Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.

Composite second-order performance improvement in optical fibre CATV transmission system using chirped fibre grating

Theoretically, we analyse the dispersion compensation characteristics of the chirped fibre grating (CFG) in an optical fibre cable television (CATV) system and obtain the analytic expression of the composite second-order (CSO) distortion using the time-domain form of the field envelope wave equation. The obtained result is in good agreement with the numerical simulation result. Experimentally, we verify the result by making use of the tunable characteristics of CFG to change the dispersion compensation amount and obtain an optimal CSO performance in a 125km fibre transmission link. Both the theoretical and experimental results show that the CSO performance can be improved by properly choosing the dispersion compensation amount for a certain fibre transmission link.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Polarization-dependent Talbot effect

The term "polarization-dependent Talbot effect" means that the Talbot self-imaging intensity of a high-density grating is different for TE and TM polarization modes. Numerical simulations with the finite-difference time-domain method show that the polarization dependence of the Talbot images is obvious for gratings with period d between 2 lambda and 3 lambda. Such a polarization-dependent difference for TE and TM polarization of, a high-density grating of 630 lines/mm (corresponding to d/lambda = 2.5) is verified through experiments with the scanning near-field optical microscopy technique, in which a He-Ne laser is used as its polarization is changed from the TE mode to the TM mode. The polarization-dependent Talbot effect should help us to understand more clearly the diffraction behavior of a high-density grating in nano-optics and contribute to wide application of the Talbot effect. (c) 2006 Optical Society of America.

Talbot effect of a grating with different kinds of flaws

The Talbot effect of a grating with different kinds of flaws is analyzed with the finite-difference time-domain (FDTD) method. The FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to obtain with the conventional Fourier transform method. The numerical results indicate that if a grating is perfect, its Talbot imaging should also be perfect; if the grating is distorted, its Talbot imaging will also be distorted. Furthermore, we evaluate high-density gratings by detecting the near-field distribution with the scanning near-field optical microscopy technique. Experimental results are also given. (c) 2005 Optical Society of America.

双折射晶体时域电光综合器

提出了一种利用电光双折射网络实现的光波波形综合器。该综合器由偏振器、多块具有电光效应的双折射晶体和补偿器组成，输入余弦信号，组成一多级电光双折射网络。利用琼斯理论对该综合器进行了理论分析，根据扩展傅里叶级数系数正向对比法，实现了其他类型的周期性时域波形。给出一类三元综合器的分析与设计方法，得到合成矩形波与三角波所需的多组结构参量，并对输入信号误差及方位角误差对波形的影响进行了分析。

FDTD analysis of Talbot effect of a high density grating

Talbot effect of a grating with different flaws is analyzed with the finite-difference time-domain (FDTD) method. The FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to obtain with the conventional Fourier transform method. The numerical results indicate that if a grating is perfect, its Talbot imaging should also be perfect; if the grating is distorted, its Talbot imaging would also be distorted. Furthermore, we can evaluate high density gratings by detecting the near-field distribution.

Measuring temporal fluctuation on femtosecond scale in a random medium

We report an observation of femtosecond optical fluctuations of transmitted light when a coherent femtosecond pulse propagates through a random medium. They are a result of random interference among scattered waves coming from different trajectories in the time domain. Temporal fluctuations are measured by using cross-correlated frequency optical gating. It is shown that a femtosecond pulse will be broadened and distorted in pulse shape while it is propagating in random medium. The real and imaginary components of transmitted electric field are also distorted severely. The average of the fluctuated transmission pulses yields a smooth profile, probability functions show good agreement with Gaussian distribution. (c) 2007 Elsevier B.V. All rights reserved.

一种使用双棱镜的动态小角度测量方法

提出一种基于正切关系和相位调制技术的动态小角度测量方法。使用双棱镜组成干涉测量臂引导两束平行光至分束棱镜处干涉,通过提取携带被测信息的干涉信号的相位实现动态的小角度测量。由于采用位置探测器(PSD)对测量臂中两平行光束的间距进行测量,简化了测量方程,消除了装置中双棱镜必须对称放置的要求。通过正弦地改变半导体激光器的注入电流在时域内实现对干涉信号的相位调制,形成准外差干涉测量模式,提高了光程差的测量精度。实验验证了该方法的可行性,并讨论了影响小角度测量精度的误差因素。研究结果表明,基于该方法的动态小角度的重

Phase interpretation for polarization-dependent near-field images of high-density gratings

It has been described that the near-field images of a high-density grating at the half self-imaging distance could be different for TE and TM polarization states. We propose that the phases of the diffraction orders play an important role in such polarization dependence. The view is verified through the coincidence of the numerical result of finite-difference time-domain method and the reconstructed results from the rigorous coupled-wave analysis. Field distributions of TE and TM polarizations are given numerically for a grating with period d = 2.3 lambda, which are verified through experiments with the scanning near-field optical microscopy technique. The concept of phase interpretation not only explains the polarization dependence at the half self-imaging distance of gratings with a physical view, but also, it could be widely used to describe the near-field diffraction of a variety of periodic diffractive optical elements whose feature size comparable to the wavelength. (C) 2008 Elsevier B.V. All rights reserved.

Esporte contemporâneo: um novo templo do capital monopolista

Esta pesquisa teve por objetivo abrir uma discussão sobre o papel do esporte contemporâneo junto ao processo de alienação humana em tempos de domínio do capitalismo monopolista e do fortalecimento da ideologia dominante. Para tal, no primeiro capítulo, analisou-se as principais transformações vividas historicamente pelo capitalismo com a intenção de identificar o impacto do capitalismo monopolista sobre o novo ordenamento da humanidade. No segundo capítulo, demonstrou-se como o esporte contemporâneo constituiu-se como uma instituição burguesa, socialmente determinada e integrada ao conjunto de normas, ideias e estratégias inerentes ao modo de produção capitalista, participando do processo de mascaramento da questão social. Destaca-se neste capítulo o uso de fontes documentais que demonstraram como o esporte contemporâneo tem ocupado lugar estratégico tanto junto à produção da ideologia dominante, quanto junto ao controle da queda da taxa de lucro. Identificou-se que sob tais condições o esporte contemporâneo compõe os processos compensatórios frente à queda tendencial da taxa de lucro e, ao mesmo tempo, integra-se ao processo de alienação humana, tendo por maior expressão a sua materialização sob a forma dos megaeventos esportivos. Neste ponto, a pesquisa concentra-se na análise dos megaeventos esportivos no Brasil e na criação das políticas do esporte, desde o primeiro governo Lula da Silva até os dias atuais. Identificou-se que os projetos de desenvolvimento do esporte no país, no período em tela, têm participado do processo de gerenciamento da crise do capital e do refluxo das lutas dos trabalhadores. O último capítulo abordou as particularidades que envolvem a ideologia pós-moderna, tendo por objetivo identificar as relações desta com fenômeno esportivo. Constatou-se que, em tempos de domínio do capitalismo monopolista e de suas políticas neoliberais, as contradições que aguçam o processo de alienação sob o qual encontra-se a classe trabalhadora de todo o mundo, coloca a humanidade em um novo patamar de alienação, ainda mais brutal e desumanizador. Nesta conjuntura, o esporte contemporâneo destaca-se por ser funcional tanto ao mercado globalizado, quanto ao projeto imperialista, impondo-se como instrumento da contenção de conflitos em nome da tolerância e da paz no mundo. A presente pesquisa pôde concluir que as condições impostas pela fase monopolista do capitalismo ocultam a natureza dialética do esporte transforma-o num instrumento eficiente ao projeto dominante de incremento da alienação humana. O esporte, sob a forma assumida na contemporaneidade, não contribui para o avanço da consciência da classe trabalhadora, pois vem colaborando para adiamento do projeto de emancipação da humanidade. Projeto este que só será produzido pela organização consciente da classe trabalhadora em busca da superação do modo de produção capitalista.

飞秒脉冲通过散射表面后的时域特性

从理论上和实验上对飞秒激光脉冲通过散射表面后的时域特性进行了研究分析。用频率分辨光学开关法对通过散射表面前后的飞秒脉冲进行了测量和对比。理论分析和实验结果表明, 由于散射表面对飞秒脉冲的散射导致飞秒脉冲的展宽和形状的畸变。输入脉冲在时间相关函数的半峰全宽为64 fs; 透射脉冲在时间相关函数半峰全宽的平均值为117 fs。对透射脉冲场的统计特性进行了讨论, 透射脉冲场实部和虚部的概率函数分布遵从高斯函数分布; 强度的概率分布遵从指数分布规律; 给出了入射飞秒脉冲强度的自相关函数分布和飞秒时域散斑场强度的互相关函数分布的实验结果, 并且对二者的时间相关函数进行了讨论。

Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal

In this paper we theoretically study the left-handed behaviors in a two-dimensional triangular photonic crystal made of elliptical rods in air. An absolute left-handed region is found in the second photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Typical left-handed behaviors such as negative refraction, flat superlensing and plano-concave lensing are demonstrated by the finite-difference time-domain simulations. These behaviors are also compared with the quasi-negative refraction and the resulted focusing effects in a square-lattice two-dimensional photonic crystal. (c) 2005 Optical Society of America

Subwavelength imaging with two symmetrical interfaces by dielectric-tube photonic crystals

As distinct from coated photonic crystals, in this paper we propose a novel one that is made of dielectric tubes arranged in a close-packet square lattice. Without metallic cores, this structure is low-loss and convenient to fabricate. A left-handed frequency region is found in the second band by dispersion characteristic analysis. Without inactive modes for the transverse electric mode, negative refraction and subwavelength imaging are demonstrated by the finite-difference time-domain simulations with two symmetrical interfaces, i.e. Gamma X and Gamma M.

基于电光调制的激光光谱整形技术

提出了一种新型的基于电光调制的激光光谱整形方案，该整形技术可以减轻啁啾脉冲放大系统中的增益窄化效应。傅立叶变换限的宽带种子激光脉冲通过光学展宽器线性展宽后，耦合到加载有整形电脉冲的集成波导调制器中进行整形，整形电脉冲由孔径耦合带状线电脉冲发生器产生。由于线性啁啾脉冲时间-频率的直接对应关系，在时域内对宽带种子激光脉冲整形，其光谱也得到了同样形状的整形。模拟了整形光谱形状，相应的整形电脉冲波形，分析了该整形技术的光谱整形分辨率，以及整形过程中引入的相位畸变。