Electrodynamics of Metamaterials by Shalaev V.M., Sarychev A.K.

By Shalaev V.M., Sarychev A.K.

Mild is in a feeling ''one-handed'' whilst interacting with atoms of traditional fabrics. the reason is, out of the 2 box parts of sunshine, electrical and magnetic, basically the electrical ''hand'' successfully probes the atoms of a fabric, while the magnetic part continues to be fairly unused as the interplay of atoms with the magnetic box part of mild is generally vulnerable. Metamaterials, i.e. synthetic fabrics with rationally designed houses, can allow the coupling of either one of the sphere elements of sunshine to meta-atoms, allowing fullyyt new optical homes and interesting functions with such ''two-handed'' gentle. one of the interesting homes is a unfavourable refractive index. The refractive index is likely one of the so much primary features of sunshine propagation in fabrics. Metamaterials with damaging refraction could lead to the improvement of a superlens in a position to imaging gadgets and their superb buildings which are a lot smaller than the wavelength of sunshine. different fascinating purposes of metamaterials contain novel antennae with stronger houses, optical nano-lithography and nano-circuits, and ''meta-coatings'' which can make items invisible. The be aware ''meta'' skill ''beyond'' in Greek, and during this feel the identify ''metamaterials'' refers to ''beyond traditional materials.'' Metamaterials are usually man-made and feature houses now not on hand in nature. what's so magical approximately this straightforward merging of ''meta'' and ''materials'' that has attracted rather a lot realization from researchers and has ended in exponential development within the variety of guides during this quarter? the reply you'll find during this publication.

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21) give an asymptotic behavior both for the effective dielectric susceptibility εe ∼ εd |∆p|−s and effective conductivity σ e ∼ σ m (∆p)t , somewhat different from the asymptotic behavior of the same quantities for the conducting stick composites given by Eqs. 19). To incorporate Eqs. 19) into the scaling model, we rewrite the scaling Eq. 22) where the scaling function f2 (z) is still given by Eq. 21), while the di2 mensionless frequency ω ∗ = (a/b) (εd /εm ) is large in an absolute value due to the large stick’s aspect ratio a/b.

8) into Eq. 15) where the polarization factors g and g⊥ are given by Eq. 14). 15) can be simplified for the case of the high-aspect-ratio conducting elongated inclusions (σ m ω, a b). The following simplifications are adopted (1) Since we are interested in the effective conductivity for the stick concentration p, which is below and in a vicinity of the percolation threshold pc ∼ b/a l, we neglect the concentration p in the first term but keep it in the second term of Eq. 15). (2) Since the concentration p 1, the effective conductivity σ e is much smaller than the stick conductivity σ e σ m , we neglect σ e in comparison with σ m in all the terms of Eq.

8 [Bergman and Stroud, 1992]. Therefore, we believe that Eq. 19) may be used for a quantitative estimation of εe (∆p) near pc . Note that the factor a/b 1 again appears in Eq. 19) due to the large polarizability of conducting sticks discussed above. As a result, the dielectric constant εe (∆p) achieves very large values in the critical region ∆p near the percolation threshold pc as shown in Fig. 2 (the dashed line in Fig. 2 indicates the position of pc ). Actually, the concentrations region, where εe (∆p) 1,largely exceeds the usual condition of the percolation theory |∆p| 1.

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