三能级光纤激光器速率方程组的阈值解析解

 在考虑了泵浦损耗及激光损耗的情况下，解析求解了阈值泵浦下的三能级光纤激光器速率方程组，获得了泵浦功率阈值的显函数解析表达式，泵浦功率沿光纤变化的隐函数表达式，以及用功率变化表示的各个能级的粒子数密度随位置变化的显函数表达式。并利用这些表达式对光纤激光器的阈值特性进行了研究，研究表明：泵浦功率阈值随泵浦损耗系数增大而增大；激光上能级粒子数密度随归一化位置呈下降趋势，而下能级粒子数密度的变化与此相反；泵浦功率阈值越大(光纤长度越长),净增益系数随归一位置下降就越快。所获得的结果适用于单包层和双包层光纤激光器。     

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。     

Theoretical analysis of multimode fiber amplifiers and lasers containing spatial filters

By the use of the coupling theory of the modes and the multimode rate equations, the performances of the multimode fiber amplifiers or lasers containing a spatial filter have been discussed. After the rate equations applicable to amplifiers are solved, the beam quality factors of the output from a multimode fiber amplifier with and without a single mode filter have been evaluated and compared. By the use of the analytical expression of the threshold pump power applicable to the multimode fiber lasers with the spatial filter and doped with quasi two-energy-level ions, and two example fibers had been selected which may guide 4 and 9 transversal modes, respectively, the threshold pump power for each transversal fiber mode has been evaluated. The results indicate that the single mode filter, does introduce a very strong discrimination for the modes between the high order modes and the fundamental mode. This should considerably favor the operation of the fundamental mode in the lasers with a homogeneously broadened active medium.     

Threshold characteristics analysis of one-end-pumped Yb3+-doped gain-guided and index-antiguided fiber laser

An exact analytical expression of the threshold pump power for the one-end-pumped Yb³⁺-doped gain-guided and index-antiguided (GG–IAG) fiber laser has been obtained by solving the improved rate equations (REs) with the additional leakage losses. The effects of Yb³⁺ concentration, fiber length, core radius and mirror reflectivity on the threshold pump power are discussed. After optimizing, the results show that the laser threshold of GG–IAG fiber laser can be greatly reduced while maintaining single mode oscillation. Compared to the numerical methods, the analytical expression has easy calculation and distinct results.     

掺铒光纤激光器输出特性的解析研究

从描述掺铒光纤激光器的速率方程组出发，对９８０ｎｍ和１４８０ｎｍ波段泵浦下掺铒光纤激光器的输出特性进行了解析研究，得到了这两个波段泵浦下下输出功率，斜效率等重要参烽的隐式或显示解析表达式。     

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.     

Novel shooting method with simple control strategy for fiber lasers

A novel shooting method with excellent simple control strategy is developed for solving the failure to convergence of the traditional shooting methods themselves in fiber lasers model. Compared with the published literature, the novel shooting method provides a clear physical understanding method for getting the threshold pump power and the exact results with given random functions in Yb³⁺-doped fiber lasers and Er³⁺-doped fiber lasers. Then, the results in Er³⁺-doped fiber lasers and Yb³⁺-doped fiber lasers demonstrate that the solutions using the novel shooting method has high accuracy of 10⁻⁸ W with several iteration steps, which have extended the applicable range of the end-pumped power even lower than 1 mW pump power. Furthermore, compared with 1480 nm pump for the threshold and slope efficiencies of the Er³⁺-doped fiber lasers, 978 nm fiber lasers can extend wider scope of application and be pump source in the coming future. Finally, the lower threshold and higher slope efficiency at 975 nm than those of 910 nm pump in Yb³⁺-doped fiber lasers, 975 nm pump laser provides for broad band excellent cladding pump source.     

强泵浦下掺Yb3+双包层光纤激光器输出特性数值分析和实验研究

对强泵浦下线形腔掺Yb3+双包层光纤激光器输出特性进行了理论和实验研究。通过数值模拟,分析了泵浦光及激光在光纤中的分布、输出功率与泵浦功率的关系、光纤长度及腔镜反射率对激光输出功率的影响。在实验中,利用D型掺Yb3+双包层光纤获得了输出功率10 6W的光纤激光输出,斜率效率达86%。测量了在不同输出耦合条件下的输出功率、阈值泵浦功率和斜率效率,理论分析与实验结果基本一致,为进一步提高光纤激光器功率提供了理论和实验依据。     

线形腔掺铒光纤激光器输出特性的理论研究

通过求解速率方程，从理论上详细地分析了形腔掺铒光纤激光器输出特性，得到了稳定条件下激光器阈值泵浦功率，输出功率和斜率效率的解析表达式；给出了构造线形腔掺铒光行激光器所需掺铒光纤最短长度和最佳长度的表达式。     

光纤环形镜线形腔掺Er3+光纤激光器输出特性的数值分析

在分析光纤环形镜工作原理的基础上,给出了基于光纤环形镜的线形腔掺Er3+光纤激光器相位和幅度的振荡条件.通过求解速率方程,理论分析了其输出特性,获得了稳态条件下激光器输出功率、阈值泵浦功率和斜率效率的解析表达式.推导出激光器工作所需掺Er3+光纤最短长度,并在给定泵浦光功率时,在特定输出波长上获得最大输出功率所需最佳掺Er3+光纤长度的表达式,且通过实验进行了验证.     

掺铒光纤环形激光器输出特性的研究

根据掺铒光纤激光器的速率方程，对环形腔光纤激光器的输出特性进行了理论分析，得到了光纤激光器在稳态条件下阈值抽运功率、激光输出功率和斜率效率的解析表达式。利用数值模拟结果对光纤激光器的这些基本特性参量进行了分析和讨论，为光纤环形激光器的优化设计提供了依据。并进行了980nm抽运的掺铒光纤激光器的实验，实验证明理论分析得到的基本特性是合理的。     

LD泵浦掺铥(Tm3+)光纤激光器的数值分析

首先从掺铥光纤激光器的速率方程和光传输方程出发,建立数学模型,通过Matlab软件进行数值计算,分析了泵浦光和激光沿光纤的分布以及各能级离子数的变化.在不同掺杂浓度下,研究了小信号增益与入纤泵浦功率的关系以及泵浦光和激光功率与增益介质长度的关系.在不同泵浦功率下,研究了输出功率与输出耦合镜反射率的关系.进一步对不同泵浦吸收系数,研究了斜率效率和泵浦阈值与光纤长度的关系.分析结果表明存在最佳光纤长度和最佳耦合输出透过率,使得激光输出功率达到最佳值.     

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.     

Semi-analytical model of Raman generation in silicon-on-insulator rib waveguide with DBR/F-P resonator

An approximate method of modelling of Raman generation in silicon-on-insulator (SOI) rib waveguide with DBR/F-P resonator including spatial field distribution and nonlinear effects such as Raman amplification and two photon absorption (TPA), is developed. In threshold analysis of steady-state Raman laser operation, an analytical formula relating threshold pump power to the system parameters is obtained. The analysis of the above threshold operation is based on an energy theorem. In exact energy conservation relation, we approximate the Stokes field distributions by that existing at the threshold, whereas the approximate pump field distributions are obtained by integrating the equations for the pump signal using the linear (threshold) pump field distributions and the threshold Stokes field distributions. An approximate, semi-analytical expression related the Raman output power to the pump power and system parameters is derived. Our calculations remain in a good agreement with the exact numerical solutions.     

环形掺铒光纤激光器输出特性的理论研究

通过求解速率方程,建立了环形掺铒光纤激光器的理论模型.获得了激光器的阈值泵浦功率、输出功率.斜率效率以及最佳掺铒光纤长度的解析解.对结果给予了清晰的物理解释     

热键合技术的Cr4+:YAG被动调Q激光器理论和实验研究

 采用数值求解被动调Q速率方程，并讨论了基于热键合技术被动调Q激光器的优化方法。通过数值仿真讨论分析了谐振腔的损耗、饱和吸收体的初始透过率、输出镜的反射率和泵浦功率等参数对激光输出的影响。结果表明：输出镜存在最佳透过率，使得输出功率最高和脉冲能量最大；减小饱和吸收体的初始透过率能有效提高脉冲能量，并压缩脉宽，但是会增加阈值泵浦功率；泵浦功率与脉冲重复率和输出功率近似成线性增加，增大泵浦功率可以压缩脉宽。并通过实验验证了理论分析的正确性。     

Efficient operation of diode-pumped single-frequency thulium-doped fiber lasers near 2 micro m

Efficient operation of diode-pumped single-frequency fiber lasers at wavelengths from 1740 to 2017 nm has been demonstrated by using a very short piece of newly developed single-mode active fiber, i.e., heavily thulium-doped germanate glass fiber. At 1893 nm, the single-frequency fiber laser has a pump threshold of 30 mW, a slope efficiency of 35%, and maximum output power of 50 mW with respect to the launched power of single-mode pump diodes at 805 nm. To the best of our knowledge, this is the highest lasing efficiency achieved in single-frequency fiber lasers operating near 2 micro m. Frequency noise of the single-frequency fiber laser at 1893 nm has been characterized and compared with that of single-frequency fiber lasers at 1 and 1.55 micro m.     

Rate equations studies on coherently combined fiber lasers connected by an optical coupler

Attempt has been made to apply the steady-state rate equations to study two coherently combined Er³⁺-doped fiber lasers joined by an optical fiber coupler. In order to establish the boundary conditions, which are necessary for solving the equations, we have taken into consideration the fact that a constructive interference at the coupler assures that the laser radiations from both constituent lasers are directed to the coupler output port to which a reflection mirror defining both lasers is attached. Consequently, effective reflectivity, provided by the coupler-mirror combination, can be specified in terms of the laser powers of both laser signals, and the rate equations describing the compound system can be solved. Using the derived solutions, quantitative investigations can be made on the influences of different laser parameters. For example, the influence of the length difference between doped fibers, the splitting ratio of the coupler and power difference between the two pump radiations have been given in this report.     

自调Q激光器的理论分析

利用速率方程，对自调Q激光二极管抽运固体激光器进行了数值模拟。通过求解析解计算了自调Q脉冲的峰值功率、单脉冲能量、脉冲宽度、能量利用率、重复频率、平均输出功率等参量。根据自调Q二极管抽运固体激光器的特点，分别得到了使抽运阈值功率最小的最佳自调Q晶体长度和使光-光效率最大的最佳自调Q晶体长度。     

Analytical and visual modeling of InGaN/GaN single quantum well laser based on rate equations

An analytical, visual and open source model based on solving the rate equations for InGaN/GaN single quantum well (QW) lasers has been carried out. In the numerical computations, the fourth-order Runge–Kutta method has been used for solving the differential rate equations. The rate equations which have been considered in this simulation include the two level rate equations for the well and separate confinement heterostructure (SCH) layers. We present a new and inexpensive modeling method with analytical, visual and open source capabilities to investigate and comprehend the QW laser characteristics such as time behavior of carriers in SCHs and QW, photon density, output power and gain, and also the output power versus current which presents the threshold current of the laser. The characteristics of the QW lasers, which include laser time response (P–t), turn-on delay time of lasing and output power–current (P–I) characteristic and related features such as threshold current and slope efficiency have been investigated. Our model accurately computes the P–t and P–I characteristics such as turn-on delay time, threshold current and slope efficiency, and also illustrates the effects of parameters such as the injection current and geometry.