PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 35 > pp. 299-314

ELECTROMAGNETIC PULSE PROPAGATION IN DISPERSIVE MEDIA

By P. Hillion

Full Article PDF (118 KB)

Abstract:
We first consider the mathematical theory of boundaryinitial value problems for Maxwell's equations with as illustration, an extensive discussion of 1D-problems, Then, with the objective to investigate electromagnetic pulse propagation in dispersive media, we analyse how to translate electromagnetic processes which take place in a bounded domain of space-time into a boundary-initial value problem of Maxwell's equations, still focusing on 1D-problems.

Citation: (See works that cites this article)
P. Hillion, "Electromagnetic Pulse Propagation in Dispersive Media," Progress In Electromagnetics Research, Vol. 35, 299-314, 2002.
doi:10.2528/PIER02021703
http://www.jpier.org/PIER/pier.php?paper=0202173

References:
1. Stratton, J. A., Electromagnetic Theory, MacGraw Hill, New York, 1941.

2. Hopkinson, J., "The residual charge of the Leyden jar," Phil. Trans. Roy. Soc. London, Vol. 167, 599-626, 1877.
doi:10.1098/rstl.1877.0016

3. Davis, P., "Hyperbolic integrodifferential equations arising in the electromagnetic theory of dielectrics," J. Diff. Eqs., Vol. 18, 170-178, 1975.
doi:10.1016/0022-0396(75)90087-X

4. Bloom, F., Ill-Posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory, SIAM, Philadelphia, 1981.
doi:10.1137/1.9781611970890

5. Doetsch, G., Guide to the Applications of the Laplace and Z Transforms, Van Nostrand, New York, 1971.

6. Erdelyi, A., Tables of Integral Transforms, Vol. 1, MacGraw Hill, New York, 1954.

7. Mc Lachlan, N. W., Complex Variable Theory and Transform Calculus, University Press, Cambridge, 1955.

8. Dahlquist, G., "A multigrid extension of the FFT for the numerical inversion of the Fourier and Laplace transforms," BIT, Vol. 33, 85-112, 1993.
doi:10.1007/BF01990346

9., Classical Electrodynamics, Wiley, New York, 1975.

10. Sommerfeld, A., "Uber die fortplanzung des lichtes in disperdieren medien," Ann. der Phys. (Lpz), Vol. 44, 177-202, 1914.
doi:10.1002/andp.19143491002

11. Brillouin, L., "Uber die fortplanzung des lichtes in disperdieren medien," Ann. der Phys. (Lpz), Vol. 44, 203-240, 1914.
doi:10.1002/andp.19143491003

12. Oughstun, K. E. and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, Springer, Berlin, 1997.

13. Jiang, B. N., J. Wu, and A. Povinelli, J. Comput. Phys., Vol. 125, 104-125, 1996.

14. Hillion, P., "Beware of Maxwell’s divergence equations," J. Comput. Phys., Vol. 132, 154-155, 1997.
doi:10.1006/jcph.1996.5629

15. Doetsch, G., Introduction to the Theory and Applications of the Laplace Transformation, Springer, Berlin, 1974.
doi:10.1007/978-3-642-65690-3

16. Bellman, R. and E. D. Denman (Eds.), Invariant Imbedding, Springer, Berlin, 1970.

17. Bellman, R. and G. M. Wing, An Introduction to Invariant Imbedding, Wiley New York, 1975.

18. Quinnez, S., P. Hillion, and G. Nurdin, "Iterative method for invariant imbedding," Appl. Math. and Comput., Vol. 4, 213-237, 1978.
doi:10.1016/0771-050X(78)90009-8

19. Hillion, P., "Invariant imbedding for block tridiagonal systems," Appl. Math. and Comput., Vol. 6, 95-122, 1980.

20. Weston, W. H., "Invariant imbedding for the wave equation in three dimensions and the applications to the direct and inverse problems," Inverse Problems, Vol. 6, 1075-1105, 1990.
doi:10.1088/0266-5611/6/6/014

21. Gustafson, M., Wave Splitting in Direct and Inverse Scattering Problems, University Press, Lund, 2000.

22. Volterra, V., "Sur les equations integrodifferentielles et leurs applications," Acta Mathematica, Vol. 35, 295-356, 1912.
doi:10.1007/BF02418820

23. Toupin, R. A. and R. S. Rivlin, "Linear functional electromagnetic constitutive relations and plane waves in hemihedral isotropic materials," Arch. Rat. Mech. Anal., Vol. 6, 188-197, 1960.
doi:10.1007/BF00276162

24. Karlsson, A. and G. Kristensson, "Constitutive relations, dissipation and reciprocity for the Maxwell’s equations in the time domain," J. Electromeg. Waves and Appl., Vol. 6, 537-551, 1992.
doi:10.1163/156939392X01309

25. Hadamard, J., La Theorie des Equations aux Derivees Partielles, Editions Scientifiques, Pekin, 1964.

26. Cessenat, M., Mathematical Methods in Electromagnetism, World Scientific, Singapore, 1996.
doi:10.1142/2938

27. Bossavit, A., Computational Electromagnetism, Academic Press, New York, 1998.

28. Eller, M. M. and J. E. Masters, "Exact controllability of electromagnetic fields in a general region," Appl. Math. Optim., Vol. 45, 99-123, 2002.
doi:10.1007/s00245-001-0030-x


© Copyright 2014 EMW Publishing. All Rights Reserved