Automatic Calculation of Band Diagrams of Photonic Crystals Using the Multiple Multipole Method
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Automatic Calculation of Band Diagrams of Photonic Crystals Using the Multiple Multipole Method摘要
In the framework of photonic crystal’s band structure calculations, we present a novel way – based on several advanced techniques for searching and tracing eigenvalues with the multiple multipole program – to compute these diagrams automatically, efficiently, and with a high accuracy. Finally, we validate the results for some well known test cases.
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参考
E. Yablanovich, “Inhibited spontaneous emission in solid-state physics and
electronics”, Phys. Rev. Lett., 58, pp. 2059-2062, 1987.
J. Mills, “Photonic crystals head toward the marketplace”, Nov. 2002,
http://optics.org/articles/ole/7/11/1/1 ,
K. Busch, S. John, “Liquid-crystal photonic-band-gap materials: the
tunable electromagnetic vacuum”, Phys. Rev. Letters, 83, pp. 967-970,
A. Figotin, Y. A. Godin, “two-dimensional tunable photonic crystals”,
Phys. Rev. B, 57, pp. 2841-2848, 1998.
R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, S. Chandra,
“Switchable orthorombic F photonic crystals formed by holographic
polymerization-induced phase separation of liquid crystal”, Optics Express,
, pp. 1074-1082, 2002.
K. Sakoda, “Optical Properties of Photonic Crystals”,Springer, Berlin, 2001.
J. D. Joannopoulos, R. D. Meade, J. N. Winn, “Molding the Flow of
Light”, Princeton University Press, 1995.
K. M. Ho, C. T. Chan, and, C. M. Soukolis, “Existance of a Photonic Gap
in Periodic Dielectric Structures”, Phys. Rev. Lett., 65, pp. 3152-3155,
S. G. Johnson, and J. D. Joannopoulos, “Block-iterative frequency-domain
methods for Maxwell’s equations in a planewave basis”, Opt. Express, 8,
pp. 173-190, 2001.
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L.
Alerhand, “Accurate theoretical analysis of photonic band-gap materials”,
Phys. Rev. B, 48, pp. 8434-8437, 1993.
H. S. Söuzüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence
problems with the plane-wave method”, Phys. Rev. B, 45, pp. 13962-
, 1992.
D. Hermann, M. Frank, K. Busch and P. Wölfle, “Photonic band structure
computations”, Opt. Express, 8, pp. 167-172, 2001.
K. Ohtaka, T. Ueta, and K. Amemiya, “Calculation of photonic bands
using vector cylindrical waves and reflectivity of light for an array of
dielectric rods”, Phys. Rev B, 57, pp. 2550-2568, 1998.
C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for
electromagnetic waves”, Phys. Rev B, 51, pp. 16 635-16 642, 1995.
M. Qui and S. He, “A non-orthogonal finite-difference time-domain
method for computing the band structure of a two-dimensional photonic
crystal with dielectric and metallic inclusions”, J. Appl. Phys., 87, pp.
-8275, 2000.
J. B. Pendry and A. MacKinnon, “Calculation of Photon Dispersion
Relations”, Phys. Rev. Lett., 69, pp. 2772-2775, 1992.
W. Axmann and P. Kuchment, “An efficient finite element method for
computing spectra of photonic and acoustic band-gap materials”, J.
Comput. Phys., 150, pp. 468-481, 1999.
ACES JOURNAL, VOL. 18, NO. 3, NOVEMBER 2003
P. A. Knipp, and T. L. Reinecke, “Boundary-element calculations of
electromagnetic band-structure of photonic crystals”, Physica E, 2, pp.
-924, 1998.
Ch. Hafner, “Post-modern Electromagnetics Using Intelligent MaXwell
Solvers”, John Wiley & Sons, 1999.
Ch. Hafner, “MaX-1: A visual electromagnetics platform”, John Wiley &
Sons, 1998.
P. R. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional
square and hexagonal lattices”, Phys. Rev. B, 46, pp. 4969-4972, 1992.
M. Plihal and A. A. Maradudin, “Photonic band structure of two-
dimensional systems: the triangular lattice”, Phys. Rev. B, 44, pp. 8565-
, 1991.
Ch. Hafner, J. Smajic, The Computational Optics Group Web Page (IFH,
ETH Zurich), http://alphard.ethz.ch/.
I. N. Vekua, “New methods for solving elliptic equations”, North-Holland,
Amsterdam, 1967.
G. H. Golub and C. F. Van Loan, “Matrix Computations”, John Hopkins
University Press, Baltimore, 1996.
F. G. Bogdanov, D. D. Karkashadze, and R. S. Zaridze, in “Generalized
Multipole Techniques for Electromagnetic and Light Scattering”, edited by
T. Wriedt, pp. 143-172, Elsevier, Amsterdam, 1999.
K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K.
Hirao, “Photonic bands of metallic systems. I. Principle of calculation and
accuracy”, Phys. Rev. B, 64, pp. 045116, 2001.
E. Moreno, D. Erni and Ch. Hafner, “Band structure computations of
metallic photonic crystals with the multiple multipole method”, Phys. Rev.
B, 65, pp. 155120: 1-10, 2002.
S. G. Johnson and J. D. Joannopoulos, The MIT Photonic-Bands Package
home page, http://ab-initio.mit.edu/mpb/ .
R. D. Meade, K.l D. Brommer, A. M. Rappe and J. D. Joannopoulos,
“Photonic band states in periodic dielectric materials”, Phys. Rev. B, 44,
pp. 13 772 – 13 774, 1991.
E. Moreno, D. Erni and Ch. Hafner, “Modeling of discontinuities in
photonic crystal waveguides with the multiple multipole method”, Phys.
Rev. B, 66, pp. 036618, 2002
