Using an electromagnetic approach based on three-dimensional Maxwell's equations coupled with electron density equation, we investigate femtosecond laser interaction with fused silica containing randomly distributed inhomogeneities. By irradiating with linearly, radially, azimuthally, circularly and mixed polarized beams, we visualize and analyze the resulting electron density distributions in glass. The numerical calculations demonstrate the local material excitation to the polarization state of light and underline the nanostructure orientation perpendicular to the local laser polarization. The advantages of using azimuthal- and radial-variant polarizations to produce the nanogratings with desirable characteristics are discussed. Circularly polarized beams are shown to be, on the contrary, beneficial to prevent the nanostructure self-organization.