volume | PIER Journals

Abstract

The transmission line transfer matrix method (TLTMM) is proposed for the analysis of planar multilayer metamaterial (MTM) structures, where a transmission line model is developed by the transfer matrix method. This novel method may consider any oblique incident plane wave at any angle of incidence, any linear polarization (TE or TM with respect to the incidence plane), circular and elliptical polarizations, any frequency range (microwave or optical frequencies), any number of layers, any combination of common materials (DPS) and MTMs (such as DNG, ENG, MNG), any layer thickness, consideration of any dispersion relations for ε and μ, etc. A unified formulation is presented for both TE and TM polarizations, which lead to the evaluation of the fields and powers inside the layers and half spaces. The objective of the paper is to analyze and design several diverse problems of multilayered structures by TLTMM and a matrix method. The results of computations by TLTMM are agreed with the literature where possible and with the matrix method.

1. Alu, A. and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency," IEEE Trans. Antennas Propagat., Vol. 51, No. 10, 2558-2571, 2003.
doi:10.1109/TAP.2003.817553

2. Veselago, V., "The electrodynamics of substances with simultaneously negative values of ε and μ," Soviet Physics Uspekhi, Vol. 10, No. 4, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699

3. Khalaj-Amirhosseini, M., "Analysis of lossy inhomogeneous planar layers using the method of moments," Journal of Electromagnetic Waves and Applications, Vol. 21, 1925-1937, 2007.
doi:10.1163/156939307783152984

4. Khalaj-Amirhosseini, M., "Analysis of lossy inhomogeneous planar layers using finite difference method," Progress In Electromagnetics Research, Vol. 59, 187-198, 2006.

5. Rothwell, E. J., "Natural-mode representation for the field reflected by an inhomogeneous conductor-backed material layer ---- TE case," Progress In Electromagnetics Research, Vol. 63, 1-20, 2006.
doi:10.2528/PIER06051801

6. Kedar, A. and U. K. Revankar, "Parametric study of flat sandwich multilayer radome," Progress In Electromagnetics Research , Vol. 66, 253-265, 2006.
doi:10.2528/PIER06111202

7. Aissaoui, M., J. Zaghdoudi, M. Kanzari, and B. Rezig, "Optical properties of the quasi-periodic one-dimentional generalized multilayer Fibonacci structures," Progress In Electromagnetics Research, Vol. 59, 69-83, 2006.
doi:10.2528/PIER05091701

8. Qing, A. and C. K. Lee, "An improved model for full wave analysis of multilayered frequency selective surface with gridded square element," Progress In Electromagnetics Research, Vol. 30, 285-303, 2001.
doi:10.2528/PIER00041803

9. Kong, J. A., "Electromagnetic wave interaction with stratified negative isotropic media," Progress In Electromagnetics Research, Vol. 35, 1-52, 2002.
doi:10.2528/PIER01082101

10. Cory, H. and C. Zach, "Wave propagation in metamaterial multilayered structures," Mic. and Opt. Tech. Lett., Vol. 40, No. 6, 460-465, 2004.
doi:10.1002/mop.20005

11. Oraizi, H. and M. Afsahi, "Analysis of planar dielectric multilayers as FSS by transmission line transfer matrix method (TLTMM)," Progress In Electromagnetics Research, Vol. 74, 217-240, 2007.
doi:10.2528/PIER07042401

12. Ishimaru, A., Electromagnetic Wave Propagation, Radiation, and Scattering, Englewood Cliffs, Prentice Hall, 1991.

13. Oraiz, H. and M. Afsahi, "Determination of correct values for propagation constant, intrinsic impedance and refraction index of metamaterials," IEEE Int. Conf. Applied Electromagnetic, 1-4, 2007.

14. Gerardin, J. and A. Lakhtakia, "Negative index of refraction and distributed Bragg reflectors," Mic. and Opt. Tech. Lett., Vol. 34, No. 6, 409-411, 2002.
doi:10.1002/mop.10478

15. Zhang, Z. M. and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," App. Phys. Lett., Vol. 80, No. 6, 1099, 2002.
doi:10.1063/1.1448172

16. Gao, L. and C. J. Tang, "Near-field imaging by a multi-layer structure consisting of alternate right-handed and left-handed materials," Phys. Lett. A,, Vol. 322, No. 5-6, 390-395, 2004.
doi:10.1016/j.physleta.2004.01.048

17. Macleod, H. A., Thin-Film Optical Filters, 94-100, Adam Hilger, London, 1969.

18. de Gennes, P. G. and J. Prost, The Physics of Liquid Crystals, Sec. 6.1.2, Clarendon Press, Oxford, 1993.

19. Ghatak, A. and K. Thyagarajan, Optical Electronics, Sec. 18.6., Cambridge University Press, Cambridge, 1989.

20. Othonos, A., "Fiber Bragg ratings," Rev. Sci. Instrum., Vol. 68, 4309-4341, 1997.
doi:10.1063/1.1148392

21. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, No. 18, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966

22. Oraizi, H. and M. Afsahi, "Lossless DNG-DPS bilayer structures for tunneling and zero reflection," PIERS Online, Vol. 4, No. 1, 69-72, 2008.

23. Ye, Z., "Optical transmission and reflection of perfect lenses by left handed materials," Phys. Rev. B, Vol. 67, No. 19, 193106: 1-4, 2003.
doi:10.1103/PhysRevB.67.193106

24. Garcia, M. and M. Nieto-Vesperinas, "Left-handed materials do not make a perfect lens," Phys. Rev. Lett., Vol. 88, No. 20, 207403: 1-4, 2002.
doi:10.1103/PhysRevLett.88.207403

25. Fu, C. and Z. M. Zhang, Radiative properties of multilayer thin films with positive and negative refractive indexes, ASME Int. Conf. Mechanical Engineering Congress & Exposition, New Orleans, USA, 2002.

26. Besso, P., M. Bozzi, L. Perregrini, L. S. Drioli, and W. Nickerson, "Deep space antenna for Rosetta mission: Design and testing of the S/X-band dichroic mirror," IEEE Trans. Antennas Propagat., Vol. 51, 388-394, 2003.
doi:10.1109/TAP.2003.808528

27. Pendry, J., A. Holden, and W. Stewart, "Magnetism from conductors and enhanced nonlinear phenomen," IEEE Trans.Microwave Theory Tech., Vol. 47, No. 18, 2075-2084, 1999.
doi:10.1109/22.798002

28. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett., Vol. 84, No. 18, 4184-4187, 2000.
doi:10.1103/PhysRevLett.84.4184

Professor Homayoon Oraizi

Dr. Majid Afsahi