Introduction To Modern Planar Transmission Lines. Anand K. Verma
compared to the extraordinary wave in all directions except along the y‐axis.
The phase velocities vp1 and vp2 of the ordinary and extraordinary waves using equations (4.7.26a) and (4.7.27a) are expressed through the following relations [B.3]:
(4.7.28)
The phase velocity vp1 of the ordinary wave is independent of the angle θ. However, the phase velocity vp2 of the extraordinary wave is dependent on the angle θ. In Figure (4.15b), both velocities are identical only for the wave propagation along the z‐optic axis.
Finally, it is possible to artificially realize a uniaxial anisotropic material with one of the permittivity components as a negative quantity, say εr⊥ = − |εr⊥|. In this case, equation (4.7.26d) shows the hyperbolic dispersion relation. This medium is known as the hypermedium. It supports the wave propagation with a larger value of wavenumbers and can convert an incident evanescent wave to the propagating waves. Such engineered materials are needed by the hyperlens [J.1, J.7]. Figure (4.15d) shows the dispersion relation of the hypermedium with phase and group velocities. In this case, y‐components of vp and vg are opposite to each other. So, the hypermedium supports the backward wave propagation, and it is a metamaterial medium. The hyperlens is discussed in the subsection (5.5.6) of chapter 5.
References
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Journals
1 J.1 Jacob, Z.; Alekseyev, L.V.; Narimanov, E.: Optical hyperlens: far‐field imaging beyond the diffraction limit, Opt. Express, Vol. 14, No. 18, pp. 8247–8256, 2006.
2 J.2 Lee, H. et al.: Development of optical hyperlens for imaging below the diffraction limit, Opt. Express, Vol. 15, pp. 15886–15891, 2007.
3 J.3 Seddon, N.; Bearpark, T.: Observation of the inverse Doppler effect, Science, Vol. 302, pp. 1537–1539, Nov. 2003.
4 J.4 Mosallaei, H.; Sarabandi, K.: Magneto‐dielectrics in electromagnetics: concept and applications, IEEE Trans. Ant. Propagat., Vol. 52, No. 6, pp. 1558–1567, June 2004.
5 J.5 Alu, A.; Engheta, N.: Pairing an epsilon–negative slab with a mu‐negative slab: anomalous tunneling and transparency, IEEE Trans. Antenna Proag., Special Issue on Metamaterials, Vol. 51, No. 10, pp. 2558–2570, Oct. 2003.
6 J.6 Lee, H.; Xiong, Y.; Fang, N.; Srituravanich, N.; Durant, S.; Ambati, M.; Sun, C.; Zhang, X.: Realization of optical superlens imaging below the diffraction limit, New Journal of Physics, Vol. 7, No. 255, pp. 1–16, 2005.
7 J.7 Kim, M.; Rho, J.: Metamaterials and imaging, Nano Convergence, Vol. 2, No. 22, pp. 1–16, 2015.
5 Waves in Material Medium‐II: (Reflection & Transmission of Waves, Introduction to Metamaterials)
Introduction
The characteristics of material media and EM‐waves propagation in unbounded media are discussed in the previous chapter 4. Continuing the topics, this chapter is about the normal and oblique incidence of EM‐waves at the interface of two media. The characteristics of both the normal and oblique incident EM‐waves are obtained using an analytical method and convenient equivalent transmission line models. Under certain conditions, the interface surface of two media could acquire the property of a perfect electric conductor (PEC), or perfect magnetic conductor (PMC), or