We explain the generation of four wave mixing (FWM) components at the front and back facets of semiconductor optical amplifiers (SOAs) based on the Bragg-scattering from the propagating gratings in the SOAs. We propose a counter-propagating cross-polarized degenerate pumping scheme for polarization-insensitive conjugate generation, simultaneously in both input and output ports of the SOA for the first time. The corresponding Bragg scattering processes along with the phase matching conditions are described and the detuning performance of the generated conjugate in either port are experimentally validated. Polarization-insensitive phase conjugate generation at both input and output ports of the SOA through Bragg scattering FWM is further demonstrated. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement