volume | PIER Journals

Abstract

The dynamic evolutions of full Gaussian and particularly the truncated Gaussian pulses in dispersive Lorentz media are studied numerically in detail. The observed qualitative phenomena lead to revised interpretation regarding both Sommerfeld and Brillouin precursors. Neither strict Sommerfeld nor Brillouin precursor is present for the case of an incident full Gaussian pulse for any finite propagation distance. In addition, the Brillouin effect can be separated into a tail and a forerunner depending on the turn-on point of the initial pulse. Moreover, the essence of an artificial precursor is discussed, which deserves caution when handling the high dynamic range problems by numerical algorithm.

1. Sommerfeld, A., "Uber die fortpflanzung des lichtes in dispergierenden medien," Ann. Phys., Vol. 44, 177-202, 1914.
doi:10.1002/andp.19143491002

2. Brillouin, L., "Uber die fortpflanzung des licht in dispergierenden medien," Ann. Phys., Vol. 44, 203-240, 1914.
doi:10.1002/andp.19143491003

3. Brillouin, L., Wave Propagation and Group Velocity, Academic, 1960.

4. Jackson, J. D., Classical Electrodynamics, 2nd Ed., John Wiley& Sons, Inc., 1975.

5. Oughstun, K. E. and G. C. Sherman, "Propagation of electromagnetic pulses in a linear dispersive medium with absorption (the Lorentz medium)," J. Opt. Soc. Am. B, Vol. 5, 817-848, 1988.
doi:10.1364/JOSAB.5.000817

6. Wyns, P., D. P. Foty, and K. E. Oughstun, "Numerical analysis of the precursor fields in linear dispersive pulse propagation," J. Opt. Soc. Am. A, Vol. 6, 1421-1429, 1989.
doi:10.1364/JOSAA.6.001421

7. Oughstun, K. E., P.Wyns, and D. Foty, "Numerical determination of the signal velocity in dispersive pulse propagation," J. Opt. Soc. Am. A, Vol. 6, 1430-1440, 1989.
doi:10.1364/JOSAA.6.001430

8. Solhaug, J. A., J. J. Stamnes, and K. E. Oughstun, "Diffraction of electromagnetic pulses in a single-resonance Lorentz medium," Pure Appl. Opt., Vol. 7, 1079-1101, 1998.
doi:10.1088/0963-9659/7/5/016

9. Balictsis, C. M. and K. E. Oughstun, "Uniform asymptotic description of ultrashort Gaussian-pulse propagation in a casual, dispersive dielectric," Phys. Rev. E, Vol. 47, 3645-3669, 1993.
doi:10.1103/PhysRevE.47.3645

10. Oughstun, K. E. and C. M. Balictsis, "Gaussian pulse propagation in a dispersive, absorbing dielectric," Phys. Rev. Lett., Vol. 77, 2210-2213, 1996.
doi:10.1103/PhysRevLett.77.2210

11. Balictsis, C. M. and K. E. Oughstun, "Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, casually dispersive medium," Phys. Rev. E, Vol. 55, 1910-1921, 1997.
doi:10.1103/PhysRevE.55.1910

12. Ni, X. and R. R. Alfano, "Brillouin precursor propagation in the THz region in Lorentz media," Optics Express, Vol. 14, 4188-4194, 2006.
doi:10.1364/OE.14.004188

13. Oughstun, K. E., "Dynamical evolution of the Brillouin precursor in Rocard-Powles-Debye model dielectrics," IEEE Transactions on Antennas and Propagation, Vol. 53, 1582-1590, 2005.
doi:10.1109/TAP.2005.846452

14. Beezley, R. S. and R. J. Krueger, "An electromagnetic inverse problem for dispersive media," J. Math. Phys., Vol. 26, 317-325, 1985..
doi:10.1063/1.526661

15. Kristensson, G., "Direct and inverse scattering problems in dispersive media — Green’s functions and invariant imbedding techniques," Methoden und Verfahren der Mathe-matischen Physik, Vol. 37, 105-119, 1991.

16. Karlsson, A., "Wave propagators for transient waves in onedimensional media ," Wave Motion, Vol. 24, No. 1, 85-99, 1996.
doi:10.1016/0165-2125(96)00008-X

17. Cossmann, S. M. and E. J. Rothwell, "Transient reflection of plane waves from a Lorentz medium half space," J. of Electromagn. Waves and Appl., Vol. 21, 1289-1302, 2007.
doi:10.1163/156939307783239456

18. Sihvola, A., "Metamaterials in electromagnetics," Metamaterials, Vol. 1, 2-11, 2007.
doi:10.1016/j.metmat.2007.02.003

19. Bigelow, M. S., N. N. Lepeshkin, H. Shin, and R. W. Boyd, "Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities," Journal of Physics: Condensed Matter, Vol. 18, 3117-3126, 2006.
doi:10.1088/0953-8984/18/11/017

20. Dvorak, S. L. and R. W. Ziolkowski, "Hybrid analytical-numerical approach for modeling transient wave propagation in Lorentz medium," J. Opt. Soc. Am. A, Vol. 15, 1241-1254, 1998.
doi:10.1364/JOSAA.15.001241

21. Ziolkowski, R. W. and J. B. Judkins, "Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams," J. Opt. Soc. Am. A, Vol. 9, 2021-2030, 1992.
doi:10.1364/JOSAA.9.002021

22. Ziolkowski, R. W., "Superluminal transmission of information through an electro-magnetic metamaterial," Phys. Rev. E, Vol. 63, 1-13, 2001.

23. Ziolkowski, R. W., "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E, Vol. 64, 1-15, 2001.

24. Sihvola, A. H., Electromagnetic Mixing Formulas and Application, 1999.

25. Pendry, J. B., A. J. Holden, D. C. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech., Vol. 47, 2075-2084, 1999.
doi:10.1109/22.798002

26. Robert, P., Electrical and Magnetic Properties of Materials, 1988.

Mr. Jiaran Qi

Dr. Ari Sihvola