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We propose a new geometry of a clad-pumped fiber amplifier/laser that includes at least one doped core which guides the signal wave and at least one clad region that guides the incoherent pump. Our proposed geometry enables the incoherent diode pump light to be efficiently absorbed by the doped glass core over very short lengths on the order of a few to tens of centimeters. The transparent cladding is realized as a narrow slab with refractive index higher than that of the core. The slab is designed to effectively capture all of the incoherent pump light and is tapered to force the highly moded incoherent guided light into the strongly absorbing core. Modes of this composite waveguide structure are analyzed. Criteria are established in terms of the refractive indices of the core, slab, and cladding that ensure efficient absorption of the pump light in the core while ensuring that only a single or few lowest order signal modes can propagate in the amplifying core. Numerical simulations with the beam propagation method and a modal expansion technique confirm that a significant enhancement of the absorption efficiency of the pump in the core can be realized by tapering the slab waveguide. Assuming a local absorption rate of 10 m-1 of the intensity of the pump in a core of radius 4.3 μm and a realistic multimode diode pump distributed over a 100-μm aperture, an absorption efficiency of 94% can be realized over an amplifier length of 2 cm. The geometry is scalable to longer lengths and multiple incoherent diode-pumped slab claddings.