Study on the Superluminal Group Velocity in a Coaxial Photonic Crystal

In this paper, the superluminal group velocity in a coaxial photonic crystal is studied. The simulation of the effective refraction index in coaxial photonic crystal is performed. The group velocity is calculated based on the transmission line equations and compared with experimental results.

Where Is Phase Velocity in Minkowski Space?

In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: vp.vg = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ, i.e. to vgt ± σ/ω, where ω is the particle angular frequency. This is the first time the phase range has been described for a massive particle.

Quantum Mechanics: Internal Motion in Theory and Experiment

Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħω (symbol definitions in footnote) and p = h/λ = ħk, to special relativity E2 = p2c2 + m2c4. Calculations on a wave-packet, that is symmetric about the normal distribution, are partly conservative and partly responsive. The complex electron wave function is chiefly modelled on the real wave function of an electromagnetic photon;while the former concept of a “point particle” is downgraded to mathematical abstraction. The computations yield conclusions for phase and group velocities, vp⋅vg = c2 with vp ≥ c because vg ≤ c, as in relativity. The condition on the phase velocity is most noticeable when p≪mc. Further consequences in dispersion dynamics are: derivations for ν and λ that are consistently established by one hundred years of experience in electron microscopy and particle accelerators. Values for vp = νλ = ω/k are therefore systematically verified by the products of known multiplicands or divisions by known divisors, even if vp is not independently measured. These consequences are significant in reduction of the wave-packet by resonant response during interactions between photons and electrons, for example, or between particles and particles. Thus the logic of mathematical quantum mechanics is distinguished from experiential physics that is continuous in time, and consistent with uncertainty principles. [Footnote: symbol E = energy;h = Planck’s constant;ν = frequency;ω = angular momentum;p = momentum;λ = wavelength;k = wave vector;c = speed of light;m = particle rest mass;vp = phase velocity;vg = group velocity].

Studies on phase and group velocities from acoustic logging

It is still argued whether we measure phase or group velocities using acoustic logging tools. In this paper, three kinds of models are used to investigate this problem by theoretical analyses and numerical simulations. First, we use the plane-wave superposition model containing two plane waves with different velocities and able to change the values of phase velocity and group velocity. The numerical results show that whether phase velocity is higher or lower than group velocity, using the slowness-time coherence （STC） method we can only get phase velocities. Second, according to the results of the dispersion analysis and branch-cut integration, in a rigid boundary borehole model the results of dispersion curves and the waveforms of the first-order mode show that the velocities obtained by the STC method are phase velocities while group velocities obtained by arrival time picking. Finally, dipole logging in a slow formation model is investigated using dispersion analysis and real-axis integration. The results of dispersion curves and full wave trains show similar conclusions as the borehole model with rigid boundary conditions.

利用啁啾飞秒激光脉冲调控金薄膜中传输表面等离激元的群延迟色散

准确评估与灵活调控表面等离激元(surface plasmon polaritons,SPP)的传输特性对基于等离激元效应设计的高速-小型化器件具有重要意义.本文从理论上推导了SPP在不同厚度金膜表面传播的群速度色散.当金膜厚度小于40 nm时,随着膜厚度的增大,SPP的群速度色散显著减小;金膜厚度为40-60 nm时,SPP的群速度色散下降趋势变缓,并在厚度大于60 nm后保持恒定.利用时域有限差分方法,数值模拟了不同传播距离下SPP的电场时间演化.通过比较不同传输距离下SPP近场强度与入射光色散量的关系确定SPP的群速度色散,并得到接近理论推导的结果,进而提出利用负啁啾脉冲激发SPP来补偿传输中产生的群延迟色散,实现不同传输距离SPP场振幅、脉宽的调控.此外,利用定制的SPP激发金属纳米天线,通过调控入射脉冲色散量与SPP在金膜中传播产生群延迟色散的传播特性相结合的手段,实现在纳米信号接收器中热点位置的fs时间灵活时空相干控制.这对于利用等离激元效应设计和控制微型片上集成系统具有重要意义.

基于超声导波技术的双层粘接结构界面质量检测

针对粘接结构界面质量难以检测的问题,提出一种超声导波检测技术方法。基于弹簧模型和波动方程建立超声导波在双层粘接结构中传播的数学模型,获得不同粘接界面的频散方程,通过求解该方程获得不同粘接界面的频散特性。利用COMSOL软件模拟了声波在不同粘接界面的传播过程。仿真结果表明,在频率为1 MHz时刚性粘接条件下,数值求解的群速度为4.632 km/s,仿真平均群速度为4.505 km/s,误差为2.74%;在滑移粘接条件下,数值求解的群速度为4.855 km/s,仿真平均群速度为5.045 km/s,误差为3.91%;在完全脱粘条件下,双层粘接结构频散曲线为单层频散曲线的叠加。通过对双层介质超声导波实验检测结果的分析,发现实验结果与数值求解和有限元仿真结果吻合较好,验证了该理论模型的正确性。

Group velocity dispersion effect on the collapse of femtosecond laser pulses in air: a revised form for Marburger's law

The influence of group velocity dispersion（GVD） on the self-focusing of femtosecond laser pulses is investigated by numerically solving the extended nonlinear Schr？dinger equation. By introducing the GVD length LGVDinto the semi-empirical, self-focusing formula proposed by Marburger, a revised one is proposed, which can not only well explain the influence of GVD on the collapse distance, but also is in good agreement with the numerical results, making the self-focusing formula applicable for more cases.

Properties of Ternary One Dimensional Plasma Photomic Crystals for an Obliquely Incident Electromagnetic Wave Considering the Effect of Collisions in Plasma Layers

An analytical study is presented on the modal dispersion characteristics, group velocity, and effective group, as well as the phase index of a ternary one dimensional plasma photonic crystal for an obliquely incident electromagnetic wave considering the effect of collisions in plasma layers. The dispersion relation is derived by using the transfer matrix method and the boundary conditions based on electromagnetic theory. The dispersion curves are plotted for both the normal photonic band gap structure and the absorption photonic band gap structure. It is found that the increase in the angle of incidence shifts the photonic band gap toward higher frequencies. Also, the cutoff frequency is independent of collisions.

G-type dispersion equation under suppressed rigid boundary:analytic approach

This paper studies dispersion of a G-type earthquake wave under the influence of a suppressed rigid boundary. Inside the Earth, the density and rigidity of the crustal layer and the mantle of the Earth vary exponentially and periodically along the depth. The displacements of the wave are found in the individual medium followed by a dispersion equation using a suitable analytic approach and a boundary condition. The prominent effect of inhomogeneity contained in the media, the rigid boundary plane, and the initial stress on the phase and group velocities is shown graphically.

Theoretical Calculation of Ultrashort-Pulse Optical Parametric Generation

A general theory of optical parametric generation that accounts for pump depletion, loss, phase mismatch, group-velocity mismatch among the pump, signal and idler pulses, and intrapulse group-velocity dispersion is proposed for coherent ultrashort pulses with arbitrary shapes and carrier chirps. The coupled differential equations are numerically solved using a symmetric split step beam-propagation method. The general solutions of these equations are obtained and the optical parametric generation process is theoretically investigated. Results show that the major factors, which remarkably affect the optical parametric conversion efficiency and durations of the pulses in phase-matched structure, are the group velocity mismatch and the intrapulse group velocity dispersion.

Determination of the Crust and Upper-Mantle Structure in Anatolia by Surface Wave Data

In this study, the crust and upper mantle structure of Anatolia have been investigated by measuring the group velocity dispersion data of discriminated seismic surface waves. In the scope of the study, it has selected the profiles between six stations located in western Anatolia of Bogazici University Kandilli Observatory Earthquake Research Institute, national network of Turkey, and records of an earthquake (having about 10°epicentral distance) occurred in the eastern of Anatolia have been used. Firstly, surface wave discrimination filter based on the polarization properties has been applied tothree-component recordsand emphasized to surface waves. Then the group velocities have been calculated by multiple filter technique. A five-layered crustal model having total thickness of 38 - 40 km and Pn-wave velocity of 8.00 km/sec in the upper-mantle has been determined through inversion of surface wave group velocity dispersion data in the period range of 10 sec to 60 sec.

Responses of a resident group to an outsider in the blue-breasted quail: A paradigm for studying social resettlement of dispersers

Dispersal is an individual life-history trait that can influence the ecological and evolutionary dynamics of both the source and recipient populations.Current studies of animal dispersal have paid little attention to how the responses of residents in a recipient population affect the social resettlement of dispersers into a new habitat.We addressed this question in the blue-breasted quail Synoicus chinensis by designing an outsider introduction experiment to simulate a scenario of interaction between residents and dispersers.In the experiment,we introduced an unfamiliar quail into a group of 3 differently ranked residents and then examined their behavioral responses to the arrival of the outsider.We found that all residents made negative responses by pecking at the outsider to maintain their pecking order,in which high-ranked residents displayed significantly greater intensity than those of lower ranks.This result highlighted that adverse behavioral responses of residents would prevent outsiders from obtaining hierarchical dominance in the recipient group.Moreover,the residents’sex ratio,their relative ages to the outsiders,and whether outsiders counter-pecked at the residents all influenced the probability of outsiders prevailing against the residents.Those outsiders that displayed counter-peck courage were more likely to gain higher dominance and hence resettle into the recipient group successfully.Our findings suggest that resident groups may impose a selection among dispersers via adverse behavioral responses.Therefore,social factors that can influence the resettlement step of dispersers in a new habitat should be accounted for in future studies of animal dispersal.

Design and analysis of a wideband photonic crystal waveguide with low group-velocity and low dispersion

The slow light propagation in a line waveguide in the two-dimensional triangular photonic crystal has been numerically studied, based on which a wideband photonic crystal waveguide with low group-velocity and low dispersion is proposed. The numerical simulation analysis shows that it is possible to maximize the group index and minimize the group-velocity dispersion in wide bandwidth by increasing the radius of the basic air hole and changing the position of the first two rows of air holes in photonic crystal waveguides. Such a photonic crystal waveguide exhibits low group velocity and low group-velocity dispersion over a broad wavelength range. A larger group index-bandwidth product is achieved in this type of waveguide structure. The numerically computed results present the normalized bandwidth as 0.32%, 0.48% and 0.642% corresponding to the group index of 85, 58 and 45, respectively.

槽波层析成像方法在煤田勘探中的应用--以河南义马矿区为例

在地下煤田的开发中,工作面内的小构造、异常体、煤层厚度变化等是需要解决的关键问题,而槽波探测则为这些问题的解决提供了重要的物探方法.本文对河南义马矿区11061工作面进行槽波透射法测量,在巷道显示的煤层厚度变化为1.5～8m,从理论频散曲线分析速度与厚度关系,确定125Hz频率槽波主要用于观测厚度约为2～5m的煤层厚度变化;有效提取了684个频散曲线,并分别拾取了125Hz时槽波群速度与走时,采用走时层析成像方法获得工作面内煤层速度、厚度以及高应力区分布特征,回采验证了结果的正确性.

半解析有限元法求解钢轨中超声导波频散曲线

钢轨中超声导波的频散曲线是采用超声导波技术进行无缝线路钢轨完整性检测的重要参考依据。通过传统的有限元模态分析方法,无法求解得到钢轨中超声导波完整的频散曲线,针对这一问题,采用了半解析有限元方法。求解时假设导波在钢轨中以简谐振动的方式传播,仅对钢轨的横截面采用三角形单元进行有限元网格划分,经理论推导得到超声导波在钢轨中传播的波动方程,通过求解特征方程,得到波数与频率的值,进而获取频率与相速度、群速度的关系,绘制出频散曲线。通过求解得到的特征向量还可以分析各导波模态的振动特性。实验结果表明,半解析有限元法求解得到的我国无缝线路CHN60钢轨的频散曲线与实际线路测试结果有很好的一致性。

半解析有限元法分析兰姆波频散特性

为了获得各向同性均质自由铝板中兰姆波的频散特性曲线,采用了半解析有限元方法。此方法仅需要在自由板的横截面进行有限元离散,而假定兰姆波沿波的传播方向以简谐振动的方式运动,由哈密顿原理推导出兰姆波在自由板中传播的波动方程,通过特征方程求解得到波数和频率的关系。通过半解析有限元方法可以绘制各向同性均质自由铝板中兰姆波的相速度频散曲线,不需模态跟踪,由特征值和特征向量可直接求解得到群速度频散曲线,由特征向量可进行兰姆波的振动模态分析,这种方法还可推广用于任意横截面形状波导介质中导波模态的求解。

华北地区三维地壳上地幔结构

本文用均等显示滤波频时分析方法分析了长周期瑞利面波资料,获得了路经中国大陆及邻区的238条混合路径的面波群速度频散,其周期范围为10.5—113s.用改进的分格反演方法从混合路径频散中提取出位于华北地区的12个4°×4°网格单元的纯路径频散并反演其地壳上地幔结构.所得结果表明,华北地区地壳上地幔结构横向变化显著;从东向西地壳逐渐变厚;位于华北东部的分格在地壳中20km深处普遍存在低速层,整个华北地区上地幔低速层埋藏较浅,一般为55—100km之间.各个网格上地幔低速层的速度不尽相同.

中国西部三维速度结构及其各向异性

本文用覆盖中国的358条勒夫面波路径资料,研究了10.45—113.80s范围内中国西部的三维SH波速度结构.结果表明,各构造单元的SH波速度结构均有明显的差别.作为稳定块体的塔里木盆地,壳内重力分异程度较高,上、中、下地壳厚度差别小,壳内无明显的低速层,地壳平均速度比较小;上地幔低速层埋深大且层中速度大;区内横向变化小.构造活动区如天山、青藏高原,其突出的特征是下地壳厚度大且速度大,上地幔盖层速度值相当高.这与西伯利亚、印支板块的挤压有密切的关系.青藏高原东部及其北、东边缘地区壳内存在低速层,上地幔低速层埋深浅,一些地区存在壳幔过渡层.面波各向异性研究表明,青藏高原、天山及印支板块北缘下存在明显的各向异性,以构造边缘地区及上地幔低速层附近最为突出.印度板块、西伯利亚板块与中国大陆间的碰撞引起强大的水平压力和一定的下插作用,是造成青藏高原隆起、地壳增厚、天山隆起的最根本的因素,同时也促成壳幔中辉石、橄榄石的定向排列和物质运移,因而出现明显的各向异性现象.

水平网格计算频散性的研究

从线性浅水方程组出发 ,在ArakawaA—E网格、Z网格和Eliassen网格上 ,分可分辨和不可分辨两种情况 ,从频率和群速方面讨论了这 7种网格的计算频散性 ,并指出了每种网格出现错误群速的水平尺度范围。结果表明 :在可分辨的情况下 ,Z、C和Eliassen网格较其它网格效果好 ;在不可分辨的情况下 。

色散、群速与群折射率

本文讨论了群折射率存在的物理意义，指出群折射率不仅包含了折射率概念而且还体现了折射率的色散性质，同样能作为材料本身的光学性质参量－ 接着指出在折射率的白光干涉法测量中存在着忽视色散作用而导致的将群折射率误认为折射率的情况－ 将群折射率与折射率区别开来，不仅可以消除折射率测量中所存在的错误，而且可以突出色散现象在光传播时间特性上的意义－ 为此建立了折射率与群折射率的相互变换关系，通过对于典型物质的折射率与群折射率变换关系的计算，说明二者在数值上的差别甚至对于气体介质来说也是不能忽略的－