We report on an air-clad large-core single-transverse-mode ytterbium-doped photonic crystal fiber with a mode-field-diameter of 35 microm, corresponding to a mode-field-area of ~1000 microm(2). In a first experiment this fiber is used to amplify 10-ps pulses to a peak power of 60 kW without significant spectral broadening due to self-phase modulation allowing for the frequency up-conversion of these pulses using narrow-bandwidth phase matched nonlinear crystals.