Introduction To Modern Planar Transmission Lines. Anand K. Verma

Free space matched lossy DNG absorber.

      Lossy DNG Slab with Conductor Backing

      Figure (5.17a) shows the obliquely incident wave on a conductor backed lossy DNG slab. The angle of refraction is negative. The incident wave could be either TE or TM‐polarized discussed in section (5.2). Following the results of equations (5.2.8c) and (5.2.16c) the reflection coefficients of both polarizations could be written as follows:

      (5.5.46)

      where θ_i = θ is the angle of incidence, is the refractive index of a DNG slab and (μ_r, ε_r) are material parameters of the DNG medium. The reflectivity for the incident TE and TM‐polarized waves is defined as and . In the case of normal incidence θ = 0^∘, the above results provide the following expression for reflectivity:

      (5.5.47)

To get no reflection, i.e. for R^nor = 0, the material parameters are n = ε_r, i. e. μ_r = ε_r. Thus, the DNG slab is impedance matched i.e. . The transmission coefficient τ^nor and transmissivity T^nor of a normally incident wave on the impedance matched DNG slab is obtained from equation (5.4.15):

(5.5.48)

      The condition 2n^″k₀d_min = 1 provides the minimum propagation depth to attenuate the absorbed RF power to 1/e:

      (5.5.49)

      The conductor backing reflects the attenuated EM‐wave that gets further attenuated by 1/e before appearing as the reflected wave from the air‐DNG interface. It degrades the absorption of the absorbing slab. An expression for the reflection coefficient is available, using the theory of multiple reflections [J.29]. However, for a thicker slab, multiple reflections can be ignored and simpler expression can be used to get the absorptivity of an absorber:

      (5.5.50)

      Lossy DNG Slab Without Conductor Backing

Figure (5.17b) shows the matched DNG slab without any conductor backing. In this case, the impedance matching of the DNG slab is also obtained for the condition μ_r = ε_r. The transmissivity of a normally incident wave is given by equation (5.5.48b). A thicker DNG slab is taken (d >> d_min) to reduce the transmissivity T almost to a negligible value.

      Both arrangements can be simulated using the Drude–Lorentz model discussed in chapter 6. We have discussed only the case of a single‐layered DNG absorber. It has a limited bandwidth, as μ_r = ε_r is obtained at one frequency. However, several thin layers of the lossy DNG could be stacked to get a wideband absorber. The multiple resonance DNG slabs provide multiband absorber also [J.32–J.35].

      The metamaterials have several other characteristics and applications. For instance, the DNG medium could be tailored to hide an object from the incident waves. It leads to the concept of cloaking. The cloak to hide any object is designed using the concept of the transformation electromagnetics [J.36]. The graded anisotropic refractive index between zero and unity is obtained through transformation electromagnetics. The metamaterials are used from microwave to optical frequency ranges, including the THz band [B.16]. Chapter 21 discusses realization and some applications of metamaterial in planar technology.

References

      Books

      1 B.1 Balanis, C.A.: Advanced Engineering Electromagnetics, John Wiley & Sons, New York, NY, 1989.

      2 B.2 Jordan, E.C.; Balmain Keith, G.E: Electromagnetic Wave and Radiating System, Prentice‐Hall India, New Delhi, 1989.

      3 B.3 Ramo, S.; Whinnery, J.R.; Van Duzer, T.: Fields, and Waves in Communication Electronics, 3rd Edition, John Wiley & Sons, Singapore, 1994.

      4 B.4 Orfanidis, S.J.: Electromagnetic Waves and Antenna, Free Book on The Web, ECE Department, Rutgers University, Piscataway, NJ, 2016.

      5 B.5 Collin, R.E.: Foundations for Microwave Engineering, IEEE Press, Wiley Student Edition, John Wiley & Sons, Singapore, 2004.

      6 B.6 Engheta, N.; Ziolkowski, R.W. (Editors): Metamaterials: Physics and Engineering Explorations, Wiley ‐ Interscience, John Wiley & Sons, Inc., Hoboken, NJ, 2006.

      7 B.7 Christophe Caloz, C.; Itoh, T.: Electromagnetic Metamaterials: Transmission line Theory and Microwave Applications (The Engineering Approach), Wiley‐ Interscience, John Wiley & Sons, Inc., Hoboken, NJ, 2006.

      8 B.8 Eleftheriades, G.I.; Balmain, K.G. (Editors): Negative‐Refraction Metamaterials: Fundamental Principles and Applications, Wiley‐ Interscience, John Wiley & Sons, Inc., Priceton, NJ, 2005.

      9 B.9 Capolino, F. (Editor): Theory and Phenomena of Metamaterials, CRC Press, Boca Raton, 2009.

      10 B.10 Marques, R.; Martin, F.; Sorolla, M.: Metamaterials with Negative Parameters. Theory, Design and Microwave Applications, Wiley, Hoboken, NJ, 2008.

      11 B.11 Sarychev, A.K.; Shalaev, V.M.: Electrodynamics of Metamaterials, World Scientific Publishing, Singapore, 2007.

      12 B.12 Smith, G.S.: An Introduction to Classical Electromagnetic Radiation, Cambridge University Press, New York, NY, 1997.

      13 B.13 Rutledge, D.B., Neikirk, D. P.; Kasilingam, D.P.: Planar Integrated Circuit Antennas, In Infrared and Millimeter Waves: Volume 10, Millimeter Components and Techniques Part II, Chapter‐1, K.J. Button, Academic Press, New York, NY, 1983.

      14 B.14 Liao, S.Y.: Microwave Devices and Circuits, 2nd Edition, Prentice – Hall of India Pvt. Ltd, New Delhi, 1989.

      15 B.15 Kraus, J.D.: Antenna, 2nd Edition, McGraw‐Hill International. Editions, New York, NY, 1988.

      16 B.16 Bass, A.F. de (Ed. In‐Chief): Nonostructured Metamaterials, European Commission, Brussels, 2018.

      Journals

      1 J.1 Holmes, J.J.; Balanis, C.A.: Refraction of the uniform plane wave incident on a plane boundary between two lossy media, IEEE Trans. Antenna Propagat., Vol. 26, No. 5, pp. 738–741, Sept. 1978.

      2 J.2 Pendry, J.B.: Negative refraction makes a perfect lens, Phys. Rev. Lett., Vol. 85, No. 18, pp. 3966–3969,