Proofs for free - parametricity for dependent types

Reynolds' abstraction theorem shows how a typing judgement in System F can be translated into a relational statement (in second order predicate logic) about inhabitants of the type. We obtain a similar result for pure type systems: for any PTS used as a programming language, there is a PTS that can be used as a logic for parametricity. Types in the source PTS are translated to relations (expressed as types) in the target. Similarly, values of a given type are translated to proofs that the values satisfy the relational interpretation. We extend the result to inductive families. We also show that the assumption that every term satisfies the parametricity condition generated by its type is consistent with the generated logic

Stochastic light concentration from 3D to 2D reveals ultraweak chemi- and bioluminescence

For countless applications in science and technology, light must be concentrated, and concentration is classically achieved with reflective and refractive elements. However, there is so far no efficient way, with a 2D detector, to detect photons produced inside an extended volume with a broad or isotropic angular distribution. Here, with theory and experiment, we propose to stochastically transform and concentrate a volume into a smaller surface, using a high- albedo Ulbricht cavity and a small exit orifice through cavity walls. A 3D gas of photons produced inside the cavity is transformed with a 50% number efficiency into a 2D Lambertian emitting orifice with maximal radiance and a much smaller size. With high-albedo quartz-powder cavity walls ( P = 99.94%), the orifice area is 1/( 1 - P) approximate to 1600 times smaller than the walls' area. When coupled to a detectivity-optimized photon-counter ( D = 0.015 photon- 1 s1/ 2 cm) the detection limit is 110 photon s- 1 L- 1. Thanks to this unprecedented sensitivity, we could detect the luminescence produced by the non-catalytic disproportionation of hydrogen peroxide in pure water, which has not been observed so far. We could also detect the ultraweak bioluminescence produced by yeast cells at the onset of their growth. Our work opens new perspectives for studying ultraweak luminescence, and the concept of stochastic 3D/2D conjugation should help design novel light detection methods for large samples or diluted emitters

Polymer microstructure waveguides on various substrates for optical interconnection and communication

Planar polymer lightguides ofpoly-(methyl methacrylate) (PMMA) are doped with a UV sensitive material and an azo dye, sensitive for green or blue light (514, 488 nm) simultaneously. The UV-sensitive material is used for recording a permanent waveguide pattern while the azo dye is meant for a reversible light induced refractive index change. Although the azo dye is partly destroyed by the UV light and the photochemical reaction during waveguide formation, a light induced phase modulation in the guide is still possible in such bifunctional materials

Thick phase hologram for optical clock distribution application on wafer scale integrated circuits

We propose the first monolithic optical clock distribution network on wafer scale integrated circuits (WSIC) . This new architecture can save real estate on VLSI chips and eliminate the packaging, alignment and interface problems of previously proposed architectures. A l-to-3 optical fan out for clock signal distribution application is demonstrated by utilizing a DCC multiplexed volume hologram on a thin quartz plate