Real-space imaging reveals symmetry-selected nonlinear energy routing in a mechanical resonator

Abstract

Nonlinear energy routing among modes underlies phenomena ranging from internal resonance and wave mixing to frequency-comb generation in micro- and nanoelectromechanical resonators, yet modal interactions are typically inferred from spectra rather than imaged in real space. This leaves unresolved how energy is spatially routed and what determines which pathways are selected. Here, we use phase-locked multi-harmonic stroboscopic interferometry to reconstruct harmonic-resolved differential displacement maps in a nearly mirror-symmetric microelectromechanical resonator. These maps reveal that harmonics generated by a driven mode can be carried by distinct spatial eigenmodes, directly resolving pathways of nonlinear energy transfer. We further show that such mode-selective routing occurs even away from integer frequency matching: generated harmonics are dominated by eigenmodes sharing the driven mode's mirror parity, whereas spectrally closer opposite-parity modes remain strongly suppressed. A nonlinear modal framework links this hierarchy to symmetry-dependent modal-overlap integrals. These results identify spatial symmetry as a selection rule for nonlinear energy routing.