Is fuck omitted to obtain a linearized form31. Although, this can potentially be a source of inaccuracy of the results, its consequences can be minimized using very tiny steps in numerical calculations. Moreover, the effects of loss are not considered in Eq. (7) since it is a complicated procedure and needs a quantum mechanical considerations. The process of including loss mechanisms in the behavior of the difference operators will be discussed soon. Equation (6) are nonlinear coupled equations with respect to the expectation values. On the other hand, Eq. (7) are linear with respect to the difference operators. To solve Eq. (6), the well-known method of Runge–Kutta can be used38. Here, items for complexity for pump depletion, complex nonlinear coupling coefficient and nonlinear phase mismatch can be taken into account. This is in sharp contrast to analytical approaches, where for simplicity, do not consider any of the above mentioned items.
