Exponential tuning of the coupling constant of coupled microcantilevers by modifying their separation

Abstract

Vibration localization in coupled nanomechanical resonators has emerged as a promising concept for ultrasensitive mass sensing. It possesses intrinsic common mode rejection and the mass sensitivity can be enhanced with no need of extreme miniaturization of the devices. In this work, we have experimentally studied the role of the separation between cantilevers that are elastically coupled by an overhang. The results show that the coupling constant exponentially decays with the separation. In consistency with the theoretical expectations, the mass sensitivity is inversely proportional to the coupling constant. Finite element simulations show that the coupling constant can be exponentially reduced by increasing the ratio of the cantilever separation to the overhang length. © 2011 American Institute of Physics. ͓doi:10.1063/1.3569588͔ Nanomechanical resonators such as vibrating cantilevers, doubly clamped beams, and trampolines to name a few geometries have been proposed for ultrasensitive mass sensing. [1][2][3][4][5] The principle is that molecular adsorption on the surface of the resonator gives rise to an increase in the active mass of the resonator that makes the resonance frequency to decrease. The continuous advancements in top-down microand nanofabrication techniques has made possible increasingly smaller nanomechanical resonators with detection limits in the zeptogram range ͑10 −21 g͒. 6 Moreover, resonant nanowires and nanotubes fabricated by bottom-up methods are on the verge of single atom resolution ͑1.6610 −24 g͒. 7,8 The main disadvantage in the fabrication of extremely small nanomechanical resonators is that the deviations and imperfections inherent to the fabrication at nanoscale makes difficult to obtain reproducible mechanical properties and responses to molecular adsorption. In addition, very large scale integration of these resonators is still technologically complex.An approach that is no longer depending on the extreme miniaturization of the devices is the use of coupled nanomechanical resonators fabricated by standard silicon technology. 9-14 When the resonators are identical, the vibration of the eigenmodes is delocalized over the array. In a similar way to the Anderson's localization, the addition of the mass on one of the resonators leads to the spatial localization of the eigenmodes. 9,10,12 Since vibration localization is insensitive to uniform adsorption, coupled nanomechanical resonators allows decoupling of unspecific and specific molecular adsorption in differentially sensitized resonators. Theoretically, the sensitivity of these devices could be enhanced by reducing the mechanical coupling constant with no need of miniaturization of the nanomechanical resonators. 12 Here we have fabricated coupled mechanical systems consisting of two silicon nitride microcantilevers elastically coupled by an overhang at their base. The aim is to study the dependence of the mass sensitivity on the coupling constant that in this work is tuned by changing the separation between cantilevers.An optical m...

Non-linear mixing in coupled photonic crystal nanobeam cavities due to cross-coupling opto-mechanical mechanisms

“…FEM allows to calculate the mechanical coupling constant, j, as a function of the gap between the nanobeams. According to previous studies, 27 the coupling constant rapidly decreases with the increasing gap. We find the value of j to be $0.13, which is similar to the values a) previously reported in the literature for mechanically coupled systems.…”

Dynamical and quantum effects of collective dissipation in optomechanical systems

“…Moreover the fact that this same mechanism is observed in other mechanical oscillators with a similar geometry [48,49], indicates that collective dissipation is relevant in closely clamped mechanical resonators. Despite the mechanical coupling strength in this device [44,45] is an order of magnitude smaller than the regime studied here, it is possible to increase it up to the analyzed values by reducing the separation of the beams' clamping points and increasing the size of the overhang or common substrate, as shown in [69]. Interestingly this last point suggests that strong mechanical coupling and collective dissipation might go hand in hand.…”

Arrays of suspended silicon nanowires defined by ion beam implantation: mechanical coupling and combination with CMOS technology

“…Here, we actually take advantage of the overhang formation to generate coupled mechanical resonator systems based on a pair of doubly clamped SiNWs and demonstrate their coupled mechanical behaviour. Coupling of suspended SiNWs has already proven suitable for the realization of ultrasensitive nanomechanical mass sensors [17,42]. In that work [42], optical lithography methods were used.…”

“…Quantitatively, the frequency split effect can be explained by using the ideal coupled harmonic oscillator's theory [42] which holds that if N resonators are coupled, N collective modes of oscillation will be generated, where individual resonators will oscillate either in phase or antiphase with respect to their adjacent neighbours. For the particular case of two parallel identical resonators (nanobeams with the same dimensions), the mechanical coupling generates two different vibration modes: symmetric, nanobeams oscillating in phase, and antisymmetric, nanobeams oscillating in antiphase.…”