We present near-field measurements of transverse plasmonic wave propagation in a chain of gold elliptical nanocylinders fed by a silicon refractive waveguide at optical telecommunication wavelengths. Eigenmode amplitude and phase imaging by apertureless scanning near-field optical microscopy allows us to measure the local out-of-plane electric field components and to reveal the exact nature of the excited localized surface plasmon resonances. Furthermore, the coupling mechanism between subsequent metal nanoparticles along the chain is experimentally analyzed by spatial Fourier transformation on the complex near-field cartography, giving a direct experimental proof of plasmonic Bloch mode propagation along array of localized surface plasmons. Our work demonstrates the possibility to characterize multielement plasmonic nanostructures coupled to a photonic waveguide with a spatial resolution of less than 30 nm. This experimental work constitutes a prerequisite for the development of integrated nanophotonic devices.