Efficient generation of Bessel-Gauss attosecond pulse trains via nonadiabatic phase-matched high-order harmonics

Abstract

Generating Bessel-Gauss beams in the extreme ultraviolet (EUV) with attosecond pulse durations poses a significant challenge due to the limitations of conventional transmission optical components. Here, we propose a novel approach to produce such beams by inducing an annular EUV source through high-order harmonic generation (HHG) under nonadiabatic phase-matching conditions. The resulting light pulse maintains temporal coherence and manifests attosecond pulse trains as confirmed by the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) measurements. Macroscopic HHG calculations reproduce the measured spatiotemporal structures, demonstrating the plasma-induced spatial modulation on the formation of an annular source. Propagation simulations further confirm the feasibility of this approach for generating attosecond Bessel-Gauss beams, presenting exciting prospects for various applications in EUV photonics and attosecond science.

Fig. 1. Formation of an attosecond Bessel-Gauss beam.

a Illustration of the annular EUV emissions resulting from the reshaping of the intense femtosecond NIR laser after propagation and harmonic generation in the nonadiabatic phase-matching regime. b Spatiotemporal structure of the NIR laser field at the exit plane. The blue lines represent contours with a laser intensity of 5 × 10¹⁴ W cm⁻². c Attosecond bursts observed at the exit plane of the interaction area. d The optical path for generating an attosecond EUV Bessel-Gauss beam using the annular EUV source. e Evolution of the Bessel-Gauss beam simulated for the annular source along the propagation axis

Fig. 2. Spatial-spectral structure of HHG from Ar gas.

a, b Measured spatial distributions of HHG spectra from Ar at pressures of 20 Torr and 80 Torr in the nonadiabatic phase-matching regime at the intensity of 5 × 10¹⁴ W cm⁻². The signals contributed by the long trajectories are indicated by red arrows. c Spatial distributions of harmonic signals for H23, H25, and H27 as a function of gas pressure. The signals are integrated over an energy range of 2 eV and normalized separately. d Gas pressure-dependent harmonics intensities for H23, H25, and H27

Fig. 3. Macroscopic propagation effect on spatial profiles.

a Annular EUV Source (H39) in ray tracing simulation. b Free propagation imaging to the front of the grating. c Captured spectrum located in the focal plane of the grating. d Experimentally measured full spectrum of HHG from Ne gas with a pressure of 80 Torr and a target position of −1 mm under a laser intensity of 10 × 10¹⁴ W cm⁻². e The divergence of H39 in experiments was obtained by: (left) varying the laser intensity at a gas pressure of 80 Torr and a target position of −1 mm, with the dashed black curve representing the Bessel distribution; (middle) varying the target position, with a pressure of 80 Torr and a laser intensity of 10 × 10¹⁴ W cm⁻²; (right) varying gas pressure, with a laser intensity of 10 × 10¹⁴ W cm⁻² and a target position of −1 mm. f Theoretical simulated divergence of H39 obtained under the same experimental conditions. The black dashed lines guide the location of the first satellite peak

Fig. 4. Temporal reconstruction of APT with Ar and Ne Sources.

a, b RABBIT spectra of Ar and Ne sources in nonadiabatic phase-matching regime. c, d Temporal structure of APT reconstructed using the RABBIT spectra from Ar and Ne sources by employing the ePIE method

Fig. 5. Spatial-spectral and temporal structure analysis of HHG source.

a, b Simulated full spectra of Ne in the near and far fields, with a pressure of 80 Torr in the laser-gas interaction region, a gas position of −1 mm and a laser intensity of 10 × 10¹⁴ W cm⁻². c, d The zoomed-in near and far fields spatial distribution of H39. e, f Intensity and phase distribution for the selected energy slice marked in (c, d). g Spatiotemporal structure of H35-H47 obtained by fast Fourier transform and the synthesized attosecond pulse trains by integrating along the spatial direction is shown in the blue line

Fig. 6. Numerical simulation of the spatial distribution of the EUV source.

a EUV Bessel-Gauss beam produced by the annular EUV source using the energy slice on H39. b Radial distribution corresponding to that from the white dotted line in (a). c Attosecond EUV Bessel-Gauss beam generated by the annular EUV source using H35-H47. d Radial section at the white dotted line in (c). e On-axis intensity and phase distribution in (a, c). The solid lines represent the energy slices on H39, and the dashed lines are the energy integrals of H35-H47. f The intensity and phase derived from the radial profiles for the distributions of (b, d)