When the incident (i) light (with wavevector k₀=2p /l ) falls onto the plane surface, it produces reflected (r) and transmitted (t) waves. Their amplitudes are given by the Fresnel formulas. If the surface is not plane but corrugated, diffracted waves also appear. Because Maxwell equations are linear, it is enough to consider only one sinusoidal Fourier harmonic of corrugation. It acts as a diffraction grating. In the first diffraction order, the anti-Stokes and Stokes waves with parallel to the surface components of the wavevector
                                                                             (1)
appear. These diffracted waves in the media interfere with the (t) wave, which results in the periodic energy deposition into the material. One can expect that the interference will be strongest near the surface, if diffracted waves in the media propagate parallel to the surface. This yields:
                                                               (2)
Another possibility for strong interference is that as a result of diffraction on a corrugation with wavevector q, surface electromagnetic wave (SEW) is excited. In many cases
,
which together with (1) results in a condition
                                                                  (3)
In some cases conditions (2) and (3) may coexist, and therefore most "dangerous" corrugation wavevectors -- i.e., those, which yield the strongest modulation of deposited energy near the surface lie on one or even two circles in the wavevector space. This simple consideration is confirmed by the more complicated calculations for the amplitudes of diffracted waves and their interference with Fresnel (zero order) transmitted wave.

    This diffraction picture can manifest itself in laser ablation experiments in the following way. If constructive interference takes place in the valleys of the corrugation, they will be heated stronger, ablated faster, and corrugation will increase in time. If it takes place in the humps of corrugation, ablation will have a stabilizing effect on it. Other feedback mechanisms are possible, thus making the consideration of the phase of diffracted waves also important.
    Thus, laser ablation (or some other feedback mechanism) may perform a wavevector selection in the initial stochastic surface profile where almost all wavevectors are present. This selection results in certain periodicity which can be analyzed in a diffraction experiments of a probe laser beam. Angular diffraction pattern almost reproduces one of the two ring structure given by (2) or (3).

Calculated dependence of modulation of energy deposition near the surface as a function of wavevector of surface corrugation. These circles are due to SEW (3). Second picture shows the phase shift between the inhomogeneous part of deposited energy and (sinusoidal) surface corrugation. Parameters: e =-3+0.6i, plane of incidence (y-z) angle of incidence q_i=45°, circular polarization. For certain material parameters rings (2) and (3) can bee seen simultaneously.

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