Abstract
A resonance model, describing an LC circuit interaction with a bipole, is established for the determination of the effective parameters of metamaterials. The dynamic descriptions of both an LC circuit and a bipole are harmonic oscillators. Their interplay will induce a frequency shift, meaning that the most efficient receiving frequency (resonance frequency) of an LC circuit (or split ring) resonator is not the LC intrinsic frequency (ΩLC=1/LC) or the atomic vibration frequency. The relationship between the susceptibilities (χ(2),χ(3)) and the frequencies, including the atomic vibration frequency (Ω0), the LC intrinsic frequency (ΩLC), and the practical emission field frequency (Ω), is obtained. Compared with the other second-order harmonics, the extra DC current is much stronger, regardless of whether the system reaches resonance or not. The third-order harmonics are more likely to approach the resonance states compared with the second-order effect. Once the combined frequency is located at the resonance frequency, it is most likely to create a negative χ(3), and with the increase of the LC intrinsic frequency, a negative χ(3) can be obtained without satisfying the resonance condition.
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