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Session 2P4 Electromagnetic Field in Optical Materials and EM Field Dispersion in Photonic Crystals Coupling Theory of Asymmetric Photonic-crystal Waveguides Chih-Hsien Huang, Wen-Feng Hsieh, Szu-Cheng Cheng, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Homogeneous Optical Fibers with Irregular Boundaries Serhend Arvas, Joseph R. Mautz, Ercument Arvas, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anomalous Microwave Transmission in a Superconducting Periodic Multilayer Structure Chien-Jang Wu, Tzong-Jer Yang, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electromagnetic Field Energy in a Metamaterial Medium Consisting of Metallic Wires and Split-ring Resonators Pi-Gang Luan, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Layered Metamaterial with Parabolic Dispersion Tzong-Jer Yang, Jin-Jei Wu, Linfang Shen, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GL EM Modeling for Electromagnetic Wave Propagation in Helix Pipe Crystals and Structures Ganquan Xie, Jianhua Li, Feng Xie, Lee Xie, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Critical Fields in Lithum Niobate Nano Ferroelectrics Asis Kumar Bandyopadhyay, P. C. Ray, V. Gopalan, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Potential-based Finite Element Method Based on Wave Scheme for Transient Maxwell’s Equations Tong Kang, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 138 139 140 141 142 143 144 145 138 Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008 Coupling Theory of Asymmetric Photonic-crystal Waveguides Chih-Hsien Huang1 , Wen-Feng Hsieh1 , and Szu-Cheng Cheng2 1 Department of Photonics, National Chiao Tung University, Hsinchu, Taiwan 2 Department of Physics, Chinese Culture University, Taipei, Taiwan Abstract— The physical properties of asymmetric photonic-crystal directional couplers are studied under the tight-binding theory, which considers the field distribution of photonic-crystal waveguides is localized around periodic defects. From this model, the analytic formulas to describe the dispersion of the coupler and the eigen mode pattern is derived, thus helping to analyze the eigen mode and energy localization of the waveguides. It also helps to explain the novel phenomenon that the mode patterns are exchanged at decoupling point but the dispersion relation curves do not cross at triangular lattice asymmetry photonic-crystal waveguides. By linearly combination of the derived wave vectors and eigen mode, the amplitudes of the electric field can be easily writing down which are consistent with the results gotten by the finite difference time domain method. Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008 139 Analysis of Homogeneous Optical Fibers with Irregular Boundaries Serhend Arvas, Joseph R. Mautz, and Ercument Arvas Department of Electrical Engineering and Computer Science Syracuse University, Syracuse, NY 13244, USA Abstract— A simple numerical technique is developed to analyze optical fibers of arbitrary cross section. The surface equivalence principle is used to replace the fiber by equivalent electric and magnetic surface currents radiating in unbounded media. Each of these equivalent surface currents has both longitudinal and transverse components. Eight coupled integral equations are obtained by applying the conditions on the tangential components of the electric and magnetic fields. They are reduced to four equations by using a combined field approach. These four integral equations are solved using the Method of Moments. The contour describing the fiber cross section is approximated by linear segments. Pulses are used as expansion functions for the longitudinal currents JZ and MZ , and triangular functions are used in expanding the lateral components of the currents JL and ML . An approximate Galerkin’s method of testing is used. The moment matrix Z is a function of the propagation constant β. The matrix becomes singular when β corresponds to a possible guided mode. These values of propagation constants are determined by monitoring the condition number of the moment matrix as β is varied. No β values corresponding to any spurious modes are detected. For a valid β value corresponding to a particular mode, the eigenvector of Z corresponding to the minimum eigenvalue is found. This eigenvector contains the expansion coefficients for the equivalent surface currents. The tangential components of the electric and magnetic fields over the boundary of the fiber can simply be found once the expansion coefficients are determined. The dispersion relationship and fields inside and outside the fiber can also be computed easily. The method can be applied to fibers with deformed boundaries, including the elliptical, chipped circle, egg shape or asymmetrical boundary. The computed results for a number of cross sections are in excellent agreement with available exact or numerical data. 140 Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008 Anomalous Microwave Transmission in a Superconducting Periodic Multilayer Structure Chien-Jang Wu1 and Tzong-Jer Yang2 1 Institute of Electro-Optical Science and Technology National Taiwan Normal University, Taipei, Taiwan 106, R.O.C. 2 Department of Electrical Engineering, Chung Hua University, Hsinchu, Taiwan 300, R.O.C. Abstract— In this work we theoretically study microwave properties of a superconductor/dielectric periodic layered structure, in which a strongly dispersive superconductor, nearly ferroelectric superconductor (NFE SC), is taken. Microwave transmittance in the dielectric-like response has been calculated based on the transfer matrix method as well as the electrodynamics of NFE SCs. Microwave response is strongly dependent on the number of periods as well as the thickness of superconductor layer. It is found that the first anomalous transmission peak can be created when the number of periods is more than five. In addition, more anomalous peaks are generated by greatly increasing the number of periods. The presence of anomalous sharp peaks can be used to design a nicely frequency-selective filter or sampler using such a multilayer structure. Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008 141 Electromagnetic Field Energy in a Metamaterial Medium Consisting of Metallic Wires and Split-ring Resonators Pi-Gang Luan Department of Optics and Photonics, National Central University, Jhong-Li 32001, Taiwan Abstract— We derive in this paper the formula of electromagnetic field energy density in a dispersive metamaterial medium with finite loss. The metamaterial consists of arrays of metallic wires and split-ring resonators. Equations of motion for the electric and magnetic dipoles are obtained by analyzing the current and charge responses of the metallic components to the incident fields. Based on the analysis, the relations between currents/charges, dipoles, and fields can be found, and hence the stored energy and energy loss in the medium can be correctly calculated and expressed using either the current/charge or field/dipole variables. We also find that the energy loss in the metamaterial are nothing else than the Joule heat generated by the resistances in the metallic structures. Space averaging the fields and dipoles under the long-wavelength assumption, the macroscopic fields E, B, D, H, P, M can be defined. The equations of motion for the polarization P and magnetization M are obtained from the corresponding equations for the electric and magnetic dipoles. An effective continuous medium theory for this metamaterial is thus established. We show that the energy density of the fields can be derived from Maxwell’s equations of the macroscopic fields (electrodynamics approach), and the result is the same as that obtained from calculating the energy stored in one unit cell (equivalent circuit approach), divided by the cell volume. Our formula gives the same result as that of Boardman’s [1] in the lossless limit, but different from theirs when energy loss cannot be neglected. We explain the physically meaning of every term appearing in the energy density formula, and compare the result with those obtained by other authors using electrodynamics [1] or equivalent circuit approach [2]. This comparison reveals that our approach is more satisfactory and physically transparent, and can be easily generalized to establish the effective medium theory of other kinds of metamaterials such as those including of both electric and magnetic resonators in one unit cell. REFERENCES 1. 2. 3. 4. Boardman, A. D. and K. Marinov, Phys. Rev. B, Vol. 73, 165110, 2006. Tretyakov, S. A., Phys. Lett. A, Vol. 343, 231, 2005. Ruppin, R., Phys. Lett. A, Vol. 299, 309, 2002. Chen, H., L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, J. Appl. Phys., Vol. 100, 024915, 2006. 5. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech., Vol. 47, 2057, 1999. Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008 142 The Layered Metamaterial with Parabolic Dispersion Tzong-Jer Yang1 , Jin-Jei Wu1 , and Linfang Shen2 1 Department of Electrical Engineering, Chung Hua University, Hsinchu 30012, Taiwan, R.O.C. 2 Department of Information Science and Electronic Engineering, Electromagnetic Academy Zhejiang University, Hangzhou, Zhejiang 310027, China Abstract— A layered meatmaterial which is predicted by the effective medium theory to have partially permittivity near zero is analyzed. It is shown that such a material has parabolic dispersion relation. This material may be viewed as a homogeneous medium but is spatially dispersive strongly. This material may also have either forward wave or backward wave, depending on the magnitude of the wave vector. Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008 143 GL EM Modeling for Electromagnetic Wave Propagation in Helix Pipe Crystals and Structures Ganquan Xie, Jianhua Li, Feng Xie, and Lee Xie GL Geophysical Laboratory, USA Abstract— We present a GL EM modeling for electromagnetic (EM) wave propagation in the helical pipe crystal and structure. The helical pipe crystal and structure can be figured as 3D periodic lattice structure. The unit cell is a structure that unit helical is embedded into the cubic crystal. Our GL EM modeling can simulate EM wave propagation in the helical pipe crystal and structure and perform its dispersion engineering. Using GL EM modeling simulation and dispersion engineering, the EM filed wave can be almost focus guiding propagation in the helical pipe crystal and structure. That is useful for making nanometer helical pipe crystal laser, artificial DNA, nanometer material device, sensor and other applications. 144 Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008 Critical Fields in Lithum Niobate Nano Ferroelectrics A. K. Bandyopadhyay1 , P. C. Ray2 , and V. Gopalan3 1 Govt. College of Engineering & Ceramic Technology, WBUT, Kolkata-700010, India 2 Dept. of Mathematics, GCE & LT, WBUT, Salt Lake, Kolkata-700098, India 3 Dept. of Materials Science and Engineering, Pennsylvania State University, USA Abstract— An important property like giant polarization with many other properties are commonly observed in ferroelectric materials, which have an wide area of applications. A typical non-linear hysteresis behaviour is observed between polarization (P ) and electric field (E). For an uniaxial ferroelectric, such as lithium niobate, we developed a discrete Hamiltonian by taking Landau-Ginzburg functional as potential energy with near-neighbour ‘interactions’ between the polarization domains. The spatio-temporal behaviour of P is then described by a non-linear Klein-Gordon equation as a governing equation as: ∂2P ∂2P ∂P − k̄ 2 − ᾱ1 (P − P 3 ) − E + γ̄ =0 2 ∂t ∂x ∂t where, k̄ is an interaction term and γ̄ is the damping term. Here, all the terms are used as non-dimensional. The ‘analytical solutions’ of the above non-linear K-G equation give rise to both slower (tan h) and faster (sec h) solitons in such photonic materials. The stability of these solitons, i.e., up to what field such solitons exist, is worked out in order to find a ‘critical field’ value, which has not been attempted so far for actual photonic crystals for non-linear device applications. This particular case of stability analysis is done at E 6= 0 and γ̄ 6= 0. Beyond this critical value, the solitons do not exist in our system. If we multiply this non-dimensional Ecrit value by the coercive field (Ec ), we obtain the optimum value of the field (V/nm) to be applied in a given nano device, which has an important relation with impurity content in such inhomogeneous ferroelectrics. This is considered to be due to break-up of Landau potential as we increase the driving force, as shown below. Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008 145 A Potential-based Finite Element Method Based on Wave Scheme for Transient Maxwell’s Equations Tong Kang School of Sciences, Communication University of China, China Abstract— In this paper, we investigate the potential-based finite element method (the Amethod) based on Wave scheme for transient three-dimensional Maxwell equation system. By appending a penalty function term in the governing equation of magnetic vector potential, we achieve the satisfaction of the Coulomb gauge and guarantee the uniqueness of the vector splitting. As distinguished from the traditional coupled scheme in which an equation system including both vector and scalar potentials is solved at every time-step after time discretization, a decoupled scheme is specially presented here. Because the vector and scalar unknowns are calculated at different equations respectively, it decreases the storage amount of non-zero entries of coefficient matrix and computational costs and achieves the better results under the equal CPU time. Some computer simulation results of the distributions of magnetic flux and electric field are demonstrated to verify the feasibility and efficiency of our algorithm. REFERENCES 1. Albanese, R. and G. Rubinacci, “Formulation of the eddy-current problem,” IEE Proceedings, 137, 16–22, 1990. 2. Bossavit, A., Computational Electromagnetism, Academic Press, 1997. 3. Jin, J. M., Finite Element Method in Electromagnetism, the 2nd Version, Academic Press, 2002. 4. Ren, Z. and A. Razek, “Comparison of some 3D eddy current formulations in dual systems,” IEEE Trans. on Magn., Vol. 36, No. 4, 751–755, 2000. 5. Yao, Y., D. Xie, J. Wang, and A. M. Osama, “A Multi-step method for 3-D nonlinear transient eddy current problems,” IEEE Trans. Magn., Vol. 37, 3194–3197, 2001. 146 Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008