Dispersion-enabled spatial scaling in multimode fibers

Modal dispersion in multimode fibers (MMFs) normally causes rapid spectral decorrelation of transmitted fields. Here, we propose and experimentally demonstrate dispersion-scaled modes (DSMs), which harness modal dispersion to realize spatial scaling of the output field under frequency tuning, including expansion, contraction, and preservation of its transverse extent. By analyzing the transmission matrix (TM) evolution under frequency tuning and spatial scaling, we construct a dispersion-scaled operator and recast the DSM condition as an eigenvalue problem. Eigenstates with eigenvalue magnitudes close to unity are selected as stable DSMs, indicating robust mode-field stability during prescribed frequency-induced spatial scaling. Experiments demonstrate invariant, magnifying, and demagnifying focal-spot evolution over a 500 GHz spectral tuning range. DSMs are further generated at different user-defined output regions while maintaining high spatial fidelity and strong energy localization, providing a route toward dispersion-enabled dynamic light control in complex media.