Laser theory with finite atom-field interacting time

Abstract

We investigate the influence of atomic transit time $\ensuremath{\tau}$ on the laser linewidth by the quantum Langevin approach. With comparing the bandwidths of cavity mode $\ensuremath{\kappa}$, atomic polarization ${\ensuremath{\gamma}}_{ab}$, and atomic transit broadening ${\ensuremath{\tau}}^{\ensuremath{-}1}$, we study the laser linewidth in different limits. We also discuss the spectrum of fluctuations of output field and the influence of pumping statistics on the output field.The influence of atomic transit time $\ensuremath{\tau}$ on laser field has not been carefully discussed before, to our knowledge. In particular, a laser operating in the region of ${\ensuremath{\gamma}}_{ab}⪡{\ensuremath{\tau}}^{\ensuremath{-}1}⪡\ensuremath{\kappa}∕2$ appears not to have been analyzed in previous laser theories. Our work could be a useful complementarity to laser theory. It is also an important theoretical foundation for the recently proposed active optical atomic clock based on bad-cavity laser mechanism.