Laser microsculpting for the generation of robust diffractive security markings on the surface of metals

AbstractWe report the development of a laser-based process for the direct writing (‘microsculpting’) of unique security markings (reflective phase holograms) on the surface of metals. In contrast to the common approaches used for unique marking of the metal products and components, e.g., polymer holographic stickers which are attached to metals as an adhesive tape, our process enables the generation of the security markings directly onto the metal surface and thus overcomes the problems with tampering and biocompatibility which are typical drawbacks of holographic stickers. The process uses 35ns laser pulses of wavelength 355nm to generate optically-smooth deformations on the metal surface using a localised laser melting process. Security markings (holographic structures) on 304-grade stainless steel surface are fabricated, and their resulted optical performance is tested using a He–Ne laser beam of 632.8nm wavelength

Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups

We define several "standard" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show how Aut(G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decompostion of Aut(G) into a subgroup of locally conjugating automorphisms by the subgroup stabilising a certain lattice of "admissible subsets" of the vertices of C. We then characterise those graphs for which Aut(G) is a product (not necessarily semi-direct) of two such subgroups.Comment: 7 figures, 63 pages. Notation and definitions clarified and typos corrected. 2 new figures added. Appendix containing details of presentation and proof of a theorem adde