Relation between nonlocal surface and bulk dark solitons

We investigate the existence and stability of nonlocal surface dark solitons at the interface formed by a nonlocal nonlinear self-defocusing medium and a linear medium. We find that nonlocal fundamental surface dark solitons are always stable in their entire existence domain, while high-order surface dark solitons are oscillatory stable. Comparing with nonlocal bulk dark solitons in amplitude and boundary conditions, nonlocal surface dark solitons can be regarded as the half of the corresponding bulk dark solitons with antisymmetrical amplitude distribution.