Laser-induced periodic surface structure. I. Theory

We develop a theory for laser-induced periodic surface structure by associating each Fourier component of induced structure with the corresponding Fourier component of inhomogeneous 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 spacing 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 calculation, 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 surface 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.