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The Goos-Hänchen effect at the non periodic surface of a negative index metamaterial

We investigate the lateral displacement (Goos-Hänchen lateral shift) of a linearly polarized Gaussian beam reflected from a corrugated surface between a conventional dielectric and a homogeneous isotropic metamaterial with a negative index of refraction. We pay particular attention to effects associated with the resonant excitation of surface plasmon polaritons. The dependence of the lateral displacement on the incident beam parameters is examined in detail and discussed in different situations among which is the total reflection case. We compare these characteristics with the limiting case of reflection of a beam from a surface with infinitely periodic corrugations.