Generation and Evolution of Phononic Frequency Combs via Coherent Energy Transfer between Mechanical Modes

Phononic frequency combs represent the mechanical analog of optical frequency combs. Several independent experimental studies have demonstrated the onset and evolution frequency comb response in a variety of micro- and nanoelectromechanical devices in recent years. A theoretical basis for exploring and understanding the conditions for comb generation and evolution with varying driving parameters is essential to enable future practical applications. Here, we present the comparison between modeling and experimental results on the generation and evolution mechanism of phononic frequency combs in a nonlinear micromechanical resonator from the perspective of coherent energy transfer between two mechanical modes. Phononic frequency combs emerge in a strong coupling regime involving nonlinear resonances when the amplitudes and phases of two coupled mechanical modes are modulated via coherent energy transfer. The spacing and number of comb teeth can be analytically estimated based on modeling the nature of the interaction of the coupled modes under the specified driving conditions. As the driving conditions are varied, the phononic frequency comb evolves into different forms and a phenomenological model for the system is established to accurately predict the evolution of phononic frequency combs. The alignment between experiment and model provides a basis for the engineering of this phenomenon in future device applications.