  We address (2+1)D surface solitons occurring at the interface between a
linear medium and a nonlocal nonlinear medium whose nonlinear contribution to
the refractive index has a initial value at the interface. We find that there
exist stable single and dipole surface solitons which do not exhibit a power
threshold. The properties of the surface solitons can be affected by the
initial value and the degree of nonlocality. When a laser beam is launched away
from the interface, the beam will be periodic oscillations.
