Threshold condition for thin-film distributed-feedback lasers

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Abstract
An exact solution to wave propagation in thin‐film periodic structures using Bloch waves is presented and from it the threshold condition for distributed‐feedback DFB lasers is derived. The form of the latter is identical to the oscillation condition of cavity lasers but with the appropriate reflection coefficients and propagation constant for Bloch waves substituted. We find that for laser action Bragg scattering alone is not sufficient but structural changes at both ends of the structure are necessary in order to produce appreciable reflection of the Bloch waves. Suggestions on how to achieve these reflections are given.