A frequency comb consists of a series of equally spaced discrete frequencies. In recent years, optical frequency combs [1][2][3][4][5][6][7][8] have emerged as a potential toolset spanning diverse applications ranging from frequency metrology [1-4] to molecular fingerprinting [8]. Specifically the ability to precisely define the frequency spacing between frequency markers and align these measurements with microwave sources through the comb generation process has led to a number of physical measurements [4] requiring very high accuracy including the observation of gravitational waves [9].Optical frequency combs have been generated by using the comb-like mode structure of modelocked lasers and more recently through the interaction of continuous-waver lasers with high Q toroidal optical microresonators mediated via the Kerr non-linearity [10].Despite the analogies between phonons and photons, a direct analogue for an optical comb in the phononic domain has not been observed and comb generation process is thought to be largely limited by the nonlinear dispersion relations of phonons. However, theoretical work [11] has recently demonstrated the possibility for generation of frequency combs in a phononic system represented by Fermi-Pasta-Ulam α (FPU-α) chains [15] where the dispersion relationship does not play a role. In this letter, we report the first experimental confirmation of a phononic frequency comb in a microfabricated structure bearing similar traits predicted by numerical simulations performed on a FPU-α chain [11]. Additionally, our resonator also captures the onset of Duffing nonlinear mechanism [12][13][14] and its interference with the nominal phononic comb.The non-linear three wave mixing mechanism resulting in the generation of frequency combs is theoretically facilitated through the excitation of non-linear resonances of various orders.Specifically, in Direct Nonlinear Resonance (DNR) as termed in [11], the interaction between the eigenmode and driven phonon mode in a non-linear lattice results in the formation of equi-spaced spectral lines at a characteristic frequency ∆ set by the drive frequency and the intrinsic phonon mode frequencies. Mathematically, the DNR phenomenon can be modelled through the coupled dynamics. Figure 1A) upon the drive level crossing a specific threshold value. Here, the displacement profile corresponding to the sub-harmonic mode can be conceived as a pre-stressed framework for the level of coupling between drive frequency and intrinsic resonance mode ( Figure 1B). That being said, the propensity for comb generation is higher at the antinodes of sub-harmonic mode. Additionally, figure 1b1 provides an evidence for the phase coherency of equidistant comb lines. In this letter, we systematically report the experimental results carried out in the extensional resonator based test bed to understand the frequency comb generation and discuss the opportunities for active tuning of comb structure.The drive amplitude dependence on the phononic comb for an off-resonant drive frequenc...
Abstract-Piezoelectric vibration energy harvesters have been widely researched and are increasingly employed for powering wireless sensor nodes. The Synchronized Switch Harvesting on Inductor (SSHI) circuit is one of the most efficient interfaces for piezoelectric vibration energy harvesters. However, the traditional incarnation of this circuit suffers from a significant startup issue that limits operation in low and variable amplitude vibration environments. This paper addresses this start-up issue for the SSHI rectifier by proposing a new architecture with SSHI startup circuitry. The startup circuitry monitors if the SSHI circuit is operating correctly and re-starts the SSHI interface if required. The proposed circuit is comprehensively analyzed and experimentally validated through tests conducted by integrating a commercial piezoelectric vibration energy harvester with the new interface circuit designed in a 0.35 µm HV CMOS process. Compared to conventional SSHI rectifiers, the proposed circuit significantly decreases the required minimum input excitation amplitude before energy can be harvested, making it possible to extract energy over an increased excitation range.Index Terms-Energy harvesting, piezoelectric transducer, synchronized switch harvesting on inductor (SSHI), rectifier.
This paper is motivated by the recent demonstration of three-wave mixing based phononic frequency comb. While the previous experiments have shown the existence of three-wave mixing pathway in a system of two-coupled phonon modes, this work demonstrates a similar pathway in a system of three-coupled phonon modes. The paper also presents a number of interesting experimental facts concomitant to the three-mode three-wave mixing based frequency comb observed in a specific micromechanical device. The experimental validation of three-mode threewave mixing along with the previous demonstration of two-mode three-wave mixing points to the ultimate possibility of multimode frequency combs.Optical frequency combs have significantly transformed modern metrology and molecular spectroscopy [1][2]. Recently, we experimentally demonstrated the existence of such frequency combs in the phononic domain [3] after its theoretical prediction in [4]. While both optical and phononic frequency combs carry similar spectral features, the dynamics describing the respective
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