Description of laser pulses using Fourier analysis

The output of lasers in various modes of operation is described in a unified way, using Fourier analysis. A novel model for treating an active Fabry-Perot cavity, including the case of high gain, is developed resulting in a more exact expression for the spectral width of the cavity modes. Simple mathematical tools are given to relate the observed pulse length with the average gain and with the initial population inversion in the laser medium. It is shown that lasers with homogeneously broadened spectral lines have cavity modes of equal width and that if the modes are locked together the resulting ultrashort pulses are of equal duration. For lasers with inhomogeneously broadened spectral lines the cavity modes vary in width along the gain curve and, when mode-locked, the ultrashort pulses increase monotonically in duration along the emitted pulse train.