volume | PIER Journals

Abstract

We show in this paper that metamaterials in which some components of the permittivity and permeability tensors can have negative real values (thus associated with left-handed metamaterials) call for a reconsideration of the common concepts of critical angle and Brewster angle. By studying the reflection coefficient for isotropic and biaxial half-spaces and slabs, we show that a metamaterial for which the Brewster angle appears beyond the critical angle is realizable. In addition, we also show that the Goos-Hänchen shift induced by left-handed isotropic slabs is not necessarily negative but could be positive when the second interface of the slab supports a surface plasmon. Finally, upon studying a bianisotropic metamaterial, we show that propagation at a negative angle can occur, although it would not if only the permittivity and permeability tensors were considered. All the results have been obtained using an eigenvalue method which we extend to bianisotropic media in this paper.

1. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, 1990.

2. Teitler, S., B. W. HenvisJ. Opt. Soc. Am., and Vol. 60, 830, Vol. 60, 1970., 1970.

3. Berreman, D. W., "Optics in stratified and anisotropic media: 4 × 4-matrix formulation," J. Opt. Soc. Am., Vol. 62, No. 4, 502-510, 1972.

4. Tsalamengas, J. L., "Electromagnetic fields of elementary dipole antennas embedded in stratified general gyrotropic media," IEEE Trans. Antennas Propagat., Vol. 37, No. 3, 399-403, 1989.
doi:10.1109/8.18739

5. Tsalamengas, J. L. and N. K. Uzunoglu, "Radiation from a dipole near a general anisotropic layer," IEEE Trans. Antennas Propagat., Vol. 38, No. 1, 9-16, 1990.
doi:10.1109/8.43584

6. Tsalamengas, J. L., "Interaction of electromagnetic waves with general bianisotropic slabs," IEEE Trans. Microwave Theory Tech., Vol. 40, No. 10, 1870-1878, 1992.
doi:10.1109/22.159623

7. Sihvola, A., Electromagnetic Mixing Formulae and Applications, IEE Electromagnetic Waves Series 47, 2000.

8. Veselago, V., "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. USPEKHI, Vol. 10, No. 2, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699

9. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett., Vol. 76, 4773-4776, 1996.
doi:10.1103/PhysRevLett.76.4773

10. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys: Condens. Matter, Vol. 10, 4785-4809, 1998.
doi:10.1088/0953-8984/10/22/007

11. Shelby, R., D. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, No. 4, 77-79, 2001.
doi:10.1126/science.1058847

12. Norgen, M., "General optimization approach to a frequency-domain inversie problem of a stratified bianisotropic slab," J. Electromagn. Waves Applicat., Vol. 11, 515-546, 1997.

13. Smith, D. R., S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B, Vol. 65, 1-5, 2002.
doi:10.1103/PhysRevB.65.195104

14. Chen, X., T. M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr., and J. A. Kong, "Improved method to retrieve the constitutive effective parameters of metamaterials," accepted for publication in Phys. Rev. E..

15. Marqués, R., F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B, Vol. 65, 1-6, 2002.

16. Norgen, M., "Optimal design using stratified bianisotropic media: Application to anti-reflection coatings," J. Electromagn. Waves Applicat., Vol. 12, 939-959, 1998.

17. Ishimaru, A., S.-W. Lee, Y. Kuga, and V. Jandhyala, "Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory," IEEE Trans. Antennas Propagat., Vol. 51, No. 10, 2550-2557, 2003.
doi:10.1109/TAP.2003.817565

18. Titchener, J. B. and J. R. Willis, "The reflection of electromagentic waves from stratified anisotropic media," IEEE Trans. Antennas Propagat., Vol. 39, No. 1, 35-39, 1991.
doi:10.1109/8.64432

19. Pacheco, J., "Theory and application of left-handed metamaterials," Ph.D. thesis, No. 2, 2004.

20. Yin, W. Y., B. Guo, and X. T. Dong, "Comparative study on the interaction of electromagnetic waves with multi-layer omega(chiro)ferrite slabs," J. Electromagn. Waves Applicat., Vol. 17, No. 1, 15-29, 2003.
doi:10.1163/156939303766975326

21. Berman, P. R., "Goos-Hänchen shift in negatively refractive media," Phys. Rev. E, Vol. 66, 1-3, 2002.

22. Ziolkowski, R. W., "Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs," Optics Express, Vol. 11, 662-681, 2003.

23. Shadrivov, I. V., A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett., Vol. 83, 2003.
doi:10.1063/1.1615678

24. Shadrivov, I. V., A. A. Sukhorukov, and Y. S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett., Vol. 82, 3820-3822, 2003.
doi:10.1063/1.1579849

25. Kong, J. A., "Electromagnetic wave interaction with stratified negative isotropic media," Progress in Electromagn. Res., Vol. 35, 1-52, 2002.
doi:10.1159/000060803

26. Kong, J. A., Electromagnetic Wave Theory, EMW, 2000.

27. Smith, D. R. and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett., Vol. 90, No. 7, 1-4, 2003.
doi:10.1103/PhysRevLett.90.077405

28. Brekhovskikh, L. M., Waves in Layered Media, second ed., 1980.

29. Lai, H. M. and S. W. Chan, "Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media," Optics Letters, Vol. 27, No. 9, 680-682, 2002.

Dr. Tomasz M. Grzegorczyk

Professor Xudong Chen

Dr. Joe Pacheco

Dr. Jianbing Chen

Dr. Bae-Ian Wu

Professor Jin Au Kong