Analytically describing pulse deformation arising from frequency dependent filling factor of wave guide amplifiers

After neglecting the frequency dependence of the material gain, the analytical expressions to the output pulses from the amplifier for the input pulses of sinc-type and Gaussian have been derived. According to the derived results, the pulse deformation arising from frequency dependent filling factor can be analyzed: for the sinc-type pulse train, the light intensity peak remains unchanged, but the valleys between the output pulse peaks cannot touch the zero floor anymore; For the Gaussian pulse, the amplifier will impose a frequency shift on the pulse, which is proportional to the first derivative of the filling factor (Γ1). Another, the analytical expression of Γ1 for the semiconductor laser amplifier has been derived. And the calculated result shows that Γ1 is a positive quantity, and the magnitude of it is about 10−3/nm. The result indicates that Γ1 is an important parameter for theoretical describing the pulse deformation of wave guide amplifier such as the ps and fs pulse amplifier.