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We discovered a new transmodal Fabry-P\'erot resonance that one elastic-wavemode is maximally transmitted to another when the phase difference of twodissimilar modes through an anisotropic layer is exactly odd multiples of{\pi}. Unlike the well-established Fabry-P\'erot resonance, the transmodalresonance must involve two coupled elastic-wave modes, longitudinal and shear.The formation of wiggly transmodal transmission spectra is due to structuralinstability appearing in anisotropic mode-coupled elastic-media. Experimentswith elastic metamaterials confirmed our findings which can play a criticalrole in shear-mode ultrasound applications.

Transmodal Fabry-P\'erot Resonance: Theory and Realization with Elastic Metamaterials