Threshold condition of DFB semiconductor lasers by the local-normal-mode transfer-matrix method: correspondence to the coupled-wave method

An analytical expression for the threshold condition of DFB semiconductor lasers is derived based on the local-normal-mode transfer-matrix method (TMM). The threshold condition is expressed in terms of an equivalent reflection coefficient of a DFB laser structure and a Bloch-wave propagation constant. It is shown that the TMM threshold condition can reproduce the one which is derived by the coupled-wave method (CWM) under certain conditions. It is also shown that the CWM can predict very accurately the spatially averaged values of the threshold modal gain and the detuning frequency which are obtained by the TMM if the coupling coefficient in the CWM is replaced by the TMM coupling coefficient.<
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