Spontaneous Raman Scattering under Vibrational Strong Coupling: The Critical Role of Polariton Spatial Mode Coherence

Resonant coupling of a vibration to a cavity mode has been reported to dramatically modify spontaneous Raman scattering, but subsequent studies have produced conflicting results. In this Letter, we develop a microscopic quantum framework that captures the spatial structure of polaritonic modes. In a homogeneously filled cavity, spatial overlap between polaritons and cavity resonances enforces selection rules that suppress the initially reported polaritonic Raman peaks, consistent with most experiments. In contrast, for a quasi-two-dimensional (2d) molecular layer, these rules are lifted, yielding Raman peaks at the polariton energies. Our work clarifies that the Raman response under vibrational strong coupling is determined by cavity-vibration spatial mode overlap and offers a framework for Raman studies of strongly coupled quasi-2d systems.