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.
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