For appropriate topclogical spaces X, Y, Z the algebra Cc(X xZY) of ℂ-valued continuous functions on the fibre product X xZY in the compact-open topology, describes the completed biprojective Cc(Z)-tensor product of Cc(X), Cc(Y).
In analogy with fibre bundles, which are locally Cartesian products, fibre tensor product bundles are objects that are locally tensor products. These can be patched together via transition maps, etc., into an object very similar to the set of sections of a locally convex algebra bundle.
We give an overview of our recent progress on the design and proof-of-concept demonstration of interfacing components for short-distance optical interconnects with a particular emphasis on their fabrication through two-photon polymerization-based laser direct writing. We show mode field conversion tapers printed on single-mode optical fibers for easy and efficient interfacing to various photonic integrated circuits, circular and square planar waveguide structures with V-groove inspired alignment structures for easy coupling to fibers, microlenses and fan-out diffractive optical elements.
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