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Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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MODAL EXPANSION FOR THE 2D GREEN'S FUNCTION IN A NON-ORTHOGONAL COORDINATES SYSTEM

By J. P. Plumey, K. Edee, and G. Granet

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Abstract:
We present an efficient modal method to calculate the two-dimensional Green's function for electromagnetics in curvilinear coordinates. For this purpose the coordinate transformation based differential method, introduced for the numerical analysis of surface-relief gratings, is directly used with perfectly matched layers (PMLs). The covariant formalism Maxwell's equations, very convenient for the non-orthogonal coordinates formulation, also gives an unified analysis of PMLs. Numerical results for a line source placed above a perfectly conducting corrugated surface are presented.

Citation:
J. P. Plumey, K. Edee, and G. Granet, "Modal Expansion for the 2D Green's Function in a Non-Orthogonal Coordinates System," Progress In Electromagnetics Research, Vol. 59, 101-112, 2006.
doi:10.2528/PIER05080701
http://www.jpier.org/PIER/pier.php?paper=0508071

References:
1. Bérenger, J., "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys., Vol. 114, 185-200, 1994.
doi:10.1006/jcph.1994.1159

2. Chew, W. C. and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microwave Opt. Technol. Lett., Vol. 7, 599-604, 1994.

3. Chew, W. C., J. M. Jin, and E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microwave Opt. Technol. Lett., Vol. 15, 363-369, 1997.
doi:10.1002/(SICI)1098-2760(19970820)15:6<363::AID-MOP8>3.0.CO;2-C

4. Teixeira, F. L. and W. C. Chew, "Differential forms, metrics, and the reflectionless absorption of electromagnetic waves," J. Electromagn. Waves Appl., Vol. 13, 665-686, 1999.

5. Derudder, H., F. Olyslager, and D. De Zutter, "An efficient series expansion for the 2-D Green's function of a microstrip substrate using perfectly matched layers," IEEE Microwave Guided Wave Lett., Vol. 9, 505-507, 1999.
doi:10.1109/75.819413

6. Silberstein, E., P. Lalanne, J.-P. Hugonin, and Q. Cao, "Use of gratings in integrated optics," J. Opt. Soc. Am. A, Vol. 18, 2865-2875, 2001.

7. Chandezon, J., D. Maystre, and G. Raoult, "A new theorical method for diffraction gratings and its numerical application," J.Optics, Vol. 11, 235-241, 1980.
doi:10.1088/0150-536X/11/4/005

8. Sacks, Z. S., D. M. Kingsland, R. Lee, and J.-F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propagat., Vol. 43, 1460-1463, 1995.
doi:10.1109/8.477075


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