Optimized Multimode Interference Fiber Based Refractometer in A Reflective Interrogation Scheme

A fiber based refractometer in a reflective interrogation scheme is investigated and optimized. A thin gold film was deposited on the tip of a coreless fiber section, which is spliced with a single mode fiber. The coreless fiber is a multimode waveguide, and the observed effects are due to multimode interference. To investigate and optimize the structure, the multimode part of the sensor is built with 3 different lengths: 58 mm, 29 mm and 17 mm. We use a broadband light source ranging from 1475 nm to 1650 nm and we test the sensors with liquids of varying refractive indices, from 1.333 to 1.438. Our results show that for a fixed wavelength, the sensor sensitivity is independent of the multimode fiber length, but we observed a sensitivity increase of approximately 0.7 nm/RIU for a one-nanometer increase in wavelength

Minkowski-type and Alexandrov-type theorems for polyhedral herissons

Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.Comment: 19 pages, 8 figures, LaTeX 2.0