A high power fiber laser system emitting a substantially diffraction limited beam with a Gaussian intensity profile includes a single mode ("SM") neodymium fiber pump source outputting a SM pump light; a seed laser operative to emit a SM signal light at a wavelength greater than that of the pump light; a SM DWM receiving and multiplexing the SM pump and signal lights. The disclosed system further includes a booster fiber amplifier which is confiugred with a frustoconically-shaped ytterbium ("Yb") doped core receiving the pump and signal lights and configured with a small diameter input end which supports only a SM and a large diameter output end which is capable of supporting the SM and high order modes (:HOM"). The booster further has a cladding surrounding and coextending with the core, the core being configured for having intensity profiles of respective SMs of pump and signal lights overlap one another so that an overlap integral substantially equals to one (1) along an entire length of the core. The SM of the light signal extracts substantially the entire energy from the pump mode leaving the HOMs without amplification necessary to affect a quality of the diffraction limited beam of the system in a MW peak power range and hundreds of watt average power range.