莫比乌斯变换及其物理应用

北京科技大学陈难先教授把数论中的一条古老定理:莫比乌斯变换推广到普通函数并创造性地用之于物理学中许多反问题,取得了巨大成功。在此以更直观和易于理解的方式导出陈氏定理,并通过一些具体实例展示其应用前景。     

Dimer statistics of honeycomb lattices on Klein bottle,Möbius strip and cylinder

Dimer statistics is a central problem in statistical physics. In this paper the enumerations of close-packed dimers of honeycomb lattices on Klein bottle, Möbius strip and cylinder are considered. By establishing a Pfaffian orientation or a crossing orientation, and then computing the determinants of the skew-symmetric matrices of the resulting orientation graphs, we obtain explicit expressions of the number of close-packed dimers of the Klein-bottle polyhex, the Möbius polyhex and the cylindrical polyhex.     

锥形光纤激发盘腔光学模式互易性研究

光学谐振腔由于其高Q值特性,作为谐振式陀螺的核心元件,有望实现谐振式陀螺的小型化、集成化,但是非互易性噪声成为制约其精度提高的不利因素. 介绍了采用传统半导体工艺制备的盘型腔与熔融法拉制的锥形光纤组成的耦合系统. 当盘型腔在光纤锥区的不同位置进行耦合谐振时,将输入输出正/反对调,观察到输出透射谱发生偏差,谐振频率、耦合效率以及Q值均发生变化,即存在非互易性现象. 用Rsoft软件对锥形光纤倏逝场分布特性进行仿真,理论分析了非互易性产生的原因. 以此可抑制谐振式光学陀螺应用中由锥形光纤与谐振腔组成的耦合系统产生的非互易性噪声. 关键词： 光学谐振腔 锥形光纤 非互易性 谐振式陀螺     

Highly selective surface-wave resonators for terahertz frequency range formed by metallic Bragg gratings

In the frame of the quasi-optical approach we solve the diffraction problem and describe surface modes confined at a metallic plate with a shallow grating of finite length. We prove that such planar grating can form a highly selective surface-wave Bragg resonator. For a given material conductivity and grating length, we find the optimum corrugation depth that provides the maximum value of Q factor. These results are applicable for developing resonators for terahertz frequency bands.     

光梯度力驱动的纳米硅基光开关

通过一道光改变另一道光的传输路线是光子集成网络中重要而长远的目标, 然而, 由于硅材料的光学非线性较弱, 在硅材料上实现开关的全光控制难以实现. 因此本文提出了一种由光梯度力驱动的纳米硅基光开关, 实现了硅基光开关的全光控制. 该光开关由一个部分悬空的微环谐振器和一个交叉波导结构构成, 当通入一道控制光时, 悬空的微环谐振器在光梯度力的作用下发生弯曲, 微环谐振器的谐振波长随之发生变化, 从而实现光信号的传输路线发生改变. 该光开关利用纳米光子制造技术在标准绝缘体上硅晶圆上制造, 实验数据得出其最小消光比为10.67 dB, 最大串扰为 -11.01 dB, 开关时间分别为180 ns和170 ns. 该光开关具有尺寸小, 响应速度快, 低损耗和可拓展等优点, 在片上集成光路、高速信号处理以及下一代光纤通信网络中具有潜在应用.     

非线性薛定谔方程N孤子数值解的递归算法

本文介绍一种新的求非线性薛定谔方程(NLS方程)N孤子数值解的方法,它是一种递归的计算方法。在实际计算过程中,该方法不但可以得到很好的孤子图像,而且简单、迅速,可以节省大量计算时间。     

Modified surface plasmonic waveguide formed by nanometric parallel lines

In this paper, two kinds of modified surface plasmonic waveguides formed by nanometric parallel lines are proposed. The finite-difference frequency-domain method is used to study propagation properties of the fundamental mode supported by these surface plasmonic waveguide structures. Results show that the transverse magnetic field of the fundamental mode is mainly distributed in the face to face region formed by two rods. With the same geometrical parameters and the same working wavelength of 632.8~nm, in the case of rods with a triangular cross-section, the degree of localization of field is strong, i.e. the mode area is small, but the fraction of the modal power in the metal increases, so the effective index increases and the propagation length of the mode decreases. With the same geometrical parameters, relative to the case of a working wavelength of 632.8~nm, when working wavelength is large, the mode area of transverse magnetic field distribution is large, i.e. the degree of localization of field is weak, and the interaction of field and silver is weak too, then the effective index decreases, so the propagation length increases. The rounded radii of rods have a great influence on the performance of the surface plasmonic waveguides with rounded triangular cross-sections, but have little influence on the performance of surface plasmonic waveguides with rounded square cross-sections. Since the distribution of transverse magnetic field, effective index, propagation length and the mode area can be adjusted by the geometrical parameters, this kind of modified surface plasmonic waveguide can be applied to the field of photonic device integration and sensors.     

Suppression of Chaotic Generation Caused by the External Optical Feedback in a Laser Diode

It is shown by computer simulation and in experiments that chaotic generation caused by the external optical feedback in a laser diode can be suppressed by means of a delayed optoelectronic feedback controlled by the injection current. The suppression of chaotic generation is realized for an AlGaAs/GaAs laser of the quantum wall structure. In the presence of the external optical feedback provided by the mirror placed at a distance of 1~mm the noise of optical intensity is of the oder of 10 W, the single mode dominates in the spectrum, and its spectral width exceeds 600 MHz. The optoelectronic feedback controlled by the injection current reduces the noise by several times and narrows the generation line width down to 80 MHz.     

高斯光束与谐振腔基模模式光路谐振匹配的分析与校准

为了降低高斯光束与谐振腔耦合过程中失调量和失配量对基于无源谐振腔测量技术精度的影响, 采用高斯光束变换规律、模式耦合有关理论以及光束传播坐标变换等相关理论, 就失调量和失配量对基模耦合效率的影响分别进行分析和模拟, 并据此给出了一般情况下两个参考量同时存在时基模耦合效率的表达式. 分析表明: 失配量的存在主要影响激光器与谐振腔的耦合效率, 而对高阶模式的激发影响较小, 因此对谐振腔的衰减线型影响较小; 失调量的存在对谐振腔高阶模式的激发起主要作用, 给测量带来严重误差. 该结论为利用腔出射光信号来确定误调参量值的实验方案提供了依据. 因此, 在考虑光源光谱线宽的情况下, 就光源光谱线宽的特性提出两种装调校准方案: 基于法布里-珀罗干涉仪法和基于多维象限探测器探测谐振腔出射光的调节回路, 这将为分析基于无源谐振腔的相关技术测量误差来源以及实现测量系统的高精度装调提供理论指导.     

Torus maps and the problem of a one-dimensional optical resonator with a quasiperiodically moving wall

We study the problem of the asymptotic behavior of the electromagnetic field in an optical resonator one of whose walls is at rest and the other is moving quasiperiodically (with d≥2 incommensurate frequencies). We show that this problem can be reduced to a problem about the behavior of the iterates of a map of the d-dimensional torus that preserves a foliation by irrational straight lines. In particular, the Jacobian of this map has (d−1) eigenvalues equal to 1. We present rigorous and numerical results about several dynamical features of such maps. We also show how these dynamical features translate into properties for the field in the cavity. In particular, we show that when the torus map satisfies a KAM theorem—which happens for a Cantor set of positive measure of parameters—the energy of the electromagnetic field remains bounded. When the torus map is in a resonant region—which happens in open sets of parameters inside the gaps of the previous Cantor set—the energy grows exponentially.     

A proposal for the generation of optical frequency comb in temperature insensitive microcavity

We numerically simulate the generation of an optical frequency comb(OFC) in a microring based on the traditional Si_3N_4 strip waveguide and a temperature compensated slot waveguide.The results show that OFCs are susceptible to temperature with strip waveguide while they can keep stable when temperature changes 10 Kin either low-Q(10~5) or highQ(10~6) microcavity with the well-designed slot waveguide,which has great superiority in practical applications where the temperature drift of the cavity due to the intense pump or surrounding change is unavoidable.     

Efficient suppression of radiation damping in individual plasmonic resonators: towards high‐Q nano‐volume sensing

Recent results on radiation damping suppression in individual plasmonic resonators using conformal bending of the structure, which suppresses the electric‐dipole response in favor of magnetic dipole one, are overviewed. It is demonstrated that bending of linear plasmonic nano‐antennas increases significantly their Q factors above the electrostatic limit while preserving the nature of resonance along with its exceptional features, such as linear size‐dependent tunability and robust field enhancement. The approach, which makes use of strong lateral confinement exhibited by the slow plasmonic modes (slow‐SPPs) bound to ultra‐narrow metallic structures, turned out to be quite general, and its experimental demonstration has been attained with circularly curved nano‐rod antennas. Furthermore, this approach suggested novel configurations of plasmonic single particle nanosensing with enhanced features, allowing record‐high figures of merit along with unprecedented spatial resolution in nanofiber‐based split‐cylinder structures.     

准光腔品质因数的标网测量与研究

采用标量网络分析仪(SNA)对毫米波段的Fabry-Perot准光腔进行了品质因数测定。通过纵向半波数的测试确定了谐振峰对应的模式,给出了AV3617测量数据并计算了相应的外观品质因数和固有品质因数,详细分析了扫频测试的误差及其误差来源。分析表明,半功率点的频率测定误差是引起准光腔品质因数测量误差的主要因素;利用扫频源HP83630A较高的频率分辨率,结合参考频标使测试数据的有效位数增加,从而提高了测试准光腔品质因数的精度。     

Two-Frequency Brillouin Fiber Laser Controlled by Temperature Difference in Fiber Ring Resonator

A Brillouin fiber laser (BFL) consisting of a fiber ring resonator with different fiber temperatures emits two-frequency light output. The two-frequency BFL yields an optical beat output which can be utilized as an optical frequency shifter. The output beat frequency is controllable by the temperature difference in the fiber ring resonator and changes with a step of a resonant frequency interval of BFL. The temperature dependence of the BFL output frequency was 2.4 MHz/°C. The stability of the output beat frequency to the temperature fluctuation was estimated as 1.04°C/2.5 MHz.     

Atomistic study of the pressure-induced phase-transition mechanism in GaAs by Möbius inversion potentials

In this work, the phase transition from zincblende (B3) to rocksalt (B1) structure in bulk GaAs is investigated by using Möbius inversion potentials. A Cm transition path is proposed from the molecular static simulation results, even though it is different from previously proposed transition paths Imm2, R3m and P3₂. The present Cm path is quite close to the previously suggested Imm2 path according to the crystal cell geometries and activation enthalpies. By comparison, the activation enthalpies along the R3m and P3₂ path are relative high. Therefore, the Imm2 mechanism, as a simplified model of the Cm one, is suggested to describe the microscopic process of the B3-B1 phase transition of GaAs. In this way, we investigate the changes of the system features during the transition process characterized by Imm2 mechanism and obtain a concise picture for the common B3-B1 transition. All the calculated results are compared to relevant experimental observations and other calculations.     

Systematical study of the trapping forces of optical tweezers formed by different types of optical ring beams

The technique of optical tweezers has been improved a lot since its invention, which extends the application fields of optical tweezers. Besides the conventionally used Gaussian beams, different types of ring beams have also been used to form optical tweezers for different purposes. The two typical kinds of ring beams used in optical tweezers are the hollow Gaussian beam and Laguerre--Gaussian (LG) beam. Both theoretical computation and experiments have shown that the axial trapping force is improved for the ring beams compared with the Gaussian beam, and hence the trapping stability is improved, although the transverse trapping forces of ring beams are smaller than that of Gaussian beam. However, no systematic study on the trapping forces of ring beam has ever been discussed. In this article, we will investigate the axial and transverse trapping forces of different types of ring beams with different parameters systematically, by numerical computation in which the ray optics model is adopted. The spherical aberration caused by the refractive index mismatch between oil and water is also considered in the article. The trapping forces for different objectives that obey the sine condition and tangent condition are also compared with each other. The result of systematical calculation will be useful for the applications of optical tweezers formed by different types of ring beams.     

All-optical control of the time delay in a one-dimensional photonic bandgap formed by double-quantum-wells

In this work, we show the feasibility of all-optical control of time delay in a Bragg grating with an active defect that consists in an asymmetric double quantum-well GaAs/Al_xGa_1−xAs. The double quantum-well is modeled as a Λ-V-type four level system. The refractive index of the defect can be modified by a control field due to the tunneling-induced quantum interference. It is shown that index changes as large as 0.4 can be obtained via cross-phase modulation. This allows for the development of a propagating mode at the selected wavelength. The existence of the mode permits the slow-down of light pulses, thus the system may act as a delay line with a group index as high as 100 operating at bandwidths of tens of GHz. We demonstrate that this defective photonic bandgap structure could enable ultrafast and ultrasensitive nonlinear all-optical switching at moderate powers of the control field.     

Surface Plasmon Resonance of Au Nanoparticles Fabricated by Negative Ion Implantation and Grid Structure toward Plasmonic Applications

Optical properties of Au nanoparticle composites and a grid structure of Cu nanoparticle composite were studied. Negative ion implantation was applied to synthesize Au and Cu nanoparticles in amorphous SiO₂ and Al₂O₃. Au nanoparticles were embedded within a depth of 30 nm by 60keV Au⁻ implantation. The surface plasmon resonance (SPR) of Au:SiO₂ and Au: Al₂O₃ composites shifted to red and to blue, respectively, compared to calculated ones by the Mie theory. Optical nonlinearity was measured with pump-probe femtosecond spectroscopy and the transient spectrum of Au: Al₂O₃ composite presented a large red shift from the SPR peak. Image mapping of far-field transmitted intensity of Cu-implanted SiO₂ with a fine grid structure drawn by laser-lithography was observed by a scanning near-field optical microscopy (SNOM) system.     

基于加权能量集中度的光条成像质量评价方法研究

线结构光视觉传感器的光条成像质量是判断摄像机曝光时间设置是否合适,系统能否达到最佳测试精度的重要因素。从横截面近似高斯分布的光条出发,综合考虑影响能量集中度的峰值灰度和光条宽度,提出了一种基于加权能量集中度的光条像质量评价方法。光条图像和背景图像作差获取差分图像,提取光条直线方程并根据法线方向旋转差分图像使得光条完全垂直于图像水平轴,获取光条的截面灰度分布情况,并计算加权能量集中度,根据经验阈值判断光条成像的质量。实验表明,随着曝光时间加大,加权能量集中度在数值上先增大后减小,因此通过阈值可以很好地评价光条成像质量。     

微腔效应对顶发射串联蓝光有机电致发光器件性能的影响

相比于传统有机电致发光器件,串联有机电致发光器件的发光效率与寿命均得到明显提升.因此,深入研究微腔效应对顶发射串联有机电致发光器件性能的影响具有重要意义.本文以蓝光器件为例,通过光学仿真模拟与实际实验相结合的方法,研究了顶发射串联蓝光器件的光学性能与电学性能变化规律.具体实验为:分别制备了顶发射串联蓝光器件,使其两个发光层位置分别位于器件光学结构中的第一与第二反节点、第二与第三反节点、第三与第四反节点.分析并确定了顶发射串联蓝光器件的两个发光层位置分别位于第二反节点与第三反节点处时,器件性能较佳.即:当器件电流密度为15 mA/cm^2时,器件电流效率为10.68 cd/A(色坐标CIEx,y=0.14,0.05),其亮度衰减到95%所需时间为1091.55 h.可能原因是:器件腔长较长时,既可以改善第一发光单元的空穴与电子平衡度、削弱表面等离激元效应,降低膜厚波动性对器件腔长的影响性;又可以在一定程度内起到包裹Partical的作用,提高效率,延长寿命.这一研究成果为设计高效率、长寿命的顶发射串联器件提供了重要依据.