Influence of the polarization mode dispersion on the propagation of ultrashort optical pulses in single-mode fiber lightguides with very weak linear birefringence and random inhomogeneities

We consider the influence of the polarization mode dispersion, which is stipulated by the presence of random inhomogeneities in single-mode fiber lightguides, on the propagation of ultrashort optical pulses in the fiber communication lines with very weak linear birefringence. Evolution of the envelope of ultrashort optical pulses and their spectra as functions of the length of a single-mode fiber lightguide with very weak linear birefringence and random inhomogeneities are obtained by the method of mathematical simulation. An increase in the pulse duration is shown to be proportional to the square root of the length of a single-mode fiber lightguide. The numerical-simulation results are compared with the results of experimental measurements of the polarization mode dispersion.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XII. Dependence of the zero drift in fiber ring interferometers in orthogonal polarization modes on the range of temperature variation in an optical fiber

Temperature dependences of the zero drift in a fiber ring interferometer (FRI) without a polarizer in the presence of random inhomogeneities in a single-mode optical fiber in the FRI loop are obtained by numerical simulation. The results are compared with known experimental data. It is shown that FRIs using a superluminescent diode as a source of nonmonochromatic radiation and a loop made of a single-mode optical fiber with weak linear birefringence can find application as low-accuracy fiber-optic gyroscopes and FRIs with a loop made of a single-mode optical fiber with strong linear birefringence can be used as medium-accuracy fiber-optic gyroscopes.     

Increase in the correlation length of nonmonochromatic radiation during propagation in a single-mode optical fiber containing random inhomogeneities and the influence of this increase on the operation of a fiber ring interferometer

An analysis is made of the conditions under which the coupling of orthogonal polarization modes at random inhomogeneities in single-mode optical fibers leads to an increase in the correlation length of a source of nonmonochromatic radiation. It is shown that when long-base fiber ring interferometers with a single-mode fiber ring system possessing weak linear birefringence are used, the correlation length of the nonmonochromatic radiation at the interferometer exit is increased, which means that the interference pattern can have satisfactory visibility even when there is an appreciable difference between the interferometer arms as a result of the Sagnac effect due to the Earth’s rotation. The calculations were made by mathematical modeling of random inhomogeneities in the fiber. Zh. Tekh. Fiz. 69, 140–143 (July 1999)     

Mode Structure and the Envelope of a Short Pulse in a Graded-Index Optical Fiber with a Longitudinal Inhomogeneity and a Spatial Bending

We consider propagation of a short optical pulse in an optical fiber whose refractive index is strongly dependent on the radial coordinate and is weakly dependent on the longitudinal coordinate with allowance for the possible weak spatial bending of the fiber axis. The three-dimensional nonlinear wave equation modelling the pulse propagation is solved asymptotically with respect to a small parameter specifying the order of magnitude of the pulse amplitude. A relationship between the propagating modes and the eigenvalues and eigenfunctions of the singular Sturm-Liouville problem is established. The pulse propagation is shown to have three scales: the high-frequency carrier is modulated by the envelope which evolves in a two-scale manner and is described by a nonlinear Schrödinger equation whose coefficients depend on the longitudinal coordinate. The transverse distribution of the wave field and the envelope soliton are obtained in terms of elementary functions for several types of transverse and longitudinal inhomogeneities of the fiber. The possibility of controlling the pulse parameters by varying the transverse and longitudinal inhomogeneities of the fiber is pointed out.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XV. Dependence of integral statistical parameters of polarization modes in single-mode optical fibers with random inhomogeneities on the wavelength of light

Spectral dependences of integral statistical elements of the Jones matrix of an extended segment of a single-mode optical fiber (SMOF) with random inhomogeneities, whose length considerably exceeds the correlation length of random inhomogeneities, are found by the method of mathematical modeling. The boundaries of the ranges of optical wavelengths are determined, within the limits of which the parameters under consideration remain quasi-constant. This allows the derivation of analytical expressions for the degree of polarization of nonmonochromatic radiation in an SMOF and for the zero drift in fiber ring interferometers with the help of the approximate method of small perturbations. It is shown that the small-perturbation method leads to adequate results for SMOFs with strong and intermediate linear birefringence.     

Methods for calculating the temperature zero drift initiated in fiber ring interferometers by random inhomogeneities in single-mode optical fibers

The specific features of the existing methods used for calculating the temperature zero drift initiated in fiber ring interferometers (FRIs) by linear coupling between polarization eigenmodes at random inhomogeneities in single-mode optical fibers are analyzed. The ranges of applicability of each method are determined. It is demonstrated that numerical simulation with a variation in the temperature of the single-mode optical fiber of the FRI loop is the most complex and, at the same time, the most universal method.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: Integrated statistical properties of polarization modes of single-mode optical fibers in the presence of random inhomogeneities

Using mathematical modeling, an explicit form is found for the Jones matrix of a segment of a single-mode optical fiber with random inhomogeneities, whose length is considerably greater than the correlation length of random inhomogeneities. It is shown that parameters of this matrix are of a statistical nature. A rational representation of the matrix is proposed. It is shown that, under certain conditions, one of the matrix parameters may be treated as constant, whereas the other parameter is assumed to be continuously distributed on the interval [0, 2π]. As the latter parameter is changed, which corresponds to a change from one random realization of inhomogeneities in a single-mode fiber to another, the ellipticity and the azimuth of the major axis of the polarization ellipse of natural polarization modes of a single-mode fiber simultaneously change.     

300 W quasi-continuous-wave diffraction-limited output from a diode-pumped Nd:YAG master oscillator power amplifier with fiber phase-conjugate stimulated Brillouin scattering mirror

A master oscillator power amplifier system comprising a cw Nd:YAG master oscillator, a quasi-cw diode-pumped power amplifier, and a fiber-based stimulated Brillouin scattering phase-conjugate mirror is reported. A 12-pass amplifier configuration is employed to achieve high gain in a small-length slab amplifier. Residual and pump-induced optical inhomogeneities in the slab are corrected by the fiber phase conjugator to achieve diffraction-limited output beam quality. 300 W quasi-cw output and a maximal attainable gain of approximately 150 for the system are obtained.     

Periodic and solitary waves in optical fiber Bragg gratings with dispersive reflectivity

The system of partial differential equations for moving optical solitons in fiber Bragg gratings are studied. The traveling wave reductions are used to look for solutions of the system of equations. The compatibility conditions for the overdetermined system of equations are analyzed and discussed. Periodic and solitary waves in optical fiber gratings are found and illustrated.     

A moment method for analysis the gain spectrum in fiber Raman amplifier with broadband pumps

The governing equations of optical fiber Raman amplifier with broadband pumps in the steady state are systems of uncountable nonlinear ordinary differential equations (NODE). In this paper, the Moment method is used to reduce the uncountable system of NODE to a system of finite number of NODE. This system of equations is solved numerically. The results are compared with that of the full numerical method. It was shown that the Moment method is a precise and efficient technique for analysis of optical fiber Raman amplifier with broadband pumps.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: X. Verification of the ergodic hypothesis for fiber ring interferometers

The problem of the validity of the ergodic hypothesis as applied to a fiber ring interferometer (FRI) is considered on the basis of a comparison between magnitudes of the zero drift of an FRI calculated upon changing temperature of the fiber and upon random realizations of inhomogeneities in a single-mode optical fiber (SMF). The physical nature and statistical characteristics of random inhomogeneities in an SMF, types of polarization nonreciprocity in an FRI, and thermo-optical parameters of an SMF are analyzed. An algorithm for calculation of the zero drift of an FRI on changing temperature is proposed. The conditions under which the ergodic hypothesis is satisfied in an FRI are formulated. In particular, it is shown that many random inhomogeneities have to be placed on the depolarization length of polychromatic radiation in the SMF loop of an FRI; otherwise, the zero drift of the FRI calculated by the method of averaging over an ensemble of independent realizations may significantly exceed its actual value. Numerical estimations are made. It is shown that thermostabilization of an FRI with a polychromatic radiation source may significantly reduce its zero drift.     

The possibility for a significant decrease in the zero drift of fiber ring interferometers with a circuit formed by a highly anisotropic optical waveguide and a broadband radiation source

It is shown that the zero drift of interference of counterpropagating waves at the output from a fiber ring interferometer can be completely eliminated in the first order of magnitude and significantly decreased in the second order of magnitude if a sufficiently broadband source of nonmonochromatic radiation is used in a fiber ring interferometer with a circuit formed by a highly anisotropic optical waveguide when the depolarization length of nonmonochromatic radiation in a single-mode fiber-optical waveguide becomes significantly shorter than the correlation length of random inhomogeneities. Numerical estimates are made.     

Optical and thermal-transport properties of an inhomogeneous d-wave superconductor

We calculate transport properties of disordered 2D d-wave superconductors from solutions of the Bogoliubov-de Gennes equations, and show that weak localization effects give rise to a finite-frequency peak in the optical conductivity similar to that observed in experiments on disordered cuprates. At low energies, order parameter inhomogeneities induce linear and quadratic temperature dependencies in microwave and thermal conductivities respectively, and appear to drive the system towards a quasiparticle insulating phase.     

类明孤子在光纤中传输特性的变分研究

应用变分法,研究了微扰对类明孤子在光纤巾非线性传输特性的影响,导出了类明孤子脉冲参量演化的动力学方程。它统一了在单模光纤、色散缓变光纤或色散控制光纤中类明孤子脉冲参量演化的动力学方程。在此基础上,计算了色散缓变光纤中的线性高阶色散微扰。结果表明：线性高阶色散对类明孤子脉冲的位置和相位有影响,而对振幅、宽度和啁啾没有影响;光纤色散缓变对类明孤子脉冲的所有参量均有影响。     

一种新型的Tapered光纤光栅

利用耦合模方程对正弦型Ｔａｐｅｒｅｄ光纤光栅的反射谱进行了较为详细的计算和分析,并从实验上进行了验证。利用叠加均匀周期光纤光栅的模板和周期性振幅光栏一次成栅的方法,获得了具有三个反射峰、中心波长间隔为０．８ｎｍ的Ｔａｐｅｒｅｄ光纤光栅,这种光栅具有类似于梳状滤波器的功能,在多波长光纤激光器等方面有重要应用。     

正弦锥光纤光栅的数值计算分析

本文利用耦合模方程对正弦锥光纤光栅的反射谱进行了较为详细的计算和分析,发现,这种光纤光栅的反射谱与普通均匀周期光栅的反射谱有着很大的不同,通过控制光栅锥的形状,可得到类似于梳状滤波器的功能,对这种新型光栅在光纤激光器等方面的应用有指导意义。     

Causal first-order equations for wave field modeling in a horizontally inhomogeneous ocean

A mathematical model is developed for acoustic fields in a horizontally inhomogeneous oceanic medium with allowance for prominent inhomogeneities. On the basis of the system of equations of linear acoustics and the ideas of the method of transverse sections, causal equations of the first order that exactly describe the horizontal components of acoustic modes are derived. These equations offer a possibility to model the situations with nonsmooth inhomogeneities, when the known approximate methods are inappropriate. The equations are characterized by a number of important advantages, which include relative simplicity, physical clarity, and suitability for numerical simulations with the use of the existing algorithms designed for solving wave problems in layered media.     

基于复Ginzburg-Landau方程的双核光纤中调制不稳定性的仿真研究

在双核光纤光学系统中,应用复Ginzburg-Landau方程,研究了连续波的不稳定性问题.双核光纤光学系统是由一个非线性离散主核和一个线性附核构成的.研究发现,在线性微扰下存在调制不稳定性.系统仿真结果表明：如果充分考虑调制不稳定性,则该系统将产生规则或者不规则的脉冲序列.反之,如果不考虑调制不稳定性它将产生一连串具有连续增长振幅的离散峰.这表明在反常群速度色散情况下,一串归零脉冲的峰值或者单一归零脉冲峰值仍然是增强的.在光纤中产生归零序列脉冲源,这一研究结果对全光纤通信有一定的价值,对光纤光学及物理学 关键词： 光孤子 复Ginzburg-Landau方程 双核光纤 调制不稳定性     

Spectral properties of waves in superlattices with 2D and 3D inhomogeneities

We investigate the dynamic susceptibility and one-dimensional density of states in an initially sinusoidal superlattice containing simultaneously 2D phase inhomogeneities simulating correlated rough-nesses of superlattice interfaces and 3D amplitude inhomogeneities of the superlattice layer materials. The analytic expression for the averaged Green’s function of the sinusoidal superlattice with two phase inhomogeneities is derived in the Bourret approximation. It is shown that the effect of increasing asymmetry in the peak heights of dynamic susceptibility at the Brillouin zone boundary of the superlattice, which was discovered earlier [15] upon an increase in root-mean-square (rms) fluctuations, also takes place upon an increase in the correlation wavenumber of inhomogeneities. However, the peaks in this case also become closer, and the width and depth of the gap in the density of states decrease thereby. It is shown that the enhancement of rms fluctuations of 3D amplitude inhomogeneities in a superlattice containing 2D phase inhomogeneities suppresses the effect of dynamic susceptibility asymmetry and leads to a slight broadening of the gap in the density of states and a decrease in its depth. Targeted experiments aimed at detecting the effects studied here would facilitate the development of radio-spectroscopic and optical methods for identifying the presence of inhomogeneities of various dimensions in multilayer magnetic and optical structures.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XIII. Conditions of applicability of the ergodic hypothesis for fiber ring interferometers

Some additional conditions of applicability of the ergodic hypothesis to fiber ring interferometers (FRIs) with a loop consisting of a single-mode optical fiber (SMOF) with random inhomogeneities are considered. It is shown by mathematical modeling that the change in the phase difference of counterpropagating waves at the FRI output with the SMOF temperature is not a stationary random process. However, in a fairly narrow temperature range, this dependence can be assumed to be locally stationary. The conditions determining this temperature range are formulated. It is shown for a fairly large ensemble of independent realizations of random inhomogeneities in an SMOF that, even when all conditions of ergodicity are satisfied with a large margin, there will always be at least one realization violating strict ergodicity. Thus, only conditional (approximate) ergodicity occurs in this case. Nevertheless, in calculation of the FRI zero drift in this situation, averaging over an ensemble of independent realizations of random inhomogeneities in the SMOF of an FRI loop can be performed with sufficient accuracy. As a result, calculations are simplified significantly. In the general case, when at least one of the conditions of ergodicity is not satisfied, averaging over temperature for each realization with subsequent averaging over the entire ensemble should be performed. It is shown also that, within this problem, we can speak only about quasi-ergodicity or emulation of ergodicity, since a change in the temperature of the SMOF of an FRI loop and successive enumeration of independent realizations of random inhomogeneities in the SMOF loop are radically different random processes. The parameters characterizing quasiperiodic temperature changes in the phase difference of counterpropagating waves at the FRI output are refined.