Abstract
A systematic dynamic theory is established to deal with the optical collective resonance in metamaterial arrays. As a reference model, we consider an infinite split ring resonator (SRR) array illuminated by a linearly polarized wave and introduce an N-degree-of-freedom forced oscillator equation to simplify the coupled-mode vibration problem. We derive a strict formula of resonance frequency (RF) and its adjustable range from the steady-state response. Unlike a single SRR possesses invariant RF, it successfully explains the mechanism of RF shift effect in the SRR array when the incident angle changes. Instead of full wave analysis, only one or two adjacent resonance modes can give an accurate response line shape. Our approach is applicable for metallic arrays with any N-particle cell at all incident angles and well matched with numerical results. It provides a versatile way to study the vibration dynamics in optical periodic many-body systems.
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