Frequency and temporal effects in linear optical quantum computing
耗散腔量子电动力学系统中量子Fisher信息和量子相干性分布
MIMO-OFDM系统中信道估计解析
题目：MIMO-OFDM系统中信道估计及信号检测算法的研究独创性（或创新性）声明本人声明所呈交的论文是本人在导师指导下进行的研究工作及取得的研究成果。
尽我所知，除了文中特别加以标注和致谢中所罗列的内容以外，论文中不包含其他人已经发表或撰写过的研究成果，也不包含为获得北京邮电大学或其他教育机构的学位或证书而使用过的材料。
与我一同工作的同志对本研究所做的任何贡献均已在论文中作了明确的说明并表示了谢意。
申请学位论文与资料若有不实之处，本人承担一切相关责任。
本人签名：关于论文使用授权的说明学位论文作者完全了解北京邮电大学有关保留和使用学位论文的规定，即：研究生在校攻读学位期间论文工作的知识产权单位属北京邮电大学。
学校有权保留并向国家有关部门或机构送交论文的复印件和磁盘，允许学位论文被查阅和借阅；学校可以公布学位论文的全部或部分内容，可以允许采用影印、缩印或其它复制手段保存、汇编学位论文。
（保密的学位论文在解密后遵守此规定）本学位论文不属于保密范围，适用本授权书。
本人签名：夺^摘要MIMO-OFDM系统中信道估计及信号检测算法的研究输入多输出（MIMO)和正交频分复用（OFDM)是LTE的两大核心技术。
多输入多输出（MIMO)技术利用各种分集技术带来的分集增益可以提高系统的信道容量、数据的传输速率以及系统的频谱利用率，这些都是在不增加系统带宽和发射功率的情况下取得的；正交频分复用（OFDM)技术是多载波调制技术的一种，其物理信道是由若干个并行的正交子信道组成，因此可有效地对抗频率选择性衰落，同时通过插入循环前缀（CP)可以有效消除由多径而引起的符号间干扰(ISI)。
由于多输入多输出（MIMO)在提高系统容量和正交频分复用（OFDM)在对抗多径衰落方面的优势，基于两者结合的MIMO-OFDM系统已经引起了广泛的关注。
信道估计算法和信号检测算法是MIMO-OFDM系统的关键技术。
其中信道估计算法对MIMO-OFDM系统接收端的相干解调和空时检测起着至关重要的作用，信道估计的准确性将影响系统的整体性能。
东南大学博士学位论文结果不同重组...
东南大学博士学位论文基因密码子使用和蛋白质结构的生物信息学分析姓名：***申请学位级别：博士专业：生物医学工程指导教师：***20040401东南大学博士学位论文摘要论文题目：基因密码子使，ｑＪ和蛋白质结构的生物信息学分析研究生姓名：顾万君导师姓名：陆祖宏（教授）学校名称：东南人学随着人类基冈组计划雨Ｉ模式生物基因组计划的完成，公共数据库中生物数据的增艮速度越来越快。
如何从海量的生物数据中解读、提取和获得有片；｜的生物信息，己成为基因组计划下一步亟待解决的问题。
本文中，我们利用生物信息学的方法对基因的周义密码子使用进行了统计分析，研究了不局物种中蛋白质结构和基因周义密码子使用间可能存在的相关性，提出了一种基于密码子的氨基酸二级结构偏向性参数。
同时，我们还在蛋白质二级结构预测的神经网络方法中引入了蛋白质编码基因的密码子使用信息．在预测大肠杆菌的蛋白质的二级结构时提高了预测的准确率。
最后，我们还提出了一种根据单倍体数据将基冈组划分成若干很少出现重组现象的块结构的新方法。
论文的主要内容如下：１．在基因组中，基因的同义密码子使用并不是随机选择的。
研究不周物种中基因的密码子使用模式以及形成这种密码子使用模式的内在因素，对于了解基因组的特征和物种的分子进化具有重要作崩。
我们对一些物种的基因密码子使用模式进行了分析，并且进一步分析了这些物种中影响密码子使用的内在因素。
●通过ＳＡＲＳ病毒基因组和进化上相近的病毒基因组的密码子使用偏性的分析，我们发现在这些病毒基冈组中尽管基因的同义密码子使用存在着偏向性，但是偏向性程度并不高。
这些病毒基因组中，影响同义密码子使用的最主要因素是进化中的碱基突变压力。
同时，基冈的功能也在一定程度上决定了这些病毒基因中密码子的选择。
但是，基因长度和基因翻译过程中的选择作用在这些病毒中并不影响基因的密码子使用。
另外，在这些病毒基囡组中，密码子使用模式在进化上是保守的。
基于密码子使用模式的进化分析表明，ＳＡＲＳ冠状病毒在进化上与其它己知的冠状病毒都不是很近。
Observation of parity–time symmetry in optics
Observation of parity–time symmetry in opticsChristian E.Rüter 1,Konstantinos G.Makris 2,Ramy El-Ganainy 2,Demetrios N.Christodoulides 2,Mordechai Segev 3and Detlef Kip 1*One of the fundamental axioms of quantum mechanics is associated with the Hermiticity of physical observables 1.In the case of the Hamiltonian operator,this requirement not only implies real eigenenergies but also guarantees probability conservation.Interestingly,a wide class of non-Hermitian Hamiltonians can still show entirely real spectra.Among these are Hamiltonians respecting parity–time (PT )symmetry 2–7.Even though the Hermiticity of quantum observables was never in doubt,such concepts have motivated discussions on several fronts in physics,including quantum field theories 8,non-Hermitian Anderson models 9and open quantum systems 10,11,to mention a few.Although the impact of PT symmetry in these fields is still debated,it has been recently realized that optics can provide a fertile ground where PT -related notions can be implemented and experimentally investigated 12–15.In this letter we report the first observation of the behaviour of a PT optical coupled system that judiciously involves a complex index potential.We observe both spontaneous PT symmetry breaking and power oscillations violating left–right symmetry.Our results may pave the way towards a new class of PT -synthetic materials with intriguing and unexpected properties that rely on non-reciprocal light propagation and tailored transverse energy flow.Before we introduce the concept of spacetime reflection in optics,we first briefly outline some of the basic aspects of this symmetry within the context of quantum mechanics.In general,aHamiltonian ˆH =ˆp 2/2m +V (ˆx )(where ˆx and ˆpare position and momentum operators respectively,m is mass and V is the potential)is considered to be PT symmetric,PT ˆH =ˆHPT ,provided that itshares common eigenfunctions with the PT operator 1,16–21.This condition corresponds to an exact or unbroken PT symmetry,as opposed to that of broken PT symmetry,where,even thoughPT ˆH =ˆHPT is still valid,ˆHand PT (or any other antilinear operator)possess different eigenvectors 22.For the case considered here,given that the action of the parity P and time T operatorsis defined as ˆp →−ˆp ,ˆx →−ˆx and ˆp →−ˆp ,ˆx →ˆx ,i →−i ,respectively,it then follows that a necessary (but not sufficient)condition for a Hamiltonian to be PT symmetric is V (ˆx )=V ∗(−ˆx ).In other words,PT symmetry requires that the real part of the potential V is an even function of position x ,whereas the imaginary part is odd;that is,the Hamiltonian must have theform ˆH =ˆp 2/2m +V R (ˆx )+i εV I (ˆx ),where V R ,I are the symmetric and antisymmetric components of V ,respectively 12–14.Clearly,if ε=0,this Hamiltonian is Hermitian.It turns out that,even if the antisymmetric imaginary component is finite,this class of potentials can still allow for both bound and radiation states,all with entirely real spectra.This is possible as long as εis below some threshold,ε<εth .If,on the other hand,this limit is crossed1ClausthalUniversity of T echnology,Institute of Energy Research &Physical T echnologies,Leibnizstr.4,38678Clausthal-Zellerfeld,Germany,2Universityof Central Florida,School of Optics-CREOL,Orlando,Florida 32816-2700,USA,3T echnion-Israel Institute of T echnology,Department of Physics,32000Haifa,Israel.*e-mail:kip@hsu-hh.de.(ε>εth ),the spectrum ceases to be real and starts to involve imaginary eigenvalues.This signifies the onset of a spontaneous PT symmetry-breaking,that is,a ‘phase transition’from the exact to broken-PT phase 7,20.In optics,several physical processes are known to obey equations that are formally equivalent to that of Schrödinger in quantum mechanics.Spatial diffraction and temporal dispersion are perhaps the most prominent examples.In this work we focus our attention on the spatial domain,for example optical beam propagation in PT -symmetric complex potentials.In fact,such PT ‘optical potentials’can be realized through a judicious inclusion of index guiding and gain/loss regions 7,12–14.Given that the complex refractive-index distribution n (x )=n R (x )+in I (x )plays the role of an optical potential,we can then design a PT -symmetric system by satisfying the conditions n R (x )=n R (−x )and n I (x )=−n I (−x ).In other words,the refractive-index profile must be an even function of position x whereas the gain/loss distribution should be odd.Under these conditions,the electric-field envelope E of the optical beam is governed by the paraxial equation of diffraction 13:i∂E ∂z +12k ∂2E ∂x 2+k 0[n R (x )+in I (x )]E =0where k 0=2π/λ,k =k 0n 0,λis the wavelength of light in vacuum and n 0represents the substrate index.Ultimately,it will be of interest to synthesize artificial periodic optical systems showing unusual features stemming from PT symmetry 13,14.Yet,it is first imperative to understand PT behaviour at a single-cell level.In integrated optics,such a single PT element can be realized in the form of a coupled system 7,12,with only one of the two parallel channels being optically pumped to provide gain γG for the guided light,whereas the neighbour arm experiences loss γL (Fig.1a).Under these conditions and by using the coupled-mode approach,the optical-field dynamics in the two coupled waveguides are described byid E 1d z −i γGeff 2E 1+κE 2=0,id E 2d z +i γL2E 2+κE 1=0(1)where E 1,2represent field amplitudes in channels 1and 2,κ=π/(2L c )is the coupling constant with coupling length L c and the effective gain coefficient is γGeff =γG −γL .From previous consider-ations,PT symmetry demands that γGeff =γL =γ.The behaviour of this non-Hermitian system can be explained by considering the structure of its eigenvectors,above and below the phase-transition point γ/(2κ)=1.Below this threshold the supermodes are given by |1,2 =(1,±exp(±i θ)),with corresponding eigenvalues being ±cos θ,where sin θ=γ/2κ.At phase transition (the ‘exceptionalConventional systemConventional coupled systemPT –symmetric coupled systemSupermodes of conventional systemPT –symmetric system above thresholdPT –symmetric system below thresholdPT –symmetric supermodes below thresholdPT –symmetric supermodes at threshold a b c Figure 1|Conventional and PT -symmetric coupled optical systems.a ,Real (n R ,red line)and imaginary (n I ,green line)parts of the complexrefractive-index distribution.b ,Supermodes of a conventional system,and of a PT -symmetric arrangement below and above threshold.c ,Optical wave propagation when the system is excited at either channel 1or channel 2.For the conventional case,wave propagation is known to be reciprocal,whereas in a PT -symmetric system lightpropagates in a non-reciprocal manner both below and abovethreshold.Intensity/phase distributionLithium niobateBeam splitterReference beamFigure 2|Experimental set-up.An Ar +laser beam (wavelength 514.5nm)is coupled into the arms of the structure fabricated on a photorefractive LiNbO 3substrate.An amplitude mask blocks the pump beam from entering channel 2,thus enabling two-wave mixing gain only in channel 1.A CCD camera is used to monitor both the intensity and phases at the output.point’),the modes coalesce to |1,2 =(1,i ),where the amplitudes in the two channels have the same magnitude 23,24.Above threshold,that is,for γ>2κ,|1,2 =(1,i exp(∓θ)),where in this range cosh θ=γ/2κand the two eigenvalues are ∓i sinh θ.We emphasize that,unlike Hermitian systems,these eigenmodes are no longer orthogonal.Instead,the basis is now skewed.This in turn has important implications for optical-beam dynamics including a non-reciprocal response and power oscillations.For a conventional Hermitian system (γ=0),any superposition of the two (symmetric and antisymmetric,see Fig.1b)eigenmodes leads to reciprocal wave propagation:obviously,the light distribution in Fig.1c (top)obeys left–right symmetry.This situation changes when the coupled system involves a gain/loss dipole.If the gain increases but is still below threshold,the relative phase differences ϑbetween the two field components increase from their initial values at 0and π,respectively,and finally,at threshold,the two modes coalesce at ϑ=π/2(see Fig.1b).More interestingly,light propagation is now obviously non-reciprocal:by exchanging the input channel from 1to 2in Fig.1c (middle)we obtain an entirely different output state.This behaviour is altered drastically above threshold (Fig.1c,bottom).In this regime light always leaves the sample from channel 1,irrespective of the input—again in a non-reciprocal fashion.This can be explained by noting that,above threshold,the system’s eigenvalues are complex,with the corresponding amplitudes either exponentially increasing or decaying.Thus only one supermode effectively survives.Here it is worth noting that any coupled system with an asymmetric gain–loss profile can be mathematically transformed into a PT -symmetric one.In particular,this is true for an asymmetric loss/loss-type potential (coupled states with low/high losses),showing a ‘passive’PT system 25.Very recently,for such a system,loss-induced optical transparency was experimen-tally demonstrated.Here we observe non-reciprocal wave propagation in an ‘active’PT -symmetric coupled waveguide system based on Fe-doped LiNbO 3.As such,this structure shows richer dynamics and enables us to explore a wider range of behaviour not previously accessible because of fixed losses.We use Ti in-diffusion to form the symmetric index profile n R (x ).Optical gain γG (the typical magnitude is a few cm −1in Fe-doped LiNbO 3)is provided through two-wave mixing using the material’s photorefractiveI 1I 2I 2I 2I 1I 1I 1,2/(I 1 + I 2)I 1,2/(I 1 + I 2)0.51.0 1.5t /Time (min)Time (min)2.02.5 1.00.80.40.201.00.80.60.20010203040204060τ0.6abFigure 3|Computed and experimentally measured response of a PT -symmetric coupled system.a ,Numerical solution of the coupled equations (1)describing the PT -symmetric system.The left (right)panel shows the situation when light is coupled into channel 1(2).Red dashed lines mark the symmetry-breaking threshold.Above threshold,light is predominantly guided in channel 1experiencing gain,and the intensity of channels 1and 2depends solely on the magnitude of the gain.b ,Experimentally measured (normalized)intensities at the output facet during the gain build-up as a function of time.nonlinearity 26,27.A mask on top of the sample is used to partiallyblock the pump light,to provide amplification in only one channel (see the experimental set-up in Fig.2).Both the output intensity and the phase relation between the two channels (using interference with a plane reference wave)are monitored by a CCD (charge-coupled device)camera.In our system,losses arise from the optical excitation of electrons from Fe 2+centres to the conduction band.On the other hand,the optical two-wave mixing gain (which is proportional to the concentration of Fe 3+centres)has a finite response time 26.Assuming an exponential temporal build-up,γG (t )=γmax [1−exp(−t /τ)]with Maxwell time constant τ,the evolution of the intensity distribution at the output facet can be monitored as a function of time t .In other words,the state of the system below,at and above threshold can be directly observed at different instants t (refs 7,13).Although equations (1)can be solved analytically,we here obtain the output intensities I 1∼|E 1|2,I 2∼|E 2|2as a function of gain γG (t )by numerical integration.Figure 3a shows results of two such simulations when γL =2κ,γmax =2.5γL ,where channel 1(Fig.3a,left-hand side)or channel 2(Fig.3a,right-hand side)has been excited.At t =0the system startsfromγG =0and shows a reciprocal response.However,as the gain builds up at t >0and the PT structure is tuned below threshold (which is reached for t /τ≈1.6),wave propagation becomes strongly non-reciprocal (with different numbers of zero-crossings,depending on the ratio L /L c ;see Fig.3a).At the threshold the two supermodes become degenerate;however,the intensities of the two fields are slightly different.The reason lies in the limited length L of our sample:at threshold,the pure coalesced eigenstate |1,2 =(1,i )of our system (excited by an input state (1,0)or (0,1),respectively)is approached adiabatically only for infinitely long propagation,L /L c →∞.Above thresholdϑϑϑ 2π2π≈ϑπ≈abcdFigure 4|PT supermode phase measurements.a –d ,Intensity distribution(upper panels)and phase relation (lower panels)of conventional (a ,b )and PT -symmetric (c ,d )systems.a ,b ,Measured relative phases of an even (a )and odd (b )eigenstate associated with a conventional system.c ,d ,Phase relation corresponding to a PT -symmetric system below (c )and above (d )threshold.Although below threshold (c )the phase difference lies in the interval [0,π],depending on the magnitude of gain,above threshold this value is fixed at π/2,as shown in d .the output of the PT system is no longer sensitive to the input conditions.In this regime,one supermode is exponentially amplified whereas the other decays.The experimental response of this LiNbO 3PT -symmetric optical system (with κ=1.9cm −1and L =2cm)is shown in Fig.3b.In all our experiments we used low input power levels (signal power ∼25nW and pump intensity I p =0.5mW cm −2when exciting channel 2,and twice these values when exciting channel 1)to avoid any index perturbations (including the situation above threshold,where intensity increases rapidly),which may in turn spoil the symmetry in n R (x )(refs 28,29).Figure 3b (left-hand side and right-hand side)depicts the temporal behaviour of the output intensity distribution when channel 1and 2is excited,respectively.We note that the build-up time constants τin these two situations are different owing to different intensities used during excitation.As a result,the threshold is reached faster (t th ,1≈10min)in the first case as compared with the latter (t th ,2≈70min).By taking this intoaccount,we find an excellent agreement between our experiments and numerical simulations.Another manifestation of PT symmetry is the relative phase dif-ferenceϑbetween the two elements of the same eigenmode—which can be measured at the output facet of the sample.These results are depicted in Fig.4.ForγG=0,the phases corresponding to the even and odd supermodes areϑ=0andϑ=π,respectively,as in conven-tional arrangements(Fig.4a,b).When the gain is further increased and the system is below threshold,the two eigenstates are not orthogonal and their phases can be anywhere(depending onγ/2κ) in the interval[0,π].An example is given in Fig.4c,where a phase difference ofϑ≈2π/3was estimated from our measurements. Finally,Fig.4d illustrates the situation slightly above the exceptional point.In this case the phase is fixed atϑ=π/2,irrespective ofγ/2κ, again in good agreement with theoretical predictions.Our results can be easily extended to transversely periodic media,enabling new intriguing effects such as PT solitons,double-refraction or synthetic systems with tailored transverse flow of optical energy,and thus pave the way for developing new non-reciprocal optical components,where light is propagating forward and backward in a different fashion.This letter has made the simplest demonstration of PT effects:just a coupled two-channel system.However,the vision is to incorporate nonlinearities and construct sophisticated PT systems,such as PT optical lattices, PT-based solitons and so st but not least,the phase-transition or exceptional point has been intriguing researchers for a long time,because the eigenmodes associated with that point are self-orthogonal,and as such their amplitudes should diverge7.In addition,in optical PT lattices,anomalous transport or discrete diffraction can occur in the neighbourhoods of such points,as indicated in ref.13.Is this self-orthogonality a physical property with truly unique and experimentally observable quantities?This and related questions are now within experimental reach. Received3August2009;accepted17December2009; published online24January2010References1.Shankar,R.Principles of Quantum Mechanics(Plenum Press,1994).2.Bender,C.M.&Böttcher,S.Real spectra in non-Hermitian Hamiltonianshaving PT symmetry.Phys.Rev.Lett.80,5243–5246(1998).3.Bender,C.M.,Böttcher,S.&Meisinger,P.N.PT-symmetric quantummechanics.J.Math.Phys.40,2201–2229(1999).4.Bender,C.M.Must a Hamiltonian be Hermitian?Am.J.Phys.71,1095–1102(2003).5.Ahmed,Z.Real and complex discrete eigenvalues in an exactly solvableone-dimensional complex PT-invariant potential.Phys.Lett.A282,343–348(2001).6.Levai,G.&Znojil,M.Systematic search for PT-symmetric potentials with realspectra.J.Phys.A33,7165–7180(2000).7.Klaiman,S.,Moiseyev,N.&Günther,U.Visualization of branch points inPT-symmetric waveguides.Phys.Rev.Lett.101,080402(2008).8.Bender,C.M.,Brody,D.C.&Jones,H.F.Extension of PT-symmetricquantum mechanics to quantum field theory with cubic interaction.Phys.Rev.D70,025001(2004).9.Goldsheid,Y.&Khoruzhenko,B.A.Distribution of eigenvalues innon-Hermitian Anderson models.Phys.Rev.Lett.80,2897–2900(1998). 10.Rotter,I.A non-Hermitian Hamilton operator and the physics of openquantum systems.J.Phys.A42,1–51(2009).11.Dembowski,C.et al.Observation of a chiral state in a microwave cavity.Phys.Rev.Lett.90,034101(2003).12.El-Ganainy,R.,Makris,K.G.,Christodoulides,D.N.&Musslimani,Z.H.Theory of coupled optical PT-symmetric structures.Opt.Lett.32,2632–2634(2007).13.Makris,K.G.,El-Ganainy,R.&Christodoulides,D.N.Beam dynamics inPT-symmetric optical lattices.Phys.Rev.Lett.100,103904(2008).14.Musslimani,Z.H.,El-Ganainy,R.,Makris,K.G.&Christodoulides,D.N.Optical solitons in PT periodic potentials.Phys.Rev.Lett.100,030402(2008).15.Mostafazadeh,A.Spectral singularities of complex scattering potentials andinfinite reflection and transmission coefficients at real energies.Phys.Rev.Lett.102,220402(2009).16.Bender,C.M.Making sense of non-Hermitian Hamiltonians.Rep.Prog.Phys.70,947–1018(2007).17.Znojil,M.PT-symmetric square well.Phys.Lett.A285,7–10(2001).18.Bender,C.M.,Brody,D.C.,Jones,H.F.&Meister,B.K.Faster than Hermitianquantum mechanics.Phys.Rev.Lett.98,040403(2007).19.Ahmed,Z.Schrödinger transmission through one-dimensional complexpotentials.Phys.Rev.A64,042716(2001).20.Mostafazadeh,A.Pseudo-Hermiticity versus PT-symmetry III:Equivalence ofpseudo-Hermiticity and the presence of antilinear symmetries.J.Math.Phys.43,3944–3951(2002).21.Günther,U.&Samsonov,B.F.Naimark-dilated PT-symmetricbrachistochrone.Phys.Rev.Lett.101,230404(2008).22.Bendix,O.,Fleischmann,R.,Kottos,T.&Shapiro,B.Exponentially fragilePT symmetry in lattices with localized eigenmodes.Phys.Rev.Lett.103,030402(2009).23.Berry,M.Mode degeneracies and the Petermann excess-noise factor forunstable lasers.J.Mod.Opt.50,63–81(2003).24.Moiseyev,M.&Friedland,S.Association of resonance states with theincomplete spectrum of finite complex-scaled Hamiltonian matrices.Phys.Rev.A22,618–624(1980).25.Guo,A.et al.Observation of PT-symmetry breaking in complex opticalpotentials.Phys.Rev.Lett.103,093902(2009).26.Kip,D.&Krätzig,E.Anisotropic four-wave mixing in planar LiNbO3opticalwaveguides.Opt.Lett.17,1563–1565(1992).27.Kip,D.Photorefractive waveguides in oxide crystals:Fabrication,properties,and applications.Appl.Phys.B67,131–150(1998).28.Thylen,L.,Wright,E.M.,Stegeman,G.I.,Seaton,C.T.&Moloney,J.V.Beam-propagation method analysis of a nonlinear directional coupler.Opt.Lett.11,739–741(1986).29.Tan,Y.et al.Formation of reconfigurable optical channel waveguides andbeam splitters on top of proton-implanted lithium niobate crystals usingspatial dark soliton-like structures.J.Phys.D41,102001(2008). AcknowledgementsThis research was supported by the German–Israeli Foundation for Scientific Research and Development.Author contributionsC.R.andD.K.performed the experiments at Clausthal.All authors contributed to the theoretical modelling and manuscript preparation.Additional informationThe authors declare no competing financial interests.Reprints and permissions information is available online at /reprintsandpermissions. Correspondence and requests for materials should be addressed to D.K.。
生物质能的研究最新
Highly Efficient and Thermally Stable Electro-Optical Dendrimers for Photonics** By Hong Ma,Sen Liu,Jingdong Luo,S.Suresh,Lu Liu,Seok Ho Kang,Marnie Haller,Takafumi Sassa,LarryR.Dalton,and Alex K.-Y.Jen*1.IntroductionThe information technology industry has expanded drasti-cally over the past few years.We are about to see the consoli-dation of computers,wireless communication,cellular phones, flat panel displays,and consumer and industrial electronics into a powerful world-wide information mesh.This merger offers new opportunities to shape the future in even more profound ways than in the technology revolution brought by transistor electronics.Over the last two decades,advances in electronics have revolutionized the speed with which we perform comput-ing and communication of all kinds.Three key technologies combined to create a platform that enabled the electronic revo-lution:semiconductor materials,the automated microfabrica-tion of integrated electronic circuits,and integrated electronic circuit design.As a result,the mass manufacturing of low-cost integrated circuits has become possible.Now,however,we are outgrowing the performance of electronics in many applica-tions.Signal propagation and switching speeds in the electronic domain are inherently limited.One area where these limita-tions are seen clearly is in telecommunications,where band-width expansion is desperately needed.To overcome these bar-riers,we must enter a new computing and communications revolutionÐthis time based on photonics.Photonics plays some crucial and complementary roles to electronics in many application domains.Examples of the successful use of photo-nics can be found in broadband communications,high-capacity information storage,and large screen and portable information display.As the demands for information bandwidth increase, information photonics is becoming more and more important in every aspect of today's technology-driven society.The suc-cess of a new technology,however,largely depends on the progress achieved in finding and fabricating new high-perfor-mance and cost-effective materials.Recently,as the knowledge base of polymeric materials has widened,new functions for polymers have been actively investigated.New and improved polymeric/macromolecular materials were found to show promise in generating,processing,transmitting,detecting,and storing light signals.[1]Nonlinear optical(NLO)materials,especially organic and polymeric ones,have attracted significant attention from researchers since the mid1980s.[2]A high NLO susceptibility, fast response time,low dielectric constant,small dispersion inAfter a brief review on electro-optical(EO)polymers,the recent development of EOdendrimers is summarized.Both single-and multiple-dendron-modified nonlinear opti-cal(NLO)chromophores in the guest±host polymer systems showed a very significantenhancement of poling efficiency(up to a three-fold increase)due to the minimizationof intermolecular electrostatic interactions among large dipole moment chromophoresthrough the dendritic effect.Moreover,multiple NLO chromophore building blockscan also be placed into a dendrimer to construct a precise molecular architecture with a predetermined chemical composition.The site-isolation effect,through the encapsulation of NLO moieties with dendrons,can greatly enhance the performance of EO materials.A very large EO coefficient(r33=60pm/V at1.55l m)and high tempor-al stability(85 C for more than1000h)were achieved in a NLO dendrimer(see Figure)through the double-end functionalization of a three-dimensional phenyl-tetracyanobutadienyl(Ph-TCBD)-containing NLO chromophore with thermally crosslinkable trifluorovinylether-containing dendrons.±[*]Prof.A.K.-Y.Jen,Dr.H.Ma,S.Liu,Dr.J.Luo,Dr.S.Suresh,Dr.L.Liu,Dr.S.H.Kang,M.Haller,Dr.T.SassaDepartment of Materials Science and EngineeringBox352120,University of WashingtonSeattle,WA98195-2120(USA)E-mail:ajen@Prof.L.R.DaltonDepartment of ChemistryBox351700,University of WashingtonSeattle,WA98195-1700(USA)[**]Financial support from the Air Force Office of Scientific Research(AFOSR)under the MURI Center(Polymeric Smart Skins)and the DUR-IP program are acknowledged.Prof.A.K.-Y.Jen thanks the Boeing-John-son Foundation for its support.the index of refraction from DC to optical frequencies,vir-tually endless possibilities for structural modification,and ease of processability are some of the properties of conjugated organic systems that make them uniquely suited to application in photonic devices such as frequency converters,high-speed electro-optical(EO)modulators,and switches.[3]In particular, a low half-wave voltage V p of0.8V has been achieved recently in a polymer waveguide modulator using highly nonlinear organic chromophores and push±pull poling and driving tech-niques.[4]This discovery,together with a recent demonstration of exceptional bandwidths(as high as150GHz)and an ease of integration with very large scale integration(VLSI)semicon-ductor circuitry and ultra-low-loss passive optical circuitry have provided a solid foundation for using polymeric materials in the next generation of telecommunications and information processing.[4]It is well-known that second-order NLO properties originate from the non-centrosymmetric alignment of NLO chromo-phores,either doped as a guest or covalently bound as side chains in poled polymers.To obtain device-quality materials, three stringent issues must be addressed:i)the design and syn-thesis of high lb(l:the chromophore dipole moment,b:the molecular first hyperpolarizability)chromophores and the realization of a large macroscopic EO activity in the chromo-phore-incorporated polymer;ii)the maintenance of long-term temporal stability in the EO response of the poled materials in addition to their high intrinsic stability toward the environ-ment,that is,heat,light,oxygen,moisture,and chemicals;iii) the minimization of optical loss from the design and processing of materials,to the fabrication and integration of devices. 2.Conventional Polymer Approaches to Developing High-Performance EO MaterialsIn the context of addressing the first issue,a quantum mechanical analysis based on a simple two-level model[5]and a bond-order alternation(BOA)principle exploiting aromati-city[6]have worked surprisingly well in providing useful struc-ture±property relationships for the design of chromophores, with ever improving molecular hyperpolarizability.Table1 provides some representative examples of the evolution of molecular optical nonlinearity over the past decade.It has been shown that very large nonlinearities can be achieved by combining heterocyclic conjugating units,such as thiophene, with tricyanovinyl or[3-(dicyanomethylidene)-2,3-dihydroben-zothiophen-2-ylidene-1,1-dioxide]electron acceptors,[7,8]or by employing extended polyene p-bridge systems with strong mul-ticyano-containing heterocyclic electron acceptors.[9]For many years,it had been suggested that EO polymers could show elec-tro-optic coefficients(r33)much larger than that of a techno-logically important crystal,lithium niobate(LiNbO3).In the past few years,using several highly nonlinear molecules(Ta-ble1)in different polymers,such as poly(methyl methacrylate) (PMMA)and polycarbonate(PC),it has been shown that very large EO coefficients(r33of greater than60pm/V measured at 1.3l m)were achievable.The r33values obtained are nearly twice the value for lithium niobate,31pm/V.In addressing the second issue,two approaches have been adopted to improve the long-term stability of the molecular orientation in poled polymers.First,very high-T g polymers were used as host matrices to incorporate NLO chromophores. The molecular orientation in the poled polymers is thermody-namically unstable and quickly decays in low-T g polymers such as PMMA,resulting in a greatly reduced nonlinearity.How-ever,if the T g of the polymer is roughly150to200 C above the ultimate operating temperature,then decay of the orienta-tion would be negligible over the device lifetime.Many kinds of NLO chromophores have been incorporated as guests in high-T g polymers,such as polyimide[10]and polyquinoline[11] thin films.After poling,the polymers showed a much improved long-term stability at elevated temperatures.Moreover,the motion of the chromophores in a polymer matrix is further restricted when the chromophores are covalently attached to polyimides[12]or polyquinolines,[13]either in the form of a main chain or as a side-chain.This approach can lead to polymers with exceptional thermal stability(>250 C)on poling-induced polar order.An alternative approach is to develop a lower T g material containing reactive functional groups,either on the chromophore or on the polymer backbone,that can be pro-cessed into optical-quality thin films,and then poled and cross-linked sequentially at higher temperatures to lock the chromo-phores and polymer in place and achieve better control over the alignment stability(Scheme1).Crosslinkable epoxyres-Alex Jen received his Ph.D.in Organic Chemistry from the University of Pennsylvania in1984 under the tutelage of Professor Michael Cava.He started his career as a Research Chemist at Allied-Signal Inc.(1984±1988),where he was responsible for the discovery of several classes of processible and thermally stable conducting polymers for optical and electronic applications.In 1988,he joined Enichem America Inc as a Principal Scientist and established the NLO materials program in the company.He moved to ROI Technology,a device and materials oriented company, in1995,where he was Vice President of materials.In1997,he joined Northeastern University as an Associate Professor at the Department of Chemistry,moving to the University of Washington at Seattle in1999.He is currently the Boeing-Johnson Chair Professor in the Department of Materials Science and Engineering and an Adjunct Professor in the Department of Chemistry.His research interests are focused on the design,synthesis and characterization of novel conjugated molecules and polymers,NLO dendrimers,highly fluorinated polymers,self-assembled monolayers and block copolymers,and nanoscale-tailoring of organic/inorganic hybrid materials.H.Ma et al./Electro-Optical Dendrimers for Photonicsins,[14]polyurethanes,[15]polyimides,[16]and poly(perfluorocy-clobutyl (PFCB)aryl ether)s [17]have all been used to enhance the orientational stability of the poled polymers.The third critical issue influencing the utilization of poly-meric electro-optic materials is that of optical loss at the com-munication wavelengths of 1.3and 1.55l m.Both absorption and scattering contribute to optical loss.The scattering loss can be reduced by controlling the homogeneities in the EO poly-mer films before and after poling,and the uniformity of the guiding and cladding films in the NLO polymeric waveguide.[18]Minimizing the optical loss associated with C±H vibrational absorptions has been the focus of scientists endeavoring to develop low-loss,passive polymer optical waveguides.[19]The optical loss for single-mode waveguides fabricated from PMMA-type polymers has been reduced to values as low as 0.1dB/cm by partial deuteration and fluorination.Active poly-Table 1.lb values for some representative NLOchromophores.ARTICLEH.Ma et al./Electro-Optical Dendrimers for Photonicsmers are unlikely to yield optical losses as low as those of pas-sive polymers,due to the requirement of chromophore incor-poration and lattice hardening to lock-in the poling-induced chromophore acentric order.Partial fluorination of NLO chro-mophores [20]and the incorporation of chromophores into fluorinated polymers such as PFCB polymers [21]have provided the potential to minimize the absorption loss of the resulting materials.Because the thermosetting reaction does not involve the formation of any O±H,N±H,or aliphatic C±H bonds,cross-linkable PFCB polymers offer the opportunity to reduce opti-cal loss due to lattice hardening.3.Dendrimer Approach to Developing High-Performance EO MaterialsEventually,all three critical materials issues,the large EO coefficients,high stability,and low optical loss,need to be simultaneously optimized for the fabrication of practical EO devices.One of the major problems encountered in optimizing polymeric EO materials is to efficiently translate the large b values of the organic chromophores into large macroscopic electro-optic activities (r 33).According to an ideal-gas model,macroscopic optical nonlinearity should scale as lb /M w (M w :the chromophore's molecular weight).[22]Therefore,EO coeffi-cients of many hundreds of picometers per volt should be expected if the molecular optical nonlinearities shown in Table 1could be effectively translated into macroscopic EO activity.However,the electric field poling of a polymer con-taining highly nonlinear chromophores is often hindered by the large dipole moment of the molecules.The experimental and theoretical data shown in Figure 1for the NLO chromophore 1illustrate the problem caused by intermolecular electrostatic interactions.At a low loading level,where the average separa-tion of chromophores is large and thus intermolecular interac-tions are weak,the EO activity increases linearly with chromo-phore number density.However,as the intermolecular electrostatic interactions start to become competitive with chromophore dipole-applied poling field interactions,the graph becomes nonlinear.Indeed,a maximum is observed and the EO activity actually decreases at higher chromophore con-centrations.As can be seen from Figure 1,the behavior is rea-sonably well reproduced by Monte Carlo and equilibrium sta-tistical mechanical calculations that explicitly take into account the many-body spatially anisotropic intermolecular interac-tions of the chromophores.[23]Theoretical analysis suggests that the maximum realizable EO activity can be enhanced by modi-fying chromophores with bulky substituent groups as spacers to prevent stacking.These groups should not influence the molecular hyperpolarizability,but they should minimize the effect of unwanted electrostatic interactions by inhibiting the side-by-side approach of chromophores along the minor axes of the prolate ellipsoidal unmodified chromophores.Theoreti-cal analysis also suggests that the ideal chromophore shape for achieving the best poling efficiency is that of a sphere.Dendrimers are a relatively new class of macromolecules and are different from the conventional linear,crosslinked,or branched polymers.Their tree-like,monodisperse structures lead to a number of interesting characteristics and features:globular,void-containing shapes,and unusual physical proper-ties.[24]Therefore,dendrimer synthesis is well-suited to obtain-ing spherical chromophore shapes,and realizing large EOcoef-Scheme 1.NLO polymers versus NLOdendrimers.Fig.1.Variation of the material electro-optic activity (r 33)with chromophore number density (N )of several guest±host materials consisting of different NLO chromophores in poly(methylmethacrylate)(PMMA).Circles:the variant (chro-mophore 1)with butyl groups attached to the thiophene of the bridge.Diamonds:the variant (chromophore 2)in which the butyl groups have been replaced by H groups.Note that the maximum achievable electro-optic activity for the simple unprotected bridge structure is smaller,and is shifted to lower loading,than that for the bridge with the butyl derivatization.This clearly indicates the shape dependence discussed in the text.Also shown are three equilibrium statistical mechanical theoretical results.The straight line represented by long dashes cor-responds to the non-interacting chromophore model.The line consisting of short dashes corresponds to full treatment of intermolecular electrostatic interactions within the frameworkof treating chromophores as spheres.The short dash line on the circles corresponds to full consideration of intermolecular interactions within the frameworkof treating chromophores as hard (non-interpenetrating)ellipsoids.Experimental data are shown for a measurement wavelength of 1.06l m,and measurements were carried out using a modified attenuated total reflection (ATR)technique.Reproduced with permission from [23a].Copyright 2000,American ChemicalSociety.H.Ma et al./Electro-Optical Dendrimers for Photonicsficients (Scheme 1).Dendritic structures can also be used to control solubility and processability,to improve chemical and photochemical stability,and to facilitate lattice-hardening schemes carried out after the electric-field poling process.In addition,by exploiting selective halogenation and isotopic sub-stitution,the large void-containing dendrimers can help mini-mize optical loss (due to light scattering or vibrational absorp-tion).In the following sections,we will highlight the recent developments of single dendron-modified NLO chromophores,multiple dendron-modified NLO chromophores,and multiple chromophore-containing,crosslinkable NLO dendrimers.3.1.Single Dendron-Modified NLO ChromophoresThree kinds of NLO chromophores 3,4,and 5were obtained by modifying one of the highly nonlinear tricyanofuran accep-tor (FTC)-based chromophores with substituents of different shapes and sizes.When compared to the t -butyldimethylsilyl side group substituted chromophore 3,the dendritic substituent on chromophore 5has a much more flexible and wide-spread-ing shape because of the branching alkyl chains connected to the phenyl group.The adamantyl group on chromophore 4has a more rigid and bulky structure.Due to the existence of an insulating methylene spacer between the active D±p ±A (do-nor±p ±acceptor)moiety and the side group,all these modified chromophores gave essentially the same absorption peak (k max ~641nm)in dioxane solution,indicating that these sub-stituents did not affect the molecular hyperpolarizability.How-ever,it is expected that these side groups will affect the poling efficiency and the macroscopic susceptibility of polymeric materials that are incorporated in these chromophores.Two aspects of the substituent effects may contributed to this:one is that substituents of different shapes and sizes will lead to sub-stantially different intermolecular electrostatic interactions among chromophores;the other is that the different rigidities and sizes of substituents will also create a variability of free volume,which in turn will affect the mobility of the chromo-phore under high electric field poling conditions.In order to study the substituent effect on the poling efficien-cy,all three chromophores were incorporated into an amor-phous polycarbonate (APC,T g =205 C)matrix with a prede-termined loading density.The resulting polymeric materials were processed,poled,and measured under the same condi-tions.Figure 2shows the dependence of the r 33value on thechromophore number density measured for each system.For chromophore 3,it exhibited a maximum value of r 33and the value decreased with increasing chromophore loading level.In addition,it stayed at a lower r 33level than the other two sys-tems,suggesting a significantly higher chromophore±chromo-phore electrostatic interaction,as expected.In comparison,chromophores 4and 5exhibited enhanced values at a much higher level (~40%of enhancement),due to the minimization of electrostatic interactions among chromophores.However,chromophore systems 4and 5contributed differently to the en-hancement of the r 33(Fig.2)and the poling efficiencies (Fig.3),with respect to similar chromophore number pared to the t -butyldimethylsilyl group on chromophore 3,the dendritic substituent on chromophore 5offers a notable enhancement for the r 33and poling efficiencies obtainable at lower chromophore number densities,whereas the adamantyl substituent on chromophore 4provides a moresignificantparison of the EO coefficients of NLO polymers incorporated with chromophores containing different loading densities and substituent modifica-tions.parison of relative poling efficiencies of EO polymers that were incorporated with chromophores containing different loading densities and sub-stituents.ARTICLEH.Ma et al./Electro-Optical Dendrimers for Photonicsimprovement for the r33and poling efficiency only at higher chromophore number densities.This is probably due to the fact that,compared to the rigid adamantyl group on chromophore 4,the flexible and bulky dendritic moiety on chromophore5 provides more free volume for the chromophore orientation mobility under high electric field poling.3.2.Multiple Dendron-Modified NLO ChromophoresIn our continuous quest for chromophores that possess both a large molecular nonlinearity and good stability,we have developed a series of highly efficient,thermally and chemically stable chromophores,such as6,based on the2-phenyl-tetra-cyanobutadienyl(Ph-TCBD)group as the electron acceptor.[25] An X-ray single-crystal structure of such a chromophore reveals that the dicyanovinylenyl moiety is linked co-planarly to the donor-substituted aryl segment and forms an efficient push±pull system.Theªsubstituentº,a-Ph-dicyanovinyl,is twisted out of the main conjugation plane.The three-dimen-sional shape of the chromophore may help to prevent mole-cules from stacking up on each other and,thus,reduce chromo-phore aggregation.This,in turn,improves the poling efficiency and lowers the optical loss caused by light scattering.In order to maximize the dendritic effect on the poling effi-ciency,chromophore6,with the above mentioned structure, was recently further modified with multiple fluorinated den-drons.The resulting dendritic chromophore,7,exhibits appre-ciably different properties,such as a blue-shifted(by29nm) absorption,a higher(by20 C)thermal stability,and a much higher(three-fold)EO activity(Fig.4),compared to the pris-tine chromophore6(Table2).Since both chromophores con-tain the same D±p±A active moiety,the blue-shift of the absorption k max is probably due to the hydrophobic,and lower dielectric environment created by the perfluorodendrons.En-capsulating the NLO chromophore in several fluorinated den-drons also improves its thermal decomposition temperature.In order to study the dendritic effects on macroscopic EO activity, both chromophores were incorporated into the APC polymer with a predetermined loading density(12wt.-%)and the re-sulting guest±host materials were processed,poled,andparison of the EO coefficient of NLO polymers that were incorpo-rated with non-dendritic chromophore6and dendritic chromophore7at differ-ent poling temperatures(12wt.-%of chromophore in APC,1.0MV/cm of poling field).parison of the properties of the non-dendritic NLO chromophore6 and dendritic NLO chromophore7.k max[nm][a]T d[ C][b]r33[pm/V][c] NLO chromophore660324510 Dendritic chromophore757426530 [a]Measured in1,4-dioxane.[b]Determined by DSC at a heating rate of10 C/ min under nitrogen.[c]At1.3l m.Poled at150 C under a field of1.0MV/cm with12wt.-%of NLO chromophore in APC.H.Ma et al./Electro-Optical Dendrimers for Photonicssured under the same conditions.Amazingly,a three-fold larg-er EO coefficient in the chromophore 7doped system was observed.This indicates that the lower dielectric environment and the site-isolation effect provided by the dendrons may sig-nificantly facilitate the poling process.Currently,several more efficient NLO chromophores,such as chromophore 8,are being modified with the similar fluori-nated dendrons in order to provide further improved macro-scopic EO properties.3.3.Multiple Chromophore-Containing,Crosslinkable NLO DendrimersIn order to create an ideal,stand-alone,and spherically shaped NLO material that does not need to involve the com-plexity of incorporating an NLO dye in a separate polymeric matrix,multiple NLO chromophore building blocks can be further placed into a dendrimer to construct a precise molecu-lar architecture with predetermined chemical composition.A crosslinkable NLO dendrimer,9,has been developed for thispurpose and it exhibits a very large optical nonlinearity and excellent thermal stability.[26]This NLO dendrimer was con-structed using a double-end functionalized,three-dimensional Ph-TCBD thiophene-stilbene-based NLO chromophore (6)as the central core and crosslinkable trifluorovinylether-contain-ing dendrons as the exterior moieties.Spatial isolation from the dendrimer shell decreases chromophore±chromophore electrostatic interactions,and thus enhances the macroscopic optical nonlinearity.In addition,the NLO dendrimer can be directly spin-coated without the usual prepolymerization pro-cess needed to build up viscosity,since it already possesses a fairly high molecular weight (4664Da).The chromophore loading density of the dendrimer is 33wt.-%,which was confirmed by elemental analysis.There are also several otheradvantages derived from this approach,such as excellent align-ment stability and mechanical properties,which are obtained through the sequential hardening/crosslinking reactions during the high-temperature electric-field poling process.A very large EO coefficient (r 33=60pm/V at 1.55l m),and long-term align-ment stability (retaining >90%of its original r 33value at 85 C for more than 1000h)were achieved for the poled dendrimer.In comparison,EO studies were performed on the guest±host system in which the non-dendron-modified (similar structure)chromophore 6(optimized loading level:30wt.-%)was formu-lated into a high-temperature polyquinoline (PQ-100).The T g of the resulting system is plasticized to approximately 165 C.After the same sequential heating and poling as that applied to the dendrimer,the guest±host system showed a much smaller EO coefficient (less than 30pm/V)and a worse temporal sta-bility (only retaining <65%of its original r 33value at 85 C after 1000h)(Fig.5).In addition,the attempt to corona polethe non-trifluorovinyl ether functionalized dendrimer showed only a very fast decay of the EO signal (<10pm/V)after the same sample was poled and measured at room temperature.This is due to the intrinsically low T g (<50 C)and very large free volume of the dendrimer.On the basis of these results,the large r 33of the poled dendrimer is largely due to the dendritic effect,which allows the NLO dendrimer to be efficiently aligned.On the other hand,the high temporal stability of the poled dendrimer mainly results from the efficient sequential crosslinking/poling process.In order to conduct a more comprehensive study on EO den-drimers,a series of crosslinkable NLO dendrimers with differ-ent cores,branches (with more active chromophore compo-nents),and shapes and sizes has been developed.For example,dendrimer 10was designed and synthesized in order to further minimize the chromophore±chromophore electrostatic interac-tions by the addition of more dendrons.The shapes and sizesof0020040060080010001.210.80.60.40.2N o r m a l i z e d r 33Time (h)Fig.5.Temporal stability of the poled/crosslinked NLO dendrimer 9and guest±host polymer system (NLO chromophore 6/PQ-100)at 85 C in a nitrogen atmo-sphere.Normalized r 33as a function of baking time.Reproduced with permission from [26a].Copyright 2001,American Chemical Society.H.Ma et al./Electro-Optical Dendrimers for Photonicsthe dendrimers were also designed not only to optimize the dendrons'folding under a high electric field,but also to im-prove processability due to their higher molecular weight and better compatibility among the core,branches,and periphery of the resulting dendrimers.The preliminary data showed that increasing the number of dendrons on the NLO dendrimers will red-shift the absorption k max ,both in its solution and solid forms,due to the more polar environment induced by the car-boxylate linkage around the chromophores (Table 3).How-ever,encapsulating the NLO chromophores with more den-drons seems to protect the active sites of the NLO chromophore from reacting with each other under heating,and thus provides better thermal stability (Fig.6).A much longer and more efficient tricyanofuran-based NLO chromophore has also been introduced into the NLO chromophore-containing dendrimer systems,for example,the structures 11,12,and 13,in which the crosslinkable trifluorovinylether groups were functionalized at either the acceptor side or at the donor end positions.This will provide great potential,not only to enhance the macroscopic EO activity further,but also to achieve a com-bination of desirable properties.4.Outlook and StrategiesCompared to common NLO polymers,dendritic NLO mate-rials provide great opportunities for the simultaneous optimiza-tion of the macroscopic electro-optic activity,thermal stability,and optical loss.For the dendron-modified NLO chromo-phore±polymer systems,the interaction between the chromo-phore and the high T g aromatic polymer should be systemati-cally investigated,in addition to the chromophore±chromophore electrostatic interactions.For thecrosslinkableTable 3.Linear optical properties of NLO chromophore 6,and dendrimers 9and 10.k max [nm]in solution (1,4-dioxane)in film NLO chromophore 6603646NLO dendrimer 9608655NLO dendrimer 10625662parison of the thermal stability of NLO dendrimers 9and 10that were heated isothermally at 150,175,200,and 225 C at a 20min interval in a nitrogen atmosphere.Normalized absorbance as a function of baking tempera-ture.H.Ma et al./Electro-Optical Dendrimers for Photonics。
REdopedglassesforopticalcommunications
Progress of optical communication
1920s : Unclad glass fiber 1958 : Laser 1960s : 1000 dB/km optical fiber 1970 : 20 dB/km fiber @ 1 mm 1970 : CW semiconductor laser (GaAs) @ room temperature 1972 : Stimulated Raman and Brillouin scattering 1973 : Soliton in optical fiber 1974 : 0.8 mm multimode fiber telecom system (50~100 Mb/s, 10 km) 1977 : 1.3 mm laser diode (InGaAsP) 1979 : 0.2 dB/km fiber @ 1.5 mm 1980 : 1.3 mm multimode fiber telecom system (100 Mb/s, 20 km) 1987 : 1.3 mm singlemode fiber telecom system (1.7 Gb/s, 50 km)
Transmission windows of silica fibers : ~ 50 THz Challenge to achieve the maximum optical transmission Capacity up to the physical limit of light and silica fibers !
MUX
Transmitter (TR)
RE TR
Electronic Amplifier
cf) coaxial system (100 Mb/s, 10km) 1990 : 1.5 mm singlemode fiber telecom system (2.4 Gb/s) 1992 : Commercialization of erbium-doped fiber amplifier 1996 : 1.3 Tb/s and 2.6 Tb/s transmissions in laboratory 1999 : 3 Tb/s transmission in laboratory 2000 : 10.9 Tb/s transmission in laboratory
量子与电子的区分
What is Hot in Quantum Optics?
From M. Vasilyev
• Generating Optical Schrodinger Kittens for Quantum Information Processing
[Ourjoumtsev et al, Science 312, 83 (2006)]
– High transparency – High slope efficiency – >100 W output
Y. Qi, et al OE 13, (2005).
• New materials – OPGaAs, BiB3O6, 2D and higher-order QPM schemes.
[Gaebel et al, Nature Physics 2, 408 (2006)]
• Mode Locking of Electron Spin Coherences in Singly Charged Quantum Dots
[Greilich et al, Science 313, 341 (2006)]
• Generation of a Superposition of Odd Photon Number States for Quantum Information Networks
[Neergaard-Nielsen et al, PRL 97, 083604 (2006)]
• Room-temperature coherent coupling of single spins in diamond
Gain=1.8 Quadrature distribution
Gain=2.3
SNLO软件说明书
How to use SNLO nonlinear optics software to select nonlinearcrystals and model their performanceArlee V. SmithSandia National Laboratories, MS 1423, Albuquerque, NM 87185ABSTRACTSNLO is public domain software developed at Sandia Nat. Labs. It is intended to assist in the selection of the best nonlinear crystal for a particular application, and to predict its performance. This paper briefly describes its functions and how to use them. Keywords: optical parametric mixing, optical parametric oscillator, nonlinearcrystals, nonlinear optics software1. INTRODUCTIONTodays powerful desktop computers make possible detailed numerical simulations of parametric mixing in nonlinear of crystals, as well as automated calculations of linear and nonlinear properties of crystals. The purpose of SNLO is to make these calculations available to the public in a free, user-friendly, windows-based package, with the hope that this will advance the state ofthe art in applications such as optical parametric oscillators/amplifiers (OPO/OPA), optical parametric generation (OPG), frequency doublers, etc. There are three types of functions in the SNLO menu, shown at the right. The first set compute crystal properties such as phase-matching angles, effective nonlinear coefficients, group velocity, and birefringence. They include functions Ref. Ind., Qmix, Bmix, QPM, Opoangles, and GVM. The second set comprisesfunctions PW-mix-LP, PW-mix-SP, PW-mix-BB, 2D-mix-LP, 2D-mix-SP, PW-OPO-LP, PW-OPO-SP, PW-OPO-BB, and 2D-OPO-LP, which model the performance of nonlinear crystals in various applications. The first names PW and 2D refer to plane-wave and two-dimensional (diffractive) models. The middle name mix indicates single pass mixing while OPO indicates mixing in a cavity, not only as an OPO but for any cavity mixing such as resonant cavity second harmonic generation. The last names LP, SP, and BB refer to long pulse, short pulse, and broad band mixing. The third set of functions, Cavity, Focus, and Help, are helper functions for designing stable cavities, computing gaussian focus parameters, and displaying help text for each of the functions. The capabilities of select functions are presented below.2. CRYSTAL PROPERTYCALCULATIONS2.1 Selecting angle-tuned crystalsThe function QMIX is the best starting place for selecting a nonlinearcrystal for your application. When you select a crystal from the list of40+ crystals, the viewing area will display its properties, including aplot of the transmission (if the information is available), references forthe Sellmeier equation, the nonlinear coefficients, the damagethresholds, etc. You enter the wavelengths for your mixing processand click on the ‘Run’ button to compute information specific to allpossible phase-matched processes for the selected crystal at thespecified wavelengths. The figure to the left shows one example.Note that for biaxial crystals only propagation in one of the principalplanes is allowed in QMIX. If you are curious about a biaxialcrystal’s properties outside the principal planes, you can explore themInvited PaperNonlinear Frequency Generation and Conversion: Materials, Devices, and Applications II,Kenneth L. Schepler, Dennis D. Lowenthal, Jeffrey W. Pierce, Editors, Proceedingsof SPIE Vol. 4972 (2003) © 2003 SPIE · 0277-786X/03/$15.00 50using BMIX. Further information on crystal properties is available in the papers listed in the bibliography ‘Crystals.pdf’ included with SNLO(look for it in the SNLO directory). It references about 1000 papers relating to nonlinear optical crystals and their applications.2.2 Selecting quasiphase-matched crystalsThe function QPM helps you find the right quasi-phasematched poling period for any of the popular quasiphase matchable crystals. It also computes temperature and pump wavelength tuning properties for the crystal. You can chose the polarizations for your processes as well, although the zzz polarization is usually the one of practical interest.2.3 Selecting angle-tuned OPO crystalsAs shown below, the function Opoangles displays a plot of the signal/idler wavelength versus crystal angle for a given pump wavelength. It also computes the nonlinear coefficient and the parametric gain versus angle. Comparing gains over the wavelength range of interest for different crystals and phase matching types gives a good indication of their relative OPO performance. Note that this function permits noncollinear phase matching. Clicking on the ‘pump tilt’ edit box displays a diagram of the noncollinear angles. The signal is assumed to remain aligned to the cavity of an OPO, the pump is tilted by a fixed angle relative to the signal, while the crystal and idler tilt by variable amounts to achieve phase match.2.4 Computing a crystal’s linear optical propertiesThe function Ref. Ind. can be used to compute refractive indices, group velocities, group velocity dispersions, and birefringent walk off for a given propagation angle, temperature, and wavelength. This is useful if you want to make your own calculations of phase matching, group velocity matching, etc.2.5 Computing group velocity matchingThe function GVM calculates the group velocity mismatch for noncollinear mixing including the possibility of slanted pulse fronts. Group velocity matching is important not only for mixing involving femtosecond pulses butProc. of SPIE Vol. 4972 51also for mixing broad band light in many cases. This function is useful, for example, in designing a chirped pulse amplifier, or in designing an optical parametric generator that maintains short pulses and broad bandwidth.3. NONLINEAR MIXING MODELS3.1 Modeling single-pass mixingThe functions with ‘mix’ in their title model single-pass mixing, as opposed to mixing in an optical cavity. The functions with the ‘PW’ prefix model plane-wave mixing, those with the ‘2D’ prefix include Gaussian spatial profiles with diffraction and birefringent walk off. The plane-wave models run much faster than the ‘2D’ models, so they can be used to arrive at an approximate set of conditions which can then be fine tuned with the diffractive models.The functions with suffix ‘LP’ ignore group velocityeffects and are appropriate for monochromatic ns andlonger pulses, or for monochromatic cw beams.Functions with suffix ‘SP’ incorporate group velocityeffects and are useful for ps and fs pulses. The suffix‘BB’ indicates that the pulses are long but broadband sothere is temporal structure on a time scale short enoughto require inclusion of group velocity effects.The figure at the left shows an example of thefunction 2D-mix-LP. Using the input parametersshown on the input form above, it computes near-52 Proc. of SPIE Vol. 4972and far-field spatial fluence profiles as well as spatial profiles and phase profiles as a function of time. Other computed parameters include spectra, power, and beam parameters focus, tilt, and M 2.Usually mixing of low power beams involves focused light, often with a confocal length comparable to the crystal length. The helper function Focus, shown above, is included to help calculate the wavefront curvature at the entrance face of the crystal for such beams. Its output values are automatically updated whenever one of the inputparameters is changed.The function PW-mix-BB can be used to model optical parametric generation (OPG) as a high-gain case of single-pass mixing in the plane-wave approximation. You must specify the correct signal and idler energies,bandwidths, and mode spacings to simulate start-up quantum noise. The mode spacing should be the inverse of the signal/idler pulse length. For example, if you have a 1 ps pump pulse, you could use 5 ps signal and idler pulses (to allow for temporal walk off) and a signal/idler mode spacing of 100 GHz. The bandwidthshould be set to several times the OPO acceptance bandwidth, and the pulse energy of the signal and idler should be set so there is one photon per mode, ie energy = h ν×bandwidth ÷(mode spacing). Because the gain is very high for OPG, the number of z integration steps must be quite large. I suggest you start with 100 steps and double it until the results converge. Each run will use different start up noise, so convergence does not mean identical results here. A good test is to look at both the irradiance and spectral plots and make sure they integration steps. The figures at right show an example of an OPG calculation. The parameters are specified in the input form above left and the output time profile and spectra are show at the right.The functions PW-mix-SP and 2D-mix-SP model single pass mixing for pulses short enough that group velocity effects are important. The figures below shows an example for the plane-wave case. In this example the signal and idler pulses are given an input energy and the pump pulse is generated in the crystal. The signal and idler pulses separate in time due to group velocity differences and reshape due to group velocity dispersion. The “movie ” button displays the pulses as they would appear inside the crystal propagating at different velocities andProc. of SPIE Vol. 4972 53changing strength through nonlinear mixing. In this function as well as most of the other functions, you can specify the energy in any of the pulses; there is no assumption regarding the type of mixing. Mixing will proceed just as in a real crystal. If there are three nonzero inputs, the direction of energy transfer will depend on the relative phase of the three beams.3.2 Model mixing in a cavity (OPO, frequency doubling, etc.)The functions with ‘OPO ’ in their title can model mixing in a cavity. Note that most of these models will handle not only OPO ’s but any mixing process in a cavity, including frequency doubling in a build-up cavity. Functions with the ‘PW ’ prefix model plane-wave mixing; those with the ‘2D ’ prefix include Gaussian spatial profiles with diffraction and birefringent walk off, and they can accommodate curved cavity mirrors. The functions with suffix ‘LP ’ ignore grouppulses or cw beams. As an example of diffractive modeling, the figure to the left compares 2D-OPO-LP modeling of a cw, stable-cavity OPO with experimental measurements by Klein et al.1 The only adjustable input parameter is the round-trip cavity loss which was not precisely measured. For cw cases the model continues to run and display a number indicating the amount of change on the last cavity pass. You terminate the run by pressing the “Stop ” button when the convergence is satisfactory. Another example may be found in one of our earlier papers 2 in which we compared the predictions of 2D-OPO-LP with measurements of a pulsed OPO, obtaining excellent agreement between experiment and model, with no adjustable parameters, for a nanosecond, KTP, ring OPO.54 Proc. of SPIE Vol. 4972The suffix ‘BB’ indicates that the pulses are of long Array duration but have a broad bandwidth so there is temporalstructure on a time scale short enough to require theinclusion of group velocity effects. The figure at the leftdemonstrates the use of PW-OPO-BB to study injectionseeding of an OPO. The top plot is the signal spectrum ofan OPO without seeding. Succeeding plots are the signalspectra with increasing seed power, demonstrating thespectral collapse to a single mode at a seed power of a fewnW. Further details are given in ref. 3.Often mixing of low power beams is done in a stablecavity formed by focusing mirrrors. Such cavities can bedesigned using the Cavity function which will also helpyou find the wavefront curvature of the input beams at theinput mirror, and the cavity round-trip phase which mustbe known to achieve exact resonance in the cavity. Thisfunction operates much like Focus in that the outputs areupdated automatically on any change of the inputparameters. A help plot of the cavity pops up with thisfunction to assist in setting the parameters.The function PW-OPO-SP, unlike the other cavitymixing functions, is limited to OPO modeling, and willnot handle general cavity mixing. More specifically it islimited to synchronously pumped OPO’s. The cavity isassumed to be a singly-resonant ring as diagrammed above, with a nonlinear crystal in one leg and a group velocitydispersion compensator in the another leg. A sample input form and resulting output pulses are shown below.Like other cw modeling, this function runs until you are satisfied with the convergence of the output and terminatethe run.Proc. of SPIE Vol. 4972 55files written by each. One example is displayed here.56 Proc. of SPIE Vol. 49724. CONCLUSIONAll of the modeling functions of SNLO are based on split-step integration methods. They are state-of-the-art in technique, and are all-numerical to cover the widest possible range of applications. More detail is available in thepapers of refs. 2-4. I have carefully validated them against analytical expressions and against each other. SNLO is public domain software written in APL programming language. It may be downloaded free of charge at web site /imrl/XWEB1128/xxtal.htm . We are translating some of the modeling functions of SNLO as well as additional related modeling functions into C++. These are also public domain and will be posted at the same web address as they become available. Only the functions PWOPOBB, shown above, and 2D-mix-SP are currently available. These C++ functions are nearly identical to their counterpart SNLO functions. AcknowledgementSandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.References1. M. E. Klein, D.-H. Lee, J.-P. Meyn, K.-J. Boller, and R. Wallenstein, “Singly resonant continuous-wave optical parametric oscillator pumped by a diode laser,” Opt. Lett. 24, 1142-1144 (1999).2. A. V. Smith, W. J. Alford, T. D. Raymond, and M. S. Bowers, “Comparison of a numerical model with measured performance of a seeded, nanosecond KTP optical parametric oscillator,” J. Opt. Soc. Am. B 12, 2253-2267 (1995).3. A. V. Smith, R. J. Gehr, and M. S. Bowers, “Numerical models of broad-bandwidth nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 16, 609-619 (1999).4. A. V. Smith and M. S. Bowers, “Phase distortions in sum- and difference-frequency mixing in crystals,” J. Opt. Soc. Am. B 12, 49-57 (1995).Proc. of SPIE Vol. 4972 57。
Basler_piA2400-17gm_EMVA_Standard_1288-1
Pour utilisateurs au Canada Cet appareil est conforme aux normes Classe A pour bruits radioe´ lectriques, spe´ cifie´ es dans le Re` glement sur le brouillage radioe´ lectrique.
You are cautioned that any changes or modifications not expressly approved in this manual could void your authority to operate this equipment. The shielded interface cable recommended in this manual must be used with this equipment in order to comply with the limits for a computing device pursuant to Subpart J of Part 15 of FCC Rules.
4.1.6 Inverse Photon Transfer . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1.7 Saturation Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 17
光学名词中英文对照
incoherence addition interference phenomenon of light coherent condition single photon interference relationship between optical path difference and phase difference wavefront-splitted interference Young＇s double-slit interference experiment Thomas Young interference pattern (fringe) order of interference nonlocalized interference nonlocalized fringe Fresnel bimirror Fresnel biprism Lloyd mirror visibility wave train coherence time coherence length temporal coherence spatial coherence critical width of light source interference aperture angle partially coherent light amplitude-splitted interference film interference equal-inclination interference equal-inclination fringes localized interference
泰勒判据 象分辨本領 物镜的分辨本領 相对孔径
Taylor criterion image resolving power resolving power of objective relative aperture
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arXiv:quant-ph/0407002v3 31 Mar 2005FrequencyandtemporaleffectsinlinearopticalquantumcomputingPeterP.Rohde∗andTimothyC.RalphCentreforQuantumComputerTechnology,DepartmentofPhysicsUniversityofQueensland,QLD4072,Australia(Dated:February1,2008)
Typicallylinearopticalquantumcomputing(LOQC)modelsassumethatallinputphotonsarecompletelyindistinguishable.Inpracticetherewillinevitablybenon-idealitiesassociatedwiththephotonsandtheexperimentalsetupwhichwillintroduceadegreeofdistinguishabilitybetweenphotons.Weconsideranon-deterministicopticalcontrolled-NOTgate,afundamentalLOQCgate,andexaminetheeffectoftemporalandspectraldistinguishabilityonitsoperation.Wealsoconsidertheeffectofutilizingnon-idealphotoncounters,whichhavefinitebandwidthandtimeresponse.
PACSnumbers:03.67.Lx,42.50.-p
I.INTRODUCTIONIthasbeenshownthatefficientquantumcomputa-tioncanbeimplementedusingonlylinearopticalele-ments,singlephotonsourcesandphotoncounters[1].Thisschemeisreferredtoaslinearopticalquantumcom-puting(LOQC)andhasrecentlybeensubjecttoseveralin-principleexperimentaldemonstrations[2,3,4,5].IntheLOQCmodelqubitsareencodedasthepres-enceinoneoftwomodesofasinglephoton(dual-raillogic).Thusalogicalzerocanbewritten|0L≡|01where|ijisatwomodestateinwhichiistheoccu-pationnumberofthefirstmodeandandjistheoccu-pationnumberofthesecondmode.Similarlyalogicaloneiswritten|1L≡|10.Oftenthesemodesaretakentobetheverticalandhorizontalpolarizationmodesofasinglespatialmode.Thenon-linearitieswhichareneces-saryforquantumcomputationareintroducedviaacon-ditioningorpost-selectionprocesswherebytheoutputsfromthesystemareonlyacceptedifcertainstatesaredetectedatextraancillaryoutputs.Thispost-selectionprocessresultsinnon-deterministicquantumgateoper-ation(i.e.gateshaveacertainprobabilityoffailing),however,throughtheuseofateleportationprotocol,itispossiblein-principletoboosttheprobabilityofsuccessarbitrarilyclosetounity[1].Itisimportanttounderstandhowcriticallynon-idealfactorsaffectbasicgateoperation.Previousstudieshavelookedattheeffectsofbeamsplitterparameters[6],de-tection[7]andancilla[8]efficienciesonvariousgatede-signs.Akeyingredientofthepost-selectionprocessisthepresenceofnon-classicalinterferenceduetophotonindis-tinguishability.Thusonewouldexpectgateoperationtobecompromisediftheinputphotonsaredistinguishableinsomeway.Inthispaperweconsidersuchaproblembyanalyzingtheeffectofnon-identicalfrequencydistribu-tionsandunsynchronizedarrivaltimesontheoperationofanon-deterministic2-qubitLOQCgate.Someprevi-2Bychoosingdifferentformsforαω,photonsproducedbyvariousphysicalsystemscanbemodeled.Wenowconsidersomeexamples.Theoutputfromanopticalcav-ityischaracterizedbyaLorentziandistribution,whichhastheform
αω=
π1
κ2+ω2(|0ω1−ωa|1ω0−ωb+|1ω0−ωa|0ω1−ωb)dω(3)whereχistheconversionefficiencyofthedown-converter,andκisagainrelatedtothebandwidthoftheoutputphotons.Weassumethatconversionisveryweaksuchthatχ≪κ.ThisjustifiesdroppinghigherordertermsinvolvinghigherphotonnumbersinEq.(3).Themodesaandbcorrespondtothetwospatialmodeswhichformtheoutputs.ItisevidentfromtheformofEq.(3)thatthedown-conversionprocessdoesnotalwayspro-ducephotonpairs,sinceitispossiblethatbothoutputswillbeinthevacuumstate.Infact,withtheassump-tionthatχissmallcomparedtoκ,thedown-converterwillproducevacuumoutputsmostofthetime.However,becausethedown-converterproducesphotonpairsifitproducesanythingatall,areliablephotonsourcecanbeconstructedbyconditioningonthedetectionofaphotonatoneoutputandusingtheotheroutputasthesource.Havingperformedconditioning,thenormalizedformofthephotonproducedattheotherdown-converteroutputis
αω=
2πχ22χκ
2κ2(5)
whereagainκisrelatedtothebandwidthofthedistri-bution.Inadditiontomodelingarbitraryfrequencydistribu-tions,wecanalsointroduceanarbitrarytime-delayontoaphotonwave-packet.UsingFouriertransformrulesthiscanbemodeledbyintroducingacomplexexponentialrotationfactorintothefrequency-domaindistributionfunction.Thiscorrespondstomakingthesubstitutionαω→eiωταω,whereτisthetime-shiftparameter.Thus,asanexample,aGaussiandistributionwithatime-shiftwouldbeexpressedas
αω=eiωτ4κ2πe−ω2