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We present a multimode longitudinal pumping scheme for integrated rare-earth-doped waveguide amplifiers which allows an efficient use of low cost multimode pump sources. The scheme is based on evanescent pump light coupling from a multimode low loss waveguide to a single mode active core. Multimode pump light is gradually coupled to the active waveguide, which is single mode at the signal wavelengths, providing population inversion along the whole amplifier length and overcoming the main limitation of conventional single mode pump butt-coupling in case of strongly absorbing active materials. We propose this pumping scheme at 477 nm for Si-nanocluster sensitized Erbium doped waveguide amplifiers, in which conventional butt-coupling is inefficient due to the strong pump absorption by the Si- nanoclusters , and top pumping by LED arrays is limited by the low pump intensity values achievable within the active region. The coupling between the multimode waveguide and the active core has been numerically studied for slab waveguide structures using a 2-D split-step finite element method.