Developing ultra-coherent mechanical oscillators through topological optimization

High quality mechanical resonators are critical for driving advances in quantum information technologies, precision sensing, and optomechanics. However, achieving compact resonator designs that maintain high performance is a key challenge. In the first part of this thesis, we present a new class of compact resonators optimized to operate at higher-order eigenmodes, achieving both high frequencies and enhanced quality factor-frequency (Qf ) products. By employing topology optimization to maximize the damping dilution factor, these resonators achieve minimized edge bending losses and enhanced intrinsic damping. Their high-(Qf ) performance and compact form factor position these resonators as promising candidates for applications in quantum information transduction, advanced opto-mechanical systems, and next-generation sensing technologies.

High pre-stress leads to higher damping dilution and thus higher Q, which is realized by stress engineering. It is usually obtained by the contrast in dimensions such as thickness, leading to a limited stress increase. The enhancement from resonator geometry, however, is seldom explored. In the second part of this work, two measures of von Mises stress are proposed, which identify the minimum and maximum stress level of a membrane resonator, respectively. Stress engineering is accomplished using topology optimization with the two measures as objective and constraint. The von Mises stress of targeted domain in the optimized design increases over 50% and is scalable in transversal dimensions, constituting a promising platform for subsequent applications integrated with, for example, phononic crystals resonators potentially with extremely high Q.