Laser Photon Statistics Caused by Outcoupling and Losses

So far quantum-mechanical laser theories used approaches based on different but equivalent formulations either relying on a density matrix description or on the Fokker-Planck equation [1], [2]. In all these descriptions an important approximation and assumption have been used since: The outcoupling of photons out of the laser resonator was modeled by a loss term in analogy to what an equivalent intra-cavity absorption of photons would cause to the laser quantum state, i.e., an uncorrelated loss of single photons, thereby incorporating the finite cavity Q-factor into the description of the laser. Although this procedure is consistent in terms of energy and average photon number it lacks the fact that a typical dielectric laser output mirror is not just a uncorrelated photon extracting device like an absorbing or scattering object. As the output coupler is a beam splitter it has a complex action on the incoming intra-cavity photon state. The photon state, therefore, reflected back into the laser resonator is not just shifted to a lower average photon number but is a rather complex combination of various number states that are binomially distributed. The goal of this paper is to investigate the consequences of these findings on the laser photon statistics of continuous-wave lasers, now described by the new master equation including the beam-splitter effect [3]. Therefrom, the detailed balance of probability fluxes (Fig. 1) obtains as and the results with the common laser theory based on absorption-like outcoupling used so far is compared.