Soliton steering in a ramp waveguide with nonlocal nonlinearity

We present an analytical and numerical investigation of a spatial soliton propagating in a waveguide with ramp linear refractive index profile (ramp waveguide) and nonlocal nonlinearity. It is shown analytically by equivalent particle approach and numerically by implicit Crank-Nicolson scheme that in a ramp waveguide with local nonlinearity, the soliton experiences negative acceleration along the waveguide where its refractive index decreases linearly. On the other hand, if the soliton propagates in a uniform medium with nonlocal nonlinear response then it will experience a self-bending in the positive direction where the bending level depends on the soliton amplitude as well as on the strength of nonlocality. By combining these two effects, rich dynamics of soliton can be achieved. In this case, the soliton may oscillate inside the waveguide, move to the left or to the right part of the waveguide or even be trapped. Such soliton steering can be controlled by the soliton amplitude or by its initial position.