  Weak gravitational lensing by the large scale structure can be used to probe the dark matter distribution in the Universe directly and thus to probe cosmological models. The recent detection of cosmic shear by several groups has demonstrated the feasibility of this new mode of observational cosmology. In the currently most extensive analysis of cosmic shear, it was found that the shear field contains unexpected modes, so-called B-modes, which are thought to be unaccountable for by lensing. B-modes can in principle be generated by an intrinsic alignment of galaxies from which the shear is measured, or may signify some remaining systematics in the data reduction and analysis. In this paper we show that B-modes in fact {\it are produced} by lensing itself. The effect comes about through the clustering of source galaxies, which in particular implies an angular separation-dependent clustering in redshift. After presenting the theory of the decomposition of a general shear field into E- and B-modes, we calculate their respective power spectra and correlation functions for a clustered source distribution. Numerical and analytical estimates of the relative strength of these two modes show that the resulting B-mode is very small on angular scales larger than a few arcminutes, but its relative contribution rises quickly towards smaller angular scales, with comparable power in both modes at a few arcseconds. The relevance of this effect with regard to the current cosmic shear surveys is discussed. 
B-modes in cosmic shear from source redshift clustering