Scattering of a surface plasmon polariton by a localized dielectric surface defect.

On the basis of a rigorous, nonperturbative, purely numerical solution of the corresponding reduced Rayleigh equation for the scattering amplitudes we have studied the scattering of a surface plasmon polariton by a two dimensional dielectric defect on a planar metal surface. The profile of the defect is assumed to be an arbitrary single-valued function of the coordinates in the plane of the metal surface, and to be differentiable with respect to those coordinates. When the defect is circularly symmetric and the dependence of the scattering amplitudes on the azimuthal angle is expressed by a rotational expansion, the reduced Rayleigh equation is transformed into a pair of one-dimensional integral equations for each value of the rotational quantum number. This approach is applied to a defect in the form of an isotropic Gaussian function. The differential cross sections for the scattering of the incident surface plasmon polariton into volume electromagnetic waves in the vacuum above the surface and into other surface plasmon polaritons are calculated, as well as the intensity of the field near the surface. These results differ significantly from the corresponding results for a metallic defect on a metallic substrate.

Dynamic stability of crack fronts: out-of-plane corrugations.

The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids 45, 591 (1997)] to study the out-of-plane stability of planar crack fronts in the framework of linear elastic fracture mechanics. We discuss a minimal scenario in which linearly unstable crack front corrugations might emerge above a critical front propagation speed. We calculate this speed as a function of Poisson's ratio and show that corrugations propagate along the crack front at nearly the Rayleigh wave speed. Finally, we hypothesize about a possible relation between such corrugations and the long-standing problem of crack branching.