The integration of optomechanics and optoelectronics in a single device opens new possibilities for developing information technologies and exploring fundamental phenomena. Gallium arsenide (GaAs) is a well-known material that can bridge the gap between the functionalities of optomechanical devices and optical gain media. Here, we experimentally demonstrate a high-frequency GaAs optomechanical resonator with a ring-type bullseye geometry that is unprecedented in this platform. We measured mechanical modes up to 3.4 GHz with quality factors of 4000 (at 77 K) and optomechanical coupling rates up to 39 kHz at telecom wavelengths. Moreover, we investigated the material symmetry break due to elastic anisotropy and its impact on the mechanical mode spectrum. Finally, we assessed the temperature dependence of the mechanical losses and demonstrated the efficiency and anisotropy resilience of the bullseye anchor loss suppression, indicating that lower temperature operation may allow mechanical quality factors over $10^4$. Such characteristics are valuable for active optomechanics, coherent microwave-to-optics conversion via piezo-mechanics and other implementations of high-frequency oscillators in III-V materials.
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