Valley-dependent Brewster angles and Goos-Hanchen effect in strained graphene

We demonstrate theoretically how local strains in graphene can be tailored to generate a valley polarized current. By suitable engineering of local strain profiles, we find that electrons in opposite valleys (K or K') show different Brewster-like angles and Goos-H\"anchen shifts, exhibiting a close analogy with light propagating behavior. In a strain-induced waveguide, electrons in K and K' valleys have different group velocities, which can be used to construct a valley filter in graphene without the need for any external fields.