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A lateral interface connecting two regions with different strengths of theBychkov-Rashba spin-orbit interaction can be used as a spin polarizer ofelectrons in two dimensional semiconductor heterostructures. [Khodas \emph{etal.}, Phys. Rev. Lett. \textbf{92}, 086602 (2004)]. In this paper we considerthe case when one of the two regions is ballistic, while the other one isdiffusive. We generalize the technique developed for the solution of theproblem of the diffuse emission to the case of the spin dependent scattering atthe interface, and determine the distribution of electrons emitted from thediffusive region. It is shown that the diffuse emission is an effective way toget electrons propagating at small angles to the interface that are mostappropriate for the spin filtration and a subsequent spin manipulation.Finally, a scheme is proposed of a spin filter device, see Fig. 9, that createstwo almost fully spin-polarized beams of electrons.Comment: 11 pages, 9 figure

Diffuse emission in the presence of an inhomogeneous spin-orbit interaction for the purpose of spin filtration