“…Where is the group velocity, is the optical confinement factor, ( ) is the coupling coefficient between the forward and backward propagation waves, is the waveguide loss (includes the absorption in both the active and cladding layer as well as any scattering), ( ) is the phase shift at position, is the gain compression coefficient (non-linear coefficient to take into account saturation effects) and is the spontaneous emission term contributed to the forward and backward propagation components, the stochastic property of the noise term ( ) is described by a random process with zero mean value and correlation function as described in [8][9] [10] satisfying the correlation:…”