Frequency combs in a MEMS resonator featuring 1:2 internal resonance: ab initio reduced order modelling and experimental validation

Abstract

This paper is devoted to a detailed analysis of the appearance of frequency combs in the dynamics of a micro-electro-mechanical systems (MEMS) resonator featuring 1:2 internal resonance. To that purpose, both experiments and numerical predictions are reported and analysed to predict and follow the appearance of the phononic frequency comb arising as a quasi-periodic regime between two Neimark-Sacker bifurcations. Numerical predictions are based on a reduced-order model built thanks to an implicit condensation method, where both mechanical nonlinearities and electrostatic forces are taken into account. The reduced order model is able to predict a priori, i.e. without the need of experimental calibration of parameters, and in real time, i.e. by solving one or two degrees-of-freedom system of equations, the nonlinear behaviour of the MEMS resonator. Numerical predictions show a good agreement with experiments under different operating conditions, thus proving the great potentiality of the proposed simulation tool. In particular, the bifurcation points and frequency content of the frequency comb are carefully predicted by the model, and the main features of the periodic and quasi-periodic regimes are given with accuracy, underlining that the complex dynamics of such MEMS device is effectively driven by the characteristics of the 1:2 internal resonance.

Effects of High-Order Nonlinearities on Phononic Frequency Combs

“…However, the follow-up studies by various research groups have employed different technologies [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] to excite PFC viz. silicon beam [8], aluminum nitride membrane [9], hybrid graphene-silicon nitride membrane [10], quartz crystal [11][12], molybdenum disulphide membrane [13][14], graphene membrane [15], silicon nitride string [16], silicon nitride membrane [17], micro-rhombic resonator [18], micro-arch resonator [19], micro-ring resonator [20] and gas bubble clusters [21][22]. PFC has also been generated in optomechanical [23], magnetomechanical [24][25] and electromechanical systems [26].…”

Generation of Soliton Frequency Combs in NEMS

“…Over the last 25 years, optical frequency combs (OFCs) have made a resounding impact, shaping fields from metrology to astronomy. − Their frequency coherence established them as essential metrology tools in laboratories worldwide. ,, Recent strides in nonlinear optical resonators have harnessed the power of optical solitons by balancing nonlinearity and dispersion to enhance the stability of the spectral lines and FCs. This advancement has far-reaching implications across disciplines, benefiting applications in timing, sensing, resonance stabilization, spectroscopy, and quantum information processing. − ,− OFCs realized within microscale nonlinear optical resonators show promise in reducing both footprint and power consumption compared to traditional FC generators. ,− However, challenges persist, including the costs and complexities of fabrication and the experimental setup. Further, the power threshold required to generate Kerr FCs is high, leading to significant thermal losses that can impact their stability and phase coherence.…”

“…This approach provides an innovative solution to fundamental problems, such as quantum transduction, − by expanding the bandwidth of the generated FCs through enhanced energy transfer between participating modes. Further, the energy exchange between modes involved in internal resonance, − where natural frequencies are integer multiples of each other ( pf 1 = q f 2 ), occur at rates orders of magnitude faster than exchanges with external sources ,, offering further stabilization to the resulting FCs. This study presents a novel approach for the generation of mechanical soliton FCs similar to those generated by nonlinear optical microresonators.…”