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2 - Light propagation through dispersive dielectric slabs

Published online by Cambridge University Press:  03 May 2011

Malin Premaratne
Affiliation:
Monash University, Victoria
Govind P. Agrawal
Affiliation:
University of Rochester, New York
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Summary

An integral feature of any optical amplifier is the interaction of light with the material used to extract the energy supplied to it by an external pumping source. In nearly all cases, the medium in which such interaction takes place can be classified as a dielectric medium. Therefore, a clear understanding of how light interacts with active and passive dielectric media of finite dimensions is essential for analyzing the operation of optical amplifiers. When light enters such a finite medium, its behavior depends on the global properties of the entire medium because of a discontinuous change in the refractive index at its boundaries. For example, the transmissive and reflective properties of a dielectric slab depend on its thickness and vary remarkably for two slabs of different thicknesses even when their material properties are the same [1].

In this chapter we focus on propagation of light through a dispersive dielectric slab, exhibiting chromatic dispersion through its frequency-dependent refractive index. Even though this situation has been considered in several standard textbooks [2, 3], the results of this chapter are more general than found there. We begin by discussing the state of polarization of optical waves in Section 2.1, followed with the concept of impedance in Section 2.2. We then devote Section 2.3 to a thorough discussion of the transmission and reflection coefficients of a dispersive dielectric slab in the case of a CW plane wave. Propagation of optical pulses through a passive dispersive slab is considered in Section 2.4, where we also provide simple numerical algorithms.

Type
Chapter
Information
Light Propagation in Gain Media
Optical Amplifiers
, pp. 28 - 62
Publisher: Cambridge University Press
Print publication year: 2011

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References

[1] B., Nistad and J., Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E, vol. 78, p. 036603 (10 pages), 2008.Google Scholar
[2] M., Born and E., Wolf, Principles of Optics, 7th ed. Cambridge University Press, 1999.Google Scholar
[3] J. D., Jackson, Classical Electrodynamics, 3rd ed. Wiley, 1998.Google Scholar
[4] B. E. A., Saleh and M. C., Teich, Fundamentals of Photonics, 2nd ed. Wiley InterScience, 2007.Google Scholar
[5] A., Taflove and S. C., Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. Artech House, 2005.Google Scholar
[6] R. W., Ziolkowski and E., Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E, vol. 64, p. 056625 (15 pages), 2001.Google Scholar
[7] J., Wei and J., Xiao, “Electric and magnetic losses and gains in determining the sign of refractive index,” Opt. Commun., vol. 270, pp. 455–464, 2007.Google Scholar
[8] M. A., Dupertius, M., Proctor, and B., Acklin, “Generalization of complex Snell–Descartes and Fresnel laws,” J. Opt. Soc. Am. A, vol. 11, pp. 1159–1166, 1994.Google Scholar
[9] P. W., Milonni, “Controlling the speed of light pulses,” J. Phys. B: At. Mol. Opt. Phys., vol. 35, pp. R31–R56, 2002.Google Scholar
[10] C. G. B., Garrett and D. E., McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A, vol. 1, pp. 305–313, 1970.Google Scholar
[11] C., Gasquet, R. D., Ryan, and P., Witomski, Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets. Springer-Verlag, 1998.Google Scholar
[12] D., Slepian, “On bandwidth,” Proc. IEEE, vol. 64, pp. 292–300, 1976.Google Scholar
[13] G. P., Agrawal, Nonlinear Fiber Optics, 4th ed. Academic Press, 2007.Google Scholar
[14] J. B., Schneider, “FDTD dispersion revisited: Faster-than-light propagation,” IEEE Microw. Guided Wave Lett., vol. 9, pp. 54–56, 1999.Google Scholar
[15] D. F., Kelley and R., Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antennas Propag., vol. 44, pp. 792–797, 1996.Google Scholar
[16] M., Okoniewski, M., Mrozowski, and M., Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microw. Guided Wave Lett., vol. 7, pp. 121–123, 1997.Google Scholar
[17] J., Young and R., Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag., vol. 43, pp. 61–77, 2001.Google Scholar
[18] M., Han, R. W., Dutton, and S., Fan, “Model dispersive media in finite-difference timedomain method with complex-conjugate pole-residue pairs,” IEEE Microw. Wireless Compon. Lett., vol. 16, pp. 119–121, 2006.Google Scholar
[19] I., Udagedara, M., Premaratne, I. D., Rukhlenko, H. T., Hattori, and G. P., Agrawal, “Unified perfectly matched layer for finite-difference time-domain modeling of dispersive optical materials,” Opt. Express, vol. 17, pp. 21180–21190, 2009.Google Scholar
[20] J., Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, pp. 185–200, 1994.Google Scholar
[21] S., Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag., vol. 44, pp. 1630–1639, 1996.Google Scholar
[22] L., Zhao and A. C., Cangellaris, “GT-PML: Generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference timedomain grids,” IEEE Trans. Microw. Theory Tech., vol. 44, pp. 2555–2563, 1996.Google Scholar
[23] M., Kuzuoglu and R., Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers,” IEEE Microw. Guided Wave Lett., vol. 6, pp. 447–449, 1996.Google Scholar
[24] J.-P., Berenger, “Numerical reflection from FDTD-PMLs: A comparison of the split PML with the unsplit and CFS PMLs,” IEEE Trans. Antennas Propag., vol. 50, pp. 258–265, 2002.Google Scholar
[25] J.-P., Berenger, “Application of the CFS PML to the absorption of evanescent waves in waveguides,” IEEE Microw. Wireless Compon. Lett., vol. 12, pp. 218–220, 2002.Google Scholar
[26] D., Correia and J.-M., Jin, “On the development of a higher-order PML,” IEEE Trans. Antennas Propag., vol. 53, pp. 4157–4163, 2005.Google Scholar
[27] Y., Rickard and N., Georgieva, “Problem-independent enhancement of PML ABC for the FDTD method,” IEEE Trans. Antennas Propag., vol. 51, pp. 3002–3006, 2003.Google Scholar
[28] S., Cummer, “Perfectly matched layer behavior in negative refractive index materials,” IEEE Antennas Wireless Propag. Lett., vol. 3, pp. 172–175, 2004.Google Scholar
[29] A. V., Oppenheim and R. W., Schafer, Digital Signal Processing. Prentice-Hall, 1975.Google Scholar
[30] D., Sullivan, “Z-transform theory and the FDTD method,” IEEE Trans. Antennas Propag., vol. 44, pp. 28–34, 1996.Google Scholar
[31] E. L., Bolda, R. Y., Chiao, and J. C., Garrison, “Two theorems for the group velocity in dispersive media,” Phys. Rev. A, vol. 48, pp. 3890–3894, 1993.Google Scholar
[32] L. D., Landau and E. M., Lifshitz, Electrodynamics of Continuous Media, 2nd ed. Course of Theoretical Physics, vol. 8. Pergamon Press, 1984.Google Scholar
[33] T. W., Gamelin, Complex Analysis. Springer, 2001.Google Scholar
[34] G., Cesini, G., Guattari, G., Lucarini, and C., Palma, “Response of Fabry–Perot interferometers to amplitude-modulated light beams,” Optica Acta, vol. 24, pp. 1217–1236, 1977.Google Scholar
[35] J., Yu, S., Yuan, J.-Y., Gao, and L., Sun, “Optical pulse propagation in a Fabry–Perot étalon: Analytical discussion,” J. Opt. Soc. Am. A, vol. 18, pp. 2153–2160, 2001.Google Scholar
[36] X. G., Qiong, W. Z., Mao, and C. J., Guo, “Time delay of a chirped light pulse after transmitting a Fabry–Perot interferometer,” Chinese Phys. Lett., vol. 19, pp. pp. 201–202, 2002.Google Scholar
[37] J., Skaar, “Fresnel equations and the refractive index of active media,” Phys. Rev. E, vol. 73, p. 026605 (7 pages), 2006.Google Scholar

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