The Photon Wave Function

The properties of a wave equation for a six-component wave function of a photon are re-analyzed. It is shown that the wave equation presents all the properties required by quantum mechanics, except for the ones that are linked with the definition of the position operator. The situation is contrasted with the three-component formulation based on the Riemann-Silberstein wave function. The inconsistency of the latter with the principles of quantum mechanics is shown to arise from the usual interpretation of the wave function. Finally, the Lorentz invariance of the six-component wave equation is demonstrated explicitly for Lorentz boosts and space inversion.

Photon Structure and Wave Function from the Vector Potential Quantization

A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.

Photon statistics of pulse-pumped four-wave mixing in fiber with weak signal injection

We study the photon statistics of pulse-pumped four-wave mixing in fibers with weak coherent signal injection by measuring the intensity correlation functions of individual signal and idler fields. The experimental results show that the intensity correlation function of individual signal（idler） field g_（s（i））^（2） decreases with the intensity of signal injection. After applying narrow band filter in signal（idler） band, the value of g_（s（i））^（2） decreases from 1.9 ± 0.02（1.9 ± 0.02） to 1.03 ± 0.02（1.05 ± 0.02） when the intensity of signal injection varies from 0 to 120 photons/pulse. The results indicate that the photon statistics changes from Bose–Einstein distribution to Poisson distribution. We calculate the intensity correlation functions by using the multi-mode theory of four-wave mixing in fibers. The theoretical curves well fit the experimental results.Our investigation will be useful for mitigating the crosstalk between quantum and classical channels in a dense wavelength division multiplexing network.

The features of band structures for woodpile three-dimensional photonic crystals with plasma and function dielectric constituents

The features of the band structures of woodpile three-dimensional （3D） photonic crystals composed of plasma and function dielectric constituents, referred to as function plasma photonic crystals （FPPCs）, are theoretically studied by a modified plane wave expansion method, and the formulas for computing the band structures are derived. The arrangement for the proposed FPPCs is that the function dielectric columns are surrounded by plasma, and the embedded dielectric columns are stacked according to the woodpile lattices, which are arrayed with facecentered-tetragonal symmetry. The relative permittivity of function dielectric rods depends on the function coefficient and space coordinates. The relationships between the parameters for inserted function dielectric rods and plasma and the band structures are also investigated. The computed results illustrate that the obtained PBG can be tuned by those parameters as mentioned above. Compared to dielectric-air PCs, function dielectric PCs and plasma dielectric PCs with the same topology, a wider bandwidth of the photonic band gap can be observed in the proposed FPPCs. The calculated results also show us another alternative way to realize reconfigurable applications with 3D FPPCs.

Comment on “Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals” by Si-Qi Zhang et al.

Recently, Zhang et al. （Chin. Phys. B 26 024208 （2017）） investigated the band gap structures and semi-Dirac point of two-dimensional function photonic crystals, and the equations for the plane wave expansion method were induced to obtain the band structures. That report shows the band diagrams with the effects of function coefficient k and medium column ra under TE and TM waves. The proposed results look correct at first glance, but the authors made some mistakes in their report. Thus, the calculated results in their paper are incorrect. According to our calculations, the errors in their report are corrected, and the correct band structures also are presented in this paper.

圆孔衍射成像的光子学诠释

用量子力学中关于光的粒子性观点,采用概率波对圆孔衍射成像过程进行了讨论,所得到的结论与采用光的波动性观点的惠更斯-菲涅耳原理及Fourier变换方法相同。通过分析,使我们进一步加深了对光的粒子性层面的认识。

光子的旋量波动方程

给出自由和非自由光子的旋量波动方程及光子自旋算符与自旋波函数.通过计算光子的螺旋度,证明存在左旋和右旋光子.由单光子自旋波函数得到两光子或多光子的自旋波函数,并给出多光子的自旋纠缠态.

二维函数光子晶体

光子晶体是由两种或两种以上不同介电常数材料所构成的周期性光学纳米结构.光子晶体结构可分为一维、二维和三维,其中二维光子晶体已成为研究的热点.可调带隙的二维光子晶体可以设计出新型的光学器件,因此,对它的研究具有重要的理论意义和应用价值.本文提出的二维新型函数光子晶体可以实现光子晶体带隙的可调性.所谓二维函数光子晶体,即组成它的介质柱的介电常数是空间坐标的函数,它不同于介电常数为常数的二维常规光子晶体.二维函数光子晶体是通过光折变非线性光学效应或电光效应使介质柱的介电常数成为空间坐标的函数.运用平面波展开法给出了TE和TM波的本征方程,由傅里叶变换得到二维函数光子晶体介电常数ε(r)的傅里叶变换ε(G),其傅里叶变换比常规二维光子晶体的复杂.计算发现当介质柱介电常数为常数时,其傅里叶变换与常规二维光子晶体的相同,因此二维常规光子晶体是二维函数光子晶体的特例.在此基础上具体研究了二维函数光子晶体TE波和TM波的带隙结构,其介质柱介电常数函数形式取为ε(r)=k·r+b,其中k,b为可调的参数.并与二维常规光子晶体TE波和TM波的带隙结构进行了比较,发现二维函数光子晶体与二维常规光子晶体TE波和TM波的带隙结构有明显的区别,二维函数光子晶体的带隙数目、位置以及宽度随参数k的变化而发生改变.从而实现了二维函数光子晶体带隙结构的可调性,为基于二维光子晶体的光学器件的设计提供了新的设计方法和重要的理论依据.

基于介电函数实验值拟合对一维光子晶体能带结构的分析与讨论

使用与在宽波段范围内TiO2,SiO2介电函数相似的指数型函数,利用数值拟合方法,给出了与实验介电函数值完全吻合的色散关系;将其直接应用于平面波展开法,计算分析了一维TiO2/SiO2色散光子晶体能带结构.与常规平面波展开法的计算结果对照发现,由两种方法分别计算得到的能带结构中均有两个较宽的光子带隙,但两者的带宽和位置均有所不同,且改进后的计算结果中未出现中间的一个窄带隙.分析认为,改进后的平面波展开法计算出的能带结构似更符合实际.

光子的量子波动方程

给出外场中粒子的Lagrange函数及其Hamilton量的相对论表达式.令静止质量m 0=0,进一步给出光子的Hamilton量及光子在介质中的势能.在此基础上,给出自由和非自由光子的量子波动方程.用该方程可研究光在光子晶体中的量子色散关系及量子透射等特性.

基于光子散射的功能成像技术

阐述了基于光子散射模型下的功能成像技术.运用蒙特卡罗方法对光子在介质中的散射路径进行了模拟和分析,从而引入光子散射的概念.通过对光子散射方程的解释引入了散射光子密度波的概念.通过无限大模型下光子密度波的波方程,引出光子密度波的异质模型.建立了基于消元的奇异值弱化重建算法,完成了对病态方程的求解,实现了对内嵌于均匀介质中异质的吸收系数分布图像的重建.在基于光散射成像技术所开发的成像系统平台下实现了异质小球的成像实验,对多个不同浓度的物体完成了成像,探测到介质中由于微小浓度改变而引起的吸收系数变化.

一种Riemann-Silberstein光子波函数及其特性

本文讨论了一种六-矢量Riemann-Silberstein光子波函数,及其分别在坐标表象和动量表象下的形式、物理意义及特性。结合光与物质微观相互作用问题,对Riemann-Silberstein光子波函数在近场光学理论研究方面的应用进行了初步探究。

光子密度波扩散方程中的格林函数

在分析有关格林函数在光子密度波扩散方程中应用情况的基础上,根据所设定的实验模型要求,将展开法与电像法相结合求解了满足扩散方程的格林函数,并详细推导了获得该函数的过程.该函数更加适合于所设定的实验模型,并便于对扩散方程进行更为精确的求解.

中医经络理论的现代方法描述

从量子力学和电动力学等现代科学的观点出发,对中医人体经络理论进行研究。论证在腧穴处存在接触电位差,在体表与内脏之间存在温差电动势,这2种电动势会推动带电粒子在人体内运动,由此产生非稳衡电磁场;其它如脑电、心电、肌电及各种细胞电位都对人体电磁场有贡献。按量子力学,人体内的电子和各种离子特别是光子的运动不能用轨道描述,要用波函数来描述,由波函数可求出这些微粒的空间几率分布和变化规律,人体经气由这些微粒波构成,故其运动不需要特定管道。

Heuristic Solution to the Conundrum of the Zitterbewegung

Assuming the Dirac wavefunction describes the state of a single particle. We propose that the relation derived by Schrödinger, which contains the Zitterbewegung term, is a position equation for an amplitude modulated wave. Namely, the elementary constituents are amplitude modulated waves. Indeed, we surmise that a second wave is associated with the particle, which corresponds to a signal. At the same time, we interpret that Broglie’s wave corresponds to a carrier. Furthermore, the quantum object is a recording medium and, like in a hologram, information encoded on its surface. We suggest a description and the cause of the Zitterbewegung heretofore never considered regarding the previous assertions. Hereunder, we shall also apply the quantum amplitude modulation interpretation to the single-photon wave function by Bialynicki-Birula. The predictions are testable, thence providing evidence for the proposed hypothesis.

应变可调二维光子晶体的力致变色效应研究

光子晶体是由两种或两种以上的透明材料周期排列构成的功能复合材料,它可以完全反射一定频率范围内的电磁波,这个性能称为光带隙。光子晶体将在光通信、数据存储以及光路设计等方面得到广泛的应用。本文设计了一种应变可调的二维光子晶体结构,通过基底产生的正应变改变光子晶体的周期性,从而改变其光带隙性能。利用平面波展开法考察了该结构的应变可调性,即其力致变色效应。结果表明,压应变会显著影响横向电波(Transerse electric waves,TE)的传播特性,打开多条光带隙。并且光带隙的宽度也正比于压应变的大小。利用这样的效应可以制成应变传感器或光学开关等器件。

多散射介质中光子密度波扩散方程的二阶求解

对于生物医学光子学领域中的新技术——扩散光子密度波技术进行了理论上的研究与扩展,给出了长为a,宽为b,高为无限大的矩形边界条件下光子密度波扩散方程的二阶微扰解析解。由于实际测到的物理量多为光通量,演算出了与入射面相对应面处的光子通量和介质中的吸收系数改变量之间的关系。并利用人体前臂肌肉组织的典型光学参数,给出了二阶微扰解的模拟计算结果,并与一阶微扰计算结果进行了比较。结果表明,二阶微扰解比原有的一阶微扰解在计算精度上有一定的提高,尤其是在异常体附近精度更是有较大的提高。所得二阶结果不仅为利用扩散方程进行生物组织成像问题提供了更加精确的理论基础,而且对于图像质量尤其是分辨异物的能力的提高具有促进作用。

椭圆芯扁六角聚合物光子晶体光纤的偏振特性

采用全矢量定域基函数模型,以聚合物PMMA为基材,研究了椭圆芯三角点阵扁六角结构光子晶体光纤(Photonic crystal fibers,PCFs)的偏振特性,分析了其相位模双折射和群模双折射与相对孔间隔比的依赖关系,并与椭圆芯三角点阵正六角结构PCFs的研究结论进行比较;研究发现,椭圆芯扁六角结构PCF的偏振特性强烈的依赖于光纤的结构参数,由于色度色散的存在,在短波长段,群双折射远远高于相位模双折射,通过适当调节光纤的相对孔径和相对孔间隔比,有望在给定波长实现高双折射和零偏振模色散单模运行．该研究为高双折射聚合物光子晶体保偏光纤的制备提供了理论依据．

外场中双光子Jaynes-Cummings模型的统计性质

考虑了在外场中的双光子Jaynes Cummings模型.将原子与外场的相互作用视为微扰,采用微扰论的方法,得到了直到一级的波函数.重点讨论了在外场作用下腔场的光子数分布和原子的布局反转等统计性质.

3维函数光子晶体的特性研究

为了研究3维函数光子晶体的光子禁带特性,采用平面波展开法计算得到色散曲线,推导了平面波展开法的相关计算公式以及介质球介电常数的函数关系式,探讨了可调参量函数系数I和介质球半径R_1对光子禁带特性的影响。结果表明,3维函数光子晶体呈立方体晶格分布,由介质球填充空气背景;与常规3维介质光子晶体相比,3维函数光子晶体不仅能得到可调谐的光子禁带,而且可以拓展禁带带宽,并增加光子禁带的数量;改变函数系数I的大小可以实现对光子禁带数量、位置和带宽的调谐;改变介质球半径R_1可以对光子禁带带宽实现展宽,并改变光子禁带的位置。该研究对设计新型可调谐器件是有帮助的。