Decoupling crossover in asymmetric broadside coupled split-ring resonators at terahertz frequencies

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Abstract

We investigate the electromagnetic response of asymmetric broadside coupled split-ring resonators (ABC-SRRs) as a function of the relative in-plane displacement between the two component SRRs. The asymmetry is defined as the difference in the capacitive gap widths ($\ensuremath{\Delta}g$) between the two resonators comprising a coupled unit. We characterize the response of ABC-SRRs both numerically and experimentally via terahertz time-domain spectroscopy. As with symmetric BC-SRRs ($\ensuremath{\Delta}g=0$ \ensuremath{\mu}m), a large redshift in the LC resonance is observed with increasing displacement, resulting from changes in the capacitive and inductive coupling. However, for ABC-SRRs, in-plane shifting between the two resonators by more than 0.375 ${L}_{o}$ (${L}_{o}$ $=$ SRR sidelength) results in a transition to a response with two resonant modes, associated with decoupling in the ABC-SRRs. For increasing $\ensuremath{\Delta}g$, the decoupling transition begins at the same relative shift (0.375 ${L}_{o}$), though with an increase in the oscillator strength of the new mode. This strongly contrasts with symmetric BC-SRRs, which present only one resonance for shifts up to 0.75 ${L}_{o}$. Since all BC-SRRs are effectively asymmetric when placed on a substrate, an understanding of ABC-SRR behavior is essential for a complete understanding of BC-SRR based metamaterials.

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