  A one dimensional theory of lateral spin-polarized transport is derived from
the two dimensional flow in the vertical cross section of a stack of
ferromagnetic and paramagnetic layers. This takes into account the influence of
the lead on the lateral current underneath, in contrast to the conventional 1D
modeling by the collinear configuration of lead/channel/lead. Our theory is
convenient and appropriate for the current in plane configuration of an
all-metallic spintronics structure as well as for the planar structure of a
semiconductor with ferromagnetic contacts. For both systems we predict the
optimal contact width for maximal magnetoresistance and propose an electrical
measurement of the spin diffusion length for a wide range of materials.
