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We construct several new families of Fano varieties of K3 type. We give a geometrical explanation of the K3 structure and we link some of them to projective families of irreducible holomorphic symplectic manifolds., 28 pages

We solve the infinitesimal Torelli problem for $3$-dimensional quasi-smooth ${\mathbb{Q}}$-Fano hypersurfaces with at worst terminal singularities. We also find infinite chains of double coverings of increasing dimension which alternatively distribute themselves in examples and counterexamples for the infinitesimal Torelli claim and which share the analogue, and in some cases the same, Hodge-diagram properties as the length $3$ Gushel-Mukai chain of prime smooth Fanos of coindex $3$ and degree $10$., Comment: Final version, to appear in Journal of Geometry and Physics

High-Q metasurfaces have attracted much interest owing to their potential application in biological sensors. FANO is a type of high-Q factor metasurface. However, it is difficult to achieve large resonant intensity and a high-Q factor at the same time. In this paper, by sharpening the tips of the asymmetrical split-ring FANO structure and letting more charges stack at the tips to enhance tip coupling, the Q factor was significantly improved without sacrificing too much resonant intensity. Simulation results showed that the Q factor increased up to 2.4 times, while the resonant intensity stayed higher than 20 dB, and the experiment results agreed with the simulations. This indicated that the tip-field-enhancement theory can be applied in time-harmonic electromagnetic-fields, and the method proposed here can be used to increase the sensitivity and accuracy of microfluidic sensors. Additionally, other types of research, such as on antenna design, could benefit from this theory.

Chiral metamaterials with asymmetric transmission can be applied as polarization-controlled devices. Here, a Mie-based dielectric metamaterial with a spacer exhibiting asymmetric transmission of linearly polarized waves at microwave frequencies was designed and demonstrated numerically. The unidirectional characteristic is attributed to the chirality of the metamolecule and the mutual excitation of the Mie resonances. Field distributions are simulated to investigate the underlying physical mechanism. Fano-type resonances emerge near the Mie resonances of the constituents and come from the destructive interference inside the structure. The near-field coupling further contributes to the asymmetric transmission. The influences of the lattice constant and the spacer thickness on the asymmetric characteristics were also analyzed by parameter sweeps. The proposed Mie-based metamaterial is of a simple structure, and it has the potential for applications in dielectric metadevices, such as high-performance polarization rotators.

We define a class of non-compact Fano toric manifolds, called admissible toric manifolds, for which Floer theory and quantum cohomology are defined. The class includes Fano toric negative line bundles, and it allows blow-ups along fixed point sets. We prove closed-string mirror symmetry for this class of manifolds: the Jacobian ring of the superpotential is the symplectic cohomology (not the quantum cohomology). Moreover, SH(M) is obtained from QH(M) by localizing at the toric divisors. We give explicit presentations of SH(M) and QH(M), using ideas of Batyrev, McDuff and Tolman. Assuming that the superpotential is Morse (or a milder semisimplicity assumption), we prove that the wrapped Fukaya category for this class of manifolds satisfies the toric generation criterion, i.e. is split-generated by the natural Lagrangian torus fibres of the moment map with suitable holonomies. In particular, the wrapped category is compactly generated and cohomologically finite. The proof uses a deformation argument, via a generic generation theorem and an argument about continuity of eigenspaces. We also prove that for any closed Fano toric manifold, if the superpotential is Morse (or a milder semisimplicity assumption) then the Fukaya category satisfies the toric generation criterion. The key ingredients are non-vanishing results for the open-closed string map, using tools from the paper by Ritter-Smith (we also prove a conjecture from that paper that any monotone toric negative line bundle contains a non-displaceable monotone Lagrangian torus). We also need to extend the class of Hamiltonians for which the maximum principle holds for symplectic manifolds conical at infinity, thus extending the class of Hamiltonian circle actions for which invertible elements can be constructed in SH(M)., 70 pages (51 pages + appendices). Version 2: rewrote the Introduction, fixed a mistake (Remark 1.15), generation theorem generalized to all admissible toric manifolds (Section 1.8)

The interaction between microscopic particles has always been a fascinating and intriguing area of science. Direct interrogation of such interactions is often difficult. Structured electromagnetic systems offer a rich toolkit for mimicking and reproducing the key dynamics that governs the microscopic interactions, and thus provide an avenue to explore and interpret the microscopic phenomena. In particular, metamaterials offer the freedom to artificially tailor light-matter coupling and to control the interaction between unit cells in the metamaterial array. Here we demonstrate a terahertz metamaterial that mimics spin-related interactions of microscopic particles in a 2D lattice via complex electromagnetic multipoles scattered within the metamaterial array. Fano resonances featured by distinct mode properties due to strong nearest-neighbor interactions are discussed that draw parallels with the 2D Ising model. Interestingly, a phase transition from single Fano resonance to hyperfine splitting of Fano spectrum is observed by manipulating the 2D interactions without applying external magnetic or electric fields, which provides a potential multispectral platform for applications in super-resolution imaging, biosensing, and selective thermal emission. The dynamic approach to reproduce static interaction between microscopic particles would enable more profound significance in exploring the unknown physical world by the macroscopic analogues.

We propose a planar metamaterial formed by four-strip metallic resonators, which can achieve high-Q Fano resonance in terahertz regime. This terahertz planar metamaterial supports a sharp Fano resonance at 0.81 THz with 25% transmission. The resonance bandwidth of the dip is 0.014 THz with the Q-factor of 58. The interference between the bright mode and dark mode leads to the Fano line shape. This sharp Fano profile is explained by the electromagnetic theory of Fano resonance. Moreover, multiple Fano resonances can be realized by adding more strips into the original structure. As an example, two Fano dips with Q-factors of 61 and 65 can be achieved via a five-strip structure. Electronic supplementary material The online version of this article (10.1186/s11671-018-2677-0) contains supplementary material, which is available to authorized users.

The detection of fluorescence with submolecular resolution enables the exploration of spatially varying photon yields and vibronic properties at the single-molecule level. By placing individual polycyclic aromatic hydrocarbon molecules into the plasmon cavity formed by the tip of a scanning tunneling microscope and a NaCl-covered Ag(111) surface, molecular light emission spectra are obtained that unravel vibrational progression. In addition, light spectra unveil a signature of the molecule even when the tunneling current is injected well separated from the molecular emitter. This signature exhibits a distance-dependent Fano profile that reflects the subtle interplay between inelastic tunneling electrons, the molecular exciton and localized plasmons in at-distance as well as on-molecule fluorescence. The presented findings open the path to luminescence of a different class of molecules than investigated before and contribute to the understanding of single-molecule luminescence at surfaces in a unified picture., Comment: 24 pages, 4 figures

We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI course "Kähler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original.

By tuning the laser photon energy in the non-linear two-photons photoemission at a single-layer graphene/Cu(111) interface, it is possible to observe a strong resonance at h upsilon = 3.5 eV along with a weaker one at h upsilon = 3.85 eV. The main resonance photon energy is consistent with a direct optical transition between the occupied Cu(111) Shockley surface state and the n = 1 image potential state, located in the real gap-space between the single-layer graphene and the Cu( Ill) surface. The large amplitude of this resonance unveils a high value of the electric dipole matrix element integral that governs this transition. Furthermore, the Lorentzian shape of this resonance implies that these two states are decoupled from the continuum of states and the lifetime of the image potential state can be estimated. (C) 2015 Elsevier B.V. All rights reserved.

We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $\alpha$-invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities., Comment: 30 pages, improved exposition, shifted numeration

In this article we prove the existence of Kähler–Einstein metrics on $\mathbb{Q}$ -Gorenstein smoothable, K-polystable $\mathbb{Q}$ -Fano varieties, and we show how these metrics behave, in the Gromov–Hausdorff sense, under $\mathbb{Q}$ -Gorenstein smoothings.

We employ an extreme ultraviolet (XUV) pulse to impulsively excite dipole polarization in atoms or molecules, which corresponds to coherently prepared superposition of excited states. A delayed near infrared (NIR) pulse then perturbs the fast evolving polarization, and the resultant absorbance change is monitored in dilute helium, dense helium, and sulfur hexafluoride (SF6) molecules. We observe and quantify the time-dependence of various transient phenomena in helium atoms,includinglaser-inducedphase(LIP),time-varying(AC)Starkshift,quantumpathinterference, and laser-induced continuum structure. In the case of dense helium targets, we discuss nonlinear macroscopic propagation effects pertaining to LIP and resonant pulse propagation, which accoun tfor the appearance of new spectral features in transient lineshapes. We then use tunable NIR photons to demonstrate the wavelength dependence of the transient laser induced effects. In the case of molecular polarization experiment in SF6, we show suppression of XUV photoabsorption corresponding to inter-valence transitions in the presence of a strong NIR field. In each case, the temporal evolution of transient absorption spectra allows us to observe and understand the transient laser induced modifications of the electronic structure of atoms and molecules.