A computational theory of short pulse generation

The semi-classical equations for the electric field and population inversion in a two-level medium are simplified for the case of a saturable absorber cell which is shorter than the length of fluctuations in the optical-pulse envelope. The spatial coordinates in the cell are effectively lumped, and the integration is reduced to the one dimension of time. The pulse is passed through an amplifying medium and frequency selective elements by a fast Fourier transform into its spectral components. The case of pulse formation in a ruby laser, starting from a noise fluctuation is computed for the parameters of a recently reported accurate measurement of pulse duration. Good agreement is obtained with experiment. Finally, a pulse length is predicted for a cavity containing an etalon which cancels gain narrowing.