【作者】 段志春；

【导师】 陈建国；

【作者基本信息】 四川大学 ， 光学， 2007， 硕士

【摘要】 与传统固体激光器相比，掺稀土光纤激光器具有其独特的优点，即具有结构紧凑、体积小巧、阈值低、光束质量好、转换效率高以及表面积／体积比率大利于散热等特性。双包层光纤激光器的问世，更加促使了高功率光纤激光器的飞速发展，并在远程光纤通信、传感、工业加工、医疗、国防和军事等领域获得了日益广泛的应用。对双包层光纤激光器的进一步研究，成为了当前相关领域研究的热点，并在实验和理论上取得了众多丰富的成果。在对光纤激光器的理论研究中，人们通常采用速率方程理论进行分析。研究表明，速率方程组正确、有效，为阐述激光器的工作原理、特点以及研究和设计激光器提供了理论指导。由于速率方程组的解析解相对数值解具有一些明显的优点，人们便尝试在各种合理近似下对速率方程组进行解析分析和讨论。然而，由于速率方程组的非线性特性，很难对之严格求解。不过，在忽略信号光损耗系数的近似情况下，人们已得到了满足下列近似情况之一的解析解：(a)抽运光损耗系数可忽略的单包层光纤激光器件；(b)上能级粒子与抽运光相互作用的再发射可以忽略的较适合于抽运光损耗系数较大的长腔双包层光纤激光器件。对于典型的足够长双包层光纤激光器，抽运光损耗系数通常是远大于再发射项所产生的增益，因而，忽略上能级粒子数是合理的。然而，对于光纤长度短到小于或约等于1米的双包层光纤激光器，或者当讨论单包层光纤激光器的时候，则可能会出现再发射项的贡献与抽运光损耗系数相当，甚至可能会大于抽运光损耗系数，在这种情况下，忽略抽运光损耗系数较为合理。不过，可以推算到，不管是同时忽略信号光损耗系数和抽运光损耗系数，还是同时忽略信号光损耗系数和再发射项，都会造成抽运阈值功率被低估而输出激光功率被高估的事实。前人文献的实验数据充分表明了近似条件下得出的阈值略小于实验测得的结果。依据前人理论基础，本文采用端面抽运准二能级掺杂光纤激光器稳态速率方程组进行了解析分析。主要做了如下工作：(1)在忽略信号光损耗系数的前提下，明确提出了要获得光纤激光器输出功率的解析表达式，关键在于求得抽运光损耗系数与抽运光场乘积的积分值。并针对典型的双包层光纤激光器的参量，在估计了上能级粒子再发射项和抽运光的影响之后，采用保留再发射贡献主导部分而只忽略更高阶小量的办法来提高可积分近似方程的精确度和可应用的腔长范围。运用简洁的方法求得了近似条件下的双包层光纤激光器输出功率的显函解析表达式，导出了激光输出功率对抽运功率的斜线表达式，以及阈值抽运功率的表达式。并给出了近似条件下的最短光纤长度表达式，求得了固定抽运功率下获得最大激光输出功率的最佳光纤长度的隐函式，并对相关的问题进行了数值模拟分析和讨论。(2)在不忽略损耗系数的情况下，对掺准二能级稀土粒子光纤激光器的抽运阈值进行了完全解析求解。求得了抽运阈值功率的显函数解析式，同时，得到了抽运光阈值功率随光纤位置变化的隐函数表达式，以及信号光功率随光纤位置变化的解析解和上能级粒子数随光纤位置变化的解析表达式。并根据所得解，与前人的理论和实验结果进行了比较分析，结果表明，不同近似条件下得到的抽运阈值功率均比实验值要低，但本文的结果却是差别最小的。(3)运用(1)中所用的近似解析方法，从理论上分析了由F-P滤波器实现的多波长双包层光纤激光器的输出特性。讨论了光纤出光端面和双色镜的反射率、F-P滤波器腔长以及抽运光波长等参数对多波长输出功率的影响。为我们在实验中优化设计性能优越的双包层多波长光纤激光器提供了理论依据。更多还原

【Abstract】 Compared to the tradition solid lasers, rare earth doped fiber lasers has it’s unique characteristics, owing to their compactness, small volume and weigh, lower threshold, superb beam quality, high conversion efficiency, and large ratio of area/ volume, in favor of heat dispersion. Following the invention of the double-clad fiber lasers, the higher and higher powers have been achieved from the fiber lasers. At present, the fiber lasers have been widely used in the fields of long-distance fiber-optic communications, sensor, industry, medical treatment, national defence, etc.. As a consequence, in-depth studies on double-clad fiber lasers have become an important research topic, and fruitful and abundant experimental and theoretical results have been achieved. In the theoretical research of the fiber lasers, people generally used the rate equations. The investigation indicates that, the rate equations are correct and effective, and most widely used and powerful tool to theoretically predict the lasers characteristics and it’s elements of working, investigate and devise fiber laser.Compared to the numerical solutions of the rate equations, the analytical solutions have some dearly strongpoints, so that, after certain justified approximations have been adopted, peole have attempted to derive the analytical results. Unfortunately, owing to the nonlinear nature of the rate equations, it is difficult to obtain the exact analytical expressions. Even though, after the neglection of the loss coefficient of the laser radiation, people have obtained the analytical results satisfying one of the following approximate conditions: (a) the loss coefficient of the pump light can be neglected, which is applicable to the single-clad fiber lasers; (b) the re-emission arising from the interaction between the pump photons and upper-level ions can be neglected, which is applicable to the larger loss coefficient of the pump light and longer cavity of double-dad fiber lasers.In typical double-clad fiber lasers with a reasonable length, the loss coefficient of pump light is usually larger than the gain provided by the re-emission arising from the interaction between the pump photons and upper-level ions. However, when the double-clad fiber length reduces down to the order of～1 m, or when the fiber used is a single-clad fiber, it may happen that the contribution of the re-emission becomes comparable to, or even larger than the loss coefficient of pump radiation. Under these circumstances, neglecting the quantity of the loss coefficient of pump radiation may be a better approximation. It is conceivable that, the neglection of the loss coefficient of pump light and the loss coefficient of the laser radiation, or the loss coefficient of the laser radiation and the upper-level population, definitely resulted in an underestimation of the threshold pump power and overestimation of the laser output power. The data of experiment have indicated that the threshold predicted by the approximated theory is slightly smaller than the measured result.In this work, based on the theoretic of the previous studies, we have made an analytical solution by using the rate equations of an end-pumped fiber lasers doped with two-energy-level ions in the steaty state. The main works are as follows:(1) After negenecting the loss coefficient of laser radiation, it becomes apparent that the key issue of finding analytical expression for the laser output is evaluating the integrations of the loss coefficient of pump radiation multiplied by the pump radiation. Using typical parameters of double-clad fiber lasers, estimations have been made on the contribution of the re-emission affect arising from the interaction between the upper-level atoms and pump light. It is realized that the retaining of the predominance, part of the re-emission can improve the accuracy and extend the application range of the integratable approximated rate equations. As a result, an explicit analytical expression for the output of the double-clad fiber lasers, together with gradient efficiency of the pump radiation, and the analytical expression to the threshold pump power has been deduced in an economic way also. And the expression of the minimum fiber length has been deduced, and a dosed-form expression to the optimum fiber length at which the laser output power takes maxmum has been obtaind, and certain issues of concern have been discussed.(2) The rate equations in the steaty state including loss coefficients describing threshold pumped fiber lasers doped with quasi two-energy-level rare-earth ions have been analytically and fully solved. An analytical expression to the threshold pump power has been deduced, following the derivation of a closed-form expression for the variation of the pump power along the fiber has also been obtained, together with analytical solutions to the laser power in terms of the pump power and the position dependent atom population density. A comparison has been made between the analytical result with the previous reported results, which indicates that various approximations have underestimated the threshold pump powers, while the theoretical predication of this work is the closest to the experimental result.(3) Using the approximations analytical method used in (1), the output performance of multiwavelength double-clade fiber lasers with a Fabry-Perot (F-P) flter is analyzed. And the parameters that may influence the output performance of multiwavelength have been discussed, such as the reflectivity of fiber facets, the reflectivity of dichroic mirror, the length of the F-P filter, and the wavelength of the pump radiation. It may offer the theoretical basis in our expirement to design a multiwavelength double-clade fiber lasers with better performances.更多还原