Theoretical Research Of An End Pumped Double-clad Fiber Lasers Doped With Quasi Two-energy-level Ions

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.