Optomechanical microwave oscillator and frequency comb generation in a full phononic bandgap 1D optomechanical crystal cavity

Laura Mércade1,∗, Leopoldo L. Martin2,, and Amadeu Griol3,Daniel Navarro-Urrios3,Alejandro Martínez3, 1Nanophotonics Technology Center, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain 2Departamento de Física, Facultad de Ciencias, Universidad de la Laguna 3MIND-IN2UB, Departament dEnginyeria Electrònica i Biomèdica, Facultat de Física, Universitat de Barcelona, Martí Franquès 1, 08028 Barcelona, Spain


Introduction
Cavity optomechanics studies the interaction between light and sound waves simultaneously confined in a cavity [1]. In an optomechanical cavity (OMC), confined mechanical waves can coherently modulate an optical signal at MHz and even GHz frequencies via optomechanical interaction, becoming relevant in microwave photonics. Furthermore, since OMCs are nonlinear elements, multiple harmonics of the fundamental mechanical vibrations can be overimposed on the optical signal [2], a phenomenon that has been interpreted theoretically as an optomechanical frequency comb (OFC) [3].

Optomechanical frequency comb
The OMC that we exploit here consist in a suspended silicon nanobeam with one-dimensional (1D) periodicity [4].
The key idea is to have OM mirrors on each nanobeam side whilst optical and mechanical resonant modes are confined in the central region, having a good overlap between them. Our structure results of an optical mode at λ r =(1522.3±0.3) nm with an optical quality factor of Q o = 5 × 10 3 , presented in Fig. 1(a), and a mechanical mode at Ω m /2π =3.897 GHz with an optomechanical coupling rate of g 0 /2π = (660 ± 70) kHz, depicted in Fig.  1(b). In addition, we have designed our structure in order to have a full phononic bandgap to reduce the phonon leakage. A simulation, in Fig. 1(c), of the phononic band diagram from the profile extracted from a Scanning Electron Microscopy (SEM) image, which is shown (see Fig.    * e-mail: laumermo@ntc.upv.es 1(d)), shows that the experimental mechanical modes lies into the total bandgap.
The mechanical mode can be driven to the phonon lasing regime under proper conditions. When driving the OMC with a blue-detuned laser with respect to the optical resonance at even higher power, higher-order harmonics can be observed in the detected signal. This closely resembles an optical frequency comb (OFC) of OM nature, recently analyzed theoretically in [3]. We measured up to the fifth harmonic, as can be seen in the optical spectrum of the generated OFC in Fig. 1(e). The theoretical dynamics generation [3] shows a good agreement with the acquired experimental optical traces in Fig. 1(f).

Optomechanical oscillator
High-quality microwave sources, which are required for a number of applications, are typically made by applying frequency multiplication to an electronic source. Amongst the different techniques to build an optoelectronic oscillator, we propose one obtained from an OM cavity when pumped with a blue-detuned laser source. In this case, since the involved mechanism is a self-sustained oscillation originated from OM interaction, from now on we will refer to it as an optomechanical oscillator (OMO). We made this experiment with the cavity proposed in the last section and we measured. For the first harmonic in Fig.2(a), the resulting noise figure evolution is presented in Fig. 2(c). For this harmonic the noise figure becomes as low as (-100±1) dBc/Hz at 100 kHz, which is a remarkable good value for an OEO oscillating at GHz frequencies. We have also measured the phase noise of the different harmonics, shown in 2(b), where the result is depicted in Fig.  2(d). In principle, the harmonic mixing process will result in an added phase noise of 20 × log(m) with respect to that of the first harmonic, which is well satisfied in our device.

Conclusions
In summary, we have demonstrated a new silicon-chip OMC with a large OM coupling rate for a GHz mode within a full phononic bandgap, which can perform as an ultracompact OMO. Operation at cryogenic temperatures would improve the phase noise [5] as a result of the enhancement of the mechanical Q factor because of the full phononic bandgap. In addition, the preliminary demonstration of the OFC paves the way towards synthesis of microwave signals beyond the generation of pure cw tones. The main advantages of the OMC approach for microwave signal processing are its extreme compactness and low weight, highly desirable in space and satellite applications, and its compatibility with silicon electronics and photonics technology.