High-Q states in acoustic apple-shaped resonators

Apples play a significant role in our culture in various points of human history: starting from Adam and Eve, going on with Judgement of Paris, it also touches such great minds as Sir Isaac Newton and Alan Turing. Beyond that apples are still extremely relevant today due to Steve Jobs. In this work we study high quality (high-Q) resonant states of apple-shaped resonators. We have found that quasi bound states in continuum (quasi-BICs) are possible in the linear acoustic domain. We show that quasi-BICs are of Friedrich-Wintgen type, i.e. accompanied with avoided crossings while elongating or shrinking the apple-shaped resonator. Finally, we build a concise theory based on the group theory approach utilizing Wigner's theorem. We illustrate that only the resonator symmetry plays major role, but not particular resonator's shape.