Signal Amplification of Surface-Enhanced Infrared Absorption Spectroscopy Using Virtual Complex Frequency Excitation

Complex frequency wave (CFW) excitation has recently emerged as a powerful method for recovering information lost due to intrinsic material dissipation. While CFWs have been applied in acoustics, elasticity, and electromagnetic systems, optical implementations have remained limited. Here, we demonstrate that a synthetic CFW excitation method, based on spectral superposition, enables substantial enhancement in reflection-mode surface-enhanced infrared absorption spectroscopy. By applying this approach to plasmonic nanogap metasurfaces, we achieve near-unity signal enhancement and recover weak molecular fingerprints, including CH3 subpeaks and protein-specific Amide I and II modes. Despite the challenge of phase retrieval in reflective geometries due to complex-plane zeros, we propose practical mitigation strategies via minimum-phase equivalence and complex conjugation. Additionally, we show that tuning the damping factor selectively amplifies individual resonances, allowing dynamic control over subpeak visibility. These findings establish synthetic CFW excitation as a robust and tunable platform for vibrational sensing. Beyond spectroscopy, this technique offers cross-disciplinary relevance for manipulating wave–matter interactions and may provide insights into thermodynamic analogies such as Wick rotation and time-domain dualities.