The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex set of each facet forms a lattice basis. Casagrande showed that any smooth d-dimensional Fano polytope has at most 3d vertices. Smooth Fano ...

We investigate Fano resonances in planar two-dimensional periodic arrays of linear trimers of plasmonic nanoparticles that appear under plane wave incidence. The observed Fano resonances are associated to resonances belonging to the trimer (metamolecule) itself, where some are found to be strongly affected by the array periodicity. We observe that array-dependent resonances appearing for obliqu...

We investigate the generic properties of optical cavities with subwavelength structured mirrors whose reflectivity profile exhibit Fano resonances. We focus in particular on short microcavities and mirrors with high quality factor Fano resonances for which the cavity free-spectral range becomes larger than the width of the Fano resonance. In this unusual regime, the transmission spectrum of the...

We propose a controllable way of tuning Fano resonances in open quantum dots in the absence of magnetic field. A quantum dot can be modified by changing the gate voltages that define the dot itself. An extra degree of freedom can be introduced by means of a controllable repulsive perturbation, such as the one induced by scanning a Atomic Force Microscope tip on a real sample. We numerically inv...

We investigate for the first time the capacity of a twodimensional periodic array (a metasurface) of circular nanoclusters (CNCs) of plasmonic nanoparticles to support magnetic Fano resonances. These resonances are characterized by narrow angular and/or spectral features in the reflection/transmission/absorption coefficients associated with a circular disposition of nanoparticles’ dipole moment...

The observation of Fano resonance phenomena is universal across several branches of physics. Photonics is one of the most important areas of physics that mainly deals with the control of light propagation and localization through its interaction with natural and artificially engineered media. In an era of miniaturization, manipulation of light at micro-nanoscales has assumed unprecedented signi...

We shall give the best possible upper bound of the Fano indices together with a characterization of those Q-Fano 3-folds which attain the maximum in terms of graded rings. 0. Introduction Q-Fano 3-folds play important roles in birational algebraic geometry. They have been studied by several authors since G. Fano. In this paper, we study Q-Fano 3-folds from the view of their Fano indices (See de...