Cross-Family Mode Coupling and Localization Reversal in Phononic Crystal Defect Dimers

Abstract

Defects in phononic crystals confine elastic vibrations within bandgaps, enabling waveguiding, sensing, and energy harvesting. Coupling defects offers control over the spatial distribution of vibration, but how interactions between nearby modal families determine defect preference remains unclear. We examine localization reversal in dimers whose single defect supports a nearby $B_1$ singlet and $E$ doublet: softening one defect shifts a continued modal branch toward its unchanged partner. In off-axis and diagonal layouts, this reversal accompanies family exchange, with opposing $B_1$ and $E$ contributions to the defect-mass difference nearly cancelling at the threshold. Deleting cross-family stiffness and mass blocks removes reversal, while omitting cross-family observable terms at fixed states preserves it, identifying modal redistribution as the dominant mechanism. At the off-axis softening endpoint, independent channels predict the opposite preferred defect despite a $0.16\%$ frequency difference from the full-order solution. Nominal operators retaining the complete singlet-doublet space predict selected softening-branch thresholds with errors below $1.1\%$ against independent full-order sign brackets, without fitting detuned trajectories. These results link localization reversal to modal-family exchange and physical defect-mass balance, and show that frequency agreement alone does not guarantee localization accuracy.