Optomechanical Frequency Comb Based on Multiple Nonlinear Dynamics

Phonon-based frequency combs that can be generated in the optical and microwave frequency domains have attracted much attention due to the small repetition rates and the simple setup. Here, we experimentally demonstrate a new type of phonon-based frequency comb in a silicon optomechanical crystal cavity including both a breathing mechanical mode ($\sim \mathrm{GHz}$) and flexural mechanical modes (tens of MHz). We observe strong mode competition between two approximate flexural mechanical modes, i.e., 77.19 and 90.17 MHz, resulting in only one preponderant lasing, while maintaining the lasing of the breathing mechanical mode. These simultaneous observations of two-mode phonon lasing state and significant mode competition are counterintuitive. We have formulated comprehensive theories to elucidate this phenomenon in response to this intriguing outcome. In particular, the self-pulse induced by the free carrier dispersion and thermo-optic effects interacts with two approximate flexural mechanical modes, resulting in the repetition rate of the comb frequency-locked to exact fractions of one of the flexural mechanical modes and the mode hopping between them. This phonon-based frequency comb has at least 260 comblines and a repetition rate as low as a simple fraction of the flexural mechanical frequency. Our demonstration offers an alternative optomechanical frequency comb for sensing, timing, and metrology applications.

Figure 1

(a) Schematic of the setup. The SEM image shows the device consisting of two nanobeam microcavities and a tapered waveguide with an OMC mirror. Electro-optic modulator (EOM); fiber polarization controller (FPC); photodetector (PD); erbiumdoped fiber amplifier (EDFA); realtime spectrum analyzer (RSA); vector network analyzer (VNA). (b) The expanded details of the device in (a). The orange and green area show a defective cavity and the 5 GHz phonon shielding structure, respectively. The bottom panel is the simulated electric field of the optical mode in the OMC cavity. (c)–(d) The transmission of optical mode and the power spectrum of mechanical modes in the OMC cavity. The insets show the in-plane flexural modes ($m_{1,2}$), and the breathing mode ($m_3$), respectively. (e) Schematic of OMFC originating from the nonlinear interactions between photons, multiple modes phonons, and self-pulse (SP).

Figure 2

The typical OMFCs. (a) The power spectrum of OMFCs with repetition rate ${\omega }_2$, which consists of the multimode phonon lasing state of mechanical modes $m_2$ and $m_3$ but without the SP. (b)–(c) The power spectrum of OMFCs with repetition rate ${\omega }_2/3$ or ${\omega }_1/2$ due to the SP process. (d)–(f) The enlarged images of three typical OMFCs near ${\omega }_3$ in (a)–(c). The purple shaded area represents the combline with the frequency of ${\omega }_3$. (g)–(i) Corresponding time domain oscillations of OMFCs in (a)–(c). The red lines are the theoretical fitting of the pulse envelope.

Figure 3

The mode competition and multimode phonon lasing. (a) The power transmission of mechanical modes when scanning the pump from far-blue detuning to resonant before exciting the SP. (b)–(c) The trajectories of excitation thresholds in the amplitude space of mechanical modes $m_1$ and $m_2$ (${\xi }_1\text{−}{\xi }_2$), $m_2$ and $m_3$ (${\xi }_2\text{−}{\xi }_3$). For points inside (outside) the threshold trajectory, the states here tend to evolve along (opposite to) the direction of the ${\xi }_j$ amplitude coordinate axis. (d)–(f) State evolution around the pink, orange, and blue crossing points of trajectories in (b)–(c).

Figure 4

Switching lasing state with the assistance of SP. (a) The dynamic evolution of the power spectrum which is continuously recorded by the RSA as scanning the pump laser further towards the resonance. The blue dashed lines I–VI indicate the different stages of dynamic evolution. (b) The typical power spectra of different stages in (a). The green dashed line illustrates the shift of the SP and interaction with the mechanical modes. Inset: enlarged image of the quasi-locked state in the orange shaded area with ${\omega }_{\mathrm{SP}}\approx \frac{2}{6}{\omega }_1\sim \frac{2}{7}{\omega }_2$.