TE Modal Dispersion in Dielectric Slab Waveguide with Lossy Left-Handed Metamaterial

Hassan S. Ashour

1Department of Physics, Al-Azhar University, Gaza, Palestine 2Department of Physics, University of Dayton, Dayton, USA.

DOI: 10.4236/jmp.2013.49156                

Abstract

In this work, we derived the modal dispersion relation for TE_m modes for a symmetric slab waveguide constructed from SiO₂ dielectric guiding core material with lossy left-handed material (LHM) as cladding and substrate, and the power confinement factor. The dispersion relations and the power confinement factor were numerically solved for a given set of parameters: allowed frequency range; core’s thicknesses; and TE_m mode order. We found that the real part of the effective refractive index decreased with thickness and frequency increase. Moreover, the imaginary part (extinction coefficient) of the effective refractive index has very small values for all thickness in the frequency ranges, which means the waveguide structure is transparent for the used frequencies. The waveguide structure offers good guiding power for all thickness in the frequency range with low power attenuation. The real part of the effective refractive index increases with the increase of mode order, and the power confinement factor decreases with the increase of mode order.

Keywords

Dispersion Relation; Left Handed Material LHM; Power Confinement; TE Surface Waves

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. J. Pendry, “Metamaterials and the Control of Electromagnetic Fields,” Conference on Coherence and Quantum Optics, Rochester, 13 June 2007.
[2]	A. I. Ass’ad and H. S. Ashour, Turkish Journal of Physics, Vol. 36, 2012, pp. 207-213.
[3]	R. A. Shelby, D. R. Smith, N. Nasser and S. Shultz, Applied Physics Letters, Vol. 78, 2001, p. 489. doi:10.1063/1.1343489
[4]	J. B. Pendry, Physical Review Letters, Vol. 85, 2000, pp. 3966-3969. doi:10.1103/PhysRevLett.85.3966
[5]	R. A. Shelby, D. R. Smith and S. Schultz, Science, Vol. 292, 2001, pp. 77-79. doi:10.1126/science.1058847
[6]	V. G. Veselago, Soviet Physics Uspekhi, Vol. 10, 1967, pp. 509-514. doi:10.1070/PU1968v010n04ABEH003699
[7]	C. Caloz and T. Itoh, “Application of the Transmission Line Theory of Left-Handed (LH) Materials to the Realization of a Microstrip LH Transmission Line,” 2002 IEEE Antennas and Propagation Society International Symposium, San Antonio, 16-21 June 2002, pp. 412-415.
[8]	C. Caloz and T. Itoh, “Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications,” IEEE Press and Wiley, New York, 2005. doi:10.1002/0471754323
[9]	C. Caloz and T. Itoh, IEEE Transactions on Antennas Propagation, Vol. 52, 2004, pp. 1159-1166. doi:10.1109/TAP.2004.827249
[10]	T. T. Tang, W. L. Liu, X. J. He and X. Y. Gao, Optik-International Journal for Light and Electron Optics, Vol. 123, 2012.
[11]	T. T. Tang, Optik-International Journal for Light and Electron Optics, 2013, in Press.
[12]	S. Otto, A. Rennings, C. Caloz, P. Waldow, I. Wolff and T. Itoh, “Composite Right/Left Handed λ-Resonator Ring Antenna for Dual-Frequency Operation,” Proceedings of IEEE AP-S USNC/URSI National Radio Science Meeting, Washington DC, 3-8 July 2005.
[13]	A. Sanada, K. Murakami, I. Awai, H. Kubo, C. Caloz and T. Itoh, “A Planar Zeroth Order Resonator Antenna Using a Left-Handed Transmission Line,” 34th European Microwave Conference, Amsterdam,12-14 October 2004, pp. 1341-1344.
[14]	M. J. Adams, “An Introduction to Optical Waveguides,” John Wiley and Sons, New York, 1981.
[15]	K. Okamoto, “Fundamentals of Optical Waveguides,” Elsevier Inc, Burlington, 2006.
[16]	J. Singh, “Optical Properties of Condensed Matter and Applications,” John Wiley, New York, 2006. doi:10.1002/0470021942
[17]	Y. Chen, P. Fischer and F. Wise, Quantum Electronics and Laser Science Conference, Baltimore, 22-27 May 2005.
[18]	P. Markos and C. Soukoulis, Physical Review E, Vol. 65, 2002, p. 8. doi:10.1103/PhysRevE.65.036622
[19]	I. Shadrivov, S. Morrison and Y. Kivshar, Optics Express, Vol. 14, 2006, p. 9344. doi:10.1364/OE.14.009344
[20]	J. Zhou, N. Eleftherios, E. Koschny, M. Costas and C. Soukoulis, Optics Letters, Vol. 31, 2006, pp. 3620-3622. doi:10.1364/OL.31.003620
[21]	J. Kong, Journal of Electromagnetic Waves and Applications, Vol. 15, 2001, pp. 1319-1320. doi:10.1163/156939301X01200
[22]	A. I. Ass’ad, H. S. Ashour and M. M. Shabat, International Journal of Modern Physics B, Vol. 21, 2007, pp. 1951-1960. doi:10.1142/S0217979207037120
[23]	A. D. Boardman, M. M. Shabat and R. F. Wallis, Journal of Physics D, Vol. 24, 1991, pp. 1702-1707. doi:10.1088/0022-3727/24/10/002