The POLAR detector is a space based Gamma-Ray Burst (GRB) polarimeter sensitive in the 15-500 keV energy range. Apart from its main scientific goal as a Gamma-Ray Burst polarimeter it is also able to detect photons from pulsars in orbit. By using the six-months in-orbit observation data, significant pulsation from the PSR B0531+21 (Crab pulsar) was obtained. In this work, we present the precise timing analysis of the Crab pulsar, together with a phase-resolved spectroscopic study using a joint-fitting method adapted for wide field of view instruments like POLAR. By using single power law fitting over the pulsed phase, we obtained spectral indices ranging from 1.718 to 2.315, and confirmed the spectral evolution in a reverse S shape which is homogenous with results from other missions over broadband. We will also show, based on the POLAR in-orbit performance and Geant4 Monte-Carlo simulation, the inferred capabilities of POLAR-2, the proposed follow-up mission of POLAR on board the China Space Station (CSS), for pulsars studies.
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