An optical amplifier for pulsed laser with short or ultra-short and energetic pulses includes an optical pumping source for generating a pump wave, an elongate amplifying medium including an input interface for receiving an optical signal to be amplified, the medium being able to amplify the optical signal propagating along the amplifying medium and to extract an amplified signal and an optical system for coupling the pump wave in the amplifying medium so as to pump the amplifying medium longitudinally. The amplifying medium has a minimum transverse dimension φ3 and the optical system focuses the pump wave inside the gain medium, the focused pump wave having a transverse dimension φ6 which is smaller than the dimension φ3 of the medium and a smaller numerical aperture than the numerical aperture of the medium, so that the pump wave propagates freely over a part of the amplifying medium and then in a confined manner over a part of the amplifying medium.