Perfect optical coherence lattices

Free-space propagation of optical coherence lattices and periodicity reciprocity.

We examine paraxial propagation of recently introduced optical coherence lattices in free space and demonstrate a novel phenomenon of periodicity reciprocity between their intensity and coherence properties. The periodicity reciprocity arises because an aperiodic source intensity profile of an optical coherence lattice evolves into a lattice-like far-field profile, while the periodic spectral d...

Jessen / Deutsch , " Optical Lattices " 1 OPTICAL LATTICES

Low dimensional strongly perfect lattices. III: Dual strongly perfect lattices of dimension 14

The extremal 3-modular lattice [±G2(3)]14 with automorphism group C2 × G2(F3) is the unique dual strongly perfect lattice of dimension 14.

Low dimensional strongly perfect lattices . II : Dual strongly perfect lattices of dimension 13 and 15

A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.

Perfect Delaunay Polytopes and Perfect Quadratic Functions on Lattices

A polytope D, whose vertices belong to a lattice of rank d, is Delaunay if it can be circumscribed by an ellipsoid E with interior free of lattice points, and so that the vertices of D are the only lattice points on the quadratic surface E. If in addition E is uniquely determined by D, we call D a perfect Delaunay polytope. Thus, in the perfect case, the lattice points on E, which are the verti...