Analytical seven-wave model for wave propagation in a degenerate dual-pump fiber phase sensitive amplifier

We develop an analytical model to describe propagation of seven continuous waves [two strong pumps, a degenerate signal and idler, two high-order idlers (HOIs), and two high-order pumps (HOPs)] through a nonlinear fiber. The model is developed considering the pumps to be much stronger than the other waves. The seven-wave system is analyzed in terms of interactions among its four-wave subsystems: (i) pumps and degenerate signal and idler, (ii) pumps and HOIs, and (iii) pumps and HOPs. First we analyze the three four-wave subsystems, and then we move to the seven-wave system and compare the two analytical models. The analytical seven-wave model reveals that a strong coupling (mediated through four-wave-mixing processes) between the subsystem with the signal and the subsystem with the HOIs leads to an important role of the HOIs in influencing the signal gain of a degenerate dual-pump fiber phase sensitive amplifier (PSA). We find that the maximum PSA gain of the signal for such an amplifier can be significantly enhanced by launching theHOIs at the fiber input along with the signal.We compare the analytical results with those of a numerical seven-wave model, and for the anomalous dispersion regime, we find good agreement between the two when the system nonlinearity is weak, i.e., total nonlinear phase less than 0.6 rad.