We develop a theory for laser-induced periodic surface structure by associating each Fourier component of induced structure with the corresponding Fourier component of inho- mogeneous energy deposition just beneath the surface. We assume that surface roughness, confined to a region of height much less than the wavelength of light, is responsible for the symmetry breaking leading to this inhomogeneous deposition; we find strong peaks in this deposition in Fourier space, which leads to predictions of induced fringe patterns with spac- ing and orientation dependent on the angle of incidence and polarization of the damaging beam. The nature of the generated electromagnetic field structures and their relation to the simple "surface-scattered wave" model for periodic surface damage are discussed. Our cal- culation, which is for arbitrary angle of incidence and polarization, applies a new approach to the electrodynamics of randomly rough surfaces, introducing a variational principle to deal with the longitudinal fields responsible for local field, or "depolarization, " corrections.
For a p-polarized damaging beam our results depend on shape and filling factors of the sur- face roughness, but for s-polarized light they are essentially independent of these generally unknown parameters; thus an unambiguous comparison of our theory with experiment is possible.