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During the last few decades, solid-core photonic crystal fibers (PCFs) have been extensively explored to generate broadband, high-coherence supercontinua (SC). Limited by the material absorption and relatively low nonlinearity of fused silica, spectral broadening in silica PCF-based SCs is usually restricted to the blue to near-infrared spectral regions, even in developed commercial sources. The output spectra of these sources are missing short wavelengths of the full range. Many efforts have been spent to break the limitation. Among them, dispersive-wave (DW) generation has been investigated for triggering new frequencies in short wavelengths. With satisfied phase-matching conditions, excessive energy can be directly transferred from solitons of the anomalous dispersion region to DWs of the short wavelengths. However, a systematical study of factors, including phase-matched DWs, strongly related to the dispersion tailoring of higher-order modes (HOMs), has rarely been shown. This study reports the experimental observations of HOM-enhanced phase-matchings for the DW generation in the deep-blue and ultraviolet regions. A solid-core PCF-based, UV-extended SC source spanning a 2.8-octave-wide (350 nm to 2500 nm) is demonstrated. Meanwhile, we carefully verify our findings via numerical calculations.