Phononic Frequency Comb via Intrinsic Three-Wave Mixing

Abstract

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...

Generation of ultralow power phononic combs

“…The major difference between optical Kerr combs and the presented acoustic is the absence of a free spectral range corresponding to the comb signal spacing. In principle, absence of the equally spaced mode structure is also a feature of combs in other mechanical systems 13 and in Whispering Gallery Mode crystals 9,43 . In the latter case, an extra half degree of freedom arises due to the Fano resonance, the phenomenon which in BAW community is known as anti-resonance 44 .…”

Excitation of coupled phononic frequency combs via two-mode parametric three-wave mixing

“…However, in contrast to the linear increase with the drive power level (cf. Figure 3 in [1]), the dependences in the current experiments are quadratic ( Figure 4B) and cubic ( Figure 4D). …”

“…Now, in this paper, we experimentally demonstrate the possibility to further excite multiple frequency combs with the same external drive through its coupling with other identical devices. In addition, we also experimentally identify interesting features associated with such a frequency comb generation process.This paper builds upon the recent experimental demonstration of the phononic counterpart of optical frequency combs in a micromechanical vibratory device [1]. The generation of these phononic frequency combs is described by a nonlinear three-wave mixing process as theoretically outlined in [2].…”

“…To understand these experimental observations in the context of previous demonstration of frequency comb in [1], the following dynamics is considered. …”

“…Such parametrically excited tone is expected to have a frequency 2 and is closer the resonant frequency of mode 2: 2 . However, the recent experiments on the two-mode three wave mixing based frequency comb [1] have indicated the possibility for …”