Quantum theory of a one-dimensional laser with output coupling. Linear theory

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Abstract
Subthreshold operation of a one-dimensional laser having output coupling is analyzed quantum mechanically under the assumption of constant population inversion. The conventional quantum Langevin theory of the laser is improved in that the spatial behavior of the field is treated exactly by use of a multimode formulation of the field of the universe. This formulation allows the thermal noise to be derived automatically without introducing any artificial damping mechanism for the field; this noise comes from the statistical nature of the initial state of the field. The analysis shows that the cavity quasimodes are excited, that the linewidth formula differs from that of a conventional theory by a factor determined by the field distribution excited in the cavity, and that, outside the cavity, the quantum-mechanical coherence function is propagated with the velocity of light.