Quadrupole plasmon and (octupolar) Fano resonances are induced in lithographically fabricated theta-shaped ring-rod gold nanostructures. The optical response is characterized by measuring the light scattered by individual nanostructures. When the nanorod is brought within 3 nm of the ring wall, a weak quadrupolar resonance is observed due to capacitive coupling, and when a necklike conductive b...

In this article the map given by the anticanonical bundle of a Fano manifold is investigated with respect to a number of natural notions of higher order embeddings of projective manifolds. This is of importance in the understanding of higher order embeddings of the special varieties of adjunction theory, which are usually bered by special Fano manifolds. An analysis is carried out of the higher...

The symmetric edge polytopes of odd cycles (del Pezzo polytopes) are known as smooth Fano polytopes. In this extended abstract, we show that if the length of the cycle is 127, then the Ehrhart polynomial has a root whose real part is greater than the dimension. As a result, we have a smooth Fano polytope that is a counterexample to the two conjectures on the roots of Ehrhart polynomials. Résumé...

Light localization in disordered systems and Bragg scattering in regular periodic structures are considered traditionally as two entirely opposite phenomena: disorder leads to degradation of coherent Bragg scattering whereas Anderson localization is suppressed by periodicity. Here we reveal a non-trivial link between these two phenomena, through the Fano interference between Bragg scattering an...

By a canonical (resp. terminal) weak Q-Fano 3-fold we mean a normal projective one with at worst canonical (resp. terminal) singularities on which the anti-canonical divisor is QCartier, nef and big. For a canonical weak Q-Fano 3-fold V , we show that there exists a terminal weak Q-Fano 3-fold X , being birational to V , such that the m-th anti-canonical map defined by | −mKX | is birational fo...

The realization and detection of Majorana fermions in condensed matter systems are of considerable importance and interest. We propose a scheme to detect the Majorana fermions by Fano resonance in hybrid nanostructures made of semiconductor quantum dots and quantum wire in proximity to superconductor. Through detailed theoretical studies of the transport properties of our hybrid nanostructures ...

A recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor P/Ī (the ratio of the noise power and the mean transmitted current) is related to the scattering matrix of the medium. This is the optical analogue of Büttiker’s formula for electronic shot noise. Scattering by itself has no effect on the Fano factor, which remains equal to ...

In the classification of Fano varieties, those which are not “Gino Fano”, i.e., where −KX is ample but not very ample, are usually annoying. In the beginning of his classification of Fano threefolds, Iskovskikh listed those for which |−KX | is not free. The purpose of this article is to see how his result extends to the canonical Gorenstein case. If X is a Gorenstein Fano threefold with at wors...

Localized surface plasmon resonances (LSPRs) in metallic nanostructures have been studied intensely in the last decade. Fano interference is an important way to decrease the resonance linewidth and enhance the spectral detection resolution, but realizing a Fano lineshape with both a narrow linewidth and high spectral contrast-ratio is still challenging. Here we propose a metallic nanostructure ...

We propose a route to the spectral separation of optical spin angular momentum based on spin-dependent Fano resonances with antisymmetric spectral profiles. By developing a spin-form coupled mode theory for chiral materials, the origin of antisymmetric Fano spectra is clarified in terms of the opposite temporal phase shift for each spin, which is the result of counter-rotating spin eigenvectors...