Nonlinear Left-Handed Metamaterials

Metamaterials are artificial structures that are designed to exhibit specific electromagnetic properties required for different applications but not commonly found in nature.The methodology of synthesizing materials composed of micro-and nano-structured components that mimic the electromagnetic response of individual atoms and molecules (meta-atoms and meta-molecules) has proven to be very productive and resulted in the development of metamaterials exhibiting strong magnetic response at microwave and optical frequencies and so-called left-handed metamaterials (LHMs) (both impossible in conventional real-world materials).LHMs are designed to exhibit simultaneously negative permittivity and permeability (Veselago, 1968;Engheta & Ziolkowski, 2006).In 2000, Smith et al. developed the first experimental left-handed structure, which was composed of metallic split-ring resonators and thin metal wires (Smith et. al., 2000;Shelby et. al., 2001).An alternative transmission line approach for left-handed materials was proposed, almost simultaneously, by several different groups (Belyantsev & Kozyrev, 2002; Caloz & Itoh, 2002;Iyer & Eleftheriades, 2002).This approach, based on nonresonant components, allows for low-loss left-handed structures with broad bandwidth.The unique electrodynamic properties of these materials, first postulated by Veselago in 1968, include the reversal of Snell's law, the Doppler effect, Vavilov-Cherenkov radiation, and negative refractive index, making theses materials attractive for new types of RF and microwave components.The range of applications for LHMs is extensive, and opportunities abound for development of new and powerful imaging and communication techniques.The most tantalizing of these potential applications is the possibility of realizing "perfect" (diffraction-free) lenses based on their inherent negative index of refraction (Pendry, 2000).The slab of LHM can act as an ideal (diffractionfree) lens and thus capable of producing images of objects without any loss of information which is impossible with conventional lenses.Most studies of LHMs have been concerned with linear wave propagation, and have inspired many applications that were unthinkable in the past (Engheta & Ziolkowski, 2006;