Reflection compensation scheme for the efficient and accurate computation of waveguide discontinuities in photonic crystals
Keywords:
Reflection compensation scheme for the efficient and accurate computation of waveguide discontinuities in photonic crystalsAbstract
We presented a novel method for the accurate and
efficient computation of the reflection and transmission coefficients
of waveguide discontinuities within planar photonic crystals (PhCs).
This method proposes a novel kind of field source that optimally
excites the dominant waveguide mode and mimics procedures that
are typically used for the measurement of reflection coefficients.
This technique may be applied to arbitrary field simulators working
in the frequency domain. The presented reflection compensation
scheme is elucidated along the Method of Auxiliary Sources (MAS).
In order to verify the results, we compare two test cases with the
rigorous connection technique provided by the Multiple Multipole
Method (MMP)
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References
E. Yablanovich, “Inhibited spontaneous emission in solid-
state physics and electronics”, Phys. Rev. Lett., 58, pp.
-2062, 1987.
E. Centeno, D. Felbacq, “Guiding waves with photonic
crystals,” Opt. Commun. 160, pp. 57-60, 1999.
H. Benisty, “Modal analysis of optical guides with two-
dimensional photonic band-gap boundaries,” J. Appl.
Phys. 79, pp.7483-7492, 1996.
R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L.
Alerhand, D. A. Smith, K. Kash, “Novel applications of
photonic band gap materials: Low-loss bends and high Q
cavities,” J. Appl. Phys. 75, pp. 4753-4755, 1994.
A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve,
J. D. Joannopoulos, “High transmission through sharp
Table 4
MMP solution MAS solutions
Case R (%) Tl (%) Tr (%) Σ (%) R (%) Tl (%) Tr (%) Σ (%)
Left 35.37 63.38 0.41 99.16 36.38 63.71 0.42 100.51
Right 36.51 0.11 63.24 99.86 36.02 0.11 63.76 99.89
D. Karkashadze, et al.: Reflection Compensation Scheme for Computation of Waveguide Discontinuities in Photonic Crystals
bends in photonic crystal waveguides,” Phys. Rev. Lett.
, pp. 3787-3790, 1996.
A. Chutinan, M. Okano, S. Noda, “Wider bandwidth with
high transmission through waveguide bends in two-
dimensional photonic crystal slabs,” Appl. Phys. Lett. 80,
pp. 1698-1700, 2002.
J. Smajic, Ch. Hafner, D. Erni, “Design and optimization
of an achromatic photonic crystal bend”, Opt. Express 11,
-1384,2003,
http://www.opticsexpress.org/abstract.cfm?URI=OPEX-
-12-1378 .
M. Koshiba, Y. Tsui, M. Hikari, “Time-domain beam
propagation method and its application to photonic crystal
circuits,” J. Lightwave Technol. LT18, pp. 102-110, 2000.
J. Yonekura, M. Ikeda, T. Baba, “Analysis of finite 2-D
photonic crystals of columns and lightwave devices using
the scattering matrix method,” J. Lightwave Technol.
LT17, pp. 1500-1508, 1999.
E. Moreno, D. Erni, Ch. Hafner, “Modeling of
discontinuities in photonic crystal waveguides with the
multiple multipole method,” Phys. Rev. E 66, 036618,
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.
A. Bijamov, I. Paroshina, D. Karkashadze, Simulation of
optical control devices based on photonic band structures.
Proceedings of the Seminar/ Workshop "Numerical
Solution of Direct and Inverse Problems of the
Electromagnetic and Acoustic Waves Theory, DIPED-
, 2003.
D.D.Karkashadze, F.G.Bogdanov, R.S.Zaridze,
A.Y.Bijamov, C.Hafner, and D.Erni. "Simulation of Finite
Photonic Crystals Made of Biisotropic or Chiral Material.
Using the Method of Auxiliary Sources". Advances in
Electromagnetics of Complex Media and Metamaterials.
Edited by Said Zouhdi, Ari Sihvola and Mohamed
Arsalane, NATO Science Series. II Mathematics, Physics
and Chemistry - Vol. 89, pp. 175-193, 2003.
K. S. Yee, “Numerical solution of initial boundary value
problems involving Maxwell’s equations in isotropic media,”
IEEE Trans. Antennas Propagat., vol. AP-14, pp. 302-307,
J. P. Berenger, “A perfectly matched layer for the
absorption of electro-magnetic waves, “ J. Comp. Phy.
, pp. 185-200, 1994.
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.
A. Wexler, “Solution of waveguide discontinuities by
modal analysis,” IEEE Trans. On Microwave Theory and
Techniques, Vol. MTT-15, pp. 508-517, 1967.
R. Sorrentino, Numerical methods for passive microwave
and milimeter-wave structures, IEEE Press, Ch. 8, New
York, 1989.
K. Rauscher, J. Smajic, D. Erni, and Ch. Hafner "The
open-supercell approach for the eigenmode analysis of 2-
D photonic crystal defect waveguides," submitted to Phys.
Rev. E., 2003.
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.
J. Smajic, Ch. Hafner, D. Erni, “On the design of photonic
crystal multi-plexers”, Opt. Express 11, pp. 566-571,
,
http://www.opticsexpress.org/abstract.cfm?URI=OPEX-
-6-566 .
G. A. Deschamps, “Gaussian Beams as a Bundle of
Complex Rays”, Electron. Lett. 7, pp. 684-685, 1971.
A. Boag, R. Mittra, “Complex Multipole Beam Approach
to 3D Electro-magnetic Scattering Problems”, J. Opt. Soc.
Am. A, Vol. 11, pp. 1505-1512, 1994.
A. Tikhonov, V. Arsenin, Solutions of ill-posed problems,
Winston and Sons., Washington DC, 1977.
