Third order dispersion compensation is studied in the framework of compressed of ultrafast pulses amplified in the parabolic regime in ytterbium-doped fibres. First, a hybrid sequence of gratings-prisms is employed to improve the compression of low energy parabolic pulses close to the asymptotic solution of the non-linear Schrödinger equation. Second, due to asymmetric temporal pulses, the non-linearities created along a high energy parabolic amplifier together with a standard grating compressor allows an almost perfect compression down to 63 fs of a 290 nJ pulse i.e. 4.6MW peak power at a central wavelength of 1050nm.
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