Domain walls are topological defects which nucleate at symmetry breaking phase transitions. Albeit domain walls are intensively studied in ferromagnetic materials, in which they describe the transition among neighbouring regions of oppositely aligned magnetic dipoles, their equivalent in optics have been poorly exploited so far. Here, we report on the existence of a universal class of polarization domain walls in conventional optical fibres. We capture the symbiotic nature of those entities for which fast polarization knots lead to two robust anticorrelated coupled twin-waves. We exploit their binding properties for optical data transmission beyond the Kerr limits of normally dispersive fibres. More fundamentally, we highlight their trapping behaviour, which manifests itself as a remarkable phenomenon of spontaneous polarization segregation in a system of incoherent random waves, in analogy with the ferromagnetic order–disorder phase transition. These results constitute the first experimental observation of kink/antikink solitary wave propagation in nonlinear fibre optics. Cover design: Loïc Brunot.