Generating intense ultrashort pulses with high-quality spatial modes is
crucial for ultrafast and strong-field science. This can be accomplished by
controlling propagation of femtosecond pulses under the influence of Kerr
nonlinearity and achieving stable propagation with high intensity. In this
work, we propose that the generation of spatial solitons in periodic layered
Kerr media can provide an optimum condition for supercontinuum generation and
pulse compression using multiple thin plates. With both the experimental and
theoretical investigations, we successfully identify these solitary modes and
reveal a universal relationship between the beam size and the critical
nonlinear phase. Space-time coupling is shown to strongly influence the
spectral, spatial and temporal profiles of femtosecond pulses. Taking advantage
of the unique characters of these solitary modes, we demonstrate single-stage
supercontinuum generation and compression of femtosecond pulses from initially
170 fs down to 22 fs with an efficiency ~90%. We also provide evidence of
efficient mode self-cleaning which suggests rich spatial-temporal
self-organization processes of laser beams in a nonlinear resonator