Generalized homogenization theory and inverse design of periodic electromagnetic metamaterials

textArtificial metamaterials composed of specifically designed subwavelength unit cells can support an exotic material response and present a promising future for various microwave, terahertz and optical applications. Metamaterials essentially provide the concept to microscopically manipulate light through their subwavelength inclusions, and the overall structure can be macroscopically treated as homogeneous bulk material characterized by a simple set of constitutive parameters, such as permittivity and permeability. In this dissertation, we present a complete homogenization theory applicable to one-, two- and three-dimensional metamaterials composed of nonconnected subwavelength elements. The homogenization theory provides not only deep insights to electromagnetic wave propagation among metamaterials, but also allows developing a useful and efficient analysis method for engineering metamaterials. We begin the work by proposing a general retrieval procedure to characterize arbitrary subwavelength elements in terms of a polarizability tensor. Based on this system, we may start the macroscopic analysis of metamaterials by analyzing the scattering properties of their microscopic building blocks. For one-dimensional linear arrays, we present the dispersion relations for single and parallel linear chains and study their potential use as sub-diffractive waveguides and leaky-wave antennas. For two-dimensional arrays, we interpret the metasurfaces as homogeneous surfaces and characterize their properties by a complete six-by-six tensorial effective surface susceptibility. This model also offers the possibility to derive analytical transmission and reflection coefficients for metasurfaces composed of arbitrary nonconnected inclusions with TE and TM mutual coupling. For three-dimensional metamaterials, we present a generalized theory to homogenize arrays by effective tensorial permittivity, permeability and magneto-electric coupling coefficients. This model captures comprehensive anisotropic and bianisotropic properties of metamaterials. Based on this theory, we also modify the conventional retrieval method to extract physically meaningful effective parameters of given metamaterials and fundamentally explain the common non-causality issues associated with parameter retrieval. Finally, we conceptually propose an inverse design procedure for three-dimensional metamaterials that can efficiently determine the geometry of the inclusions required to achieve the anomalous properties, such as double-negative response, in the desired frequency regime.Electrical and Computer Engineerin

A Sparse Graph-Structured Lasso Mixed Model for Genetic Association with Confounding Correction

While linear mixed model (LMM) has shown a competitive performance in correcting spurious associations raised by population stratification, family structures, and cryptic relatedness, more challenges are still to be addressed regarding the complex structure of genotypic and phenotypic data. For example, geneticists have discovered that some clusters of phenotypes are more co-expressed than others. Hence, a joint analysis that can utilize such relatedness information in a heterogeneous data set is crucial for genetic modeling. We proposed the sparse graph-structured linear mixed model (sGLMM) that can incorporate the relatedness information from traits in a dataset with confounding correction. Our method is capable of uncovering the genetic associations of a large number of phenotypes together while considering the relatedness of these phenotypes. Through extensive simulation experiments, we show that the proposed model outperforms other existing approaches and can model correlation from both population structure and shared signals. Further, we validate the effectiveness of sGLMM in the real-world genomic dataset on two different species from plants and humans. In Arabidopsis thaliana data, sGLMM behaves better than all other baseline models for 63.4% traits. We also discuss the potential causal genetic variation of Human Alzheimer's disease discovered by our model and justify some of the most important genetic loci.Comment: Code available at https://github.com/YeWenting/sGLM

The Y(2175) State in the QCD Sum Rule

We study the mass of the state Y(2175) of J^{PC} = 1^{--} in the QCD sum rule. We construct both the diquark-antidiquark currents (ss)(s_bar s_bar) and the meson-meson currents (s_bar s)(s_bar s). We find that there are two independent currents for both cases, and derive the relations between them. The OPE convergence of these two currents is sufficiently fast, which enables us to perform good sum rule analysis. Both the SVZ sum rule and the finite energy sum rule lead to a mass around 2.3+-0.4 GeV, which is consistent with the observed mass within the uncertainties of the present QCD sum rule. The coupling of the four-quark currents to lower lying states such as \phi(1020) turns out to be rather small. We also discuss possible decay properties of Y(2175) if it is a tetraquark state.Comment: 10 pages, 6 figures, revised version to appear in Phys. Rev.

The hidden-charm pentaquark and tetraquark states

In the past decade many charmonium-like states were observed experimentally. Especially those charged charmonium-like $Z_c$ states and bottomonium-like $Z_b$ states can not be accommodated within the naive quark model. These charged $Z_c$ states are good candidates of either the hidden-charm tetraquark states or molecules composed of a pair of charmed mesons. Recently, the LHCb Collaboration discovered two hidden-charm pentaquark states, which are also beyond the quark model. In this work, we review the current experimental progress and investigate various theoretical interpretations of these candidates of the multiquark states. We list the puzzles and theoretical challenges of these models when confronted with the experimental data. We also discuss possible future measurements which may distinguish the theoretical schemes on the underlying structures of the hidden-charm multiquark states.Comment: Review accepted by Physics Reports, 152 pages, 66 figures, and 29 table

Bottom Baryons

Recently CDF and D0 collaborations observed several bottom baryons. In this work we perform a systematic study of the masses of bottom baryons up to $1/m_Q$ in the framework of heavy quark effective field theory (HQET) using the QCD sum rule approach. The extracted chromo-magnetic splitting between the bottom baryon heavy doublet agrees well with the experimental data.Comment: 8 pages, 5 figures, 3 tables. More discussions and references adde

A review of the open charm and open bottom systems

Since the discovery of the first charmed meson in 1976, many open-charm and open-bottom hadrons were observed. In 2003 two narrow charm-strange states $D_{s0}^*(2317)$ and $D_{s1}(2460)$ were discovered by the BaBar and CLEO Collaborations, respectively. After that, more excited heavy hadrons were reported. In this work, we review the experimental and theoretical progress in this field.Comment: Review accepted by Reports on Progress in Physics, 161 pages, 53 figures, 23 tables, more references added and review on heavy baryons adde