Frequency-shift free optical phase conjugation using counter-propagating dual pump four-wave mixing in fiber

Abstract

We propose and numerically verify a novel scheme of frequency-shift free optical phase conjugation by counter-propagating dual pump four-wave mixing in nonlinear fiber. The two counter-propagating pumps create a Bragg grating inside the fiber, which diffracts the forward propagating signal and generates a backward propagating idler wave whose phase is conjugate of signal phase. The two pump frequencies are placed symmetrically about signal frequency to ensure that idler wave will have same frequency as that of signal wave. Since the signal and idler waves appear at opposite ends, the idler is easily filtered out from the rest of the spectrum. Using nonlinear Schrödinger equation, we derive equations of signal and idler evolution. We obtain expressions for idler phase and show that perfect phase conjugation is achieved at an optimum length of fiber for a given pump power. We study the effect of fiber length and pump power on phase conjugation. Simulation results show the perfect phase conjugation at optimum fiber length under lossless conditions and small phase-offset when fiber loss and self and cross phase modulations are included. The small phase-offset is avoided by choosing fiber length smaller than optimum fiber length. Simulation results exhibit close agreement to theoretical values, which validates our simulations.