Gold nanoparticles deposited on self-organized nano-ripple quartz substrates have been studied by spectroscopic Mueller matrix ellipsometry. The surface was found to have biaxial anisotropic optical properties. For electric field components normal to the ripples the periodic and disconnected nature of the in plane nanowires gives rise to an optical response dominated by the localized plasmon resonance. In the direction parallel to the ripples the gold nanoparticles are aligned closely leading to localized plasmon resonances in the infrared. As Au was deposited at an angle oblique to the surface normal, the gold nanoparticles were formed on the side of the ripples facing the incoming evaporation flux. This makes the gold particles slightly inclined, correspondingly the principal coordinate system of the biaxial dielectric tensor results tilted. The anisotropic plasmonic optical response results in a strong polarizing effect, making it suitable as a plasmonic nanowired grid polarizer.