Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers

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Abstract
A theory of spontaneous emission noise is presented based on classical electromagnetic theory. Unlike conventional theories of laser noise, this presentation is valid for open resonators. A local Langevin force is added to the wave equation to account for spontaneous emission. A general expression is found relating the diffusion coefficient of this force to the imaginary part of the dielectric function. The fields of lasers and amplifiers are found by solving the wave equation by the Green's function method. The lasing mode is a resonant state associated with a pole in Green's function. In this way, noise in lasers and amplifiers is treated by a unified approach that is valid for either gain guiding or index guiding. The Langevin rate equations for the laser are derived. The theory is illustrated with applications to traveling wave and Fabry-Perot amplifiers and Fabry-Perot lasers. Several new results are found: optical amplifier noise increases inversely with quantum efficiency; spontaneous emission into the lasing mode is enhanced in lasers with low facet reflectivities; and the linewidth of a Fabry-Perot laser with a passive section decreases as the square of the fraction of the cavity optical length that is active.