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Four-wave mixing (FWM) in few-mode fibers (FMFs) has been extensively investigated to develop mode-related alloptical signal processing, such as wavelength conversion, parametric amplification and mode conversion. Compared to the FWM processes in single-mode fibers, intermodal FWM in FMFs shows more flexible phase-matching condition by tailoring the modal dispersion of each optical mode. Generally, there are two mainly different types of FWM processes, namely, Bragg scattering (BS) and phase conjugation (PC). In this paper, we focus our interest on the PC-FWM in both graded-index (GI) and step-index (SI) FMFs to probe mode conversion. In the PC-FWM, the energy transfers from pump modes to both signal and idler waves. From the point of phase matching, the modal dispersions of the two FMFs is firstly optimized by genetic algorithm (GA) to design optimal core radius and core-cladding refractive difference. We then investigate the effect of the small deviations of these two parameters from their optimal values upon the phase mismatch. Numerical results show that both SI and GI fibers are able to convert the LP01 mode to the LP02 mode with the phase matching condition of the SI fiber being more sensitive to the changes of fiber parameters. In addition, we analyze the dependence of mode conversion performance (bandwidth and efficiency) on fiber length and pump level. It is shown that the 3dB-bandwidth increases with the pump power in the PC-FWM, which can be attributed to the nonlinear phase shift induced by the high pump power compensate for the linear phase mismatch.
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