Beam splitters in inhomogeneous nonlocal media

We numerically investigate the dark soliton interaction in an inhomogeneous nonlocal medium and find that the variation of the longitudinal nonlocality disturbs the pair of dark solitons and splits them into two separate dark solitons with the same escape angle but opposite deflection directions. In particular, the escape angle monotonically increases with an increase of the inhomogeneous variation rate. We show that the waveguide induced by the dark soliton interaction yields a complete family of beam splitters for trapped linear beams. Interestingly, a weak probe signal is split into two beams in this waveguide, and the two beams have different powers, which could be controlled by adjusting the nonlocality variation rate.