## Combined fictitious-sources–scattering-matrix method

JOSA A, Vol. 21, Issue 8, pp. 1417-1423 (2004)

http://dx.doi.org/10.1364/JOSAA.21.001417

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### Abstract

We describe a way to combine the method of fictitious sources and the scattering-matrix method. The resulting method presents concurrently the advantages of these two rigorous methods. It is able to solve efficiently electromagnetic problems in which the structure is made up of a jacket containing an arbitrary set of scatterers. The method is described in a two-dimensional case, but the basic ideas could be easily extended to three-dimensional cases.

© 2004 Optical Society of America

**OCIS Codes**

(050.1960) Diffraction and gratings : Diffraction theory

(260.2110) Physical optics : Electromagnetic optics

**History**

Original Manuscript: November 14, 2003

Revised Manuscript: February 18, 2004

Manuscript Accepted: February 18, 2004

Published: August 1, 2004

**Citation**

Gérard Tayeb and Stefan Enoch, "Combined fictitious-sources–scattering-matrix method," J. Opt. Soc. Am. A **21**, 1417-1423 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-8-1417

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### References

- D. Felbacq, G. Tayeb, D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994). [CrossRef]
- D. Felbacq, E. Centeno, “Theory of diffraction for 2D photonic crystals with a boundary,” Opt. Commun. 199, 39–45 (2001). [CrossRef]
- T. P. White, B. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002). [CrossRef]
- D. Maystre, M. Saillard, G. Tayeb, “Special methods of wave diffraction,” in Scattering, P. Sabatier, E. R. Pike, eds. (Academic, London, 2001).
- G. Tayeb, R. Petit, M. Cadilhac, “Synthesis method applied to the problem of diffraction by gratings: the method of fictitious sources,” in Proceedings of the International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 95–105 (1991). [CrossRef]
- G. Tayeb, “The method of fictitious sources applied to diffraction gratings,” Special issue on Generalized Multipole Techniques (GMT) of Appl. Computat. Electromagn. Soc. J. 9, 90–100 (1994).
- F. Zolla, R. Petit, M. Cadilhac, “Electromagnetic theory of diffraction by a system of parallel rods: the method of fictitious sources,” J. Opt. Soc. Am. A 11, 1087–1096 (1994). [CrossRef]
- F. Zolla, R. Petit, “Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical diffraction mounts,” J. Opt. Soc. Am. A 13, 796–802 (1996). [CrossRef]
- Y. Leviatan, A. Boag, “Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model,” IEEE Trans. Antennas Propag. AP-35, 1119–1127 (1987). [CrossRef]
- A. Boag, Y. Leviatan, A. Boag, “Analysis of two-dimensional electromagnetic scattering from a periodic grating of cylinders using a hybrid current model,” Radio Sci. 23, 612–624 (1988). [CrossRef]
- A. Boag, Y. Leviatan, A. Boag, “Analysis of diffraction from echelette gratings using a strip-current model,” J. Opt. Soc. Am. A 6, 543–549 (1989). [CrossRef]
- A. Boag, Y. Leviatan, A. Boag, “Analysis of electromagnetic scattering from doubly periodic nonplanar surfaces using a patch-current model,” IEEE Trans. Antennas Propag. AP-41, 732–738 (1993). [CrossRef]
- C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston, Mass., 1990).
- C. Hafner, “Multiple multipole program computation of periodic structures,” J. Opt. Soc. Am. A 12, 1057–1067 (1995). [CrossRef]
- V. D. Kupradze, “On the approximate solution of problems in mathematical physics,” original (Russian), Uspekhi Mat. Nauk 22(2), 59–107 (1967); English translation, Russian Mathematical Surveys 22, 58–108 (1967). [CrossRef]
- D. Kaklamani, H. Anastassiu, “Aspects of the method of auxiliary sources (MAS) in computational electromagnetics,” IEEE Antennas Propag Mag.June2002, pp. 48–64.
- W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes in FORTRAN: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
- A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. M. de Sterke, N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 046612 (2001). [CrossRef]
- M. Abramovitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).
- D. Maystre, M. Cadilhac, “Singularities of the continuation of the fields and validity of Rayleigh’s hypothesis,” J. Math. Phys. 26, 2201–2204 (1985). [CrossRef]
- http://institut.fresnel.free.fr/fs_ssm/index.htm , or contact the authors.

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