Self-Injection Locked and Phase Offset-Free Micromechanical Frequency Combs

Pure mechanical frequency combs attracted a lot of attention recently due to the intriguing nonlinear dynamics and potential of miniatured precision timekeeping but are currently limited by narrow spectra and missing frequency locking physics. In this Letter, we report the design and experiment of a self-injection locked micromechanical frequency comb that is further intrinsically immune to phase offset. We show that by tuning the pump frequency of a pair of nonlinearly coupled flexural and torsional oscillations, self-injection locking could be achieved via aligning the comb teeth from neighboring harmonic clusters, leading to decade-wide cascading of hundreds of equidistant teeth. Inside the injection locking region, the stability of the comb spacing and the phase noise are significantly improved. Moreover, the phase offset in the temporal signal also disappears because all comb lines are locked as integer multiples of the comb spacing and the first tooth is locked to the d.c. frequency due to the comb origination from harmonics. The observation of self-injection locking and zero phase offset in mechanical frequency combs greatly promotes their value for precision applications.