Download Session 2P4 Electromagnetic Field in Optical Materials and

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, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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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
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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.
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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.
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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.
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Progress In Electromagnetics Research Symposium Abstracts, Cambridge, USA, July 2–6, 2008