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Designing acoustic resonators at ultra-high frequencies is a promising pathway for important technological advancements, including quantum technologies. Resonators operating in the tens-of-gigahertz range are usually based on semiconductor multi-layered Distributed Bragg Reflectors (DBRs). However, their inherent lack of tuning capability imposes constraints on specific applications, such as sensing. Mesoporous materials, with pores at the nanoscale, could potentially bridge the gap for responsive acoustic resonators. These cost-effective materials support gigahertz acoustic resonances, and their high surface-to-volume ratio allow for engineering resonators with novel functionalities, such as optoacoustic sensors or switches. For instance, the infiltration of liquids and vapors into the pores modifies the material’s optical and elastic parameters, leading to direct modification of the acoustic resonances. Here, we theoretically propose open-cavity multi-layered acoustic resonators based on SiO2 mesoporous materials that are responsive to the environment, e.g., relative humidity changes. The resonators are formed by a DBR of dense SiO2/TiO2 multilayers, followed by a Ni acousto-optical transducer, to both generate and detect acoustic phonons, and finalized by the mesoporous as the last layer, so it has access to the environment. In this design, gigahertz acoustic phonons can be effectively confined at the mesoporous layer. On one hand, the acoustic DBR prevents their leakage toward the substrate, and on the other hand, they cannot propagate through the air, creating an ideal acoustic mirror at the mesoporous-air interface. We present two case studies based on this approach and show, by numerical simulations using transfer matrix method, the responsiveness and tunability of such resonators upon ambient humidity changes. The simulation results also indicate that these devices can be characterized through transient reflectivity experiments. Our study could guide the way for designing effective nanoacoustic sensing and adaptable devices, utilizing cost-effective fabrication techniques.
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