The Crab optical and ultraviolet polarimetry

Polarisation measurements of pulsars and of their pulsar wind nebulae (PWNe) are uniquely able to provide deep insights into the highly magnetised relativistic environment of young, rotationpowered isolated neutron stars (INSs). Besides the radio band, optical observations are primarily suited to providing such insights. The first INS for which optical polarisation observations were performed is the Crab pulsar which is also the brightest one (V = 16.5). For this reason, the Crab pulsar is also the only INS for which repeated, phase-resolved polarisation measurements have been performed through the years. Moreover, it is the only case, together with the much fainter and distant PSR B0540−69 in the Large Magellanic Cloud (LMC), of an optical pulsar embedded in an optical PWN. Thus, the Crab is a perfect test case to study the optical polarisation properties of pulsars and of their PWNe. In this paper, we review the polarisation properties of the Crab pulsar and of its PWN in the optical and ultraviolet domains, we summarise the state of the art of the polarisation observations of other INSs, and we outline perspectives for INS polarisation studies with present and future generations of optical telescopes.