Virtually coupled resonators with modal dominance for improved sensitivity and bandwidth.

Mode-localized sensors have attracted significant attention due to their exceptional sensitivity and inherent ability to reject common-mode noise. This high sensitivity arises from the substantial shifts in resonator amplitudes induced by energy confinement in weakly coupled resonators. Despite their promising attributes, there has been limited research on the mechanisms of energy confinement. This paper presents both qualitative and quantitative analyses of energy confinement within weakly coupled resonators and concludes them as the concept of modal dominance. This concept elucidates that mode frequencies are predominantly dictated by the natural frequencies of the internal resonators, facilitating spatial energy confinement. Based on this modal dominance, a novel concept of virtually coupled resonators is proposed, which obviates the need for physical coupling structures. Instead, energy confinement is achieved through a frequency offset between two independent resonators, resulting in a similar amplitude ratio output and enhanced sensitivity. To further enhance performance, a double-closed-loop control scheme is developed for virtually coupled resonators, expanding the bandwidth in comparison to weakly coupled resonators. Experimental results validate the feasibility of virtually coupled resonators and the double-closed-loop control, demonstrating a 2.7-fold improvement in amplitude ratio sensitivity and at least a four-fold enhancement in bandwidth relative to weakly coupled resonators with identical parameters.