Energy velocity and effective gain in distributed−feedback lasers

Here, we establish a relation G = gv/vℰ between the effective gain coefficient G in a periodic medium (for a Bloch wave) and the ordinary gain coefficient g in a corresponding uniform medium (for an ordinary plane wave). In distributed−feedback (DFB) lasers, G is greater (or smaller) than g because the energy velocity vℰ of a Bloch wave is smaller (or greater) than the phase velocity v of a plane wave. The relation between G and g can be regarded as a first principle for DFB lasers. We can use this principle to test the validity of a DFB−laser theory and to guide us to a correct interpretation of the theoretic result.