We demonstrate theoretically and experimentally that Fano resonances can be obtained in terahertz metamaterials that are composed of periodic continuous metallic wires dressed with periodic split ring resonators. An asymmetric Fano lineshape has been found in a narrow frequency range of the transmission curve. By using a transmission line combined with lumped element model, we are able to not o...

Smooth toric Fano varieties are classified up to dimension 4. In dimension 2, there are five toric Del Pezzo surfaces: P, P1×P1, and Si, the blowup of P in i points, for i = 1, 2, 3. There are 18 toric Fano 3-folds [2, 20] and 124 toric Fano 4-folds [4, 17]. In higher dimensions, little is known about them and many properties that hold in low dimensions are not known to hold in general. Let X b...

A tunable microwave scattering device is presented which allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. We observe a non-monotonic evolution of resonance parameters that is explained in terms of interacting resonances. The dissipation of radiation in the cavity walls leads to decoherence and thus to a modification of the Fano profile. We...

Systems with coupled cavities and waveguides have been demonstrated as optical switches and optical sensors. To optimize the functionalities of these optical devices, Fano resonance with asymmetric and steep spectral line shape has been used. We theoretically propose a coupled photonic crystal cavity-waveguide structure to achieve Fano resonance by placing partially reflecting elements in waveg...

From an octonion algebra $\mathbb{O}$ over a field $k$ of characteristic not two or three, we show that the fundamental representation ${\rm Im}(\mathbb{O})$ derivation Der}(\mathbb{O})$ and spinor $\mathfrak{so}({\rm Im}(\mathbb{O}))$ are special orthogonal representations. They have particular geometric properties coming from their similarities with binary cubics covariants these representati...

Since its discovery, the asymmetric Fano resonance has been a characteristic feature of interacting quantum systems. The shape of this resonance is distinctively different from that of conventional symmetric resonance curves. Recently, the Fano resonance has been found in plasmonic nanoparticles, photonic crystals, and electromagnetic metamaterials. The steep dispersion of the Fano resonance pr...

Combining the connectedness principle of Shokurov and Kollár with the technique of hypertangent divisors, we develop a new technique of studying birational maps of natural Fano fiber spaces. We prove that the only structures of a rationally connected fibration on direct products of typical Fano varieties are projections onto the factors. In particular, the groups of biregular and birational sel...

Any smooth projective Fano variety in characteristic zero is rationally connected and hence contains a very free rational curve. In positive characteristic a smooth projective Fano variety is rationally chain connected. However, it is not known whether such varieties are separably rationally connected, or equivalently, whether they have a very free rational curve. This is an open question even ...

The modern study of the birational properties of Fano varieties started with the works of Iskovskikh; see the surveys [Isk01, Che05] and the many references there. A key concept that emerged in this area is birational rigidity. Let X be a Fano variety with Q-factorial, terminal singularities and Picard number 1. Roughly speaking, X is called birationally rigid if X can not be written in terms o...

Statistical coding techniques have been used for a long time in lossless data compression, using methods such as Huffmans algorithm, arithmetic coding, Shannon’s method, Fano’s method, etc. Most of these methods can be implemented either statically or adaptively. In this paper, we show that although Fano coding is sub-optimal, it is possible to generate static Fano-based encoding schemes which ...