Solution to rate equations of a double-clad fiber laser

In order to obtain more exact analytical solution to study the output characteristics of double-clad fiber lasers,according to the continuous-wave rate equations of fiber lasers,using typical parameters of double-clad fiber lasers(DCFLs),the contribution of the re-emission effect arising from the interaction between the upper-level atoms and pump light was estimated.Taking into account the predominant part of the re-emission to improve the accuracy of the integration approximated rate equations,the integration of the product of the loss and radiation should be found and explicit analytical expressions for the output of the DCFLs and gradient efficiency of the pump radiation,were deduced,and certain issues of concern were discussed.As an example,for laser wavelength 1090nm,if the pump wavelength is 915nm,920nm,and 975nm,respectively,the gradient efficiency of 975nm is the maximum and it is about 87%.The result shows that the analytical solutions are fit to investigate the output characteristics of fiber lasers extending the application range.