Light transfer between a curved single-mode fiber and a two-mode planar waveguide is investigated experimentally with respect to its dependence on the refractive index and the thickness of the planar waveguide and for different polishing depths. The behavior of this distributed coupler is treated theoretically with a coupled-mode model, which takes into account the two dimensions of the waveguide configuration, as well as the even or the odd symmetry of the planar waveguide mode field. Coupling of a fiber to a multimode planar waveguide is also considered.