Microwave oscillator and frequency comb in a silicon optomechanical cavity with a full phononic bandgap

Abstract

Cavity optomechanics has recently emerged as a new paradigm enabling the manipulation of mechanical motion via optical fields tightly confined in deformable cavities. When driving an optomechanical (OM) crystal cavity with a laser blue-detuned with respect to the optical resonance, the mechanical motion is amplified, ultimately resulting in phonon lasing at MHz and even GHz frequencies. In this work, we show that a silicon OM crystal cavity performs as an OM microwave oscillator when pumped above the threshold for self-sustained OM oscillations. To this end, we use an OM cavity designed to have a breathing-like mechanical mode at 3.897 GHz in a full phononic bandgap. Our measurements show that the first harmonic of the detected signal displays a phase noise of ≈−100 dBc/Hz at 100 kHz. Stronger blue-detuned driving leads eventually to the formation of an OM frequency comb, whose lines are spaced by the mechanical frequency. We also measure the phase noise for higher-order harmonics and show that, unlike in Brillouin oscillators, the noise is increased as corresponding to classical harmonic mixing. Finally, we present real-time measurements of the comb waveform and show that it can be fitted to a theoretical model recently presented. Our results suggest that silicon OM cavities could be relevant processing elements in microwave photonics and optical RF processing, in particular in disciplines requiring low weight, compactness and fiber interconnection.

Phonons Manipulation in Silicon Chips Using Cavity Optomechanics

“…It mus be pointed out that the main results presented in this chapter can also be found at Ref. [101].…”

“…Here, we can see an appreciable difference between these two cases as the thermally driven mode had a very low amplitude, thus resulting in a huge contribution of frequency noise sources related to the white noise. Once either P1 or P2 is in the self-oscillating regime, we observe that, in both cases, the different noise contributions are the ones that can be expected in OM oscillators: the white phase (1/f 0 ), white frequency (random phase walk, 1/f 2 ), and flicker frequency (1/f 3 ) noise types [101], in good agreement with the Leeson's model [112]. Phase noise values around -100 dBc/Hz at 100 kHz were observed, on par with other OM microwave oscillators [44,101,111,114,117] as well as with our results in the previous chapter.…”

“…Once either P1 or P2 is in the self-oscillating regime, we observe that, in both cases, the different noise contributions are the ones that can be expected in OM oscillators: the white phase (1/f 0 ), white frequency (random phase walk, 1/f 2 ), and flicker frequency (1/f 3 ) noise types [101], in good agreement with the Leeson's model [112]. Phase noise values around -100 dBc/Hz at 100 kHz were observed, on par with other OM microwave oscillators [44,101,111,114,117] as well as with our results in the previous chapter. From the fit of the random phase walk (1/f 2 ) at Fig.…”

“…We can see that our system performs in close vicinity of the best OM cavities reported in the literature. The labeled points correspond to different works, corresponding to a - [64], b - [100], c -(This work) [101], d - [44], e - [67], f - [102], g - [103] and h - [104].…”

“…Even though operation in the sideband-resolved regime seems unattainable, the large values of g 0 would ensure transduction of the GHzscale mechanical modes as well as its manipulation either by cooling or heating them. In particular, blue-detuned laser driving at high power could ensure the formation of broad (> 100 GHz) optical frequency combs [101] in a wavelength-sized structure, opening the door towards ultra-compact microwave photonics. Notice also that the dimensions of the disks under study are smaller than those reported in [156,158], which support high-Q optical and mechanical whispering gallery modes.…”