2-Resonant fullerenes

A fullerene graph $F$ is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set $\mathcal{H}$ of disjoint hexagons of $F$ is called a resonant pattern (or sextet pattern) if $F$ has a perfect matching $M$ such that every hexagon in $\mathcal{H}$ is $M$-alternating. $F$ is said to be $k$-resonant if any $i$ ($0\leq i\leq k$) disjoint hexagons of $F$ form a resonant pattern. It was known that each fullerene graph is 1-resonant and all 3-resonant fullerenes are only the nine graphs. In this paper, we show that the fullerene graphs which do not contain the subgraph $L$ or $R$ as illustrated in Fig. 1 are 2-resonant except for the specific eleven graphs. This result implies that each IPR fullerene is 2-resonant.Comment: 34 pages, 25 figure

Graphene-like optical light field and its interaction with two-level atoms

The theoretical basis leading to the creation of a light field with a hexagonal honeycomb structure resembling graphene is considered along with its experimental realization and its interaction with atoms. It is argued that associated with such a light field is an optical dipole potential which leads to the diffraction of the atoms, but the details depend on whether the transverse spread of the atomic wave packet is larger than the transverse dimensions of the optical lattice (resonant Kapitza-Dirac effect) or smaller (optical Stern-Gerlach effect). Another effect in this context involves the creation of gauge fields due to the Berry phase acquired by the atom moving in the light field. The experimental realization of the light field with a honeycomb hexagonal structure is described using holographic methods and we proceed to explore the atom diffraction in the Kapitza-Dirac regime as well as the optical Stern-Gerlach regime, leading to momentum distributions with characteristic but different hexagonal structures. The artificial gauge fields too are shown to have the same hexagonal spatial structure and their magnitude can be significantly large. The effects are discussed with reference to typical parameters for the atoms and the fields

Pattern formation in 2-frequency forced parametric waves

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different 3--wave resonant interactions. They occur either as symmetry--breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by 4--wave interactions that arise when symmetry constraints rule out 3--wave resonances.Comment: The paper contains 34 pages and 53 figures and provides an extensive review of both the theoretical and experimental work peformed in this syste

Planar k-cycle resonant graphs with k=1,2

AbstractA connected graph is said to be k-cycle resonant if, for 1⩽t⩽k, any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M-alternating cycle. The concept of k-cycle resonant graphs was introduced by the present authors in 1994. Some necessary and sufficient conditions for a graph to be k-cycle resonant were also given. In this paper, we improve the proof of the necessary and sufficient conditions for a graph to be k-cycle resonant, and further investigate planar k-cycle resonant graphs with k=1,2. Some new necessary and sufficient conditions for a planar graph to be 1-cycle resonant and 2-cycle resonant are established

Controlled Synthesis of Organic/Inorganic van der Waals Solid for Tunable Light-matter Interactions

Van der Waals (vdW) solids, as a new type of artificial materials that consist of alternating layers bonded by weak interactions, have shed light on fascinating optoelectronic device concepts. As a result, a large variety of vdW devices have been engineered via layer-by-layer stacking of two-dimensional materials, although shadowed by the difficulties of fabrication. Alternatively, direct growth of vdW solids has proven as a scalable and swift way, highlighted by the successful synthesis of graphene/h-BN and transition metal dichalcogenides (TMDs) vertical heterostructures from controlled vapor deposition. Here, we realize high-quality organic and inorganic vdW solids, using methylammonium lead halide (CH3NH3PbI3) as the organic part (organic perovskite) and 2D inorganic monolayers as counterparts. By stacking on various 2D monolayers, the vdW solids behave dramatically different in light emission. Our studies demonstrate that h-BN monolayer is a great complement to organic perovskite for preserving its original optical properties. As a result, organic/h-BN vdW solid arrays are patterned for red light emitting. This work paves the way for designing unprecedented vdW solids with great potential for a wide spectrum of applications in optoelectronics

Field enhancement and spectral features of hexagonal necklaces of silver nanoparticles for enhanced nonlinear optical processes

Access to the online abstract in the journal: https://doi.org/10.1364/OE.26.022394 © 2018 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reservedThe nonlinear properties of hybrid metallic-dielectric systems are attracting great interest due to their potential for the enhancement of frequency conversion processes at nanoscale dimensions. In this work, we theoretically and experimentally address the correlation between the near field distribution of hexagonal plasmonic necklaces of silver nanoparticles formed on the surface of a LiNbO3 crystal and the second harmonic generation (SHG) produced by this nonlinear crystal in the vicinities of the necklaces. The spectral response of the hexagonal necklaces does not depend on the polarization direction and is characterized by two main modes, the absorptive high-energy mode located in the UV spectral region and the lower energy mode, which is strongly radiant and extends from the visible to the near infrared region. We show that the spatial distribution of the enhanced SHG is consistent with the local field related to the low energy plasmon mode, which spectrally overlaps the fundamental beam. The results are in agreement with the low absorption losses of this mode and the two-photon character of the nonlinear process and provide deeper insight in the connection between the linear and nonlinear optical properties of the hybrid plasmonic-ferroelectric system. The study also highlights the potential of hexagonal necklaces as useful plasmonic platforms for enhanced optical processes at the nanoscaleSpanish Ministry of Economy and Competitiveness (MINECO) under project MAT2016- 76106-R and the Comunidad de Madrid (grant S2013/MIT-2740). C.T. acknowledges funding from the VILLUM Foundation (Villum Investigator, grant no. 16498). L.E.B and M.O.R also acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through The “María de Maeztu” Programme for Units of Excellence in R&D (MDM-2014-0377