光子晶体简介英文版
光子晶体水凝胶的英文
光子晶体水凝胶的英文Photonic crystal hydrogels are pretty cool materials. They're like the combo of two amazing things: photonics and hydrogels. You know, photonics deals with light and its interaction with matter, while hydrogels are those super-absorbent polymers that can hold a lot of water.When you put them together, you get something that can manipulate light in a really unique way. Imagine being able to control how light passes through a material just by changing its water content. That's what photonic crystal hydrogels allow you to do.These materials are also really responsive. They can change their properties based on external stimuli like temperature or pH. So, not only can you control light, but you can also make the material respond to its environment.Photonic crystal hydrogels are super versatile, too. You can use them in sensors to detect chemicals or indisplays that change color based on some input. The possibilities are endless!Plus, they're just so fascinating to look at. The way the light dances through the crystal structure is like a mini light show. It's like nature's own version of a laser light display, but much more subtle and elegant.In a nutshell, photonic crystal hydrogels are a marriage of science and beauty. They're not just useful materials; they're also a visual treat. Who knows, maybe one day we'll see them everywhere, from our smartphones to our homes, adding a bit of magic to our daily lives.。
_英文_-短波长三维光子晶体
第29卷第2期 光 子 学 报 V o1129N o12 2000年2月 A CTA PHO TON I CA S I N I CA Feb ruary2000 SHORT-W AVEL ENGTH THREE-D I M ENSI ONALPHOT ON I C CRY STAL SQ uyang Zhengb iao,L i J ingzhen,Sun Y iling,L in M inD ep t.Op to2E lectron ic E ng g.,S chool of S ci.&T ech.,S henz hen U n iv.,S henz hen518060,P.R.Ch inaAbstract A new k ind of th ree2di m en si onal p ho ton ic crystal,called as com b ined th ree2di m en si onal p ho ton ic crystal,is p resen ted and show n to be p ractical th rough theo reticalanalyses.T he com b ined th ree2di m en si onal p ho ton ic crystal is an enclo sed so lid struc2tu re m ade of several p ieces of one2di m en si onal p ho ton ic crystals.It is found ou t that,under p resen t techno logy,there ex ists no difficu lty in the fab ricati on of the p ropo sedcom b ined th ree2di m en si onal p ho ton ic crystals w o rk ing in sho rt w avelength s,includingtho se in the visib le.T h ree p ractical schem es are given and discu ssed. Keywords Pho ton ic crystal;Sho rt2w avelength;T h ree2di m en si on0 I n troduction Pho ton ic crystals(PC s)are of great in terest in recen t years fo r their po ten tial w ide app lica2 ti on s1～10.It is found that spon taneou s radiati on of atom s and m o lecu les in PC s can be con tro lled, w h ich m akes it po ssib le to ach ieve zero2th resh2 o ld sem iconducto r lasers and h igh efficiency ligh t em itting di odes1～2.T he band2gap characteristics of PC s can be app lied to design single m ode h igh Q m icro2cavities,ligh t em itting di odes of laser quality ou tp u t,h igh quality directi onal an tennas, efficien t ligh t w avegu ides,and h igh p erfo rm ance ligh t2w ave filters3～6.Fu rtherm o re,non linear PC s are u sefu l fo r sp litting coup ling,dem u lti p lex ing m u lti p lex ing and all2op tical s w itch ing of ligh t2 w aves in op tical comm un icati on s,and fo r the generati on of second harm on ics7～10.M uch p rogress is m ade in tw o2and th ree2di2 m en si onal PC s w o rk ing in the long w avelength regi on ranging from m icrow ave to the near in2 frared11～14.T h ree2di m en si onal(32D)PC s op erat2 ing in op tical w avelength s has also been investi2 gated bo th theo retically and exp eri m en tally15～17. Yet,un til now there still ex ist p len ty of techn ical difficu lties in the fab ricati on of32D PC s op erat2 ing in the sho rt w avelength regi on,esp ecially inthe visib le ligh t w avelength regi on.In th is p ap er,w e p resen t a new k ind of p ractical schem e fo r con structing32D PC s that m ay op erate in the regi on s from m icrow ave to the visib le ligh t2w ave.Each of the p ropo sed new 32D PC s con sists of a num ber of one2di m en si onal (12D)PC s.It is know n that there ex ists no diffi2 cu lt in fab ricating12D PC s op erating bo th in long w avelength s and in sho rt w avelength s.So ou r schem es are of p ractical sign ificance fo r p ro2 ducing32D PC s that m ay op erate in a w ide range of w avelength s,esp ecially,in the visib le ligh t w avelength s.1 Theoretica l m odel and ana lysis T he essen tial characteristic of12D PC s is that the tran s m issi on of electrom agnetic w aves is p roh ib ited in the directi on s in one di m en si on. W h ile in32D PC s,the tran s m issi on of electro2 m agnetic w aves is fo rb idden in all directi on s in th ree di m en si on s.F rom these essen tial charac2 teristics of12D and32D PC s,w e m ay get the idea that som e structu res con sisted of several p ieces of12D PC can p lay the ro le of32D PC s and can be con sidered as a new k ind ofR eceived date:1999-09-2032D PC .T h is new k ind of 32D PC s is advan ta 2geou s fo r its si m p licity in configu rati on and fab 2ricati on ,w h ich is sp ecially u sefu l fo r ob tain ing 32D PC s that op erate in the visib le ,becau se 12D PC s w o rk ing in the visib le can be fab ricated w ithou t m uch difficu lty by conven ti onal tech 2n iques .W e find that the necessary and sufficien t conditi on fo r a structu re m ade of 12D PC s to be 2have like a 32D PC is that the in tersecting su r 2faces of the 12D PC s in the system are enclo sed in sp ace by these 12D PC s .T h is can be show n to be true from the fo llow ing th ree asp ects .111 The m otion of Photon s i n an UnclosedStructure L et ′s con sider the m o ti on of p ho ton s in a general unclo sed system m ade of a few p ieces of 12D PC s ,as show n in F ig .1.T ak ing no tice of the fact that the su rface of a 12D PC behaves like a m irro r to inciden t p ho ton s ,from F ig .1(a )～(c )it can be easily seen that p ho ton s over a w ide range of directi on s in the structu re w ill escap e ou t of it .T h is m ean s that the m o ti on of the p ho 2ton s in the system is divergen t .T hu s an unclo sed system con sisted of a few p ieces of 12D PC s is no t a su itab le structu re that can serve as a 32D PC .H ere the unclo sed structu re is referred to be that the in tersecting su rfaces of differen t 12D PC s are unclo sed in sp ace.F ig .1 T he mo ti on of pho ton s in an unclo sed structu re ,w here ( )～( )rep resen t differen t 12D PC s ,w here V 1and V 2are respectively the inciden t and ou tgo ing velocities of the pho ton s112 The m otion of photon s i n the i n tersecti ngreg ion of 1-D PCs w ith an acute i n tersect -i ng angleTo analyze the m o ti on of p ho ton s in an en 2clo sed structu re by several p ieces of 12D PC s ,w e first con sider the m o ti on of p ho ton s in the cro ss 2ing regi on of th ree p ieces of 12D PC s w ith a cro ssing angle being acu te ,as show n in F ig . 2.L et ′s fo llow and analyze the m o ti on of a p ho ton starts from an arb itrary po in t A in F ig .2at an arb itrary directi on of m o ti on .Suppo se Η1be thein tersecti on angle of the tw o cro ssing p ieces of12D PC s ( )and ( ).W e m ay w rite the inci 2den t angle of the p ho ton at the su rface S 1of thebo ttom 12D PC as Ηi n (n =1,2,3…),w h ile that at the su rface S 2of the upp er 12D PC as Βi n (n =1,2,3…)1T hen from F ig .2w e can ob tainΗi n =2Η1+Ηi (n -1)=2(n -1)Η1+Ηi1 (n =1,2,3,…+)(1) Βi n =2Η1+Βi (n -1)=2(n -1)Η1+Βi1 (n =1,2,3,…+)(2)F ig .2 T he mo ti on of pho ton s near the in tersectingarea of 12D PC s w ith an acu te in tersecting angle ,w here regi on s ( )～( )are differ 2en t 12D PC sEqs .(1)and (2)tell u s that Ηi n and Βi n w illbe greater than 90°fo r certain large values of n .T h is m ean s that th rough certain ti m es of reflec 2ti on by the su rfaces of the in tersecting 12D PC s ,the inciden t p ho ton w ill m ove tow ards the directi on aw ay from the cro ssing regi on of the 12D PC s .W e can say that the inciden t p ho ton is reflected back by the acu te angle .113 The m otion of photon s i n the i n tersecti ngreg ion of 1-D PCs w ith a non -acute i n ter -secti ng angleN ow w e tu rn to analyze the m o ti on of p ho 2ton s in the cro ssing regi on of 12D PC s w ith the in tersecting angle being non 2acu te ,as show n in F ig .3.It is easy tosee from F ig .3(a )～(d )F ig .3 T he mo ti on of pho ton s near the in tersecting areaof the th ree p ieces of 12D PC s ( )2( )w ith a non 2acu te in tersecting angle ,w here V 1,V 2and V 3are the velocities of pho ton s3112期 Q uyang Zhengb iao ,et al .Sho rt 2w avelength th ree 2di m en si onal pho ton ic crystalsthat all p ho ton s m oving tow ards the in tersecting area of the th ree p ieces of 12D PC s w ith a non 2a 2cu te in tersecting angle w ill be reflected aw ay from the regi on near the in tersecting angle .F rom the above analyses w e m ay conclude that p ho ton s in side an enclo sed strucu re con sisted of several p ieces of 12D PC s are w ho lly fo rb idden in the enclo sed sp ace .In the sam e w ay w e m ay get the conclu si on that p ho ton s ou tside the enclo sed sp ace are p roh ib ited to p enetrate in 2to the in side of the structu re .T hu s an enclo sed structu re m ade of 12D PC s can serve as a 32D PC .2 Exam ples of conf igura tion ofpractica l 3-D photon ic crysta lsA s show n in the above secti on s ,any en 2clo sed structu re m ade of several p ieces of 12D PC s can serve as a 32D PC .T hu s a lo t of schem es can be ob tained acco rding to th is p rinci p le .H ere w e ju st give th ree exam p les to save p ages ,asshow n in F ig .4～6.A so lid cub ic structu re m ade of five p ieces of 12D PC s is show n in F ig .4.It shou ld be po in t 2ed ou t that the effective sp ace fo r fo rb idding p ho ton s in the structu re show n in F ig .4(d )is the vo lum e of the cen tral 12D PC b lock [W ].T h is structu re can be fab ricated acco rding to the fo llow ing step s :first the cen tral b lock ,then the fou r ou tside b lock s one by one ,either th roughdepo siting ,grow ing o r fil m coating techn iques.F ig .4 A cub ic structu re (d )m ade of th ree typesof 12D PC s :[U ],[V ]and [W ]show n in (a ),(b )and (c ),respectivelyA so lid cylinder configu rati on con sisted of tw o p ieces of 12D PC s is p resen ted in F ig .5.H ere the effective sp ace fo r fo rb idding p ho ton s in th is structu re is the vo lum e of the cen tral cylinder m ade of several dielectric discs .T he cen tral cylinder of th is structu re can be ob tained th rough laser cu tting of an o rdinary 12D PC .T he ,12,can be p rep ared by dielectric grow ing around the cen tral cylinder .T h assu re good quality ,one m ay ro tate the cen tral cylinder w h ile grow ing di 2electrics around it.F ig .5 A cylindrical structu re m ade of tw o specialk inds of 12D PC s ,w here (b )is a secti onal view of (a )A nd a so lid sp herical structu re is given in F ig .6.T he dielectric con stan t in the structu re varies p eri odically in the radial directi on s ,w ith 2ou t any dep endence on the o ther tw o coo rdi 2nates .T hu s th is structu re is theo retically a 12D PC .B u t it is easily seen that th is structu re is en 2clo sed and the p ho ton s in side the sp here are fo r 2b idden in it .A lso ,p ho ton s ou tside the sp here w ill no t be ab le to p enetrate the sp here .A ctual 2ly ,it can be con sidered as a structu re m ade of an infin ite num ber of 12D PC p ieces .T hu s th is structu re can serve as a 32D PC.F ig .6 A spherical structu re m ade of dielectric sphericalshells ,w here (b )is the secti onal view of (a )H ere w e po in t ou t that ,in conven ti onalsen se ,the structu res given above are no t 32D PC s .B u t they have the sam e functi on s as tho seconven ti onal 32D PC s .So ,fo r si m p licity ,w e m aystill call the structu res p resen ted above 32D PC s .To avo id confu si on ,w e m ay call the new 32D PC s p ropo sed in th is p ap er as com b ined 32D p ho ton ic crystals (PC s ).T he calcu lati on of p ho ton ic band gap s is no t given in th is p ap er becau se the p ropo sed 411 光 子 学 报 29卷calcu lati on of p ho ton ic band gap s in 12D PC s can be found elsew here .3 Conclusion sA new idea is p resen ted and show n to be u sefu l that an enclo sed structu re m ade of several p ieces of 12D PC s ,called as a com b ined 32D PC ,can serve as a 32D PC .T he advan tage of the newidea is that it b rings techn ical si m p licity in fab ri 2cati on ,being esp ecially m ean ingfu l fo r the p ro 2ducti on of 32D PC s op erating in sho rt w ave 2length s as in the visib le ,becau se there ex ists no techn ical difficu lty in the fab ricati on of 12D PC sw o rk ing in sho rt w avelength s.References1 Fan S ,et al .H igh ex tracti on efficiency of spon taneou s em issi on from slab s of pho ton ic crystals .Phys R ev L ett ,1997,78(17):3294～32972 Kopp V I ,et al .L ow th resho ld lasing at the age of a pho ton ic stop band in cho lesteric liqu id crystals .Op t L ett ,1998,23(21):1707～17093 Sm ith D R ,et al .Band gap cavity .A pp l Phys L ett ,1994,65(5):645～6474 L ei X Y ,et al .N oval app licati on of a pertu rbed pho ton ic crystal :h igh quality filter .A pp l Phys L ett ,1997,71(20):2889～28915 B loem er M J ,Scalo ra M .T ran s m issive p roperties of A g M gF 2pho ton ic band gap s.A pp l Phys L ett ,1998,72(14):1676～16786 Barkou S E ,et al .Silica 2air pho ton ic crystal fiber design that perm itsw avegu iding by a true pho ton ic band gap effect .Op t L ett ,1999,24(1):46～487 L in H 2B ,et al .Tw o di m en si onal pho ton ic band gap op tical li m iter in the visib le .Op t L ett ,1998,23(2):94～968 Enoch S ,A khouayri H .Second 2harmon ic generati on in m u lti layered devices :theo retical too ls .J Op t Soc Am B ,1998,15(3):1030～10419 Ko saka H ,et al .Pho ton ic crystals fo r m icro ligh t w ave circu its u sing w avelength 2dependen t angu lar beam steering .A pp l Phys L ett ,1999,74(10):1370～137210 T ran P .A ll 2op tical s w itch ing w ith a non linear ch iral pho ton ic band gap structu re .J Op t Soc Am B ,1999,16(1):70～7311 Yab lonovitch E ,et al .Pho ton ic band structu re :the face 2cen tered 2cub ic case emp loying non 2spherical atom s .PhysR ev L ett ,1991,67(17):2259～226212 A nderson C M ,Giap is K .L arger tw o 2di m en si onal pho ton ic band gap s .Phys R ev L ett ,1996,77(14):2949～295213 Feiertag G ,et al .Fab ricati on of pho ton ic crystals by deep X 2ray lithography .A pp l Phys L ett ,1997,71(11):1441～144314 Sievenp i per D F ,Yab lonovitch E ,32D m etallo 2dielectric pho ton ic crystals w ith strong capacitive coup ling betw eenm etallic islands.Phys R ev L ett ,1998,80(13):2829～283215 V lasov Y A ,et al .Ex istence of a pho ton ic p seudo 2gap fo r visib le in syn thetic opals .Phys R ev (B ),1997,55(20):R 13357～1336016 Ro sner B T ,et al .In terferom etric investigati on of pho ton ic band 2structu re effects in pu re and doped co llo idal crys 2tals .J Op t Soc Am (B ),1998,15(11):2654～265917 M iguez H ,et al.B ragg diffracti on from indium pho sph ide infilled fcc silica co llo idal crystals .Phys R ev (B ),1999,59(3):1563～15665112期 Q uyang Zhengb iao ,et al .Sho rt 2w avelength th ree 2di m en si onal pho ton ic crystals短波长三维光子晶体欧阳征标 李景镇 孙一翎 林 敏(深圳大学科技研究院光电子技术工程系,深圳518060)收稿日期:1999—09—20摘 要 本文提出了一种新型三维光子晶体—组合式三维光子晶体,它是由数块一维光子晶体组合而成的封闭式结构1从理论上论证了它的可行性1指出在短波长工作区域,这种新型光子晶体的制造工艺简单易行1文中给出并讨论了三个例子1 关键词 光子晶体;短波长;三维;光子材料 Ouyang Zhengb i ao w as bo rn in Dongkou ,H unan P rovince on Feb .20,1963.H e received h is Ph .D in electron p hysics and devices from the U n i 2versity of E lectron ic Science and T echno logy of Ch ina in 1988.A t p re 2sen t ,he is an associate p rofesso r .H is research in terests in recen t years include p ho ton ic m aterials ,quan tum op tics ,laser di ode and non linear op 2tics .H e has p ub lished m o re than 20academ ic p ap ers .611 光 子 学 报 29卷。
光子晶体及运用
1.00
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Wavenumber(cm-1)
可见光透射光谱
Transmission
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Light Sneaks through Small Holes
J. A. Porto, et al., Phys. Rev. Lett. 83, 2845 (1999)
修饰发射特性：红外隐身
发 射 率
光子晶体 热辐射材料
黑体辐射
实际材料
有光子晶体
频率
Photonic Molecule
Photons confined within the photonic molecule are restricted to a set of discrete energies, like electrons in a real molecule
S. A. Jenekhe and X.L. Chen, Science 283, 372 (1999)
Sonic bandgap material
J.V. Sanchez-Perez et al., Phys. Rev. Lett. 80, 5325 (1998).
波晶体
波
波能带
周
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波禁带
电磁波、声波、水波、 地震波 …...
光子晶体简介
第六组
一、光子晶体简介 二、光子晶体中的量子理论 三、光子晶体的发展历程 四、光子晶体的应用
五、光子晶体的发展前景
信息技术革命
标志：半导体技术
趋势：微型化和高度集成化
限制：纳米尺度的量子效应
摩尔定律 ：自从1970年以来，可以被放置 到微电子芯片的电子元件数量以18月翻一 番的速度增长，这保证了计算机运算速度 在同时期随之翻番，价格减半。
T k 设E 0，H 0， E， H 分别是E和H的振幅 和初相位：
~ E 0 E 0 e i E ~ i H H 0 H 0e
2
代入波动方程，即可得： k r 0 r 0
2
定态下的电磁波波动方程为 2 2 Er k E r 0
半导体微纳米制造法
Layer by layer method
由一维等距排列的棒逐层叠加而成，层与 层间棒取向是垂直的，次相邻层的棒相对 于第一层均平移了1/2棒间距，以四层为 一个重复单元，构成面心四方结构。d为 每一层中棒的间距，w表示棒宽度，c表示 一个重复单元的尺寸。 Ozbay et al Appl. Phys. Lett., 1994, 64, 2059; Ozbay et al Appl. Phys. Lett., 1996, 69, 3797.
在二十年内，应该制造出第一个光子晶 体逻辑电路 。 再接下来，光子晶体驱动的光子计算机 可能会出现 。 由光子晶体制造的光通讯器件将会改变 光通讯的现状，光子晶体技术的发展必将对 光通信技术产生重大而深远的影响。
2 2 r rr r 2 ' c2 r E r c2 r E r
光子晶体
缺陷真的是不完美吗？——光子晶体的理论计算、制作工艺以及器件应用（综述报告）Do defects really mean imperfection?On theory, fabrication and applications of photonic crystals（Review）胡小龙034698无研01摘要光子晶体材料的介电系数在空间中呈周期分布，这种材料存在光子带隙，引入缺陷对光有局域效应，为更好地控制光和利用光提供了新的方法。
本文综述了近几年来光子晶体理论和实验方面研究进展，包括：理论计算方法、制作工艺以及器件应用。
AbstractThe dielectric coefficient of photonic crystals is periodic in space. Photonic bandgap exits and light can be localized in the defect. The emergence of this new material provides new methods and possibilities for the control and manipulation of light. A brief overview of the progress in both theoretical and experimental research in recent years is presented, including: theoretical computation methods, fabrication and applications.§1 引言在刚刚过去的50年里，半导体物理以及相关技术迅猛发展，影响并推动了整个社会现代化的进程。
人们通过控制材料导电特性、改变电子能带实现了各种各样功能卓越的电子器件。
如果能找到合适的材料来改变（tailor）光子能带，那么是不是同样对光进行控制呢？光子晶体的概念是1987年由S.John[1]和E.Yablonovitch[2]等人分别提出来的。
光子晶体
1
光子晶体简介
散射矩阵法：
散射矩阵法假定光子晶体由各向同性的介质组成，其中充满了各种开头和 尺寸的没有重叠的光学散射中心。通过对所有的散射中心的散射场应用傅 立叶－贝塞尔展开来求解亥姆霍兹方程，从而计算出在光子晶体中传输的
三 维 金 刚 石 结 构 禁 带 计 算 结 果
光子晶体由折射率为 3.6 的球形介 质构成金刚石结构 ,分布在空气中 , 介质的填充比( 所占空间体积的比) 为 0.34。
研究指出：光子晶体可以抑制自发辐射，我们知道，自发辐射的几率与光子所在 频率的态的数目成正比。当原子被放在一个光子晶体里面 ，而它自发辐射的光频率正 好落在光子禁带中时 ，由于该频率光子的态的数目为零 , 因此自发辐射几率为零，自 发辐射也就被抑制. 反过来 , 光子晶体也可以增强自发辐射，只要增加该频率光子的态 的数目便可实现。如在光子晶体中加入杂质 ,光子禁带中会出现品质因子非常高的杂质 态，具有很大的态密度，这样便可以实现自发辐射的增强。
为解决这一问题，人们发明了反蛋白石结构,又称为模板法,即利用二氧化硅、 聚苯乙烯等生长出的胶体晶体作为模板，再往其空隙中填充高折射率材料的有机或 无机材料,如染料、金属纳米粒子、硅等, 多次填充后通过高温煅烧 或刻蚀除去模板,留下反蛋白石三维周期结构。
4
光子晶体的应用
1. 光电元件中的应用—光子晶体发光二极管
构复杂或处理有缺陷的体系时，可能因为计算能力的限制而不能计算或者
难以准确计算。而且如果介电常数不是常数而是随频率变化，就没有一个 确定的本征方程形式，这种情况下
传输矩阵法：
传输矩阵法是将磁场在实空间的格点位置展开，将麦克斯韦方程组化成传
光学性质的光子晶体PhotonicCrystal
光学性质的光子晶体PhotonicCrystal美国科学家研发出了一种新方法，改变了半导体的三维结构，使其在保持电学特性的同时拥有了新的光学性质，并据此研制出了首块光学电学性能都很活跃的新型光子晶体(Photonic Crystal)，为以后研制出新式太阳能电池、激光器、超材料等打开了大门。
研究发表在最新一期《自然·材料学》杂志上。
光子晶体(Photonic Crystal)材料具有独特的物理结构，它能采用不同于传统光学材料和设备的特殊方式诱发非同寻常的现象并影响光子的行为，可广泛应用于激光器、太阳能设备、超材料等中。
之前由科学家们研制出的光子晶体(Photonic Crystal)只能得到用光学方法激活的设备，这些设备能引导光，但无法被电所激活，因此，其无法将电变成光或相反。
伊利诺斯大学材料科学和工程学教授保罗·布劳恩领导的科研团队研制出的最新光子晶体(Photonic Crystal)却兼具光学和电学性质。
该研究的参与者埃里克·尼尔森解释道，新光子晶体(Photonic Crystal)可以让光学和电学性能同时达到最优化，这就使人们能更好地控制光的散射、吸收以及增强。
为了制造出该三维光子晶体(Photonic Crystal)，科学家们先让一些细小的球簇拥在一起形成一块模板，接着，他们将一种广泛应用于半导体中的材料砷化镓(GaAs)沉积在模板上，让砷化镓通过模板填充球之间的缝隙。
砷化镓作为单个晶体开始从下往上生长，这个过程被称作外延生长技术，工业界一般使用该技术来制造平的、二维的单晶体半导体薄膜，但布劳恩团队却对这种技术进行了升级改造，用来制造错综复杂的三维结构。
这种自下而上的外延生长技术消除了制造三维光子结构普遍采用的自上而下构造方法可能导致的很多缺陷。
另一个好处是，它让制造出层层堆积而成的半导体异质结构变得更方便。
例如，可以通过先用砷化镓部分填充该模板，再用另一种材料填满，从而将一个量子势阱层引入光子晶体(Photonic Crystal)中。
光子晶体课件
下面是两能带各自的concentration factor
A Square Lattice of Dielectric Veins
X点的集中 参数
TM模式的band1把能量集中在vein的交叉点，TE模式把能量集中在vein 的交叉点之间连线上，能量都集中在高介电常数区域，所以不会出现 gap。而对于TE模式，band1电场线集中在穿过交叉点的vein上，而 band2必须穿入空气，所以出现gap。
Electromagnetism
Symmetry
1D PhC (Layer)
2D PhC (Slab)
3D PhC
macroscopic Maxwell equations
Constitutive relations
ρ = 0 and J = 0; ignorable nonlinearity
Electromagnetism
The photonic band structures for on-axis propagation
The low frequency modes concentrate their energy in the high-ε regions, and the h-igh frequency modes have a larger fraction of their energy in the low-ε regions.
Off-Axis Propagation
1.离轴方向上没有明显的禁带
与on-axis传播 相比的区别 2.原on-axis传播的旋转对称性不存在了 存在旋转对称性的时候TE模、TM模是简并的，虽然离轴时旋转 对称性不存在了，但有可能存在其他对称性，如镜面对称性等
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光子局域：
在光子晶体中引入杂质和缺陷时，与缺陷态频率符合 的光子会被局限在缺陷位置，而不能向空间传播。
光子带隙
• 光子带隙是一个频率区域，当入射光的频 率落在其中时，它被完全反射，不能穿过 光子晶体。 • 物理上，光子带隙来源于被周期性介电结 构强散射的光之间的干涉。 • 1、光子晶体的空间结构---能否相干 • 2、构成的光子晶体材料介电常数之比---散 射强度。
具有不同介电常数的介质 材料随空间呈周期性的变 化时，在其中传播的光波 的色散曲线将成带状结构 ，当这种空间有序排列的 周期可与光的波长相比位 于同一量级，而折射率的 变化反差较大时带与带之 间有可能会出现类似于半 导体禁带的“光子禁带 ”(photonic band gap) 。
光子晶体特性
光子带陷：
~ E 0 E 0 e i E ~ i H H 0 H 0e
2
代入波动方程，即可得： k r 0 r 0
2
定态下的电磁波波动方程为 2 2 Er k E r 0
如果介质为非磁性介质，则r 1.
对于非均匀介质，尤其是其介电常数 是周期性变化时，有
光纤晶体简介
报告人
主要内容
• 光子晶体理论 • 特性 • 在实际中应用
光子晶体
• 光子晶体（photonic crystal） 是一种介电常数随空间周期性变化的新 型光学微结构材料。
光子晶体--自然界中的例子
Butterfly
Opal
Sea mouse
结构显色！！！
二、光子晶体中的量子理论
电磁波可表示为：
~ ~ E E e 0 ~ ~ i ωt k z H H e 0 i ωt k z
和k分别为角频率和波数，它们与周期T
和波长的关系为：
2 T 2 k
波的传播速度（相速）为：
T k 设E 0，H 0， E， H 分别是E和H的振幅 和初相位：
图1 TIR-PCF的典型结构
图2 PBG-PCF的典型结构
实物图
光子晶体光纤（PCF）的特性 ：
• (1)无截止单模( Endlessly Single Mode)
• (2)不同寻常的色度色散 • (3)极好的非线性效应 • (4)优良的双折射效应
光子晶体激光器
• 优点： • 光纤激光器比传统的固体激光器和气体激 光器有着很多优点, 比如稳定性高、体积小、重量轻、转换效 率高、散热效果好等,
激光器示意图
主要应用了掺杂光纤的单模特性。源自 与周期场中电子运动方程比较
V (r R) V (r )
2
2m
2 V (r ) E
电子转载周期场中的结论
E
( 0) k
k2 2m
2
考虑周期场后：
对比到光波周期场种情况
光子的能量 E p kc 因此其色散关 系的特点是E p 和k呈线性关系
理论上得到结论
光子局域
应用
• 微波天线 • 高效率低反射透镜 • 微谐振腔 • 高效率发光二极管和低阈值激光震荡 • 宽带带阻滤波器和极窄带滤波器 • 非线性光子器件和光子存储器
光子晶体光纤
• 两种类型：
TIR-PCF 是通过全反射原理来导光，与普通光纤类似； PBG-PCF则是通过光子带隙效应导光，即把光限制在光 子晶体的缺陷即空气孔中导光。
r r kn
可将相对介电常数写为两个部分之和： 平均介电常数 r 和变动介电常数 2 则有： k 2 ( r r ' ) 2
带入波动方程可得：
2 2 2
' r
c
' E (r ) 2 r E (r ) 2 r E (r ) c c 2 2 ( 2 2 r ' ) E (r ) 2 r E (r ) c c