On translation lengths of Anosov maps on the curve graph of the torus

Geometriae Dedicata - We show that an Anosov map has a geodesic axis on the curve graph of the torus. The direct corollary of our result is the stable translation length of an Anosov map on the...     

Right-angled Artin groups in the C∞ diffeomorphism group of the real line

We prove that every right-angled Artin group embeds into the C^∞ diffeomorphism group of the real line. As a corollary, we show every limit group, and more generally every countable residually RAAG group, embeds into the C^∞ diffeomorphism group of the real line.     

Nanostructured gradient-index antireflection diffractive optics

We describe the fabrication and characterization of a nanostructured diffractive element with near-zero reflection losses. In this element, subwavelength nanostructures emulating adiabatic index matching are integrated on the surface of a diffractive microstructure to suppress reflected diffraction orders. The fabricated silicon grating exhibits reflected efficiencies that are suppressed by 2 orders of magnitude over broad wavelength bands and wide incident angles. Theoretical models of the fabricated structure based on rigorous coupled-wave analysis and effective medium theory are in agreement with the experimental data. The proposed principles can be applied to improve the performance of any diffractive structures, potentially leading to more efficient Fresnel lenses, holographic elements, and integrated optical systems.