Kramers-Kronig causality in integrated photonics: The spectral tension between ultraviolet transition and mid-infrared absorption
Dispersion engineering via geometric confinement is essential to integrated photonics, enabling phenomena such as soliton microcombs, supercontinua, parametric oscillators, and entangled photons. However, prevailing methodologies rely on semi-empirical Sellmeier models that assume idealized material purity, neglecting the pronounced dispersion shifts induced by residual impurities like hydrogen-related bonds. Here, we demonstrate that these residual bonds fundamentally alter the dispersion landscape spanning from the ultraviolet (UV) to the mid-infrared (MIR) spectra. Specifically, they introduce MIR vibrational absorption while simultaneously modifying UV electronic transition, shifting the bandgap and UV pole. We show that the spectral tension between these UV and MIR modifications dictates the group velocity dispersion from the visible to the near-infrared (NIR) via the Kramers-Kronig causality. We experimentally validate this phenomenon through systematic characterization of broadband loss and dispersion in ultralow-loss silicon nitride photonic integrated circuits. By rigorously incorporating these effects, we bridge the gap between empirical fitting and predictive physical modelling. Our study resolves long-standing discrepancies in dispersion engineering, providing precision control essential for next-generation integrated photonics.