Ultrashort-Pulse Generation by $Q$-Switched Lasers

We have undertaken the complete temporal description of pulsed emission by a homogeneously broadened laser, including the effects of spontaneous emission, the detailed geometry of the laser cavity, and the variation of atomic polarization and level populations over wavelength distances. The model is based on traveling-wave equations which are derived from Maxwell's equations and solved in conjunction with boundary conditions imposed at the cavity mirrors. Thus, any direct assumptions concerning the nature of the laser's longitudinal mode structure is avoided. Variations in polarization and population over wavelength distances are treated by means of expansions in spatial Fourier series, having as fundamental a half optical wavelength. The Fourier series are truncated after the first harmonic. The treatment differs from earlier work in that the dephasing of the dipole moment is treated exactly without a rate-equation approximation. Spontaneous emission is simulated both as to spectrum and Gaussian character by including in the dipole equations stochastic shot-noise sources. The model equations are solved numerically, and results include the details of $Q$-switched pulse evolution from noise for both passive and active switching. In the case of an actively switched laser, the two-photon fluorescence intensity pattern has been calculated. It reveals a well-defined structure of subsidiary intensity maxima, even though subcavities are not assumed in the calculation. The pattern can be correlated directly with the emission pulse structure, and should vary from shot to shot. No single point in the pattern is suitable for a peak-to-background ratio determination. However, if the background is averaged over a distance in the fluorescing medium equal to twice the separation between cavity mirrors, the peak-to-background ratio would be ≈ 1.6, indicating a highly uncorrelated spectrum.