It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie group G with a bi-invariant metric and a generating function Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra g of G so that G and g form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on g is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper.Acknowledgments We would like to thank Hung-Wen Chang for very helpful discussions, Thom Curtright for sharing with us his joint work with C. Zachos, and Marco Monti for help with Xfig.

Special fibrations of toric varieties have been used by physicists, e.g. the school of Candelas, to construct dual pairs in the study of Het/F-theory duality. Motivated by this, we investigate in this paper the details of toric morphisms between toric varieties. In particular, a complete toric description of fibers -both generic and non-generic -, image, and the flattening stratification of a toric morphism are given. Two examples are provided to illustrate the discussions. We then turn to the study of the restriction of a toric morphism to a toric hypersurface. The details of this can be understood by the various restrictions of a line bundle with a section that defines the hypersurface. These general toric geometry discussions give rise to a computational scheme for the details of a toric morphism and the induced fibration of toric hypersurfaces therein. We apply this scheme to study the family of complex 4-dimensional elliptic Calabi-Yau toric hypersurfaces that appear in a recent work of Braun-Candelas-dlOssa-Grassi. Some directions for future work are listed in the end.

In this paper, we examine the electromagnetic (EM) wave tunneling and filtering characteristics of multi-layer structures composed of an arbitrary number of ɛ-negative (Epsilon-negative or ENG) metamaterial layers sandwiched by very thin double-positive (DPS) layers with high dielectric constant values. We explain the phenomenon of EM wave tunneling through this propagation barrier by drawing an analogy between this problem and a generalized coupled resonator system. Using this analogy, we demonstrate that a multi-layer structure composed of N DPS layers (N ≥ 2 is an integer number) that sandwich N-1 ENG layers can not only be made transparent in a frequency range where the ENG layers are normally opaque but also be designed to provide a desired spectral filtering characteristics. Furthermore, we present an analytical method for synthesizing such multi-layer spectral filters from the characteristics of their desired responses. The proposed synthesis procedure can be used to develop spatial filters operating throughout the microwave and mm-wave frequency bands as well as multi-layer metallo-dielectric filters at optical wavelengths. We demonstrate the validity of the proposed analytical synthesis method using full-wave numerical electromagnetic simulations. Finally, using the duality principle, we expand these analytical results to the problem of EM wave tunneling through multiple μ-negative layers surrounded by thin DPS layers with high relative permeability values.

Recently, smart stents have been developed by integrating various sensors with intravascular stents for detecting vascular restenosis or monitoring intravascular biomedical conditions such as blood pressure or blood flow velocity. The information on biomedical signals is then transmitted to external monitoring systems via wireless communications. Due to the limited volumes of blood vessels and limited influence of blood flow, antennas with good radiation performance are required for intravascular applications. In this paper, we propose a stent antenna composed of multiple rings containing crowns and struts, where each ring is connected with one connector. Unlike a conventional stent, wherein each ring is connected with several connectors, the single connector prevents the random distribution of electrical current and thus achieves good radiation performance. The implantable stent antenna is designed for the frequency range of 2 to 3 GHz for minimum penetration loss in the human body and tissues. Mechanical FEM simulations were conducted to ensure that the mechanical deformation was within specific limits during balloon expansions. A prototype was fabricated with laser cutting techniques and its radiation performance experimentally characterized. It was demonstrated that the fabricated stent antenna had an omnidirectional radiation pattern for arbitrary receiving angles, a gain of 1.38 dBi, and a radiation efficiency of 74.5% at a resonant frequency of 2.07 GHz. The main contribution of this work was the manipulation of the current distributions of the stent for good EM radiation performances which needed to be further examined while inserted inside human bodies. These research results should contribute to the further development of implantable wireless communications and intravascular monitoring of biomedical signals such as blood pressure and blood flow velocity.

In this paper, we experimentally investigate the phenomenon of electromagnetic wave tunneling through ϵ-negative (ENG) metamaterial layers surrounded by double-positive layers. Initial experiments are conducted by using a rectangular waveguide, which operates below its cutoff frequency to emulate an ENG layer. This ENG layer is then sandwiched by two dielectric substrates with relatively high dielectric constants and it is shown that the entire setup acts as a classical microwave filter with a second-order bandpass response. The power handling capability of this filter is examined experimentally using a high-power magnetron source with a frequency of 9.382 GHz, a pulse duration of 1 μs, and a peak power of 25 kW. Based on the results of this experiment, two methods for improving the power handling capability of these multi-layer structures are proposed. In particular, it is demonstrated that emulating the ENG layers with thin perforated metallic sheets with sub-wavelength holes significantly enhances their peak power handling capability. A prototype of such a device is designed, fabricated, and experimentally characterized and it is demonstrated that it can handle extremely high peak power levels. The results presented in this work are expected to be useful in designing microwave filters and frequency selective surfaces that can handle extremely high peak power levels.