“…(1) . (2) where E is the traveling optical wave (frontward or backward), v g the group velocity, B the propagation constant, T the confinement factor, g m the material gain, a the linewidth enhancement factor, a s the modal loss, S the spontaneous emission, n(z) the carrier density, N s (z) and N(z) the photon rates of signal and spontaneous emission (N=|E| 2 ), I the injected current, K the normalization factor of random spontaneous emission and L, d, W are the waveguide length, thickness and width, respectively.…”