[en] We investigate the incident angle-dependent spin polarisation transport in a ballistic nonmagnetic nanojunction with interfacial spin–orbit (SO) coupling by means of the mode-matching approach. In the absence of interfacial SO coupling, for both delta function and square-shaped barriers, the probabilities of transmission for spin up and spin down are the same and are even functions of the injection angle. On the other hand, in the presence of interfacial SO coupling, the transmission probabilities for spin up and spin down are different and are asymmetric with respect to the direction of the normal incidence. Moreover, we study the total transmission properties and analyse the spin polarisation properties of these systems. In particular, for the case of interface with SO coupling, we find that the spin polarisation oscillates with respect to the incident angle. This characteristic offers an efficient way to achieve the spin injection device without using ferromagnets. (paper)