Femtosecond laser writing of birefringent subwavelength nanostructures in dielectrics has been studied for almost two decades since it is of interest for a number of practical applications such as optical memory, optical waveguides, microfluidic channels, etc. In this work, a numerical modeling of the formation of plasma periodic nanostructures in fused silica in the direction of propagation of a focused laser beam is carried out. It is shown that the focused beam creates a plasma layer with a supercritical concentration of electrons which provides an effective reflection of the incident laser pulse, leading to the formation of a standing wave of ionization. Effective ionization occurs in the bungles of wave, that forms a plasma lattice with a period equal to the period of the standing wave in the medium. Modeling allows us to determine the conditions under which the proposed regime of nanostructuring is possible. Keywords: laser microstructuring in dielectrics, birefringent nanostructures, fused silica, electron-hole plasma, nano- and micromodifications, multiphoton ionization in strong fields.