Kramers-Kronig Causality in Integrated Photonics: The Spectral Tension between Ultraviolet Transition and Midinfrared Absorption.

Dispersion engineering via geometric confinement is essential to integrated nonlinear photonics. However, prevailing methodologies rely on semiempirical 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 midinfrared (MIR) spectra. Specifically, they introduce MIR vibrational absorption while simultaneously modifying UV electronic transitions, shifting the band gap 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 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 modeling. Our Letter resolves long-standing discrepancies in dispersion engineering, providing precision control essential for next-generation integrated photonics.