Influence of crystal thickness on THz phonon dynamics in sodium mesitylene sulfonate (SMS, C₁₈H₂₄Na₂O₇S₂) crystal using terahertz time-domain spectroscopy (THz-TDS)

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Abstract
We report a systematic study on the angular and thickness-dependent phonon mode behaviour in SMS, single crystals using terahertz time-domain spectroscopy (THz-TDS) at room temperature. The SMS crystal was rotated over a full 0°–360° range with its crystallographic a-axis initially aligned parallel to the THz electric field and the THz wave propagating along the [001] direction. A strong correlation is observed between the polarization angle, emergence of phonon modes' and spectral splitting. An increase in crystal thickness results in enhanced phonon mode splitting: the 0.18 mm and 0.35mm-thick crystals exhibit a single resonance within the 0.7–1.2 THz range, while the 0.65, 1.06 and 1.27 mm-thick crystals display well-resolved mode splitting. To interpret this thickness-dependent behavior, we consider the formation of bulk phonon-polaritons. The single resonance at 0.94 THz, which dominates the thin-sample spectra, is the TO phonon mode (ω TO ) of the SMS lattice. In a polar crystal, this TO phonon couples strongly to photons, creating a hybrid polariton with a characteristic dispersion relation defined by a LPB and an UPB, separated by the Reststrahlen band. In the thin crystals (L ≤ 0.35 mm), the interaction path length is insufficient to fully resolve the bulk polariton dispersion, resulting in a single absorption feature. However, as the thickness increases (L ≥ 0.65 mm), the system transitions to a bulk-like response where the propagating LPB and UPB modes are clearly resolved. The observed splitting increases with thickness, consistent with other polar material systems and models of polaritons in finite-sized media, where the vacuum Rabi splitting scales with the interaction volume. This transition from a single-phonon peak to a split polariton doublet demonstrates how sample thickness gates the strong light-matter coupling regime. The 0.65 mm-thick crystal exhibits four distinct anisotropic lobes centred near 0.94 THz, emphasizing the inherent anisotropic phonon response of the SMS crystal.

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