Fig. 1. Experimental setup. EA, energy attenuator; BS, beam splitter; lens, f=2  m; M1–M5, 800 nm high reflection mirrors; SLM, spatial light modulator; ND, neutral filter; TFSP, thin fused silica plate; AM, aluminum mirror; Filters, suitable bandpass filters, short-pass filters, and long-pass filters. Inset, the phase map composed of a vortex phase with m=1 and a Fresnel lens phase with f=2  m.

Fig. 2. Simulated evolution of peak intensity and electron density in the plates and air. The pulse energy of the femtosecond vortex beam is 420 μJ, and topological charge m=1.

Fig. 3. (a) Simulated full-path spectrum evolution. (b) Transverse phase distribution of different spectral components for the femtosecond vortex beam with topological charge m=1.

Fig. 4. (a) Pulse shapes of the femtosecond vortex beam at several longitudinal positions. (b) The temporal intensity (solid lines) and phase (dashed lines) profiles at different transverse positions (marked by black stars in the inset) after plate 6.

Fig. 5. Normalized transverse fluence distribution in the six plates. The first row denotes the front surface, and the second row denotes the back surface.

Fig. 6. (a) Experimentally measured spectra of pump laser and supercontinuum after each plate. (b) Measured intensity distribution and (c) interference patterns after passing different filters. BP, bandpass; SP, short-pass; LP, long-pass. (d) The detected spectra after different filters. The pulse energy before the first plate is 468 μJ, and the topological charge m=1.

Fig. 7. (a) Simulated transverse phase of different spectral components. (b) Measured interference patterns after passing different filters; the filters are the same as in Fig. 6. The pulse energy before the first plate is 660 μJ, and the topological charge m=2. Five plates with thicknesses 300 μm, 300 μm, 200 μm, 200 μm, and 100 μm are used. Their spacings are 18 mm, 14 mm, 10 mm, and 16 mm.