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A NEW INTEGRAL EQUATION FORMULATION FOR SCATTERING BY PENETRABLE diffraction gratings

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Journal of Computational Mathematics 2018年第1期36卷 110-127页

作者： Ruming Zhang Bo Zhang Center for Industrial Mathematics University of Bremen Bremen 28359 Germany LSEC and Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 10049 China

This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formula- tion is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the NystrSm method for the new integral equation. Nu- merical examples are also shown to illustrate the applicability of the new integral equation formulation.

关键词： Scattering problem Transmission condition Periodic interface diffraction gratings Boundary integral equations Helmholtz equation.

On a Fast Integral Equation Method for diffraction gratings

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Communications in Computational Physics 2006年第6期1卷 984-1009页

作者： A.Rathsfeld G.Schmidt B.H.Kleemann Weierstrass Institute for Applied Analysis and Stochastics Mohrenstr.3910117 BerlinGermany Carl Zeiss AG Corporate Research and TechnologyOptical Design73446 OberkochenGermany

The integral equation method for the simulation of the diffraction by optical gratings is an efficient numerical tool if profile gratings determined by simple crosssection curves are considered.This method in its recent version is capable to tackle profile curves with corners,gratings with thin coated layers,and diffraction scenarios with unfavorably large ratio period over wavelength.We discuss special implementational issues including the efficient evaluation of the quasi-periodic Green kernels,the quadrature algorithm,and the iterative solution of the arising systems of linear equations.Finally,as an example we present the simulation of echelle gratings which demonstrates the efficency of our approach.

关键词： diffraction gratings integral equation method preconditioning

Multi-Mode Coupling in Long-Period Fibre gratings

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Chinese Physics Letters 2004年第8期21卷 1549-1552页

作者：刘子熹杨昌喜 DepartmentofPrecisionInstruments TsinghuaUniversityBeijing100084

We report multi-mode coupling in long-period fibre gratings (LPFGs). The analytical solution to three-mode coupling equations is presented for the first time. A 3×3 transmission matrix is attained and can be used to calculate the transmission spectra of nonuniform gratings in a way much faster than direct numerical integration. It is shown that when the resonant wavelengths of cladding modes are far from each other, two-mode coupling model can still be used. Otherwise we can only choose a multi-mode coupling model. Theoretically fitting of the result from the multi-mode coupling equations agrees well with the experimental one for mechanically-induced LPFGs.

关键词： diffraction gratings

Sensitivity Analysis of a Bioinspired Refractive Index Based Gas Sensor

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Journal of Bionic Engineering 2011年第3期8卷 323-334页

作者： Yang Gao Qi Xia Guanglan Liao Tielin Shi Wuhan National Laboratory for Optoelectronic Wuhan 430074 P. R. Chinao State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan 430074 P. R. China

It was found out that the change of refractive index of ambient gas can lead to obvious change of the color of Morpho butterfly＇s wing. Such phenomenon has been employed as a sensing principle for detecting gas. In the present study, Rigorous Coupled-Wave Analysis （RCWA） was described briefly, and the partial derivative of optical reflection efficiency with respect to the refractive index of ambient gas, i.e., sensitivity of the sensor, was derived based on RCWA. A bioinspired grating model was constructed by mimicking the nanostructure on the ground scale of Morpho didius butterfly＇s wing. The analytical sensitivity was verified and the effect of the grating shape on the reflection spectra and its sensitivity were discussed. The results show that by tuning shape parameters of the grating, we can obtain desired reflection spectra and sensitivity, which can be applied to the design of the bioinspired refractive index based gas sensor.

关键词： bioinspired gas sensor sensitivity diffraction gratings refractive index subwavelength structures

Flexible subwavelength gratings fabricated by reversal soft UV nanoimprint

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Chinese Optics Letters 2012年第9期10卷 9-12页

作者：葛良进王旭迪陈火耀邱克强付绍军 National Synchrotron Radiation Laboratory University of Science and Technology of China School of Mechanical and Automotive Engineering Hefei University of Technology

We present a replication process, named reversal soft ultraviolet （UV） nanoimprint, to fabricate a high- aspect-ratio flexible subwavelength grating （SWG） on a polyurethane acrylate （PUA）. This nanopatterning technique consists of casting, reversal UV imprint, and dry release. The UV curing process of PUA to avoid pattern collapse is investigated. Revalpha film acts as the supporting and sacrificial layer during the whole process due to its special surface energy property. The free-standing PUA structures with a period of 200 nm and a depth of 350 nm can be automatically released from the Revalpha film by heating. The PUA resist is well suited to replicate fine patterns of the mold with high aspect ratio and large area precisely and uniformly for low surface energy and low viscosity. The measured transmittance is compared with the calculation results based on rigorous coupled-wave analysis in the wavelength region ranging from 500 to 800 nm. The experimental results agree well with the theoretical calculations.

关键词： 050.1950 diffraction gratings 050.6624 Subwavelength structures 220.4241 Nanostructure fabrication

Reflex optical sensor based on dual metal gratings with high angular sensitivity

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Chinese Optics Letters 2011年第6期9卷 17-20页

作者：许吉程晨白强陈璟丁剑平 Nanjing National Laboratory of Microstructures and School of Physics Nanjing University School of Physics and Key Laboratory of Weak Light Nonlinear Photonics Nankai University State Key Laboratory of Functional Materials for Informatics Shanghai Institute of Microsystem and Information Technology Chinese Academy of Sciences

An interesting reflection phenomenon in a dual metal grating （DMG） structure is studied, which is related to the competition between Fabry-Prot （F-P） resonance effect and evanescent-field coupling effect inside the gap between the two composing single metal gratings. This competition leads to high angular sensitivity in response to the refractive index variation of the sample solution in the gap. A reflex optical sensor with high sensitivity based on DMG for detecting the change in refractive index is proposed and its performance theoretically is discussed.

关键词： Competition diffraction gratings Light refraction Optical sensors Refractive index Refractometers

Micrograting Displacement Sensor with Integrated Electrostatic Actuation

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Chinese Physics Letters 2014年第7期31卷 214-217页

作者：姚保寅冯丽爽王潇刘惟芳刘美华 Key Laboratory of Micro-nano Measurement-Manipulation and Physics (Ministry of Education) Beihang University Beijing 100191 Fundamental of Science on Novel Inertial Instrument & Navigation System Technology Laboratory Beihang University Beijing 100191

A high-resolution micro-grating displacement sensor with diffraction-based and integrated electrostatic actuation is proposed and experimentally demonstrated. The Ai reflecting membrane is fabricated at the bottom of a silicon moving part and the Au micro-gratings are patterned on a transparent substrate. This structure forms a phase sensitive diffraction grating, providing the displacement sensitivity of the micro-grating interferometer. It shows sensitivity adjustment and self-calibration capabilities with electrostatic actuation. Additional system components include a coherent light source, photodiodes, and required electronics. Experimental results show that the displacement sensor has a sensitivity of about 1.8 m V /nm and a resolution of less than 1 nm in the linear region. This displacement sensor is very promising in the fields requiring high sensitivity, broad dynamic range, and immunity to electromagnetic interference.

关键词： diffraction gratings

Silicon-on-Insulator-Based Compact Optical Demultiplexer Employing Etched diffraction Grating

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Chinese Physics Letters 2004年第7期21卷 1265-1267页

作者： WANGWen-Hui TANGYan-Zhe WANGYun-Xiang QUHong-Chang WUYa-Ming LITie YANGJian-Yi WANGYue-Lin LIUMing StateKeyLaboratoriesofTransducerTechnology ShanghaiInstituteofMicrosystemandInformationTechnologyChineseAcademyofSciencesShanghai200050 DepartmentofInformationScienceandElectronicsEngineering ZhejiangUniversityHangzhou310027 MicroelectronicsR&DCentre ChineseAcademyofSciencesBeijing100029

A compact optical demultiplexer with etched diffraction grating (EDG) is designed and fabricated on a silicon-on-insulator (SOI) material. Several 90° turning mirrors are used to bend the waveguides, and the size of the EDG-based demultiplexer is minimized to only 16×1.7mm2. The crosstalk is about -18dB. The on-chip loss is about 18.2dB, which is composed of about 16.9dB excess loss and 1.3dB diffraction loss. Measures to improve the performance are discussed.

关键词： diffraction gratings

Wide band polarizer with suspended germanium resonant grating

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Chinese Optics Letters 2012年第11期10卷 77-79页

作者：曹武刚麻健勇周常河 Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences Graduate University of Chinese Academy of Sciences

An ultra broad band polarizer that operates in the telecommunication wavelength band is proposed. This device, which consists of a single suspended germanium resonant grating layer, is designed using the inverse mathematical method and the rigorous vector diffraction theory. Calculated results indicate that the ultra broad band polarizer exhibits extremely high reflection （R 〉 99%） for TE polarization light and high transmission （T 〉 99%） for TM polarization at the wavelength range greater than 300 nm, and it has an extinction ratio of approximately 1 000 at the 1 550-nm central wavelength. The results of the rigorous coupled wave analysis indicate that the extremely wide band property of the TE polarization is caused by the excitation of strong modulation guided modes in the design wavelength range,

关键词： diffraction gratings Germanium Light transmission Polarization Wavelength