted to compute nonlinear response functions in the frequency domain. The basic idea is to develop the response as Fourier series and to solve equations linking Fourier coefficients. One specific HBM feature is that response accuracy improves as the number of harmonics increases, at the expense of larger computational time. Thus this paper presents an original adaptive HBM which adjusts the number of retained harmonics for a given precision and for each frequency value. The new proposed algorithm is based on the observation of the relative variation of an approximate strain energy for two consecutive numbers of harmonics. The developed criterion takes the advantage of being calculated from Fourier coefficients avoiding time integration and is also expressed in a condensation case. However, the convergence of the strain energy has to be smooth on tested harmonics and this constitutes a limitation of the method. Condensation and continuation methods are used to accelerate calculation. An application case is selected to illustrate the efficiency of the method and is composed of an asymmetrical two cantilever beam system linked by a bolted joint represented by a nonlinear LuGre model. The practice of adaptive HBM shows that, for a given value of the criterion, the number of harmonics increases on resonances indicating that nonlinear effects are predominant. For each frequency value, convergence of approximate strain energy is observed. Emergence of third and fifth harmonics is noticed near resonances both on vibratory responses and on approximate strain energy. Parametric studies are carried out by varying the excitation force amplitude and the threshold value of the adaptive algorithm. Maximal amplitudes of vibration and frequency response functions are plotted for three different points of the structure. Nonlinear effects become more predominant for higher force amplitudes and consequently the number of retained harmonics is increased.     

Resonant coupling of surface plasmons to radiation modes by use of dielectric gratings

Efficient outcoupling of surface-plasma waves to radiation modes by use of dielectric diffraction gratings on a flat metallic surface is discussed. The dielectric gratings, which have a surface-relief structure with only several tens of nanometers in peak-to-trough height on a flat metal surface, can efficiently extract radiation modes propagating in free space from the surface-plasmon modes. An outcoupling efficiency of 50% is estimated with the rigorous coupled-wave diffraction theory, and it is confirmed by the experiment.     

Influence of the characteristic curve of the material on the diffraction efficiency of holographic volume phase gratings

The behaviour of the diffraction efficiency of holographic gratings is discussed on the basis of the multiwave coupled-wave approach, taking into consideration the photoinduced change in the refractive index of the recording medium. The cases of Bragg and off-Bragg reconstruction in Bragg and mixed diffraction are considered. The influence of the higher harmonics of the refractive index modulation profile on the diffraction efficiency is shown.     

Phase conjugation via unequal amplitude multiple gratings in photorefractives: A simple shooting method for numerical solution

We present a simple shooting method to obtain numerical solutions of the nonlinear coupled-wave equations for degenerate four-wave mixing in photorefractive crystals when four different types of the index gratings of unequal amplitudes are responsible for phase-conjugation. Our analysis includes the effects of pump depletion and absorption in the medium. Intensities of the four beams, both inside and at the output surface, are obtained as a function of four unequal coupling strengths and absorption coefficient. Intensity of the generated phase-conjugate beam is shown as a function of both the small and wide ranges of signal beam intensity. It is found that the multigrating operation with a careful choice of coupling constants and their combinations may improve the phase-conjugate wave generation. Also the presence of absorption reduces the phase-conjugate intensity more significantly when all the gratings are operative than when a single grating is allowed. Numerical results obtained from the computer calculations are presented in graphical form.     

Higher-order extremely asymmetrical scattering

Extremely asymmetrical scattering (EAS) is a type of Bragg scattering in periodic gratings, that occurs when the diffracted order satisfying the Bragg condition (scattered wave) propagates parallel to the grating boundaries. Previous studies were concerned only with first-order EAS that was shown to be a highly unusual type of scattering, characterised by a strong resonant increase of the scattered wave amplitude (i.e. the amplitude of the first diffracted order). In this paper, a rigorous numerical study of higher-order EAS is presented for the case of bulk TE electromagnetic waves in planar holographic gratings of various amplitudes and widths. In particular, it is demonstrated that typical scattered wave amplitudes in higher-order EAS are significantly smaller than those in first-order EAS, and display strongly different dependencies on grating width, grating amplitude, distance from the front grating boundary, etc. Similar to first-order EAS, second-order EAS is shown to be strongly sensitive to small variations of mean structural parameters at the grating boundaries. EAS in non-sinusoidal gratings is investigated in detail with special focus on the transition between first-order EAS and second-order EAS in such gratings. Tolerance of second-order EAS to the presence of the second grating harmonic is analysed. The effect of phase of the second grating harmonic on transitional EAS is investigated. Physical explanation of the predicted effects is presented.     

Perovskite-type oxide films combined with gratings for reduction of material consumption and improvement of thermochromism property

Combination of thermochromism of perovskite-type materials and gratings can result in some interesting variations of the spectral properties of structured surfaces. This paper aims at investigating thermal absorptive/radiative characteristics of structured thermochromic material La_0.825Sr_0.175MnO₃ (LSMO) with metallic and/or dielectric gratings. Numerical computation is conducted to obtain the distribution of the spectral absorptance of such structured surfaces with different structural parameters. The directional and temperature dependence of absorptance are also analyzed. The results reveal that compared with bulk LSMO material, the structured surface of LSMO achieves an improved thermochromic performance and much thinner layer of a structured LSMO film by combining the film with one-dimensional Al and SiO₂ gratings. Therefore, the other advantage of such structured surface is that the reduction of material consumption and weight is achieved due to the smaller LSMO layer thickness, which may be vital for thermal management of space vehicles.