We present an analysis of the nonlinear, power-dependent resonance frequency shift for two metamaterial mediums consisting of arrays of varactor-loaded split ring resonators (VLSRRs). We confirm that, over a limited range of power, a VLSRR medium can be described by its second and third order nonlinear susceptibilities, making it a useful analog medium for the quantitative investigation of other nonlinear phenomena that might be achieved using inherently nonlinear materials integrated into metamaterials. Experimental measurements of the resonance frequency shift with power from fabricated VLSRR samples are found to be in excellent agreement with the analytical model.
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