Abstract

Continuous-wave (cw) lasers are often described by the laser rate equation, in which the stimulated-emission equals the photon-decay rate. Frequently neglected is the spontaneous-emission rate into the lasing resonator mode [1]. Consequently, the gain would equal the losses, the emitted laser light would be a pure sine wave, its linewidth would become a delta function, and coherent photons would exist only above the threshold. The finite laser linewidth [2,3] is then recovered a posteriori via the phase change induced by spontaneous emission [4]. We generalize the existing theory by a priori considering spontaneous emission in the laser rate equation [5], derive the correct laser linewidth below and above the threshold, and show that the Schawlow-Townes linewidth [3] is a three-fold approximation that does not represent a lower limit to the laser linewidth [5].

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