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In this paper, we demonstrate the generation of periodic surface structures on a technologically important material, tungsten, at both 400 and 800 nm, despite that the table values of dielectric constants for tungsten at these two wavelengths suggest the absence of surface plasmons, a wave necessary for forming periodic structures on metals. Furthermore, we find that the structure periods formed on tungsten are significantly less than the laser wavelengths. We believe that the dielectric constants of tungsten change significantly due to intense laser pulse heating and surface structuring and roughening at nanometer scales, permitting surface plasmon excitation and periodic structure formation.