M ay 2 01 0 Analytical theory of dark nonlocal solitons

Spatial dark optical solitons are localized light intensity dips in the infinite constant background [1–3]. Like their bright counterparts, they propagate preserving their spatial profile. This is a result of a balance between diffraction which tends to broaden their size and nonlinearity of the medium which counteracts this process. The existence of dark spatial solitons requires the nonlinearity of the medium to be negative, or self-defocusing, i.e. refractive index of the medium must decrease with light intensity [1]. In the simplest case of Kerr medium the change of the refractive index is just proportional to the light intensity. In this special situation and in one-dimensional case the soliton amplitude u(x, z) is described analytically by the following relation u(x, z) = B tanh(x− vz) + iA, (1)