Enhanced parametric processes in binary metamaterials

Extensive studies of microwave properties of composite metallic structures led to the experimental demonstration of left-handed metamaterials [1] suggested long time ago [2]. Such metamaterials are created by resonant magnetic elements and operate for the wavelengths much larger than the period, allowing for the macroscopic effective medium description. The parameters of the effective medium depend on the microscopic structure of the metallic composites. Moreover, nonlinear response of the metamaterial can become substantial [3–5], and their transmission characteristics can be effectively controlled by external fields [6–8]. Nonlinearities of metamaterials suggest their novel applications such as frequency conversion [5, 9], tunable transmission [8], second-harmonic imaging [10], nonlinear beam focusing and soliton propagation [11], etc. In contrast to nonlinear optical media, composite metamaterials possess nonlinear magnetic response that can be engineered by inserting nonlinear elements (e.g., diodes) into the resonant conductive elements [3, 4]. In this Letter we suggest a novel type of composite metamaterials with double-resonant response and demonstrate that in the nonlinear regime such binary metamaterials are ideally suited for the first observation of the enhanced phase-matched parametric interaction and second-harmonic generation. Indeed, the quadratic nonlinear magnetic susceptibility is proportional to a product of linear magnetic susceptibilities at the frequencies of interacting waves. For conventional single-resonant nonlinear metamaterials, the magnetic susceptibility of the fundamental wave is relatively large, since it corresponds to the backward wave near the resonance [9] while the susceptibility of the second-harmonic wave is rather small. In the metamaterial with several resonances, it is possible to enhance the nonlinear response, so that both linear susceptibilities of interacting waves can become large. To create a double-resonant metamaterial we suggest to mix two types of resonant conductive elements (RCEs) with different resonant frequencies [12], as shown schematically in Fig. 1 for the structure consisting of two lattices of different split-ring resonators. First, we study linear properties of the binary metamaterials. For large wavelengths, each RCE can be described as a resonant circuit (see, e.g., [13, 14]) characterized by selfa