Femto-Second Transform Limited Pulse Generation with Higher Order Dispersion Effects for Dispersion-Shifted Optical Communication System

The paper deals with the influence of higher-order effects of dispersion on the femto-second transform limited pulse generation by compensating for linear chirp of self-phase modulation spectra in the dispersion-shifted fibers. It has been shown that the minimum propagation length with first-order dispersion term is 23 m, as reported earlier. If the higher-order dispersion effects are taken into consideration, this length is reduced to 11.5 m. With compensation of the first-order dispersion term, this length can be enhanced to 6.8161 × 10³ km. This length can further be improved to 6.0343 × 10⁹ km by compensation of first- and second-order dispersion terms together. The minimum pulse width and linewidth product without dispersion, with dispersion including higher-order dispersion effects, and with dispersion compensation, is found to be 0.44, 0.4418, and 0.4411, respectively.     

微扰论与平均Hamiltonian理论Ⅰ.场相关化学位移

本文应用平均Hamiltonian理论讨论了异核偶极相互作用引起的场相关化学位移,对照二阶微拢论的结果,发现计入了"A"项的额外影响。说明在讨论非久期项效应时,一级平均Hamiltonian比只用二阶微扰论的结果更精确。文中,应用平均Hamiltonian理论还讨论了同核偶极相互作用产生的场相关化学位移。     

Femto-Second Transform Limited Pulse Generation with Higher Order Dispersion Effects for Dispersion-Shifted Optical Communication System

The paper deals with the influence of higher-order effects of dispersion on the femto-second transform limited pulse generation by compensating for linear chirp of self-phase modulation spectra in the dispersion-shifted fibers. It has been shown that the minimum propagation length with first-order dispersion term is 23 m, as reported earlier. If the higher-order dispersion effects are taken into consideration, this length is reduced to 11.5 m. With compensation of the first-order dispersion term, this length can be enhanced to 6.8161 × 10³ km. This length can further be improved to 6.0343 × 10⁹ km by compensation of first- and second-order dispersion terms together. The minimum pulse width and linewidth product without dispersion, with dispersion including higher-order dispersion effects, and with dispersion compensation, is found to be 0.44, 0.4418, and 0.4411, respectively.     

KdV孤子的含时微扰理论

研究了周期性含时微扰对KdV(Korteweg de Vries)孤子的影响. 将微扰项展为时间变量的傅里叶级数,发现其常数项是导致长期项的根源. 在一阶近似下,消除长期项,求出了孤子参数(高度、宽度和速度)随时间的缓慢变化. 傅氏级数中的其他项决定了微扰对孤子波形的一阶修正. 关键词： KdV孤子 孤子微扰论     

Polariton resonant absorption in a bigrating: Exact theory compared to recent experiments and to perturbation theory

A nonperturbative theory of light scattering from a bigrating, with resonant excitation of surface polaritons, has been implemented to fit the results of a recent experiment. The experiment measured light absorption in Ag, with results that showed some discrepancies with first-order perturbation theory — particularly at 2-polariton peaks. The exact theory has accounted for some but not all of the discrepancies, indicating that their cause is not entirely due to perturbation theory's underestimating higher-order processes. A comparison of the Fourier coefficients of the surface profile function as determined by the two theories indicates that perturbation theory may develop problems in dealing with the cross-terms in the expansion of 2-dimensional profiles, even for small corrugation strengths.     

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Accelerated higher order radiative perturbation computation: an application of GDOM

In a previous paper by the authors, the computational expressions for the higher order terms of the radiative perturbation series have been developed, and numerical results have been obtained. In this paper, new computational expressions are developed that use the analytic Green's function and the GDOM code, which were developed recently by Qin and Box. Our analysis and numerical computations indicate that the new scheme dramatically improves the efficiency of the computation (by reducing the CPU-time to less than 2% of that required by the previous scheme), and the huge demand on memory usage has been completely removed. This new scheme allows us to expand the high order perturbation computations to more general cases, for example, to include azimuth dependence, and to use the perturbation theory in more potential applications.     

Improved uncoupled Hartree-Fock perturbation theory

Various uncoupling schemes used in the first-order Hartree-Fock perturbation theory are compared. The analysis and extraction of the most important terms in the coupled Hartree-Fock perturbation scheme leads to a definition of the new functional for the determination of the first-order perturbed orbitals. This new functional represents an alternative uncoupling scheme for the first-order Hartree-Fock perturbation theory. Some special cases of real and pure imaginary perturbations and also the connections with previously proposed uncoupling schemes are discussed.

The uncoupling procedure proposed in this paper is illustrated by electric dipole polarizability calculations for some Be- and Ne-like atomic systems. The results obtained are almost as good as those calculated by using coupled Hartree-Fock perturbation theory.     

EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS

A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.     

Quantum backreaction of quantum fluid in Bose Einstein condensates

In this paper, with the full field operator \hat ψ expressed in terms of a particle-number-conserving mean-field ansatz, we investigate the dynamical behaviour of Bose--Einstein condensates from microscopic physics. Including the first-order term correction from single-particle excitation and the remaining higher-order term correction from collective excitations simultaneously, we obtain the formulation for a closed local expression of quantum backreaction Q, and discuss the influence on static Bose--Einstein condensates. Even though the quantum backreaction is small, it still has some influence on its dynamics.     

What is measured in the scanning gate microscopy of a quantum point contact?

The conductance change due to a local perturbation in a phase-coherent nanostructure is calculated. The general expressions to first and second order in the perturbation are applied to the scanning gate microscopy of a two-dimensional electron gas containing a quantum point contact. The first-order correction depends on two scattering states with electrons incoming from opposite leads and is suppressed on a conductance plateau; it is significant in the step regions. On the plateaus, the dominant second-order term likewise depends on scattering states incoming from both sides. It is always negative, exhibits fringes, and has a spatial decay consistent with experiments.     

Calculation of the interruption function in the third order of the perturbation theory

A procedure for calculating the higher-order contributions of the perturbation theory to the interruption function S(b) is considered, and the final expressions for the third-order terms are derived. It is shown that, in the general case, the new resonance functions for the higher orders of the interruption function can be obtained by the Fourier transform of the coefficients of the intermolecular interaction potential.     

Global square-well free-energy model via singular value decomposition

ABSTRACT

The free energy of the square-well (SW) fluid is a quantity of great interest in thermodynamics and statistical mechanics. Several authors have calculated by simulations the first four terms in the high-temperature perturbation expansion for SW ranges from λ = 1 up to λ = 2.5 or 3. Besides, the asymptotic form of the first two terms in the expansion, for λ large, is known analytically. The information gathered so far seems to indicate that a range of λ = 3 is not far from this asymptotic van der Waals regime. In this work, we use the technique of singular value decomposition (SVD) to provide us with expressions of the SW free energy valid for all ranges of 1 ≤ λ and, for the higher-order terms, covering the density range upto the random close-packed state. Besides rendering unified expressions of the free energy for all ranges, the SVD allows us to separate the perturbation terms into a sum of products of functions of density and range, so that one can discern the most important contributions and extract the underlying density and range profiles.     

Cumulative solutions of nonlinear longitudinal vibration in isotropic solid bars

Based on the strain invariant relationship and taking the high-order elastic energy into account, a nonlinear wave equation is derived, in which the excitation, linear damping, and the other nonlinear terms are regarded as the first-order correction to the linear wave equation. To solve the equation, the biggest challenge is that the secular terms exist not only in the fundamental wave equation but also in the harmonic wave equation （unlike the Duffing oscillator, where they exist only in the fundamental wave equation）. In order to overcome this difficulty and to obtain a steady periodic solution by the perturbation technique, the following procedures are taken： （i） for the fundamental wave equation, the secular term is eliminated and therefore a frequency response equation is obtained; （ii） for the harmonics, the cumulative solutions are sought by the Lagrange variation parameter method. It is shown by the results obtained that the second- and higher-order harmonic waves exist in a vibrating bar, of which the amplitude increases linearly with the distance from the source when its length is much more than the wavelength; the shift of the resonant peak and the amplitudes of the harmonic waves depend closely on nonlinear coefficients; there are similarities to a certain extent among the amplitudes of the odd- （or even-） order harmonics, based on which the nonlinear coefficients can be determined by varying the strain and measuring the amplitudes of the harmonic waves in different locations.     

Further Theoretical Investigations for Laser Relative Intensity Noise with Fiber Nonlinearities and Higher-Order Dispersion

In this article, we theoretically investigate relative intensity noise (RIN) in optical communication systems with fiber nonlinearities due to optical Kerr effects and higher-order dispersion. The impact of modulation frequencies, launch power, and laser bias current on RIN has been illustrated. We show that RIN increases with modulating frequencies up to the resonance frequency, launch power, and decrease in the laser bias current. We also show that higher-order dispersion terms have no impact on the RIN, but with first-order dispersion compensation the higher-order dispersion terms have significant impact at high modulating frequencies. The RIN with and without fiber nonlinearities is further investigated. It has been shown that the RIN with fiber nonlinearity is more than the RIN without nonlinearity and the effect of nonlinearity appears at higher modulation frequencies only.     

Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method

In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the first-order solvability condition. The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.     

Comparative Study on Large and Small Signal Theory for Intensity Modulation Response of Semiconductor Lasers Including Higher-Order Dispersion Terms

In this article, the comparison of large signal theory and small signal theory has been done with dispersive propagation of optical signal with IMDD (Intensity Modulation Direct Detection) systems for semiconductor lasers with higher-order dispersion terms. The expressions for an exact large signal theory and small signal theory including higher-order dispersion terms for propagation of an optical wave with sinusoidal amplitude and frequency modulation in a dispersive fiber have been derived. It is observed that small signal theory is more sensitive compared to large signal theory in terms of intensity modulation/direct detection systems. Also, it is reported that for large signal analysis the higher-order effects of dispersion can be ignored, whereas for small signal theory, the higher-order effects can be ignored for lower modulation frequencies only. The variation in the transfer function for various values of modulation indices are greater for small signal analysis than for large signal analysis. Also, as the intensity modulation index is increased, there is a decrease in the value of transfer function. The large signal model approximates the small signal model for lower values of the intensity modulation index.     

Fermi energy of a metal nanowire with elliptical cross section

The influence of the geometrical shape of the cross section on the energy characteristics of a metal nanowire has been investigated theoretically. The size oscillations of the Fermi energy have been calculated within the model of an infinite potential well in terms of the perturbation theory. The calculations have been carried out for Au and Al. It has been shown that the cross-sectional ellipticity with a low eccentricity can be taken into account in the first-order perturbation theory by modifying the boundary conditions for the radial wave function of electrons.