Design procedure for photonic crystal fibers with ultra-flattened chromatic dispersion

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光子晶体自组装结构色

光子晶体自组装结构色English:## Photonic Crystal Self-Assembly for Structural Color.Photonic crystals (PCs) are periodic structures that can control the propagation of electromagnetic waves. They have been widely used in various applications, such as optical filters, lasers, and solar cells. One of the most promising applications of PCs is in the field of structural color, where they can be used to create vibrant and durable colors without the use of pigments or dyes.Self-assembly is a powerful technique that can be used to fabricate PCs with complex and precise structures. In self-assembly, individual components spontaneously organize into a well-defined structure without the need for external guidance or templates. This approach has several advantages over traditional fabrication methods, such as lithography, etching, and deposition, including lower cost, higherthroughput, and the ability to create structures with sub-wavelength features.There are several different methods for self-assembling PCs. One common method is to use colloidal particles. Colloidal particles are small particles that are dispersed in a liquid. When the particles are close enough to each other, they can interact with each other and self-assemble into a PC structure. The size, shape, and material of the colloidal particles can be controlled to tune the optical properties of the PC.Another method for self-assembling PCs is to use block copolymers. Block copolymers are polymers that consist of two or more different types of monomers. When the block copolymers are heated, they can self-assemble into avariety of different structures, including PCs. The structure of the PC is determined by the composition and molecular weight of the block copolymers.Self-assembled PCs have been used to create a variety of different structural colors. For example, researchershave created PCs that mimic the colors of butterfly wings, peacock feathers, and abalone shells. These colors are created by the interaction of light with the periodic structure of the PC. The wavelength of the light that is reflected from the PC is determined by the spacing of the PC's features.Self-assembled PCs are a promising technology for a variety of applications, including displays, sensors, and anti-counterfeiting. They offer a number of advantages over traditional fabrication methods, including lower cost, higher throughput, and the ability to create structures with sub-wavelength features.Chinese:## 光子晶体自组装结构色。

仿生材料论文综述大学生Biomimetic materials

Biomimetic materialsAbstract ：this article is about the biomimetic materials, including what is the bionics , Lotus leaves and their biomimetic materials, Rice leaves and their biomimetic materials, Butterfly wings and their biomimetic materials, Water strider legs and their biomimetic materials, The Study of Biomimetic Materials about Conch Nacre Structure. What’s more, there is also talking about the design criteria for tissue engineering and the Bio-inspired ceramics processing. In the final, the future about biomimetic materials is presented.Key words ：Biomimetic materials, bionics, Lotus leaves, Rice leaves , Butterfly wings, Water strider legs, Conch Nacre Structure, design criteria, ceramics processing1 IntroductionBionics is a term mad e by the Steele according to the Latin word “BIOS” (meaning the way of life) and the suffix "NIC" Bionics is the science which studys the structure and properties of biological systems in order to provide the designing idea and working principle。

纳米光子学-第8讲

The Bragg fiber
Using multilayer-film reflection to replace metal and create a light pipe. The boundary condition for EM field at the boundary of core-film boundary can be designed to be rather similar to that at the metal boundary.
behavior
Asymptotic single mode guiding behavior
For TE0l mode, the fraction of the power in cladding scales as 1/R3. For TM and mixed polarization mode, the fraction of the power in the cladding scales as 1/R
Smith et al, Nature, 424, 657 (2003)
core PCF
Core modes vs. surface modes in air-core PCF
H. Kim, J. Shin, S. Fan, M. Digonnet, G. S. Kino, IEEE J. Quantum Electronics, 40, 552 (2004)
S. G. Johnson et al, Opt. Express. 9, 748 (2001)
Hollow optical fiber, experiments
Guiding of intense CO2 laser light at 10 micron wavelength range for high power applications

The design and synthesis of photoactive materials

The design and synthesis ofphotoactive materialsPhotoactive materials refer to those substances that can undergo chemical or physical changes when exposed to light, such as photovoltaic materials, photochromic materials, and photopolymer materials. These materials have been widely used in various fields such as solar energy, information storage, and optoelectronic devices. The design and synthesis of photoactive materials are the key factors that determine their properties and applications. In this article, we will discuss the principles and methods of designing and synthesizing photoactive materials.1. Principles of designing photoactive materialsThe design of photoactive materials is based on the understanding of the mechanism of photoinduced processes. The photoinduced process refers to the process of light absorption, excitation, and subsequent energy conversion or chemical reaction. Therefore, the principle of designing photoactive materials is to choose the appropriate chromophores or energy conversion modules and construct them into a composite system. The key factors to be considered in the design process are the absorption wavelength, absorption strength, energy level, and the nature of the reaction products.For photovoltaic materials, the most commonly used chromophores are organic dyes or inorganic semiconductors. The design principle is to choose the chromophores with high light absorption efficiency and extend the absorption range to the visible and near-infrared region. The energy level of the electron transfer process should match the energy level of the electron transport materials, such as TiO2 or ZnO. The interface between the chromophores and the electron transport materials should be well-designed to reduce the energy loss due to recombination and increase the photoelectric conversion efficiency.For photochromic materials, the design principle is to choose the chromophores with reversible isomerization or reversible bond breaking properties. The absorption spectrum of the photochromic chromophore should match the wavelength of the incident light. Themolecular structure of the chromophore should be designed to facilitate the reversible isomerization or bond breaking process. The stability and color contrast of the two isomers should be considered to achieve the desired photochromic effect.For photopolymer materials, the design principle is to choose the monomers or oligomers with polymerizable functional groups and photoinitiators. The monomers or oligomers should have suitable molecular weight, rigidity, and compatibility to form the desired polymer structure. The photoinitiators should be designed to initiate the polymerization process upon exposure to light, with high efficiency and low toxicity.2. Methods of synthesizing photoactive materialsThe synthesis of photoactive materials is the key process to realize the design principles. The synthesis methods can be roughly divided into two categories: top-down and bottom-up. The top-down method refers to the modification of existing materials or structures to achieve the desired photoactive properties. The bottom-up method refers to the construction of photoactive materials from smaller molecules or atoms.The top-down method is commonly used in the synthesis of photovoltaic materials. The most common method is the dye-sensitized solar cell (DSSC) system, which uses organic dyes anchored on the surface of mesoporous TiO2 films. The organic dyes are usually synthesized in solution and then immobilized on the TiO2 surface through covalent or non-covalent interactions. The TiO2 films can be prepared by sol-gel or electrodeposition methods. The DSSC system has high efficiency, low cost, and good stability, and has attracted extensive attention in the field of solar energy conversion.The top-down method is also applied in the synthesis of photochromic materials. A typical example is the spiropyran-based photochromic compound, which can be synthesized by modifying the molecular structure of spiropyran. Spiropyran is a colorless compound that can be isomerized to the colored merocyanine form upon UV light irradiation. The photochromic effect can be adjusted by changing the substituents on the spiropyran ring, such as electron-donating or electron-withdrawing groups, or the size of the ring.The bottom-up method is commonly used in the synthesis of photopolymer materials. The most common method is the photopolymerization of monomers or oligomers with appropriate functional groups and photoinitiators. The photopolymerization can be initiated by UV or visible light irradiation, depending on the absorption properties of the photoinitiators. The resulting polymer can have various structures and properties, such as crosslinked or linear, hydrophilic or hydrophobic, elastic or stiff, and can be used in various applications such as coatings, adhesives, and biomedical materials.3. Challenges and future prospectsThe design and synthesis of photoactive materials face various challenges and opportunities. The challenges include the low efficiency, poor stability, and toxic or scarce materials used in some systems. The opportunities include the discovery of new materials and mechanisms, the development of efficient and sustainable synthesis methods, and the integration of photoactive materials into practical applications such as wearable devices, smart windows, and energy storage systems.To address the challenges and seize the opportunities, interdisciplinary research and collaboration are needed among scientists and engineers from different fields such as chemistry, physics, materials science, electrical engineering, and computer science. The research should focus on the fundamental understanding of the photoinduced processes, the optimization of the design and synthesis methods, and the exploration of new applications and markets. The progress in the design and synthesis of photoactive materials will contribute to the development of a sustainable and green society, and benefit human beings with cleaner energy, higher efficiency, and better quality of life.。

光子晶体波导折射率传感器灵敏度优化设计说明书

计算结果表明光子透射带上边沿的偏移量与传感区折射率的大小存在一定关系，在相同的折射率变化量下通过改变波导两侧缺陷处圆孔的相关几何参数可极大提高光子透射带上边沿的偏移量，即提高折射率传感器的灵敏度。

通过优化设计，传感器的灵敏度由折射率变化区间0.0~1.0的55nm/RIU(RIU表示折射率单元)与1.1~2.0的36nm/RIU分别提高到对应的405nm/RIU以及222nm/RIU。

关键词光学器件；折射率传感器；灵敏度优化；光子晶体波导；光子带隙；时域有限差分法中图分类号O436文献标识码A doi:10.3788/LOP51.052304Optimizing Design for Sensitivity Improvement of Refractive Index Sensors Based on Photonic Crystal WaveguideKe Lintong Chen Weiye Zhang Yang Li Rongsheng Shen Yifeng Department of Physics,China University of Mining and Technology,Xuzhou,Jiangsu221116,ChinaAbstract The transmission spectrum of a two-dimensional photonic crystal waveguide with edge defects of different refractive indexes(RIs)is analyzed,and accordingly a proposal to improve the sensitivity of RI sensor is put forward.The simulations and calculations show that the offset of the upper band edge of the transmission band is related to the RI of the analyte.For the same RI variation,the shift of the upper band edge of the transmission band can be greatly improved by changing the related geometrical parameters of holes at the defect area near both sides of the ly,the sensitivity of the RI sensor is enhanced.In this paper the sensitivity is respectively improved from55nm/RIU(RIU means refractive index unit)to405nm/RIU and36nm/ RIU to222nm/RIU corresponding to the range of the variation of RI(D n)from0.0to1.0and1.1to2.0after the optimizing process.Key words optical devices;refractive index sensor;sensitivity optimization;photonic crystal waveguide;photonic band gap;finite-different time-domain methodOICS codes230.5298;280.4788;130.5296；350.42381引言John等[1-4]于20世纪80年代提出了光子晶体这种新型材料的概念。

光子晶体导波基本原理说明书

More informationFundamentals of Photonic Crystal GuidingIf you’re looking to understand photonic crystals,this systematic,rigorous,and peda-gogical introduction is a must.Here you’llﬁnd intuitive analytical and semi-analyticalmodels applied to complex and practically relevant photonic crystal structures.Y ou willalso be shown how to use various analytical methods borrowed from quantum mechanics,such as perturbation theory,asymptotic analysis,and group theory,to investigate manyof the limiting properties of photonic crystals,which are otherwise difﬁcult to rationalizeusing only numerical simulations.An introductory review of nonlinear guiding in photonic lattices is also presented,as are the fabrication and application of photonic crystals.In addition,end-of-chapterexercise problems with detailed analytical and numerical solutions allow you to monitoryour understanding of the material presented.This accessible text is ideal for researchersand graduate students studying photonic crystals in departments of electrical engineering,physics,applied physics,and mathematics.Maksim Skorobogatiy is Professor and Canada Research Chair in Photonic Crystals atthe Department of Engineering Physics in´Ecole Polytechnique de Montr´e al,Canada.In2005he was awarded a fellowship from the Japanese Society for Promotion of Science,and he is a member of the Optical Society of America.Jianke Yang is Professor of Applied Mathematics at the University of Vermont,USA.Heis a member of the Optical Society of America and the Society of Industrial and AppliedMathematics.Fundamentals of Photonic Crystal GuidingMAKSIM SKOROBOGATIY 1JIANKE YANG 2´Ecole Polytechnique de Montr ´e al,Canada 1University of Vermont,USA2More informationMore informationcambridge university pressCambridge,New Y ork,Melbourne,Madrid,Cape Town,Singapore,S˜a o Paulo,DelhiCambridge University PressThe Edinburgh Building,Cambridge CB28RU,UKPublished in the United States of America by Cambridge University Press,New Y orkInformation on this title:/9780521513289C Cambridge University Press2009This publication is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published2009Printed in the United Kingdom at the University Press,CambridgeA catalog record for this publication is available from the British LibraryLibrary of Congress Cataloging in Publication dataSkorobogatiy,Maksim,1974–Fundamentals of photonic crystal guiding/by Maksim Skorobogatiy and Jianke Y ang.p.cm.Includes index.ISBN978-0-521-51328-91.Photonic crystals.I.Y ang,Jianke.II.Title.QD924.S562008621.36–dc222008033576ISBN978-0-521-51328-9hardbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication,and does not guarantee that any content on suchwebsites is,or will remain,accurate or appropriate.More informationM.Skorobogatiy dedicates this book to his family.He thanks his parentsAlexander and Tetyana for never-ceasing support,encouragement,andparticipation in all his endeavors.He also thanks his wife Olga,his children,Alexander junior and Anastasia,andhis parents for their unconditional love.J.Yang dedicates this book to his family.More informationContentsPreface page xiAcknowledgements xii1Introduction11.1Fabrication of photonic crystals21.2Application of photonic crystals41.2.1Photonic crystals as low-loss mirrors:photonicbandgap effects41.2.2Photonic crystals for out-of-bandgap operation10References112Hamiltonian formulation of Maxwell’s equations(frequency consideration)142.1Plane-wave solution for uniform dielectrics162.2Methods of quantum mechanics in electromagnetism182.2.1Orthogonality of eigenstates192.2.2Variational principle202.2.3Equivalence between the eigenstates of twocommuting Hamiltonians222.2.4Eigenstates of the operators of continuous anddiscrete translations and rotations232.3Properties of the harmonic modes of Maxwell’s equations302.3.1Orthogonality of electromagnetic modes322.3.2Eigenvalues and the variational principle322.3.3Absence of the fundamental length scale in Maxwell’sequations342.4Symmetries of electromagnetic eigenmodes352.4.1Time-reversal symmetry352.4.2Deﬁnition of the operators of translation and rotation352.4.3Continuous translational and rotational symmetries382.4.4Band diagrams432.4.5Discrete translational and rotational symmetries44More informationviii Contents2.4.6Discrete translational symmetry and discreterotational symmetry522.4.7Inversion symmetry,mirror symmetry,and other symmetries532.5Problems553One-dimensional photonic crystals–multilayer stacks593.1Transfer matrix technique593.1.1Multilayer stack,TE polarization593.1.2Multilayer stack,TM polarization613.1.3Boundary conditions623.2Reﬂection from aﬁnite multilayer(dielectric mirror)633.3Reﬂection from a semi-inﬁnite multilayer(dielectricphotonic crystal mirror)643.3.1Omnidirectional reﬂectors I683.4Guiding in aﬁnite multilayer(planar dielectric waveguide)693.5Guiding in the interior of an inﬁnitely periodic multilayer703.5.1Omnidirectional reﬂectors II803.6Defect states in a perturbed periodic multilayer:planarphotonic crystal waveguides823.7Problems864Bandgap guidance in planar photonic crystal waveguides934.1Design considerations of waveguides with inﬁnitelyperiodic reﬂectors934.2Fundamental TE mode of a waveguide with inﬁnitelyperiodic reﬂector964.3Inﬁnitely periodic reﬂectors,ﬁeld distribution in TM modes984.3.1Case of the core dielectric constantεc<εhεl/(εh+εl)984.3.2Case of the core dielectric constantεl≥εc>εhεl/(εh+εl)1014.4Perturbation theory for Maxwell’s equations,frequencyformulation1034.4.1Accounting for the absorption losses of the waveguidematerials:calculation of the modal lifetime and decay length1044.5Perturbative calculation of the modal radiation loss in aphotonic bandgap waveguide with aﬁnite reﬂector1064.5.1Physical approach1064.5.2Mathematical approach1085Hamiltonian formulation of Maxwell’s equations for waveguides(propagation-constant consideration)1105.1Eigenstates of a waveguide in Hamiltonian formulation1105.1.1Orthogonality relation between the modes of a waveguide madeof lossless dielectrics111More informationContents ix5.1.2Expressions for the modal phase velocity1145.1.3Expressions for the modal group velocity1145.1.4Orthogonality relation between the modes of a waveguide madeof lossy dielectrics1155.2Perturbation theory for uniform variations in a waveguide dielectric proﬁle1165.2.1Perturbation theory for the nondegenerate modes:example ofmaterial absorption1185.2.2Perturbation theory for the degenerate modes coupled byperturbation:example of polarization-mode dispersion1205.2.3Perturbations that change the positions of dielectric interfaces1235.3Problems126References127 6Two-dimensional photonic crystals1296.1T wo-dimensional photonic crystals with diminishingly smallindex contrast1296.2Plane-wave expansion method1326.2.1Calculation of the modal group velocity1346.2.2Plane-wave method in2D1346.2.3Calculation of the group velocity in the case of2Dphotonic crystals1356.2.4Perturbative formulation for the photonic crystallattices with small refractive index contrast1386.2.5Photonic crystal lattices with high-refractive-index contrast1426.3Comparison between various projected band diagrams1426.4Dispersion relation at a band edge,density of states andVan Hove singularities1446.5Refraction from photonic crystals1476.6Defects in a2D photonic crystal lattice1486.6.1Line defects1486.6.2Point defects1586.7Problems167References171 7Quasi-2D photonic crystals1727.1Photonic crystalﬁbers1727.1.1Plane-wave expansion method1727.1.2Band diagram of modes of a photonic crystalﬁber1767.2Optically induced photonic lattices1777.2.1Light propagation in low-index-contrast periodicphotonic lattices1787.2.2Defect modes in2D photonic lattices with localized defects1817.2.3Bandgap structure and diffraction relation for the modes of auniform lattice182More informationx Contents7.2.4Bifurcations of the defect modes from Bloch band edges forlocalized weak defects1857.2.5Dependence of the defect modes on the strength oflocalized defects1887.2.6Defect modes in2D photonic lattices with nonlocalized defects1927.3Photonic-crystal slabs1957.3.1Geometry of a photonic-crystal slab1957.3.2Eigenmodes of a photonic-crystal slab1977.3.3Analogy between the modes of a photonic-crystal slab and themodes of a corresponding2D photonic crystal2007.3.4Modes of a photonic-crystal slab waveguide2047.4Problems207References208 8Nonlinear effects and gap–soliton formation in periodic media2108.1Solitons bifurcated from Bloch bands in1D periodic media2118.1.1Bloch bands and bandgaps2118.1.2Envelope equations of Bloch modes2128.1.3Locations of envelope solitons2158.1.4Soliton families bifurcated from band edges2168.2Solitons bifurcated from Bloch bands in2D periodic media2188.2.1T wo-dimensional Bloch bands and bandgaps of linearperiodic systems2198.2.2Envelope equations of2D Bloch modes2208.2.3Families of solitons bifurcated from2D band edges2238.3Soliton families not bifurcated from Bloch bands2268.4Problems227References228Problem solutions230Chapter2230Chapter3236Chapter5244Chapter6246Chapter7257Chapter8260 Index263More informationPrefaceTheﬁeld of photonic crystals(aka periodic photonic structures)is experiencing anunprecedented growth due to the dramatic ways in which such structures can control,modify,and harvest theﬂow of light.The idea of writing this book came to M.Skorobogatiy when he was developingan introductory course on photonic crystals at the Ecole Polytechnique de Montr´e al/University of Montr´e al.Theﬁeld of photonic crystals,being heavily dependent onnumerical simulations,is somewhat challenging to introduce without sacriﬁcing thequalitative understanding of the underlying physics.On the other hand,exactly solvablemodels,where the relation between physics and quantitative results is most transpar-ent,only exist for photonic crystals of trivial geometries.The challenge,therefore,wasto develop a presentational approach that would maximally use intuitive analytical andsemi-analytical models,while applying them to complex and practically relevant pho-tonic crystal structures.We would like to note that the main purpose of this book is not to present the latestadvancements in theﬁeld of photonic crystals,but rather to give a systematic,logical,andpedagogical introduction to this vibrantﬁeld.The text is largely aimed at students andresearchers who want to acquire a rigorous,while intuitive,mathematical introductioninto the subject of guided modes in photonic crystals and photonic crystal waveguides.The text,therefore,favors analysis of analytically or semi-analytically solvable problemsover pure numerical modeling.We believe that this is a more didactical approach whentrying to introduce a novice into a newﬁeld.To further stimulate understanding of thebook content,we suggest many exercise problems of physical relevance that can besolved analytically.In the course of the book we extensively use the analogy between the Hamiltonian for-mulation of Maxwell’s equations and the Hamiltonian formulation of quantum mechan-ics.We present both frequency and propagation-constant based Hamiltonian formula-tions of Maxwell’s equations.The latter is particularly useful for analyzing photoniccrystal-based linear and nonlinear waveguides andﬁbers.This approach allows us touse a well-developed machinery of quantum mechanical semi-analytical methods,suchas perturbation theory,asymptotic analysis,and group theory,to investigate many ofthe limiting properties of photonic crystals,which are otherwise difﬁcult to investigatebased only on numerical simulations.M.Skorobogatiy has contributed Chapters2,3,4,5,and6of this book,and J.Y anghas contributed Chapter8.Chapters1and7were co-authored by both authors.More informationAcknowledgementsM.Skorobogatiy would like to thank his graduate and postgraduate program mentors,Professor J.D.Joannopoulos and Professor Y.Fink from MIT,for introducing him intotheﬁeld of photonic crystals.He is grateful to Professor M.Koshiba and ProfessorK.Saitoh for hosting him at Hokkaido University in2005and for having many excitingdiscussions in the area of photonic crystalﬁbers.M.Skorobogatiy acknowledges theCanada Research Chair program for making this book possible by reducing his teachingload.J.Y ang thanks the funding support of the US Air Force Ofﬁce of Scientiﬁc Research,which made many results of this book possible.He also thanks the Zhou Pei-Yuan Centerfor Applied Mathematics at Tsinghua University(China)for hospitality during his visit,where portions of this book were written.Both authors are grateful to their graduate andpostgraduate students for their comments and help,while this book was in preparation.Especially,J.Y ang likes to thank Dr.Jiandong Wang,whose help was essential for hisbook writing.。

Adjustable photonic crystal and method of adjustin

专利名称：Adjustable photonic crystal and method of adjusting the index of refraction of photoniccrystals to reversibly tune transmissionswithin the bandgap发明人：Ming Li,Makoto Ishizuka,DanielHogan,Xinbing Liu申请号：US10328841申请日：20021224公开号：US06898358B2公开日：20050524专利内容由知识产权出版社提供专利附图：摘要：A photonic crystal comprising a waveguide made of material. The waveguide has a periodic set of holes. The material proximate to at least one of the holes in the periodic set of holes exhibits an index of refraction that has been modified by the application of laser energy relative to the material proximate to other holes in the periodic set of holes. The photonic crystal is tuned to temporarily transmit a specific wavelength of light to create an on-off switch for the specific wavelength. Multiple photonic crystals are used to form a multiplexer and a demultiplexer.申请人：Ming Li,Makoto Ishizuka,Daniel Hogan,Xinbing Liu地址：Chelmsford MA US,Belmont MA US,Acton MA US,Acton MA US国籍：US,US,US,US代理机构：RatnerPrestia更多信息请下载全文后查看。

大直径聚苯乙烯小球自组织方法制备高质量opal晶体

大直径聚苯乙烯小球自组织方法制备高质量opal 晶体3张　琦　孟庆波　程丙英　张道中(中国科学院物理研究所和凝聚态物理中心,北京　100080)(2003年3月7日收到;2003年4月21日收到修改稿) 通过改进样品池的结构和其他实验条件,用气压法制备了大直径聚苯乙烯小球(直径为1μm 和700nm )的人造蛋白石(opal )样品,并测量了其能带特性.对于制备能带位置在红外波段的三维光子晶体,这一实验结果将有很广阔的用途.关键词:光子晶体,光子带隙,人造蛋白石(opal )PACC :4225B ,4270Q ,7820P3国家重点基础研究发展规划项目(973)(批准号:2001C B610402)和国家自然科学基金(批准号:10174089)资助的课题.E 2mail :zhangdz @11引言在光子晶体这一概念被提出[1,2]以来,光子晶体由于其特殊的性质,已经吸引了越来越多的关注.光子晶体这种材料在空间存在介电常数的周期性调制,使得对于在特定方向上传播的一定频率的光被散射而无法通过晶体.对二维[3—6]和三维[7,8]光子晶体的研究都在广泛的进行.在制备三维光子晶体的探索中,对实验室制备人造蛋白石(opal )及其反结构(inverse opal )[8-17]的研究越来越多.用人工制备的opal 作为模版,向其结构的空隙中填充高折射率的材料,再去除原模版材料以得到空气小球在高折射率背景材料中周期排列的反opal 结构[8,10],这是一种在三维结构中构造完全光子带隙的相对容易实现的方法之一.在这种方法中,高质量的opal 模版的制备是非常重要的,模版结构周期性的好坏在很大程度上决定了最终所得样品的能带质量,模版所用小球的直径和所使用的高折射率填充材料及填充比是决定反opal 能带位置的关键因素.通常的opal 模版制备方法是用直径为亚微米或微米量级的介质材料小球的单分散悬浊液,通过自组织(self-assembly )方法,得到小球按照面心立方结构(fcc )排列的样品.常见的方法有重力沉降法[8]、气压法[9,10]等等,而且新的制备方法还在不断地出现,如Sato 等提出的提拉生长法[12,16]等等.但是当希望制备能带位置在近红外区的反opal 晶体时,需要使用直径在500nm 到1μm 左右的小球制备opal 模版.在这种条件下,小球所受的重力过大,如果不采用某些特殊的实验条件,则其沉降速度会非常快,所得样品的质量也会很差.为了解决这一问题,人们采用了各种方法,比如改变环境的湿度温度[14]、利用液体在固体表面的浸润特性[17]等等,但这些方法通常都或者只能应用于通过重力沉降法制备二氧化硅或其他密度较大材料的小球样品的过程中,或者只能制得厚度很小的光子晶体薄膜,而对于用密度比较小的聚苯乙烯(PS )小球悬浊液制备厚度较大的晶体则不甚适用.本文利用改进的气压法,采用了重新制备的样品池,制得了大直径聚苯乙烯小球的opal 晶体并测量了其能带结构,结果相当令人满意.2.实验方法我们首先使用直径为1μm 的PS 小球悬浊液制备样品.样品池与制备小直径小球时所用的样品池结构[10]基本相同,由上下两片具有光学平面的玻璃圆片叠合而成,其结构如图1(a )所示,一个O 形的分隔环将上下两片玻璃基片隔开,在其间形成样品生长的空间,小球的单分散悬浊液通过一根穿过上基片的玻璃管注入样品池.在O 形分隔环远离玻璃第53卷第1期2004年1月100023290Π2004Π53(01)Π0058204物　理　学　报ACT A PHY SIC A SI NIC AV ol.53,N o.1,January ,2004ν2004Chin.Phys.S oc.管的一端预留下可以供浊液中水分流出的孔隙.原方法中的样品池中所用分隔环厚度和出水通道都比较大,这在使用直径较小的聚苯乙烯小球悬浊液(小球直径小于500nm )时是没有问题的,此时的基本制备方法是将Duke 公司(Duke Scientific C orporation )的悬浊液注入样品池,通过玻璃管用氮气稍加压力,并将样品池放入超声振荡器中加以微弱振荡,就可以在样品池中形成质量相当好的opal 晶体.但是在小球直径增大至500nm 以上时,由于重力的作用,小球在悬浊液中的下降速度将会比直径较小的情况下大很多,这时如果在不改变其他条件的前提下继续使用未经稀释的原悬浊液和同样的样品池,小球将会迅速的“堆积”在玻璃管的下端和样品池的出水口处,其沉降速度将远大于使用小直径浊液时样品的生长速度.这将直接导致所得样品的周期性极差,其透过谱中无任何光子能带结构.图1　样品池结构示意图为克服这一困难,我们改变了原样品池中分隔环的结构.在自组织的基本原理不变的前提下,为了能够尽可能的使小球的沉积速度变慢,我们使用了结构如图1(b )所示的分隔环:在下基片的上表面的四周上用光刻胶镀上厚度为十几个微米、宽度为2mm 左右的一个圆环,在圆环的一段预留宽度约为5mm 的出水口,在这段区域用光刻的方法刻上数十条深度和宽度均为100nm 左右的通道,连通分隔环所围成的样品池区域和外面.这些通道可以允许悬浊液中的水在毛细作用和外加氮气的压力下缓慢地从池中流出,同时却能够挡住悬浊液中直径比较大的聚苯乙烯小球,使之留在样品池中.先把玻璃管穿过上基片上预先打好的小孔,用环氧树脂固定好;然后将上基片与下基片叠合在一起并使分隔环上刻有出水刻槽的一端位于远离玻璃管的位置;之后用少量环氧树脂固定上下基片,注意不要堵塞出水通道.这样制备好的样品池即可用来生长opal 晶体.我们所使用的悬浊液为Duke 公司的直径1μm 的聚苯乙烯小球悬浊液产品,其中所含小球的平均直径为1.020μm ,标准误差为±0.022μm ,悬浊液中所含小球占浊液的体积比例为1.0%.经实验,如果直接使用该浊液加入样品池,其沉降速度仍然过快.因此,我们用二次蒸馏水将浊液稀释到原浓度的110—120,然后对稀释后的浊液进行5min 的强超声振荡以保证其单分散性.将稀释好的浊液注入连接样品池的玻璃管中,然后利用氮气通过玻璃管向样品池中加上微弱的压力.在压力的作用下,浊液中的水会缓慢地从出水口处渗出样品池.在这同时对样品池加以微弱的振荡.在这样的条件下,根据自组织原理,聚苯乙烯小球会在出水口的内缘处开始排列成面心立方结构(fcc )的晶体.由于出水口的刻槽宽度和深度都很小,保证了浊液中水流出的速度会很慢,样品的生长速度也就因此得以放慢,改善了所得样品的品质.我们所用的样品池上下两玻璃基片的直径为1cm ,在这种条件下生长一个直径1μm 聚苯乙烯小球样品(样品的宽度约为5mm )的时间约为3至4周.之后我们又使用了同样为Duke 公司产品的700nm 聚苯乙烯小球悬浊液,其平均直径为701nm ,标准误差为±6nm ,悬浊液中所含小球占浊液的体积比为1.0%.由于小球直径的减小,其自然沉降速度也减小了很多,除了采用如上所介绍的样品池和实验条件外,也可以使用如图3所示的分隔环,951期张　琦等:大直径聚苯乙烯小球自组织方法制备高质量opal 晶体图2　700nm样品所用样品池分隔环结构示意图用厚度为几十个微米的胶环构成分隔环,在出水口处没有胶,而是用二氧化钛粉(Aldrich Chimica公司的产品,粒径约为1μm)堵住样品池的出水口,浊液中的水可以从二氧化钛粉末间的孔隙中流出,这样可以起到与在胶环上刻槽同样的作用.这样做的好处是浊液中水流出的速度比较快,适合这种小球直径相对较小的样品制备,且准备样品池相对简单.具体的制备过程则同1μm小球样品的制备基本相同.两种直径的小球制得的样品在自然光下观察,都可以观察到彩色闪光.3.能带位置的理论估算与测量根据布拉格散射公式:λ=2neffd,其中n eff为材料的有效折射率,d为垂直于光线入射方向的晶面间距,λ为带隙中心波长.面心立方结构小球的占空比为74%,在近红外波段聚苯乙烯的折射率约为1157,在样品不含水的情况下有效折射率n eff =εPS・74%+εair・26%≈1144.估算可得1μm小球样品的能带位置在2.35μm附近,700nm小球样品的能带应该在1.65μm附近.而对于浸泡在水中的样品,其背景介质不再是空气而是水,因此有效折射率变为neff=εPS・74%+ε水・26%≈1151,在这时1μm和700nm小球样品的能带中心位置应分别为2147μm和1.73μm.我们采用分光光度计(型号Cary2390)测量了样品的透过谱.所测得的结果如图3所示,图3(a),(b),(c)分别为1μm PS小球含水的样品、1μm PS 小球不含水的样品和700nm小球含水的样品的透过谱.(a)(b)两图中波长2.6μm后为样品池所用玻璃的吸收边,因此之后的样品透过谱无法测量.其中,(a)中能带中心位置约为2.51μm,(b)中能带中心位置约为2.37μm,(c)中能带中心位置约为1746 nm.与以上的估算对比可见,所测得的样品能带位置与估算所得结果吻合得相当好.图3　样品的透过谱由图3中还可以看出,700nm的样品的能带特性比1μm样品要好得多,这也和我们经验是一致06物理学报53卷的,即在一定范围内,悬浊液中小球直径越小,小球的沉积速度就越慢,所生长出的样品的晶格结构越好.41总结综上所述,我们用气压法,通过改进的样品池和实验条件,成功制得了质量较高的大直径聚苯乙烯小球opal 晶体,其能带处于近红外波段.这个结果对于以后制备红外波段的反opal 光子晶体提供了很好的实验基础.[1]Y ablonovitch E 1987Phys .Rev .Lett .582059[2]John S 1987Phys .Rev .Lett .582486[3]Jin C J ,Cheng B Y,M an B Y,Li ZL and Zhang D Z 2000Phys .Rev .B 6110762[4]Jin C J ,Fan S H ,Han S Z and Zhang D Z 2003IEEE J Quant .Elec .39160[5]He YJ et al ,2001Acta Phys .Sin .50892(in Chinese )[何拥军等2001物理学报50892][6]Zhuang F ,Wu L and He S L 2002Chin .Phys .11834[7]Y ablonovitch E ,G mitter T J and Leung K M 1991Phys .Rev .Lett .672295[8]Ni P G,D ong P ,Cheng B Y,Li X Y and Zhang D Z 2001Adv .Mater .13437[9]Park S H ,Qin D and X ia Y 1998Adv .Mater .101028[10]Ni P G,Cheng B Y and Zhang D Z 2002Chin .Phys .Lett .19511[11]Vlas ov Y A ,Bo X ,S turm J C and N orris D J 2001Nature 414289[12]M eng Q ,G u Z ,Sato O and Fujishima A 2000Appl .Phys .Lett .774313[13]Braun P V and W iltzius P 2001Adv .Mater .13482[14]G oldenberg L M ,W agner J ,S tum pe J ,Paulke B and G rnitz E 2002Langmuir 183319[15]H olland B T ,Blan ford C F and S tein A 1998Science 281538[16]G u Z ,Fujishima A and Sato O 2002Chem .Mater .14760[17]T essier P M ,Velev O D ,K alambur A T ,Lenhoff A M ,Rabolt J F ,and K aler E W 2001Adv .Mater .13396Preparation of high -quality large diameter polystyrenesphere s opal by self -a ssembly method 3Zhang Qi M eng Qing -Bo Cheng Bing -Y ing Zhang Dao-Zhong(Laboratory o f Optical Physics ,Institute o f Physics and Centre for Condensed Matter Physics ,Chinese Academy o f Sciences ,Beijing 100080,China )(Received 7M arch 2003;revised manuscript received 21April 2003)AbstractBy upgrading the cell ’s structure and other conditions in experiment ,we have prepared the large diameter (1μm and700nm )artificial opal crystals with the operation of the nitrogen pressure and gently rock ,and measured the sam ples ’band gap property.This experimental result will be useful in preparation of the photonic crystal with in frared band gap.K eyw ords :photonic crystal ,photonic band gap ,opal PACC :4225B ,4270Q ,7820P3Project supported by the National K ey Basic Research S pecial F oundation of China (G rant N o.2001C B610402)and the National Natural Science F oundation of China (G rant N o.10174089).161期张　琦等:大直径聚苯乙烯小球自组织方法制备高质量opal 晶体。

带隙可调各向同性蛋白石光子晶体的制备与研究

带隙可调各向同性蛋白石光子晶体的制备与研究于晓伟;郭金宝;魏杰【摘要】In this study, polystyrene microspheres assembling photonic crystals were fabricated by spin coating. Features of photonic crystals were studied, and the influence of different parameters on photonic band gap with a certain size microspheres was analyzed. The results showed that; photonic crystals fabricated by spin coating presented isotropic characteristics, and the photonic band gap of photonic crystal could be controlled by changing parameters. The reflection band of photonic crystal depended on mass fraction of microspheres, and the intensity depended on layers of spin coating. Consequently, we can control the photonic band gap via changing mass fraction of microspheres and layers of spin coating according to the requirement during designing the photonic crystal.%用旋涂法将聚苯乙烯微球组装成光子晶体,研究了此光子晶体的特点,并分析了在单一微球粒径下旋涂参数对光子带隙的影响.结果表明:旋涂法制备的光子晶体具有各向同性特点,其光子带隙由旋涂参数决定.光子晶体的反射波段取决于乳液中微球的质量分数,而反射强度取决于旋涂层数.因此,在设计光子晶体时,可以根据需要,通过微球的质量分数和旋涂层数的改变实现对光子带隙的控制.【期刊名称】《影像科学与光化学》【年(卷),期】2012(030)005【总页数】7页(P358-364)【关键词】旋涂法;垂直沉降法;各向同性;三维有序;可调光子带隙;光子晶体【作者】于晓伟;郭金宝;魏杰【作者单位】北京化工大学材料科学与工程学院,北京100029;北京化工大学材料科学与工程学院,北京100029;北京化工大学材料科学与工程学院,北京100029【正文语种】中文【中图分类】TQ31光子晶体［1］是由两种不同介电常数的介质材料在空间上周期排列形成的，因而光子晶体满足布拉格反射，导致某些频率的电磁波无法透过，产生光子带隙效应.光子带隙主要取决于光子晶体中介质材料折射率的差别、各介质材料所占的比率以及它们在空间的排列结构.光子带隙的存在使光子晶体成为制造新一代光波导、光转化器、生物和化学传感器及高密度存储器等光电器件的基础材料［2］.可调光子带隙光子晶体由于在传感器方面具有相当大的潜力，因而受到广泛关注.光子带隙的调节机理是外场的变化引起光子晶体的晶格常数的改变或者内部填充材料的折射率改变从而导致光子带隙的移动.外场的变化包括离子浓度［3，4］、光［5］、电场［6－8］、磁场［9，10］、温度［11，12］、机械力［13］等的改变.因此，光子晶体传感器的应用领域十分广阔.目前，可调光子带隙光子晶体大多是在三维有序光子晶体的基础上实现的.三维有序光子晶体主要是通过微球在重力、静电力或毛细力的作用下自组装形成的.由于自组装形成的空间排列结构难以改变，所以光子晶体的光子带隙取决于微球粒径，只有用不同粒径的微球才能制备出不同光子带隙的光子晶体.如果用一种粒径的微球能组装成光子带隙不同的光子晶体，那么光子晶体的可控制备甚至彩色图案化［14］都将很容易实现.用旋涂法［15－17］制备光子晶体时可通过改变参数控制微球的排列间距，从而形成微球在空间上的排列结构差异，引起光子带隙的变化，实现由一种粒径的微球制备出具有不同光子带隙的光子晶体.本研究中，用旋涂法制备光子晶体，并讨论了旋涂参数对光子带隙的影响.试剂：聚苯乙烯（PS）微球乳液（罗门哈斯公司）；过氧化氢（分析纯，北京化工厂）；浓硫酸（分析纯，北京化工厂）；无水乙醇（分析纯，北京化学试剂公司），以上实验药品无需处理，直接使用.仪器：KW－4A型台式匀胶机（中科院电子研究所）；AS5150B型超声波清洗机（天津奥特赛恩斯仪器有限公司）；WS－301型调温调湿箱（天津市天宇实验仪器有限公司）；AvaSpec－2048型光纤光谱仪（北京爱万提斯科技有限公司）；SFG－02.500型电热恒温鼓风干燥箱（黄石市恒丰医疗器械有限公司）和S4700型扫描电子显微镜（HITACHI公司）.1.2.1 基材的处理为除去载玻片上附着的各种杂质，将载玻片浸泡于双氧水和浓硫酸的混合溶液（体积比为1∶3）中，4 h后取出载玻片，用去离子水冲洗，并用氮气吹干.1.2.2 乳液的制备将PS微球乳液用去离子水稀释，配成一定质量分数的PS微球乳液后，超声波处理使PS微球在去离子水中均匀地分散.旋涂法所需的乳液微球质量分数为5%、10%、15%和20%，垂直沉降法所需的乳液微球质量分数为0.2%.1.2.3 光子晶体的制备用旋涂法制备光子晶体：将洗净的载波片置于匀胶机上，在旋涂速度达到3000转／min时滴加乳液，后旋涂30 s.用垂直沉降法制备光子晶体：将洗净的载波片垂直插入微球乳液中，放置到温度90℃和湿度70%的调温调湿箱中24 h.采用光纤光谱仪表征光子晶体的反射光谱，扫描电子显微镜（SEM）表征微球的排列形貌.将非单分散的PS微球（无法垂直沉降制备有序光子晶体）旋涂组装成光子晶体，此，旋涂法制备的光子晶体称为各向同性的光子晶体.经光纤光谱仪表征，其反射峰位于700 nm处（如图1）.与垂直沉降组装、反射峰在700 nm左右的光子晶体相比，旋涂法选择的PS微球平均粒径为433 nm，而垂直沉降法选择的微球粒径为313 nm，但最终都制备出反射峰在700 nm的光子晶体.因此，两种方法制备的光子晶体中微球在空间上的排列结构不同.SEM进一步表征：旋涂法制备的光子晶体，微球呈现各向同性排列（如图2A），而垂直沉降法制备的光子晶体，微球呈有序排列（如图2B），此结构具有长程有序性和各向异性.因由于旋涂制备的光子晶体中微球排列不是有序的，而是各向同性的，因而在改变参数以控制微球的排列间距时，各向同性光子晶体的结构不会被破坏.因此，相对于垂直沉降法，旋涂法更容易组装成具有不同光子带隙的光子晶体.旋涂组装的参数包括乳液中微球的质量分数、旋涂层数和旋涂速度.但由于旋涂速度只有控制在3000转／min左右时，才能获得无缺陷的多层旋涂光子晶体.所以本文主要探讨微球的质量分数和旋涂层数两个参数变化对各向同性光子晶体光子带隙的影响.采用微球质量分数［w（微球）］为5%、10%、15%和20%的4种乳液进行旋涂，制备出相应的各向同性光子晶体，以光纤光谱仪表征4种光子晶体的反射光谱.如图3，四种体系的光子晶体反射峰分别为634 nm、702 nm、770 nm和802 nm，实现了由一种粒径的微球制备出具有不同光子带隙的光子晶体，且随着w（微球）值的增大，光子晶体的反射波段发生红移.通过SEM表征微球的排列来进行分析.图4中A、B、C和D分别对应w（微球）值为5%、10%、15%和20%的乳液制备的光子晶体的SEM图，可以看出：随着w（微球）值的增大，水平方向上微球的间距会逐渐的减小.以微球间距的差异建立微球在垂直方向上的排列模型（如图5）进行辅助分析.通过模型图可知：水平方向上微球的间距l的变化，将引起垂直方向上微球层间距d的变化.A图微球间距l1大于B图微球间距l2，从而导致了A图微球层间距d1小于B图微球层间距d2.即微球间距l增大时，微球层间距d减小.由布拉格衍射公式2d sinθ＝λ可知，晶面间距与反射峰的波长成正比，所以微球间距l减小时，反射峰的波长增大.因此，随着w（微球）值的增大，各向同性光子晶体的反射峰发生红移.综上所述，微球质量分数通过对微球排列紧密性的影响实现了对光子带隙的调节.当w（微球）值增大时，各向同性光子晶体中微球的间距变小，层间距增加，光子晶体的反射峰波长也增大，光子带隙发生红移.由于用旋涂法制备光子晶体时，层数较少的光子晶体反射强度较小，光纤光谱仪无法表征其反射光谱，因而本研究中主要讨论旋涂3层以上的光子晶体.采用w（微球）值为10%的乳液进行旋涂，制备出层数为4—8的光子晶体.对不同层数的光子晶体进行反射光谱的分析，如图6A.随着旋涂层数的增加，光子晶体的反射强度逐渐增加.对w（微球）值为15%的乳液制备的不同层数光子晶体进行反射光谱的分析，如图6B.随着旋涂层数的增加，光子晶体的反射强度仍逐渐增加. 通过SEM对w（微球）值为15%的乳液所制备的光子晶体进行断面表征.图7中箭头所指方向为顶层方向，由图7A中标记处可知：当层数从1增加到8层时，微球在垂直方向上的排列基本保持一致，光子晶体的反射强度增强；当层数增加到8层以上时，垂直方向上的一致性逐渐消失，微球排列无序态增加，光子晶体的反射强度减弱.因此，旋涂法制备的光子晶体在层数为8层时反射强度最大.而垂直沉降法制备的光子晶体中，微球在垂直方向上的排列始终是一致的，因此，光子晶体具有较高的反射强度.综上所述，旋涂层数通过对反射强度的影响实现对光子带隙的调节.当微球在垂直方向上的排列一致时，旋涂层数增加，光子晶体的反射强度增强；当微球排列的一致性消失时，旋涂层数增加，光子晶体的反射强度降低.旋涂法可将聚苯乙烯微球组装成各向同性光子晶体，并通过旋涂参数（微球的质量分数和旋涂层数）控制其光子带隙，实现由一种粒径的微球制备出具有不同光子带隙的光子晶体.光子带隙的反射波段可通过乳液中微球的质量分数控制.质量分数增大时，光子晶体的反射波段红移.本研究中，微球质量分数由5%增大到20%时，光子晶体的反射峰从634 nm红移到802 nm.光子带隙的反射强度可通过旋涂层数控制，旋涂层数增加时，光子晶体的反射强度先增大后减小.本研究中，用质量分数为15%的微球乳液旋涂8层制备的光子晶体，具有最高的反射强度.因此，旋涂法可实现带隙可调各向同性光子晶体的制备.【相关文献】［1］ Yablonovitch E.Inhibited spontaneous emission in solid－state physics and electronics［J］.Phys.Rev.Lett.，1987，58：2059－2062.［2］ John S.Strong localization of photons in certain disordered dielectric superlattices ［J］.Phys.Rev.Lett.，1987，58：2486－2489.［3］ Lee Y J，Braun P V.Tunable inverse opal hydrogel p H sensors［J］.Adv.Mater.，2003，15：563－566.［4］ Hong W，Hu X B，Zhao B Y，et al.Tunable photonic polyelectrolyte colorimetric sensing for anions，cations and zwitterions［J］.Adv.Mater.，2010，22：5043－5047. ［5］ Arsenault A C，Puzzo D P，Ozin G A，et al.Photonic－crystal full－colour displays ［J］.Nature，2007，1：468－472.［6］ Xia J Q，Ying Y R，Foulger S H.Electric－field－induced rejection－wavelength tuning of photonic－bandgap composites［J］.Adv.Mater.，2005，17：2463－2467. ［7］ Puzzo D P，Arsenault A C，Ozin G A，et al.Electroactive inverse opal：A single material for all colors［J］.Angew.Chem.Int.Ed.，2009，48：943－947.［8］ Hwang K S，Kwak D W，Kang C J，et al.Electrically tunable hysteretic photonic gels for nonvolatile display pixels［J］.Angew.Chem.Int.Ed.，2011，50：1－5.［9］ Zhu C，Chen L S，Xu H，et al.A magnetically tunable colloidal crystal film for reflective display［J］.Macromol.Rapid Commun.，2009，30：1945－1949.［10］ Ge J P，Hu Y X，Yin Y D.Highly tunable superparamagnetic colloidal photonic crystals［J］.Angew.Chem.Int.Ed.，2007，46：7428－7431.［11］ Takeoka Y，Watanabe M.Tuning structural color changes of 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新型太赫兹光子晶体OAM_光纤设计

第 21 卷第 12 期2023 年 12 月Vol.21，No.12Dec.，2023太赫兹科学与电子信息学报Journal of Terahertz Science and Electronic Information Technology新型太赫兹光子晶体OAM光纤设计杨婧翾1，李巍2，成利敏1(1.廊坊师范学院电子信息工程学院，河北廊坊065000；2.北华航天工业学院电子与控制工程学院，河北廊坊065000)摘要：太赫兹通信兼具微波通信和光波通信的优势，是解决通信容量紧缺难题的最有效技术手段之一。

针对太赫兹波段吸收损耗严重及抗外在扰动差，难以支持长距传输问题，设计了一种基于环形光子晶体光纤(PCF)结构的新型太赫兹光纤。

以现有常见材料作为光纤基底材质，通过创新光纤结构中空气孔排布方式，抵消材料高吸收损耗，以支持高性能轨道角动量(OAM)模式传输。

选择最优参数，实现6个OAM模式群的高模式质量、低限制损耗和宽带宽的稳定传输。

在0.2~0.9 THz宽波段内，实现模式纯度超过88.9%，限制损耗小于10-7 dB/m。

通过软件仿真实验设计，解决了太赫兹与OAM技术相结合的关键问题，为模分复用(MDM)技术在太赫兹通信系统的应用奠定了理论研究基础。

关键词：轨道角动量；太赫兹通信；光子晶体光纤；模分复用中图分类号：TN914 文献标志码：A doi：10.11805/TKYDA2023089Design of new terahertz photonic crystal fiber forOrbital Angular Momentum modes transmissionYANG Jingxuan1，LI Wei2，CHENG Limin1(1.School of Electrical Information Engineering，Langfang Normal University，Langfang Hebei 065000，China；2.School of Electronic and Control Engineering，North China Institute of Aerospace Engineering，Langfang Hebei 065000，China)AbstractAbstract：：Terahertz communication has the advantages of both microwave communication and optical communication, which is one of the most effective technical means to solve the problem ofcommunication capacity shortage. In order to solve the problems of serious absorption loss and poorexternal disturbance resistance in terahertz band, a new terahertz fiber based on circular PhotonicCrystal Fiber(PCF) structure is designed to support high performance Orbital Angular Momentum(OAM)modes transmission. The existing common materials are used as the fiber base material, and the highabsorption loss of materials is offset by the innovation of hollow porosity arrangement in the fiberstructure. The optimal parameters are selected to realize the stable transmission of six OAM mode groupswith high mode quality, low confinement loss and wide bandwidth. The mode purity is above 88.9% andthe confinement loss is below 10-7 dB/m in the 0.2~0.9 THz band. Through simulation, the key problemof combining terahertz and OAM technology is solved, which lays a theoretical foundation for theapplication of Mode Division Multiplexing(MDM) technology in terahertz communication system.KeywordsKeywords：：Orbital Angular Momentum；terahertz communication；Photonic Crystal Fiber；Mode Division Multiplexing随着信息互联网技术创新的快速发展，人工智能、高清视频、直播等新的应用方式受到了社会各界的广泛关注[1-3]。

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Design procedure for photonic crystalﬁbers with ultra-ﬂattened chromatic dispersionHuizhen Xu()1,2∗,Jian Wu()1,Yitang Dai()1,Cong Xu()1,and Jintong Lin()11Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),Ministry of Education,Beijing100876,China2College of Science,Jimei University,Xiamen361021,China∗Corresponding author:elimshee@Received November1,2010;accepted December14,2010;posted online January1,2011A simple design procedure is used to generate photonic crystalﬁbers(PCFs)with ultra-ﬂattened chromatic dispersion.Only four parameters are required,which not only considerably saves the computing time, but also distinctly reduces the air-hole quantity.The inﬂuence of the air-hole diameters of each ring of hexagonal PCFs(H-PCF,including1-hole-missing and7-hole-missing H-PCFs),circular PCFs(C-PCF), square PCFs(S-PCF),and octagonal PCFs(O-PCF)is investigated through simulations.Results show that regardless of the cross section structures of the PCFs,the1st ring air-hole diameter has the greatest inﬂuence on the dispersion curve followed by that of the2nd ring.The3rd ring diameter only aﬀects the dispersion curve within longer wavelengths,whereas the4th and5th rings have almost no inﬂuence on the dispersion curve.The hole-to-hole pitch between rings changes the dispersion curve as a whole. Based on the simulation results,a procedure is proposed to design PCFs with ultra-ﬂattened dispersion. Through the adjustment of air-hole diameters of the inner three rings and hole-to-hole pitch,aﬂattened dispersion of0±0.5ps/(nm·km)within a wavelength range of1.239–2.083µm for5-ring1-hole-missing H-PCF,1.248–1.992µm for5-ring C-PCF,1.237–2.21µm for5-ring S-PCF,1.149–1.926µm for5-ring O-PCF,and1.294–1.663µm for7-hole-missing H-PCF is achieved.OCIS codes:220.4000,060.2280,060.4005.doi:10.3788/COL20110901.0000.Since photonic crystalﬁbers(PCFs)wereﬁrst reported in1996[1],diﬀerent kinds of PCF cross section structures, such as hexagonal PCF(H-PCF)[2],octagonal PCF(O-PCF)[3],square PCF(S-PCF)[4],and so on,have been developed.The dispersion properties of PCFs are sig-niﬁcantly diﬀerent from those of conventionalﬁbers be-cause the cross section structures consisting of an array of air holes allow forﬂexible tailoring of the dispersion curves,which cannot be realized in conventional opti-calﬁbers.Control of the chromatic dispersion in PCFs is of huge importance for applications in opticalﬁber communications[5],dispersion compensation,supercon-tinuum generation[6,7],and so on.Many PCF designs have been proposed to achieve ultra-ﬂattened chromatic dispersion.In Ref.[8],the chromatic dispersion in conventional PCFs was con-trolled by changing the air holes,which are arrayed in a regular hexagonal structure with the same diame-ters in the cladding region.A PCF with a dispersion of0±0.6ps/(nm·km)from1.24to1.44µm was real-ized.Because the air-ﬁlling fraction is too small to real-ize ultra-ﬂattened dispersion,more than20rings of air holes(up to455holes)are required to signiﬁcantly re-duce the conﬁnement loss,thereby causing extreme com-plexity in the manufacturing process.Moreover,the achievement of this kind(same air-hole size)of ultra-ﬂattened dispersion over such a large wavelength range involves highly accurate control of air-hole diameter and pitch[9].To reduce the quantity of air holes and real-ize ultra-ﬂattened dispersion,many designs discussed in literature have the following characteristics:diﬀerently spaced rings of holes[3]and diﬀerent sizes of holes[10].In Ref.[3],the authors presented an eight-ring O-PCF. After optimization of the diameters of the1st ring,the outer seven rings,and the air-hole pitch,PCFs with a dispersion of0±0.5ps/(nm·km)in a wavelength range of1.46–1.66µm were obtained.In Ref.[10],a new de-sign with four orﬁve rings of gradually increasing air-hole diameters for each ring was proposed for achieving ultra-ﬂattened dispersion.Through optimization,a four-ring PCF with aﬂattened dispersion of0±0.5ps/(nm·km) for a wavelength of1.19–1.69µm,and aﬁve-ring PCF with aﬂattened dispersion of0±0.4ps/(nm·km)for a wavelength1.23–1.72µm were proposed.This design considerably reduces the ring number of air holes,but the design procedure becomes complicated because sev-eral geometrical parameters,ﬁve(four air-hole diameters and one pitch)for the four-ring PCF and six(ﬁve air-hole diameters and one pitch)for theﬁve-ring type,are needed to simultaneously optimize dispersion properties. Several studies have already used the genetic algorithm to determine global minima for ultra-ﬂattened design[11,12]. However,the genetic algorithm entails considerable com-puting time because it requires numerous iterations.In Ref.[12],for example,the algorithm required40individ-uals and13generations.In this letter,a simple procedure for diﬀerent kinds of PCFs is presented to obtain ultra-ﬂattened disper-sion.This design procedure requires only four parame-ters(three air-hole diameters and one hole-to-hole pitch), considerably saving the computing time.In addition, it requires only one array layout cross section structure and four orﬁve rings of air holes,tremendously reducing complexity in the manufacturing process.This design1671-7694/2011/010xxx-03c 2011Chinese Optics Lettersprocedure is suitable not only for1-hole-missing PCFs (including conventional H-PCFs,C-PCFs,S-PCFs,and O-PCFs),but also for7-hole-missing PCFs,which are large-mode-areaﬁbers.To improve dispersion properties and reduce opera-tional complexity,a simple design procedure was used for dispersion control.Figure1shows the cross sections of H-PCF,C-PCF,S-PCF,O-PCF,and7-hole-missing H-PCF with uniform air holes that are taken into consider-ation.These four kinds of PCFs have a two-dimensional (2D)silica core andﬁve air-silica cladding rings.In the ﬁgure,d n(n=1–5)is the air-hole diameter of the N th air-hole ring;Λis the hole-to-hole pitch for H-PCF,S-PCF,and the air-hole pitch between rings for C-PCF and O-PCF.During the simulations,the beam propa-gation method(BPM)[13]was used to calculate the dis-persion curves of the PCFs.The BeamPROP module of the commercial software package RSoft(RSoft Design Group,New York)was used for the simulations.The iterative function method[14]was used to obtain modal characteristics.During the simulations,the transparent boundary condition[15]was adopted.The simulations were performed in a window of12×12µm within the transverse x–y plane of the PCF,in steps of∆z=0.1µm and∆x=∆y=0.05µm.The tolerance for n eﬀconver-gence was as low as1×10−7to guarantee numerical pre-cision.The refractive index of silica is given by the Sell-meier dispersion equation[16]:n2m(λ)=1+li=1A iλ2cd2R e(n eﬀ)Fig.3.Design procedure for H-PCF with ultra-ﬂattened dis-persion.(a)Λ=2µm,f2=f3=0.8,f4=f5=0.95;(b)Λ=2µm,f1=0.37,f3=0.8,f4=f5=0.95;(c)f1=0.37, f2=0.65,f3=0.8,f4=f5=0.95;(d)Λ=1.35µm,f1=0.37, f2=0.65,f4=f5=0.95.with each other within the shorter wavelength range when f3varies.f3only slightly aﬀects the dispersion curves within the longer wavelength range.As shown in Fig.2(d),f4and f5have no inﬂuence on the dispersion proﬁle.In accordance with the simulation results above,a sim-ple design procedure was used to control dispersion prop-erties.Because only the air-hole diameters of the inner three rings inﬂuence the dispersion curves,only the three parameters need to be changed without regard for the4th and5th rings’air-hole diameters.The large values of f4 and f5are beneﬁcial to better conﬁnement of PCFs[10,18], although they have no inﬂuence on the dispersion pro-ﬁle.Therefore,f4and f5were set to0.95and remained unchanged during the subsequent simulations.Figure3 shows the design procedure.Figure2(a)shows that when f1=0.4,the dispersion curveﬂattens within the longer wavelength range.Therefore,f1was varied from0.34to 0.4to determine a more suitable value.Figure3(a)shows that although the dispersion value of curve f1=0.37is nearly the same as that of curve f1=0.4within the longer wavelength range,the former is smaller within the shorter wavelength range.The curve slope of f1=0.34is more steep than those of the other two.Therefore,f1=0.37 was chosen for the next optimization.Next,f2was var-ied to optimize the dispersion proﬁle within medium and longer wavelength ranges.Figure3(b)illustrates that the decrease in f2reduces the dispersion value andﬂat-tens the curves more than that in Fig.3(a)within about 1.4–2.0µm wavelengths.However,theﬂattened disper-sion values are much higher than zero.To generate a dispersion value near zero,the pitchΛis modiﬁed.Fig-ure3(c)clearly shows that changingΛwhile keeping all other parameters constant changes the curve as a whole. In addition,the dispersion value of the entire curve de-creases asΛdecreases.ForΛ=1.35µm,the dispersion value is near zero between about1.2and1.8µm wave-lengths.However,the curve is still a little steep within longer wavelengths.In the last section,f3only slightly aﬀects the dispersion curve within the longer wavelength range.Therefore,f3was varied toﬂatten the longer wavelength range.Figure3(d)shows that the dispersion value decreases with decreasing f3.The curve of f3=0.5 is muchﬂatter within the longer wavelength range than the other two curves.Finally,throughﬁne adjustments in the four parameters(inner three rings’air-hole diame-ters and pitch),an ultra-ﬂattened dispersion wavelength within broader wavelengths is obtained.C-PCFs have been discussed in our previous work[19], in which we concluded that the inﬂuence of air-hole diam-eter on the dispersion curve gradually weakened from the inside ring to the outside.Through the same procedure as H-PCF,4-ring and5-ring C-PCFs with ultra-ﬂattened dispersion are obtained.The cross section of S-PCF with uniform air holes is shown in Fig.1(c).After the investigation on the vari-ation in each ring air-hole diameter,we found that they had the same inﬂuence on the dispersion curve as H-PCF and C-PCF did.Therefore,S-PCF with ultra-ﬂattened dispersion can be obtained using the same procedure. Razzak et al.proposed an O-PCF for ultra-ﬂattened dispersion and obtained a dispersion of0±0.5ps/ (nm·km)in a wavelength range[3]of1.46–1.66µm.The same procedure was applied to O-PCF in the simulations, and ultra-ﬂattened dispersion wasﬁnally obtained.The design and discussion above are limited to1-hole-missing PCFs.Now we extend our conclusion to7-hole-missing H-PCFs,which are large mode areaﬁbers.After using the same design procedure,ultra-ﬂattened disper-sion can be achieved.However,the wavelength range withﬂattened dispersion is narrower than that in1-hole-missing PCF due to its large high-index core.Table1.PCFs with Ultra-Flattened Dispersion0±0.25ps/(nm·km)0±0.4ps/(nm·km)0±0.5ps/(nm·km)Fig.4.Dispersion of4-ring C-PCF,5-ring C-PCF,5-ring H-PCF,5-ring S-PCF,5-ring O-PCF,and7-hole-missing H-PCF.Through the optimization procedure above,PCFs with ultra-ﬂattened dispersion are obtained.Table1lists the geometrical parameters.In theﬂattened dispersion wavelength range of the1-hole-missing H-PCF,C-PCF, S-PCF,O-PCF,and7-hole-missing H-PCF,we used the proposed design procedure.Figure4shows the chro-matic dispersion of these six pared with the abovementioned references,theﬂattened dispersion wavelength ranges of these PCFs are precisely broadened through the design procedure.The optimization process for PCFs with ultra-ﬂattened dispersion can be summarized as follows.Step1.The air-hole diameter values of the outer rings (except the inner three rings)are set to a larger value for better conﬁnement.Then,the airﬁlling fraction of the 1st ring is scanned to determine a relativelyﬂat disper-sion curve.Step 2.The airﬁlling fraction of the2nd ring is scanned,and the variation in f2ﬂattens the dispersion curve to a greater extent within the longer wavelength range.Step3.The adjustment of the hole-to-hole pitch causes the dispersion curve to move as a whole.The curve near zero is then moved through the change ofΛ.Step.4.Finally,the dispersion value within the longer wavelength range can be improved through adjustment in the airﬁlling fraction of the3rd ring.In conclusion,the inﬂuence of air-hole diameters on the dispersion curve is investigated for conventional H-PCFs (including1-hole-missing and7-hole-missing),C-PCFs, S-PCFs,and O-PCFs.Regardless of the kind of PCF cross section structure,the inﬂuence of air-hole diameters on dispersion curves is similar.The1st ring air-hole di-ameter has the greatest inﬂuence on the dispersion curve, aﬀecting the dispersion curve within the entire wave-length range considered.Within the shorter wavelength range,the dispersion value decreases as f1decreases, whereas the curve shape changes minimally.However, within the longer wavelength range,the variation in f1 aﬀects not only the dispersion value but also the curve shape.The2nd ring air-hole diameter more considerably aﬀects the dispersion curve within the longer wavelength range than within the shorter wavelength range,whereas the3rd ring has only minimal inﬂuence on the dispersion curve within the longer wavelength range.The4th and 5th rings’air-hole diameters have almost no inﬂuence on the dispersion curve but play an important role in conﬁnement loss.According to the diverse eﬀects of dif-ferent ring air-hole diameters on the dispersion curve,a design procedure is used to achieve ultra-ﬂattened dis-persion.The air-hole diameters of the inner three rings and the pitch are scanned to search for minima in each step.Through the proposed procedure,aﬂattened dis-persion of0±0.5ps/(nm·km)within a wavelength range of 1.239–2.083µm for5-ring1-hole-missing H-PCF, 1.212–1.830µm for4-ring C-PCF,1.248–1.992µm for 5-ring C-PCF,1.237–2.21µm for5-ring S-PCF,1.149–1.926µm for5-ring O-PCF,and1.294–1.663µm for 7-hole-missing H-PCF is achieved.This design proce-dure is simple and tremendously saves the computing time.In addition,it requires only four parameters(the air-hole diameters of the inner three rings and the pitch) and considerably reduces the quantity of air-hole rings. 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