An approximate analytic solution of strongly pumped Yb-doped double-clad fiber lasers without neglecting the scattering loss

A theoretical analysis of strongly pumped Yb-doped double-clad fiber lasers is presented and an approximate analytic function of distributed laser along the whole fiber with the scattering loss is obtained for the first time. A comparison is made between the analytic solution and the exact numerical solution. The results have shown that the analytic function of distributed laser within the fiber is accurate and explicit. With the analytic solution the losses caused by laser scattering are shown in three different pump modes. The results verify that the backward pumping can get the highest output power in strongly pumped fiber lasers.     

Threshold characteristics of linear cavity Yb-doped double-clad fiber laser

The threshold characteristics of linear cavity Yb³⁺-doped double-clad fiber laser have been studied theoretically and experimentally. By solving rate equations, the expression for threshold pump power is obtained. The effects of fiber length, mirror reflectivity, pump wavelength, laser wavelength and Yb³⁺ concentration on threshold pump power are discussed. Then, the Yb³⁺-doped double-clad fiber laser with linear cavity is developed. By using various output couplers, threshold pump power has been measured. The experimental results are in accord with theory.     

掺Yb3+双包层光纤激光器的数值分析

 对掺Yb³⁺双包层光纤激光器不同参数情况下的输出功率和增益分布进行了数值模拟，分析了一端泵浦和双端泵浦方式下输出特性的差异，激光沿光纤长度方向的分布，输出功率与光纤长度、腔镜反射率及泵浦功率的关系。结果显示：两端泵浦较一端泵浦增益更加平坦，输出功率也稍高；当泵浦光波长为975nm时，输出激光功率对光纤长度更为敏感，最佳光纤长度相对于泵浦光波长为915nm时短且转化效率高；在大功率长光纤的情况下，光纤有损耗时输出功率随输出腔镜反射率的增加单调地减小，无损耗时输出功率不随输出腔镜反射率变化。     

Dual-wavelength high-power Yb-doped double-clad fiber laser based on a few-mode fiber Bragg grating

We report a high-power dual-wavelength Yb-doped double-clad fiber laser based on a few-mode fiber Bragg grating (FMFBG). The FMFBG was fabricated by using a piece of fiber in a length of fiber with a cutoff wavelength of 1225 nm, which supported two modes at 1060 nm. The laser was pumped by a fiber pigtailed laser diode working at 915 nm. Single-wavelength, dual-wavelength and triple-wavelength laser oscillations were observed when the fiber laser operated under different low pump powers. However, stable dual-wavelength operation was achieved at higher pump power of 3.9 W and remained unchanged until the output power reached 5.67 W under the maximum available pump power of 10.7 W. The laser wavelengths were centered at 1059.12 and 1060.80 nm with a full-width at half-maximum of 37 and 43 pm, respectively. The signal-to-noise-ratio was greater than 50 dB and the beam quality factor (M²) was about 1.9.     

掺镱双包层高功率光纤激光器热效应的理论研究

针对高功率掺镱双包层光纤激光器（DCFL）的热效应,由热传导方程并借助速率方程模型导出温度分布的解析解,研究了泵浦方式和泵浦吸收系数对DCFL腔内温度的影响。结果表明：温度沿径向的变化与轴向相比可以忽略;采用传统端面泵浦会导致DCFL局部温度过高,实际中应使用两端对称泵浦方式;而减小泵浦吸收系数虽可改善温度特性但会降低系统的输出功率。进一步分析得出,综合采用分段泵浦方式和不均匀泵浦吸收系数可实现温度分布和输出功率的最佳匹配。     

掺镱双包层高功率光纤激光器热效应的理论研究

 针对高功率掺镱双包层光纤激光器（DCFL）的热效应,由热传导方程并借助速率方程模型导出温度分布的解析解,研究了泵浦方式和泵浦吸收系数对DCFL腔内温度的影响。结果表明：温度沿径向的变化与轴向相比可以忽略;采用传统端面泵浦会导致DCFL局部温度过高,实际中应使用两端对称泵浦方式;而减小泵浦吸收系数虽可改善温度特性但会降低系统的输出功率。进一步分析得出,综合采用分段泵浦方式和不均匀泵浦吸收系数可实现温度分布和输出功率的最佳匹配。     

Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers

Numerical analysis is investigated for the high-power double-clad fiber lasers and experimental results using different microscope objectives for focusing into a Nd-doped rectangular double-clad fiber also performed. The numerical analysis includes dependence of output power on output mirror reflectivity, absorbed pump power, loss, and fiber length and pump power distribution for the cases of one-end and two-end pumps with 20 dB/km loss. Calculated conversion efficiencies are 76.36%, 69.73%, and 63.84% for lossless, two-end pump, and one-end pump fiber lasers, respectively. Slope efficiencies from absorbed pump power/output powers measured using microscope objectives are 16.8%/182 mW, 53.8%/351 mW, 24.9%/1240 mW, and 13.9%/649 mW for magnifications of 5×, 10×, 20×, and 40×, respectively.     

掺镱双包层光纤激光器典型参数对斜线效率的影响

 分析了双包层光纤激光器(DCFL)耦合方程的解析解，并对信号光散射损耗、后腔镜泵浦反射率等影响掺镱DCFL斜线效率的典型参数进行了理论研究。结果表明，斜线效率并不是随着后腔镜泵浦反射率的升高而单调增大，因为泵浦反射率的升高会影响光纤的最佳长度，从而降低斜线效率。所以在优化斜线效率时应该考虑到泵浦反射率和光纤最佳长度之间的匹配。同时，提高纤芯掺杂浓度、减小信号光散射损耗也能增大斜线效率。     

A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution

In this paper, we proposed a novel numerical algorithm for cascaded Raman fiber laser (CRFL) using the approximate analytic results as the initial values for shooting method, which effectively reduces the calculating time from several hours to a few minutes. With the algorithm, we obtained a numerical solution of the bilateral-pumping Ge-doped fifth-order CRFL which can avoid the so-called “end face damage” phenomenon efficiently. At the same time, we also simulated the unilateral-pumping one as a comparison, which showed both the characteristics of them are similar with each other.     

多点侧面泵浦双包层光纤激光器的对称夹层结构

 利用基于亚波长衍射光栅理论的介质-金属-介质的对称夹层结构,对掺杂的双包层光纤进行多点泵浦,根据严格的电磁场衍射理论和光栅方程,分析了多点泵浦时,这种耦合结构的泵浦光泄露的问题,证明了多点泵浦时泵浦光的泄露率仅为15.52%,而对信号光则不存在泄露。这种对称夹层结构可以用于多个大功率激光二极管阵列的多点侧面泵浦双包层掺杂光纤中,以制作各种大功率(数kW级)稀土光纤激光器,其最大耦合效率可以达到80%以上。     

The analytical investigation of the super-Gaussian pump source on the thermal, stress and thermo-optics properties of double-clad Yb:glass fiber lasers

Fiber lasers have attracted considerable attention when their power can realistically be scaled to kilowatt level and beyond. In this paper, we assumed that the fiber core and first clad are exposed to a pump source with a super-Gaussian profile of order four. The effects of this non-uniform heat deposition on thermal, stress and thermooptics properties such as temperature-dependent change of refractive index and thermally induced stress have been comprehensively studied and their equations analytically derived.     

Theoretical and experimental investigation of thermal effects in a high power Yb-doped double-clad fiber laser

In this paper, based on the thermal conduction equations and the steady-state rate equations, a theoretical and numerical analysis of thermal effects is investigated for a single end pumped Yb-doped double-clad fiber laser (YDDC). The distributions of signal power and temperature for different pump powers and fiber parameters are compared. According to the results, the parameters of the optical-cavity have been optimized and an effective method has been adopted to reduce the thermal effects in an experimental investigation. As a result, an output power of 621 W has been obtained with a slope efficiency of 78%.     

侧面泵浦高功率双包层光纤激光器的表面弧形金属槽结构的制作和分析

侧面耦合高功率泵浦光技术是获得高功率稀土光纤激光器的关键技术之一。介绍了一种用于侧面泵浦高功率双包层光纤激光器的表面弧形金属槽结构的制作工艺,并且针对已经实验制作出来的表面连续弧形金属凹槽的侧面耦合结构进行了严格的矢量电磁场理论计算,将120°弧形凹槽等效近似为多层等高不等宽的矩形槽并运用透射矩阵算法对这种近似后的多层矩形结构进行优化设计。这种结构可以用于大功率激光二极管阵列的侧面泵浦中,尤其可用于条形半导体激光器侧面泵浦双包层掺杂光纤,以制作各种大功率稀土光纤激光器。     

������������ɫɢ��ϵ��һ�ָ߾��ȿ����㷨

建立了等离子体-绝缘管-真空结构的等离子体天线物理模型,推导了新的色散关系方程,通过几何诠释,给出了一种新的高精度快速收敛求解方法,计算机仿真验证了结论的正确性和有效性。利用算法研究了当电子密度按线性律减小时,圆柱等离子体天线的色散关系,并绘制了方向图。这些结果对等离子体天线的分析与设计具有重要的参考价值。     

等离子体天线色散关系的一种高精度快速算法

建立了等离子体-绝缘管-真空结构的等离子体天线物理模型,推导了新的色散关系方程,通过几何诠释,给出了一种新的高精度快速收敛求解方法,计算机仿真验证了结论的正确性和有效性。利用算法研究了当电子密度按线性律减小时,圆柱等离子体天线的色散关系,并绘制了方向图。这些结果对等离子体天线的分析与设计具有重要的参考价值。     

一种求解级联拉曼光纤激光器的方法

根据适应度函数的具体情况改进了微粒群算法,与基本微粒群算法相比,其复杂函数的寻优能力得到了提高。利用改进的微粒群算法对不同结构的拉曼光纤激光器理论模型对应的适应度函数进行了算法测试,保证适应度函数精度(10-5)的情况下,计算时间不超过15 s。与Newton-Raphson打靶算法配合时,有效地缩短计算时间、提高打靶算法稳定性和计算精度。最后,利用该算法数值分析了二阶掺磷拉曼光纤激光器输出端反射率、光纤长度和泵浦功率对输出功率的影响。     

An improved shooting algorithm and its application to high-power fiber lasers

An improved shooting algorithm for high-power fiber laser is proposed based on the relation of the two-end boundary laser powers. By the improved shooting algorithm, the evolutions of the pump and laser powers along the fiber position for Yb-doped and Tm-doped high-power double-clad fiber lasers with the laser scattering loss are analyzed. The results prove that the improved shooting algorithm can be efficient even if the pump power is up to kilowatt level, and the initial value can all be fast convergent as long as the initial guessed laser power is smaller than the truth value. So, this improved shooting algorithm can be used in high-power double-clad fiber lasers efficiently.     

Approximate analytic solutions for a generalized Hirota—Satsuma coupled KdV equation and a coupled mKdV equation

<正>This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries(KdV) equation and a coupled modified Korteweg-de Vries(mKdV) equation. This method provides a sequence of functions which converges to the exact solution of the problem and is based on the use of the Lagrange multiplier for the identification of optimal values of parameters in a functional.Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.     

掺Yb光纤激光器阵列谱合成系统的光束传输模型及光束特性分析

建立了由掺Yb光纤激光器阵列、变换透镜、闪耀光栅和输出耦合镜组成的光束谱合成系统的光束传输模型.在考虑光栅角色散、光栅刻槽倾角误差和光栅衍射效率情况下,利用光线追迹法、衍射积分方法、光束非相干叠加原理和强度二阶矩方法,推导出高斯光束非平行倾斜入射到闪耀光栅的相位变化公式以及谱合成光束的光强分布解析表达式.分析了高斯光束非平行倾斜入射到光栅后,光栅角色散、光栅衍射效率和光栅刻槽倾角误差对掺Yb光纤激光器谱合成系统输出光束特性的影响.研究结果表明,谱合成光束具有与单根光纤激光器几乎相同的光束质量;光栅角色散对合成光束特性的影响可忽略;随着光栅刻槽倾角误差的增大,谱合成光束的光束质量明显变差;当光栅刻槽倾角误差较大时,必须考虑光栅衍射效率对合成光束特性的影响. 关键词： 掺Yb光纤激光器 非平行倾斜入射 光束谱合成 光束质量     

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system. The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics, and a new algorithm—algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method. In the new algorithm, the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator. The exact analytical piece-like solution of the ordinary differential equations is expressed in terms of Taylor series with a local convergent radius, and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.