  In this Letter, we demonstrate, to the best of our knowledge, the first
spatiotemporally mode-locked fiber laser with self-similar pulse evolution. The
multimode fiber oscillator generates parabolic amplifier similaritons at 1030
nm with 90 mW average power, 2.3 ps duration, and 37.9 MHz repetition rate.
Remarkably, we observe experimentally a near-Gaussian beam quality (M^2<1.4) at
the output of the highly multimode fiber. The output pulses are compressed to
192 fs via an external grating compressor. Numerical simulations are performed
to investigate the cavity dynamics which confirm experimental observations of
self-similar pulse propagation. The reported results open a new direction to
investigate new types of pulse besides beam shaping and nonlinear dynamics in
spatiotemporal mode-locked fiber lasers.
