PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 69 > pp. 305-322

EFFICIENT NUMERICAL APPROACH TO ELECTROMAGNETIC SCATTERING FROM THREE-DIMENSIONAL PERIODIC ARRAY OF DIELECTRIC SPHERES USING SEQUENTIAL ACCUMULATION

By A. Matsushima, Y. Momoka, M. Ohtsu, and Y. Okuno

Full Article PDF (229 KB)

Abstract:
An effective numerical solution is presented for the plane wave scattering by multilayered periodic arrays of dielectric spheres. The treated structure is a fundamental model of photonic crystals having three-dimensional periodicity. The problem is analyzed by the mode matching method, where the electromagnetic fields in the air and dielectric regions are approximated by using the Floquet harmonics and vector spherical wave functions, respectively. They are matched on the junction surfaces in the least squares sense. Introduction of sequential accumulation in the process of QR decomposition reduces the computation time from O(Q3) to O(Q1) and the memory requirement from O(Q2) to O(Q1), with Q being a number of sphere layers. Numerical results are given for CPU time, speed of convergence, and some band gap characteristics.

Citation: (See works that cites this article)
A. Matsushima, Y. Momoka, M. Ohtsu, and Y. Okuno, "Efficient Numerical Approach to Electromagnetic Scattering from Three-Dimensional Periodic Array of Dielectric Spheres Using Sequential Accumulation," Progress In Electromagnetics Research, Vol. 69, 305-322, 2007.
doi:10.2528/PIER06123002
http://www.jpier.org/PIER/pier.php?paper=06123002

References:
1. Venakides, S., M. Haider, and V. Papanicolaou, "Boundary integral calculations of 2-d electromagnetic scattering by photonic crystal Fabry-Perot structures," SIAM J. Appl. Math., Vol. 60, No. 5, 1686-1706, 2000.
doi:10.1137/S0036139999350779

2. Yamasaki, T., T. Hinata, and T. Hosono, "Scattering of electromagnetic waves by columnar dielectric gratings with elliptically layered media," Trans. IEE Japan, Vol. 122-A, No. 1, 28-33, 2002.

3. Yasumoto, K., H. Toyama, and T. Kushta, "Accurate analysis of two-dimensional electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique," IEEE Trans. Antennas Propagat., Vol. AP-52, No. 10, 2603-2611, 2004.
doi:10.1109/TAP.2004.834440

4. Matsushima, A., "Equivalent circuit parameters for gratings composed of dielectric circular cylinders," IEICE Trans. Electron. (Japanese Edition), Vol. J88-C, No. 7, 585-588, 2005.

5. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2062, 1987.
doi:10.1103/PhysRevLett.58.2059

6. Ho, K. M., C. T. Chan, and C. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett., Vol. 65, No. 25, 3152-3155, 1990.
doi:10.1103/PhysRevLett.65.3152

7. Li, X.-J., W.-X. Zhang, L.-G. Zheng, and P. Lu, "The stratified dielectric gratings used as 3-D EBG structure," J. of Electromagn. Waves and Appl., Vol. 18, No. 10, 1347-1359, 2004.
doi:10.1163/1569393042954956

8. Fu, Y. and N. Yuan, "Accurate analysis of electromagnetic bandgap materials using moment methods," J. of Electromagn. Waves and Appl., Vol. 19, No. 5, 629-653, 2005.
doi:10.1163/1569393053305026

9. Hattori, H. T., A. Kazmierczak, V. M. Schneider, and C. L. Barbosa, "Photonic crystal micro-cavity based radiation filter," J. of Electromagn. Waves and Appl., Vol. 19, No. 11, 1525-1534, 2005.

10. Boag, A., Y. Leviatan, and A. Boag, "Analysis of electromagnetic scattering from doubly periodic arrays of penetrable bodies using a patch-dipole current model," Radio Sci., Vol. 26, No. 2, 603-610, 1991.

11. Okuno, Y., "The mode-matching method," Analysis Methods for Electromagnetic Wave Problems, 1990.

12. Davies, J. B., "A least-squares boundary residual method in the numerical solution of scattering problems," IEEE Trans. Microwave Theory Tech., Vol. MTT-21, No. 2, 99-104, 1973.
doi:10.1109/TMTT.1973.1127931

13. Ikuno, H. and K. Yasuura, "Improved point-matching method with application to scattering from a periodic surface," IEEE Trans. Antennas Propagat., Vol. AP-21, No. 5, 657-662, 1973.
doi:10.1109/TAP.1973.1140592

14. Ohtsu, M., Y. Okuno, A. Matsushima, and T. Suyama, "Combination of up-and down-going Floquet modal functions used to describe the field inside grooves of a deep grating," Progress In Electromagnetics Research, Vol. 64, 293-316, 2006.
doi:10.2528/PIER06071401

15. Lawson, C. L. and R. J. Hanson, Solving Least Squares Problems, Ch. 27, SIAM, Philadelphia, PA, 1995.

16. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, "QR decomposition," Numerical Recipes in FORTRAN 77: The Art ofScientific Computing, 1992.

17. Stratton, J. A., Electromagnetic Theory, Ch. 7, McGraw-Hill, NY, 1941.

18. Schelkunoff, S. A., Electromagnetic Wave, Ch. 3, Van Nostrand, NY, 1943.


© Copyright 2014 EMW Publishing. All Rights Reserved