Analytical Method for Calculation of the Photon Lifetime and External Coupling Coefficient in Index-Coupled Phase-Shifted DFB Lasers

An analytical expression for the photon lifetime in index-coupled distributed feedback laser is derived and studied at, and below, the threshold condition. It is shown that the photon lifetime considerably varies with the frequency detuning in the vicinity of the dominant laser mode. The increase in the structural parameters, such as grating coupling constant and length of the DFB structure, leads to the increase in both the photon lifetime and the magnitude of its variation due to frequency detuning, while the increase in material gain has the opposite effect. The spectral dependence of the photon lifetime has important implications on calculation of the external coupling coefficient of DFB lasers.