Abstract
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable an inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators (SRRs) with packaged varactors embedded in the capacitive gaps, in a manner similar to that of Wang et al (2008 Opt. Express 16 16058). Because the SRRs exhibit a predominantly magnetic response to electromagnetic fields, the varactor-loaded SRR composite can be described as a magnetic material with nonlinear terms in its effective magnetic susceptibility. Treating the composite as a nonlinear effective medium, we can quantitatively assess the performance of the medium to enhance and facilitate nonlinear processes, including second harmonic generation, three- and four-wave mixing, self-focusing and other well-known nonlinear phenomena. We illustrate the accuracy of our approach by predicting the intensity-dependent resonance frequency shift in the effective permeability of the varactor-loaded SRR medium and comparing with experimental measurements.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Various nonlinear phenomena such as harmonic generation, parametric down-conversion, or tunability have been demonstrated experimentally in metamaterials incorporating nonlinear elements. A diverse spectrum of nonlinear phenomena in negative index materials (NIM) has been also analyzed theoretically, assuming a homogeneous NIM layer with presumed values of linear and nonlinear response. In this way a variety of novel effects have been predicted arising from the specific electromagnetic properties that negative-index media possess. For further practical applications, the design and optimization of nonlinear metamaterial-based devices requires a more quantitative approach, one that relates the particular metamaterial geometry incorporating nonlinear elements to the nonlinear properties of the resulting effective medium.
Main results. We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable an inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators with packaged varactors embedded in the capacitive gaps.
Wider implications. Within the range of applicability the approach allows the development of the model of a homogeneous analog nonlinear medium that aligns with the same concept in nonlinear optics.