An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient

The analysis of steady state Brillouin scattering in a long single mode optical fiber is presented. Meanwhile, an approximate analytical functions of distributed Brillouin scattering and pump wave along the fiber with the fiber attenuation coefficient are obtained for the first time. A comparison is made among the analytical solutions with the attenuation coefficient, the analytical solutions without the attenuation coefficient and the exact numerical solutions. The results show that the analytical solutions with fiber attenuation coefficient are more close to the numerical solutions, which can be used to describe the power distribution of the pump wave and the Stokes wave along the long distance single mode optical fiber accurately.     

光纤光栅法布里-珀罗腔中受激布里渊散射的理论研究

对光纤光栅法布里-珀罗腔中稳态受激布里渊散射模型进行了理论分析,在其耦合强度方程组基础上,推导出仅产生一阶斯托克斯波时,耦合强度方程组的解析表达式,由此计算出光纤光栅法布里-珀罗腔中抽运波与斯托克斯波透射功率和反射功率。对于光纤光栅法布里-珀罗腔中二阶斯托克斯波的产生,推导出光纤光栅法布里-珀罗腔入射端抽运波的解析表达式和忽略光纤损耗时能量守恒方程,利用Shooting和L-M算法数值求解出耦合强度方程组。分析讨论了抽运波,一阶斯托克斯波和二阶斯托克斯波的反射与透射功率随着入射波功率变化的情况。最后,仿真出光纤光栅法布里-珀罗腔中,抽运波与斯托克斯波沿腔长分布的情况。     

New Ansaetze for Obtaining Exact Solutions of Nonlinear Schroedinger-Type Equation

We propose two simple ansaetze that allow us to obtain different analytical solutions for two generalizeal versions of the nonlinear Schrodinger equation, such as the averaged dispersive-managed fiber system equation and the extended nonlinear Schrodinger equation which describe the femtosecond pulse propagation in monomode optical fiber. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media.     

New Ans(a)tze for Obtaining Exact Solutions of Nonlinear Schr(o)dinger-Type Equation

We propose two simple ans(a)tze that allow us to obtain different analytical solutions for two generalized versions of the nonlinear Schr(o)dinger equation, such as the averaged dispersive-managed fiber system equation and the extended nonlinear Schr(o)dinger equation which describe the femtosecond pulse propagation in monomode optical fiber.Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media.     

Analytical solutions to rate equations including losses describing threshold pumped fiber lasers

An exact analytical expression to the threshold pump power has been deduced for rate equations including loss coefficients applicable to fiber lasers doped with quasi two-energy-level ions. Following the derivation of a closed-form expression for the variation of the pump power along the fiber, together with analytical solutions to the position dependent atom population density and laser power in terms of the pump power, we have analytically and fully solved rate equations describing threshold pumped fiber lasers. A comparison has also been made between the exact analytical result with the previous reported results, which indicates that various approximation have underestimated the threshold pump powers.     

Pulse amplification characteristics of multimode fiber amplifier

Under small signal situation, the analytical expression for describing the output signal emitted from an Yb³⁺-doped fiber amplifier with a Gaussian input pulse signal is deduced, by full considering both fiber guided modes’ propagation constant and filling factor, which depend on the signal frequency. Pumped by continue wave (CW) source, the analytical expressions of the small signal gain and each guided mode's output power are obtained. Based on these analytical expressions, the various intensity distributions of output pulses amplified by the fiber amplifier with different Gaussian input pulse widths are analyzed.     

准二能级阈值泵浦光纤激光器的理论分析

 根据含损耗系数的稳态速率方程组,对掺准二能级稀土粒子光纤激光器的泵浦阈值进行了分析和完全解析求解。求得了泵浦阈值功率的显函数解析式,得到了泵浦光阈值功率随光纤位置变化的隐函数表达式,以及信号光功率和上能级粒子数随光纤位置变化的解析表达式。对所得的解进行了数值分析,并与已有的理论和实验结果进行了比较分析。结果表明：由于忽略了信号光和泵浦光损耗系数,不同近似条件下给出的泵浦阈值功率均比实验值低,但所导出的理论研究结果与已有实验结果的差异最小。     

Optimization of Yb3+-doped double-clad fiber lasers using a new approximate analytical solution

We investigated the properties of continuous wave (CW) Yb³⁺-doped double-clad fiber lasers (DCFLs) with linear-cavities theoretically and numerically using the rate equations. Under steady-state conditions, a new approximate analytical solution for CW Yb³⁺-doped double-clad fiber lasers (DCFLs) with consideration of the scattering losses were deduced. Good agreement between the proposed solution and the numerical simulation was demonstrated. Compared with the known approximate solutions published in the literature, the proposed solution has a briefer expression, higher accuracy and wider scope of application, which extends the applicable range of the analytical result to low reflective feedback mirror configurations. The solution provides a clear physical understanding of the optimal design of the CW Yb³⁺-doped DCFLs and can be applied to different pump and output configurations. Using the proposed solution, the optimal design of the CW Yb³⁺-doped DCFLs was discussed. If cavity reflectivities are given in advance, the optimal fiber length is found to be independent of the pump power. When the pump power and reflectivity of the feedback end are known in advance, the results show that the optimal fiber length increases and the optimal reflectivity of output mirror decreases with increase in pump power. Furthermore, when the feedback mirror is highly reflective, there exists a certain tolerance of the optimal parameters, in which the conversion efficiency decreases only slightly. But the conversion efficiency is sensitive to reflectivity of output mirror if feedback mirror has low reflectivity.     

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

In the framework of nonlinear wave optics,we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schr?dinger equation.The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method.Taking advantage of the analytical expression,we analyze the influences of various physical parameters on the breathing wave propagation,including the propagation loss and the input power on the beam width,the beam intensity,and the wavefront curvature.Also,the corresponding analytical solutions are obtained.The validity of the analysis results is verified by numerical simulation.This study provides some new insights for investigating beam propagation in lossy nonlinear media.     

Heat dissipative solitons in optical fibers

We propose a one-dimensional model governing the propagation of heat waves in an optical fiber (the “fiber fuse”). The model has solutions in the form of high temperature localized waves moving towards the input end of the fiber, fueled by the laser power. These waves can be ignited by local heating at any point along the fiber. The effect of such a wave is irreversible damage to the fiber core. The phenomenon was observed earlier by Hand and Russell, when locally heating a fiber through which CW light of modest intensity was propagating. This induced self-destruction of the optical fiber core.     

Power-independent technique to extract the dispersion parameters of an optical fiber using four wave mixing

Conventional methods which extract dispersion parameters of an optical fiber using four wave mixing rely on the measurement of optical power in the generated wavelengths, and hence are prone to measurement errors. We propose and demonstrate a power-independent method to extract the dispersion curve of a fiber using four wave mixing (FWM). The analytical equations that have been traditionally used to estimate the phase mismatch in FWM are modified to cater to low-dispersion fibers, and are verified. Experiments to obtain the dispersion curve of a low-dispersion and highly nonlinear fiber are discussed and the results are analyzed. Limitations of any FWM-based method to extract the dispersion curve of a fiber are presented for the first time.     

Analytical and Approximate Solutions for Complex Nonlinear Schrödinger Equation via Generalized Auxiliary Equation and Numerical Schemes

This article studies the performance of analytical, semi-analytical and numerical scheme on the complex nonlinear Schr¨odinger(NLS) equation. The generalized auxiliary equation method is surveyed to get the explicit wave solutions that are used to examine the semi-analytical and numerical solutions that are obtained by the Adomian decomposition method, and B-spline schemes(cubic, quantic, and septic). The complex NLS equation relates to many physical phenomena in different branches of science like a quantum state, fiber optics, and water waves. It describes the evolution of slowly varying packets of quasi-monochromatic waves, wave propagation, and the envelope of modulated wave groups, respectively. Moreover, it relates to Bose-Einstein condensates which is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero. Some of the obtained solutions are studied under specific conditions on the parameters to constitute and study the dynamical behavior of this model in two and three-dimensional.     

Spectral broadening in Raman fiber lasers

We present an analytical theory based on wave kinetic equations that describes a Raman fiber laser (RFL) generation spectrum. It is shown both theoretically and experimentally that the quasi-degenerate four-wave mixing between different longitudinal modes is the main broadening mechanism in the one-stage RFL at high powers. The shape and power dependence of the intracavity Stokes wave spectrum are in excellent quantitative agreement with predictions of the theory.     

Dark solitons in optical fiber with inhomogeneous effects

We study the nonlinear wave propagation in an inhomogeneous optical fiber core in the normal dispersive regime. In order to include the inhomogeneous physical effects, the nonlinear Schrödinger equation (NLSE), which governs the solitary pulse propagation in optical fiber, is modified by adding terms for phase modulation and power gain or loss. The modified NLSEs are bilinearized and exact dark soliton solutions are obtained. The results are discussed.     

Turbulence-induced square-root broadening of the Raman fiber laser output spectrum

The output characteristics of the conventional one-stage Raman fiber laser (RFL) are described in an optical wave turbulence formalism. Simple analytical expressions describing RFL output power and its spectral shape are presented, and square-root law for the output spectrum broadening law has been discovered. The indications of the turbulent-like spectral broadening in other types of cw fiber lasers and propagation phenomena in fibers are also discussed.     

内腔级联拉曼光纤激光器输出特性的实验研究

采用标准单模石英光纤作为拉曼增益介质，光纤布拉格光栅作为谐振腔镜，研制了一台内腔级联拉曼光纤激光器。利用掺Yb双包层光纤激光器作为抽运源，实现了二级拉曼转换，在波长1176.8nm获得了309mW的最大输出功率，斜率效率接近51.5％。在小抽运功率下，发现拉曼光纤激光器的输出中存在重复周期约为2.9μs的脉冲序列；当抽运功率大于某一值时，上述脉冲消失，获得了十分稳定的连续输出。     

Analytical treatments of the space–time fractional coupled nonlinear Schrödinger equations

Under investigation in this work is a (\(2+1\))-dimensional the space–time fractional coupled nonlinear Schrödinger equations, which describes the amplitudes of circularly-polarized waves in a nonlinear optical fiber. With the aid of conformable fractional derivative and the fractional wave transformation, we derive the analytical soliton solutions in the form of rational soliton, periodic soliton, hyperbolic soliton solutions by four integration method, namely, the extended trial equation method, the \(\exp (-\,\Omega (\eta ))\)-expansion method and the improved \(\tan (\phi (\eta )/2)\)-expansion method and semi-inverse variational principle method. Based on the the extended trial equation method, we derive the several types of solutions including singular, kink-singular, bright, solitary wave, compacton and elliptic function solutions. Under certain condition, the 1-soliton, bright, singular solutions are driven by semi-inverse variational principle method. Based on the analytical methods, we find that the solutions give birth to the dark solitons, the bright solitons, combine dark-singular, kink, kink-singular solutions with fractional order for nonlinear fractional partial differential equations arise in nonlinear optics.     

N信道高密度波分复石英光纤传输系统中受激喇曼散射产生的串话

本文利用前向稳态ＳＲＳ耦合波理论，给出Ｎ信道ＤＷＤＷ石英光纤传输系统中各信道光的喇曼串话的解析表达式。同时给出估算系统极限参数的普遍表达式。这些结果适用于具有任意初始光功率、任意信道总数和任意信道间隔的系统。最后应用以上结果计算ＤＷＤＭ石英光纤传输系统的极限参数。     

Analytical Model of Non-dispersion-limited Transient Stimulated Raman Scattering in Single-mode Silica Fiber in WDM Optical Communication System

The non-dispersion-limited analytic solutions of unidirectional N-channel transient stimulated Raman scattering (SRS) coupling wave equation which governing the propagation of the optical signals in single-mode (SM) silica fiber have been presented. Taking into account the SRS cross coupling among the N-channels, the analytic solutions are applicable to the system with arbitrary channel separation and input signal light power.     

Formulas for compression wave and oscillating flow in circular pipe

This paper shows analytical solutions for compression wave and for steady-state oscillating flow in a pipe with a circular cross section. We considered the compression wave to be one of fluid phenomena, and paid our attention to the equation of fluid motion and of continuity. Pressure and flow velocity are directly treated in analytical solutions. Not only either of them but also flow rate may be chosen as an input and outputs by easy rearrangement of the formulas. This paper enables us to express various behavior of the compression wave by using analytical solutions with the phase velocity and the spatial absorption coefficient. Those analytical solutions enable us to reduce computation time and analysis cost on not only duct acoustics but also water hammer and combustion instabilities. Of course, our formulas may contribute to designing of microdevices such as MEMS strongly influenced by wall-viscosity.