Abstract

The Kuizenga-Siegman-Haus¹ theory of mode locking is extended through three simple ordinary differential equations to treat the full transient evolution of three pulse parameters; the pulse width and chirp, amplitude and phase, and pulse position offset from the modulation peak, respectively. Application of the theory to the parametrically driven mode-locked semiconductor laser² produces several important results. The transient buildup of the pulse from an infinite width to a final steady-state value is discussed neglecting mirror dispersion. The inclusion of facet (mirror) dispersion results in pulse widths either greater or less than the steady-state value, depending on the sign of the dispersion coefficient. This is quantitatively and intuitively understood in terms of an ABCD Gaussian pulse parameter analysis to trace the pulse width and chirp around the laser cavity. For mirrors which compress on reflection we show that the pulse widths in the cavity depend critically on the accuracy with which the mirror dispersion compensates the dispersive effects of the laser amplifying medium, a compensation error of ~10⁻⁴ limiting pulse widths to the 100-fs range for a typical semiconductor laser. Finally, we show that such compensation to shorten the pulses internally results in a threshold increase of the laser.

© 1985 Optical Society of America