Pedestrian Analysis of Harmonic Plane Wave Propagation in 1D-Periodic Media
Pierre Hillion
DOI: 10.4236/jmp.2011.24027   PDF    HTML     5,865 Downloads   10,239 Views  


The propagation of TE, TM harmonic plane waves impinging on a periodic multilayer film made of a stack of slabs with the same thickness but with alternate constant permittivity is analyzed. To tackle this problem, the same analysis is first performed on only one slab for harmonic plane waves, solutions of the wave equa- tion. The results obtained in this case are generalized to the stack, taking into account the boundary condi- tions generated at both ends of each slab by the jumps of permittivity. Differential electromagnetic forms are used to get the solutions of Maxwell’s equations.

Share and Cite:

P. Hillion, "Pedestrian Analysis of Harmonic Plane Wave Propagation in 1D-Periodic Media," Journal of Modern Physics, Vol. 2 No. 4, 2011, pp. 188-199. doi: 10.4236/jmp.2011.24027.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. D. Joannopoulos, R. D. Meade and J. N.Winn, “Photonic Crystals,” University Press, Singapore, 1995.
[2] H. Rignault, J. M.Loutioz, C. Delalande and A Levinson, “La nanophotonique,” Lavoisier, Paris, 2005.
[3] A. Foroozesh and L. Shafai, “Wave Propagation in 1D EBGs: Periodic Multilayer Films Consisting of Two Different Materials,” IEEE Antennas and Propagation Magazine, Vol. 50, No. 2, 2008, pp. 175-182. doi:10.1109/MAP.2008.4563628
[4] M. Born and E. Wolf, “Principles of Optics,” Pergamon, Oxford, 1965.
[5] M. Nevière and E Popov, “Light Propagation in Periodic Media,” Marcel Dekker, New York, 2003.
[6] I. V. Lindell, “Differential Forms in Electromagnetics,” IEEE Press, Piscataway, 2004.
[7] F. W. Hecht and Yu. N. Obukhov, “Foundations of Classical Electrodynamics,” Birkausen, Boston, 2003.
[8] Bossavit, “Differential Forms and the Computation of Fields and Forces in Electromagnetism,” European Journal Mechanics. B/Fluids, Vol. 10, No. 5, 1991, pp. 474-488.
[9] S. Linden and M. Wegener, “Photonic Metamaterial,” International Symposium on Signals, ISSSE. 2007, pp. 147-150.
[10] J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Physical Review Letters, Vol. 85, No. 18, 2000, pp. 3966-3969. doi:10.1103/PhysRevLett.85.3966
[11] R. W. Ziolkowski and E. Heyman, “Wave Propagation in Media Having Negative Permittivity and Permeability,” Physical Review E, Vol. 64, No. 5, 2001, pp. 1-15. doi:10.1103/PhysRevE.64.056625

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.