Observation of mechanical bound states in the continuum in an optomechanical microresonator

Micro- and nanomechanical resonators with small mass and strong couplings to light and matter are central to precision metrology and macroscopic quantum studies. Their performance depends critically on minimizing mechanical dissipation to extend coherence times. Conventional approaches isolate modes from the continuum using material or periodic-structure bandgaps, or, for individual nonperiodic resonators, by minimizing supporting structures, which increases fabrication difficulty and limits applicability (e.g., fragile devices in fluids). Bound states in the continuum (BICs) offer a route to infinite-lifetime states overlapping the radiation continuum through symmetry or interference. While BICs have been demonstrated in optics and acoustics—often in periodic structures—and in individual optical and acoustic resonators, experimental demonstration in an individual mechanical resonator has been lacking. This work targets that gap by realizing a mechanical BIC in a compact, individual optomechanical microresonator via symmetry breaking that couples two dissipative modes to achieve destructive interference of dissipation (Friedrich–Wintgen condition).

The BIC concept originated in quantum mechanics and has been extended to optics, acoustics, and mechanics, enabling applications such as low-threshold lasing, ultrasensitive sensing, and vortex beam generation. Most experimental BICs in optics and mechanics rely on periodic structures and symmetry protection, leading to large footprints and modal volumes/effective masses. Individual resonators can confine fields strongly at the micro/nanoscale, benefiting metrology and quantum experiments. BICs have been shown in individual optical and acoustic resonators, but not experimentally in individual mechanical resonators prior to this study. Conventional mechanical Q-enhancement relies on phononic bandgaps or minimizing supports to reduce clamping loss, which constrains robustness and application environments.

Theory and design: The system is modeled as two dissipative mechanical modes coupled dispersively and dissipatively, with complex Hamiltonian H = [[ω1 − jγ1, κ − j√(γ1γ2)]; [κ − j√(γ1γ2), ω2 − jγ2]]. When the Friedrich–Wintgen condition κ(γ1γ2) = √(γ1γ2)(ω1 − ω2) is satisfied near an anticrossing, one hybrid mode becomes lossless (mechanical BIC). The device starts from a ring-shaped thin-plate silicon resonator (thickness h = 220 nm, outer radius R = 26.1 µm) supporting a fundamental radial-contour mode (A) and a 4th-order wine-glass mode (B). To enable coupling, azimuthal symmetry is broken by making the inner boundary elliptical with semi-axes rx and ry, producing hybrid modes A′ and B′ at the anticrossing. Regions of near-zero displacement in the hybrids guide where to place supports to suppress clamping loss. Device architecture and simulation: A realistic wheel-shaped resonator is formed by adding two supporting rods to the symmetry-broken ring, seated on a SiO2 pedestal on substrate. Key parameters: rod width d, center disk radius rs, semi-axes rx and ry, outer radius R, and thickness h. Finite-element simulations compute modal frequencies and mechanical Q versus rx for various d (0.5–8 µm), identifying anticrossings and calculating Q to locate the BIC (max-Q point). The design shows robust BIC formation across large variations in d, with simulated BIC Q > 1e8 for 0.5–8 µm. Fabrication: Devices were fabricated on a silicon-on-insulator wafer using CMOS-compatible processes, producing wheel-shaped silicon resonators on SiO2 pedestals. A bus waveguide is fabricated adjacent to the resonator to couple light for optomechanical readout. Optomechanical measurement: Optical whispering-gallery modes of the resonator are used for transduction of thermomechanical motion. The setup includes a tunable semiconductor laser (around 1550–1560 nm), fiber polarization controller, variable optical attenuator, erbium-doped fiber amplifier, and a photodetector connected to a signal analyzer. Optical transmission spectra provide optical Q (example loaded Q ≈ 2.3 × 10^5 at ~1558.4 nm). Mechanical spectra are measured in a vacuum chamber with controllable ambient pressure (1.0 × 10^−5 to 6.0 × 10^−3 Pa) to suppress air damping and assess residual losses. A series of devices is fabricated with fixed d = 5 µm, ry = 14.7 µm, R = 26.1 µm, and varying rx to traverse the anticrossing and identify the BIC condition experimentally.

- Experimental observation of a mechanical BIC in an individual, wheel-shaped optomechanical silicon microresonator via azimuthal symmetry breaking that couples a radial-contour mode and a 4th-order wine-glass mode, achieving destructive interference of dissipation under the Friedrich–Wintgen condition. - Simulations show clear anticrossing of modes A′ and B′ versus rx and predict drastic Q enhancement at the BIC point, robust over rod widths d from 0.5 to 8 µm, with simulated BIC mechanical Q > 10^8 across this range. - Fabricated devices exhibit optical whispering-gallery resonances with a loaded optical Q ≈ 2.3 × 10^5 (near 1558.4 nm). - Measured mechanical mode frequencies versus rx agree well with simulations, confirming identification of modes A′ and B′. - At rx = 20.8 µm (for d = 5 µm), the mechanical Q of mode A′ peaks at 9453 at an ambient pressure of 6.0 × 10^−3 Pa, consistent with the predicted BIC point; mode B′ shows Q ≈ 882. Displacement noise spectra fitted by Lorentzians corroborate these Q values. - Pressure-dependent measurements indicate that, once clamping loss is eliminated by the BIC design, air damping dominates residual loss (Q decreases as pressure increases, with a stronger effect above ~1 Pa). Material loss remains as a pressure-independent floor at a given temperature (room temperature in the experiment).

The study demonstrates that coupling two dissipative mechanical modes via deliberate azimuthal symmetry breaking can fulfill the Friedrich–Wintgen condition, yielding a mechanical BIC that eliminates clamping loss in an individual microresonator. The agreement between simulated and measured frequencies and the pronounced Q peak for mode A′ at the predicted rx confirm the BIC’s formation. The robustness to large support widths contrasts sharply with conventional approaches that require either phononic bandgap shielding or ultrathin/minimized tethers, thereby simplifying fabrication, improving mechanical robustness, and expanding application environments (e.g., tolerance to handling and thermal loads). The pressure-dependent Q behavior shows that, after suppressing clamping loss, air damping becomes the primary limitation, with material loss setting the vacuum-limited floor. These findings validate symmetry-broken, nonperiodic resonators as a practical platform for long-lived phonons, with implications for low-noise oscillators, sensitive sensors, and optomechanical/quantum information systems where high-Q and sturdy supports are simultaneously desired.

This work reports the experimental realization of a mechanical bound state in the continuum in an individual, wheel-shaped silicon optomechanical microresonator by engineering modal coupling through azimuthal symmetry breaking. The resulting Friedrich–Wintgen BIC robustly suppresses clamping loss and enables high mechanical Q with large, fabrication-friendly supports, verified by simulations (Q > 1e8 across wide support widths) and experiments (Q ≈ 9.45 × 10^3 at low pressure). The approach opens a new route for phonon trapping in compact devices with dissipation channels and is compatible with CMOS processes. Potential future directions include: optimizing geometry and materials to further suppress material loss; integrating phononic or acoustic shielding to mitigate residual air damping for operation at higher pressures; exploring cryogenic operation for quantum regimes; extending the BIC strategy to other mechanical mode families and multi-mode interference; and leveraging the robust high-Q platform for precision sensing, stable mechanical oscillators, and hybrid quantum systems.

The Friedrich–Wintgen BIC strategy specifically eliminates clamping loss but does not directly reduce other dissipation channels. In experiments, the measured BIC Q (≈9453 at ~6 × 10^−3 Pa) is lower than simulated values due to residual air damping and material loss. Pressure-dependent measurements indicate air damping dominates above ~1 Pa, while material loss provides a temperature-dependent floor even in high vacuum. The reported results are under vacuum; performance in ambient conditions is limited by air damping.