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12b. Thus, such a NIM slab has been called a “superlens”. The unique properties of such superlenses have stimulated an enormous interest as well as debates among researchers (Pendry [2000], ’t Hooft [2001], Williams [2001], Garcia and NietoVesperinas [2002], Shen and Platzman [2002], Ye [2003], Lagarkov and Kissel [2004], Merlin [2004], Larkin and Stockman [2005], Podolskiy and Narimanov [2005a], Jacob, Alekseyev and Narimanov [2006], Taubner, Korobkin, Urzhumov, Shvets and Hillenbrand [2006], Blaikie, Melville and Alkalsi [2006]).

1) can be written as follows: 4πω12 χ (2) μ1 dA1 A3 A∗2 exp(i kz), = −i dz c 2 k1 4πω22 χ (2) μ2 dA2 A3 A∗1 exp(i kz), =i dz c 2 k2 where k = k3 − k1 − k2 , ω2 = ω3 − ω1 . 13) 1, § 6] “Backward” phase-matching conditions: Implications for nonlinear optics 43 Fig. 21. (a,b) Schematics of optical parametric amplification in (a) NIMs and (b) PIMs. (c,d) The phase-matched amplification factor for the signal wave, and the conversion factor for the idler wave in (c) NIM and (d) PIM with absorption (α1 L = 1, α2 L = 1/2); (d) represents the dependence schematically.

21. (a,b) Schematics of optical parametric amplification in (a) NIMs and (b) PIMs. (c,d) The phase-matched amplification factor for the signal wave, and the conversion factor for the idler wave in (c) NIM and (d) PIM with absorption (α1 L = 1, α2 L = 1/2); (d) represents the dependence schematically. (Adapted from Popov and Shalaev [2006b]). Since loss is one of the major problems in existing NIMs, and especially in those operating at optical frequencies, optical parametric amplification has been proposed as a means to overcome dissipative losses (Popov and Shalaev [2006a]).

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