Simplified Empirical Equations to Coefficients of Linear and Nonlinear Gain of InGaAsP/InP Semiconductor Lasers and Application in Simulation of Noise

This paper presents modeling of the linear and nonlinear gain of long-wavelength In 1− x Ga x As y P 1− y /InP laser basing on a third-order perturbation approach using the density matrix analysis. We modify the perturbation approach in literature by taking account of electronic transitions between the conduction band and both the heavy and light-hole bands of the active layer. The obtained results on gain characteristics of this complicated approach are simplified by empirical equations that function in the bandgap energy of the active layer. Therefore, the gain characteristics of the laser can be simply calculated at the bandgap energy that corresponds to arbitrary compositions x and y of In 1− x Ga x As y P 1− y /InP 1− y supposing lattice matching with the base InP material. The results show that both the linear gain and nonlinear gain coefficients decrease with the increase of the bandgap energy. The obtained relationships of the gain characteristics are then used in the rate equation model to simulate the spectral properties of the relative intensity noise (RIN) of InGaAsP laser as a function of the bandgap energy over the relevant ranges of compositions x and y . Moreover, we introduce fitting equations to the RIN levels around the relaxation frequency of the laser as well as in the low-frequency range as functions of the bandgap energy. These RIN levels are shown to increase with the increase of the bandgap energy and are associated with a decrease in the relaxation frequency of the laser.