线性参数估计中一个值得注意的问题

测量量(x_i,y_i)满足一定条件的线性函数 y=α+βx (1)的最小二乘参数估计值为■的方差为 其中(?)=1/n sum from 1 to n(x_i),(?)=1/n sum from 1 to n(y_i),σ~2=D(y_i)。普通物理实验的数据处理中有很多这类问题。测量量(x‘,y‘)满足一定条件的线性函数最佳估计量,应改用下式计算y=a+刀x(1)万 乙(y‘一a)x‘一1(5)戈乙1的最小二乘参数估计值为 a=y一刀x(2)D(少(6) X.名i声干(劣一劣)(y‘一y)名(x。一x)“(3)从数学上看,(3)式与(5)式的差刀的方差为 D(刀) az名(x‘一x)2别仅在于解正规方程(4)。a+名二‘刀==兄夕‘习x‘a+习x蓄刀=习x‘…     

集成光学

集成光学、波导理论TN2522006021319径向折射率周期性分布波导的传播模式=Circularwaveguide propagation mode of refractionindex periodical-ly distributed radius[刊,中]/陈义万(湖北工业大学理学院.湖北,武汉(430068)),张群芝…∥光学与光电技术.—2005,3(5).—56-58,61在截面为圆形,沿半径方向折射率n1、n2分层周期性分布的波导中,n1折射率层中电磁场为振荡型,n2折射率层中电磁场为衰减型。将相邻n1、n2层作为一个单元,用转移矩阵法进行了计算,得到了单层(m=0)、4层(m=2)、10层(m=5)3种情况下的β-λ关系。虽然多层介质中有衰减层,…     

利用Lucas-Biquard效应测量声速和声压的实验

本文介绍在超声驻波场内,利用激光光束的Lucas-Biquard效应测量声速和声压的实验。一、Lucas-Biquard效应用高频电压驱动固有频率低于1MHZ的锆钛酸铅PZT—4换能器,在特制的液槽内,可以使透明液体发出超声驻波。假定把声波考虑成在x方向传播的平面波,那么,驻波场内的介质密度ρ、压强P、以及折射率n都只是坐标x和时间t的函数。由于光速远大于声速,所以当光束垂直于x通过声场时,可以认为介     

Er3+:YAlO3晶体中Λ型四能级系统的量子相干左手性

用相干量子干涉和电磁感应透明(Electromagnetically induced transparency,EIT)效应在Er3+:YAlO3晶体中计算得到了Thommen,Mandel和Kastel对原子气提出的Λ型四能级系统的负折射率.计算结果得到的负折射率对应的频带宽度约为1 MHz,比先前报道的103 Hz量级要宽得多.通常而言对应于折射/吸收比Re[n]/lm[n]≈1,而计算所得结果是Re[n]/lm[n]为4.6,表明吸收被EIT效应很好地抑制.Im[n]出现的负值可能与Er3+的4I13/2→4I15/2跃迁的受激发射有关.由此可知,稀土离子掺杂材料具有丰富的能级和各种不同的电磁跃迁,也是电磁感应负折射率材料中出色的应用材料的候选者.     

径向折射率周期性分布波导的传播模式

在截面为圆形,沿半径方向折射率n1、n2分层周期性分布的波导中,n1折射率层中电磁场为振荡型,n2折射率层中电磁场为衰减型。将相邻n1、n2层作为一个单元,用转移矩阵法进行了计算,得到了单层(m=0)、4层(m=2)、10层(m=5)三种情况下的β-λ关系。虽然多层介质中有衰减层,但它们的β-λ关系与单层的类似。     

用压缩态理论导出偶-奇数阶厄密多项式的无穷和

利用有序算符内积分技术,用压缩态理论导出偶数阶厄密多项式H2n(x)和奇数阶H2n+1(x)的无穷和。并提出用量子力学算符Hermite多项式方法计算奇-偶相干态的波函数。我们用的新途径具有物理意义鲜明的特点。     

BaFClxBr1－x:Sm2+中5D2→7F0跃迁几率及其对烧孔效率的影响

本文以BaFClxBr1－x:Sm2+中5D2→7F0的跃迁几率随x变化为中心对BaFClxBr1－x:Sm2+体系4f5d带的激发光谱、5D2→7F0跃迁的荧光衰减随温度的变化特性、5D2→7F0的跃迁几率等进行了研究。从而得出结论:在BaFClxBr1－x:Sm2+中,随Br含量的增大,4f5d带与5D2能级更加接近,使7F0→5D2的吸收截面增大,从而可能提高在5D2:能级烧孔的效率。     

光纤通信光开关的物理基础(续)

4　热光开关热光开关和电光开关的结构可以相同 ,但是产生开关效应的机理不同 .这里的热光效应是指通过电流加热的方法 ,使介质的温度变化 ,导致光在介质中传播的折射率和相位发生改变的物理效应 .折射率随温度的变化关系为n(T) =n0 +Δn(T) =n0 + n TΔT=n0 +αΔT(6 9)式中 n0 为温度变化之前的折射率 ,ΔT为温度的变化 ,α为热光系数 ,它与材料的种类有关 .表 3是几种材料的热光系数 .表 3　几种材料的热光系数材料 α/ (10 - 4K- 1 )L i Nb O30 .0 4 3Si 2Si O2 1.1聚合物 1　　Δn将引起相位变化为Δφ=2 πΔn L/ λ0 =2 παL…     

光折变材料的带隙结构研究

利用光子晶体的概念和时域有限差分方法计算了当光折变材料的空间折射率呈一维正弦变化时其内部的带隙结构情况,表明在光折变材料中存在极窄的光子带隙。最后讨论了折射率(n)、折射率调制幅度(△n)、周期长度(D)及周期数(N)对光子带隙的影响。     

用掠入射法测量透明介质折射率的探讨

本文介绍了掠入射法测量各种透明介质折射率的实验过程与方法,并用钠光源掠入射法测量乙醇、纯净水和丙三醇的折射率,在实验拓展中对空气、三棱镜的折射率测量进行了探讨。     

Measuring optical properties of an eye lens using magnetic resonance imaging

We compare the focal lengths of porcine lenses measured optically and by using a novel MRI technique. The geometric properties of the lenses were also measured and compared. The MRI technique exploits the dependence of both the lens refractive index and relaxation rates on the local protein concentration. By measuring the refractive index and corresponding values of R2 (=1/T2) for samples of lens homogenates with different protein concentrations, the dependence of refractive index on R2 was determined empirically. R2 maps, constructed from monoexponential fits to multiecho images of a slice through the lens containing the optical axis, were converted to refractive index maps using this relationship. A simulated ray trace through the refractive index map provided an estimate of lens focal length that was compared to a direct optical measurement of focal length using a laser ray-tracing method. It was found that the mean focal lengths estimated from the two techniques agreed within experimental uncertainty. The refractive index profile along the optical axis was found to be well described by a simple function of the form n=n0 + n1 x ra where r is the (normalized) lens radius.     

Tm:YVO4晶体的光谱参数计算

由测量的Tm :YVO4晶体的吸收光谱 ,考虑到单轴晶体在各个方向上的吸收不同和折射率随波长的变化 ,根据Judd Ofelt理论计算了Tm3 +在YVO4中的强度参数、各个能级的振子强度、自发辐射几率、荧光分支比、积分发射截面等参数。强度参数为Ω2 =1 9416× 10 - 2 0 (cm2 ) ,Ω4=0 15 6 8× 10 - 2 0 (cm2 ) ,Ω6=0 396 3× 10 - 2 0 (cm2 )。计算结果表明 ,1 D2 → 3 F4的跃迁几率远大于1 D2 向其他各个能级的跃迁几率     

Slot-waveguide biochemical sensor

We report an experimental demonstration of an integrated biochemical sensor based on a slot-waveguide microring resonator. The microresonator is fabricated on a Si3N4-SiO2 platform and operates at a wavelength of 1.3 microm. The transmission spectrum of the sensor is measured with different ambient refractive indices ranging from n=1.33 to 1.42. A linear shift of the resonant wavelength with increasing ambient refractive index of 212 nm/refractive index units (RIU) is observed. The sensor detects a minimal refractive index variation of 2x10(-4) RIU.     

Dispersion of the nonlinear refractive index in sapphire

The nonlinear refractive index, n2, of sapphire was experimentally measured in the 550-1550-nm wavelength range by use of a picosecond Z-scan technique. It was found that in this spectral region the value of n2 decreases monotonically from approximately 3.3 x 10(-16) to approximately 2.8 x 10(-16) cm2/W. An empirical expression for the wavelength dependence of the nonlinear refractive index in the 270-1550-nm range was obtained.     

Measurement of local field effects of the host on the lifetimes of embedded emitters

We report experimental results on the variation of the radiative lifetime of Eu3+ ion embedded in a dielectric with the refractive index n. We dope 1 mol % of Eu3+ into the binary glass system xPbO-(1-x)B2O3. By varying x we have achieved a fairly large variation of the refractive index from 1.7 to 2.2. This enables us to study the local field effects for the first time for ions doped in a solid glassy material. Our measurements are in agreement with the so-called real cavity model. The present measurements are free from the complications arising from reorganizational effects in solvents.     

Excess molar volumes, viscosities, and refractive indices for binary and ternary mixtures of {cyclohexanone (1) + N,N-dimethylacetamide (2) + N,N-diethylethanolamine (3)} at (298.15, 308.15, and 318.15) K

Densities ρ, viscosities η, and refractive indices n_D, of the binary and ternary mixtures formed by cyclohexanone + N,N-dimethylacetamide + N,N-diethylethanolamine were measured at (298.15, 308.15, and 318.15) K for the liquid region and at ambient pressure for the whole composition ranges. The excess molar volumes V_m^E, viscosity deviations Δη, and refractive index deviations Δn_D, were calculated from experimental densities and refractive indices. The excess molar volumes are positive over the mole fraction range for binary mixtures of cyclohexanone(1) + N,N-dimethylacetamide (2) and N,N-dimethylactamide (2) + N,N-diethylethanolamine (3) and increase with increasing temperatures from (298.15 to 318.15) K. The excess molar volumes of cyclohexanone (1) + N,N-diethylethanolamine (3) are S-shaped dependence on composition with negative values in the N,N-diethylethanolamine rich-region and positive values at the opposite extreme and increase with increasing temperatures from (298.15 to 318.15) K. The excess molar volumes are positive over the whole mole fraction ranges for the ternary mixtures at all temperatures. Viscosity deviations are negative over the mole fraction range for all binary and ternary mixtures and decrease with increasing temperatures from (298.15 to 318.15) K. Refractive index deviations are negative over the mole fraction range for all binary and ternary mixtures and increase with increasing temperatures from (298.15 to 318.15) K. The experimental data of constitute were correlated as a function of the mole fraction by using the Redlich–Kister equation for binary and , Cibulka, Jasinski and Malanowski , Singe et al., Pintos et al., Calvo et al., Kohler, and Jacob–Fitzner for ternary mixture, respectively. McAllister^'s three body, Hind, and Nissan–Grunberg models were used for correlating the kinematic and dynamic viscosity of binary mixtures. The experimental data of the constitute binaries are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.     

The proton inventory technique in a dual mechanistic system: the spontaneous hydrolysis of ethyl formate

Ethyl formate undergoes spontaneous hydrolysis through two parallel mechanistic pathways: water catalysis and specific hydrogen-ion catalysis. The proton inventory of the water reaction at 37.0 ( degrees )C was determined from the overall conversion curves, in H(2)O/D(2)O mixtures of deuterium atom fraction n, resulting in k(1)(n)=(2.1+/-0.1)x10(-5) s(-1) (1-n+0.42 n) (1-n+0.83 n)(2), in agreement with the results of six other cases of carboxylic acid derivatives. This result contributes to the validation of the accuracy of the proton inventory technique.     

Direct measurement of electrostriction in optical fibers

The electrostriction contribution to the nonlinear refractive index in optical fiber was theoretically calculated and measured. Nonlinearity was induced directly by insertion of the optical fiber into an intense external electric field. With this technique both the Kerr and the electrostrictive contributions to the intensity dependence of the nonlinear refractive index in a step-index fiber were measured. Good agreement between calculated and measured values was observed. These results should confirm and explain the differences observed in measurement of n(2) at different bit rates.     

Non-linear refractive indices of CS2-CCI4 mixtures

We have determined the two independent fast non-linear refractive indices for liquid mixtures of CS₂ and CCI₄ to within 5% relatively and 8% absolutely over their range of more than a decade. These indices describe non-linear propagation of optical pulses of arbitrary polarisation, which are of a too short duration to be affected by electrostriction. We report measurements, having relative accuracy better than 1 %, of the static Kerr constants of these mixtures. We combine these results with recent data on Rayleigh wing depolarisation ratios for the same mixtures to deduce the desired non-linear indices with the aid of molecular theory. The non-linear refractive index for linearly polarised light is shown to be two-thirds (±5%) of the index difference measured by the Kerr effect, at least for molar concentrations of CS₂ greater than 10%. Our measured relative values of the mixture Kerr constants are predicted to within experimental error if one simply replaces the Lorentz local field factors in the classical theory by their 0.6 powers.