chap12 008

# chap12 008 - 12.26 CHAPTER 12 WAVES AT PLANE BOUNDARIES...

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Unformatted text preview: 12.26 CHAPTER 12. WAVES AT PLANE BOUNDARIES 12.9 Advanced Topic: Metamaterial Boundaries The unusual metamaterial values of permittivity and permeability of were introduced in Section 10.13. One of the properties found when both the permittivity and permeability were negative was that the phase velocity was negative. This also means that the material will have a nega— tive index of refraction and that a wave enter» ing such a material produces a transmitted wave vector on the same side of the normal to the in— terface as the incident wave, thereby obeying the familiar Snell’s Law but with a negative angle. This is illustrated in Figure 12.15 by comparing transmitted wave directions for conventional ma- terials and a metamaterial for which the index of refraction is negative. An additional striking result is that the phase velocity 1),, = w/k re— verses sign upon transversal of the wave into the . . metamaterial, yet the group velocity :29 = dw/dk Figure 1215' remains positive, i.e., the power ﬂow is in a direc— tion opposite to that of the phase velocity. Cu— riously, this also occurs in atmospheric waves in which wave energy propagates upward while the phase velocity is downward (see Problem 10.41 and Kelley [1989]). Illustration of metamaterial differences. If we recall lens optics for normal materials, a convex lens can image objects when rays from a given point are focused on a point in the image plane. The resolution for such images is at best A/2 because of the ﬁnite size of the lens and the loss of information in the evanescent modes created by the interface between air and the lens. With a metamaterial lens with a negative index of refraction, the rays form an image plane inside the metamaterial as wellas in the image plane on the opposite of the lens from the object. Materials for which ,u and a are both complex and for which the characteristic impedances are equal to that of free space (17 = no) make an object disappear. With its impedance matched to free space, there is no reﬂection and with the complex per- mittivity and permeability, the wave is lossy. Covering the surfaces of a jet ﬁghter or bomber with such a material makes it invisible to radar, i.e., stealthy. Apparently the Klingons will eventually adapt this technology as a way to control the stealthiness of their spaceships by turning their cloaking on and off! ...
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