Surface plasmon polariton propagation across a gentle silver step

Surface plasmon polaritons (SPPs) are excited with light of wavelength lambda (1) = 632.8 nm on or near a gentle Ag/Ag step structure using focused beam, prism coupling and detected using a bare, sharpened fibre tip. The tip-sample separation is controlled by means of an evanescent optical field at wavelength lambda (2) = 543.5 nm in a photon scanning tunnelling microscope (PSTM). The SPP propagation properties are first characterised on both the thin and thick sections of the Ag film structure either side of the step, both macroscopically, using attenuated total reflection, and microscopically from the PSTM images; the two techniques yield very good agreement. It is found that the SPP propagation length is similar to 10-11 mum across the step in each direction (thick to thin and vice versa) as observed in the PSTM images. Thus, with reference to the propagation lengths of 14.2 and 11.7 mum for the thick and thin planar parts of the Ag film respectively, it is concluded that the SPPs negotiate the step reasonably successfully. Importantly, also, it is shown that images may be produced, displaying SPPs with either an artificially enhanced (similar to 15-20 mum) or truncated (5-8 mum) propagation length across the step. Consideration of such images leads us to suggest the possibility that the photon tunnelling occurs in a local water environment. (C) 2001 Elsevier Science B.V. All rights reserved.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.