Self-Frequency Pumping for Chaotic Micromechanical Frequency Comb Generation via Multimodal Internal Resonance

This work presents the first realization of multimodal internal resonance with a frequency ratio of 1: 3:6 between the first three flexural modes of a clamped-clamped beam resonator. Following the multiple-stepped beam profile designed in our previous work that achieves a 1: 6 ratio between the 1st and 3<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> modes, this work further tailors the geometric parameters based on an optimized finite element model (FEM) for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.35-\mu \mathrm{m}$</tex> CMOS-MEMS process platform to allow simultaneous coupling between the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1^{\mathrm{s}\vert }$</tex>, 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup>, and 3<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> modes and trigger coherent energy transfer. As a result, driving the resonator with a single-tone excitation at the fundamental mode, the multimodal interaction enables self-pumping and generates period-doubled or chaotic frequency combs near or in the region where the 3 modes are aligned, eliminating the need for multiple pumping inputs typically required for the generation of complex dynamics.