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Chin. Phys. B, 2023, Vol. 32(1): 014203    DOI: 10.1088/1674-1056/ac8cea

Effect of laser focus in two-color synthesized waveform on generation of soft x-ray high harmonics

Yanbo Chen(陈炎波)1, Baochang Li(李保昌)1, Xuhong Li(李胥红)1, Xiangyu Tang(唐翔宇)1, Chi Zhang(张弛)1, and Cheng Jin(金成)1,2,†
1 Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China;
2 MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing, Nanjing University of Science and Technology, Nanjing 210094, China
Abstract  Synthesis of multi-color laser pulses has been developed as a promising way to improve low conversion efficiency of high-order harmonic generation (HHG). Here we systematically study the effect of laser focus in a two-color waveform on generation of macroscopic HHG in soft x-rays. We find that the dependence of HHG yields on laser focus at low or high gas pressure is sensitive to the characteristics of single-atom harmonic response, in which "short"-or "long"-trajectory emissions can be selectively controlled by changing the waveform of two-color synthesized laser pulse. We uncover the phase-matching mechanism of HHG in the gas medium by examining the propagation of the two-color waveform and the evolution of time-frequency emissions of high-harmonic field. We further reveal that the nonlinear effects, such as geometric phase, atomic dispersion, and plasma defocusing, are responsible for modification of two-color waveform upon propagation. This work can be used to find better macroscopic conditions for generating soft x-ray HHG by employing two-color optimized waveforms.
Keywords:  high-order harmonic generation      two-color waveform      soft x-rays      macroscopic propagation      laser focus  
Received:  23 July 2022      Revised:  25 August 2022      Accepted manuscript online:  26 August 2022
PACS:  42.65.Ky (Frequency conversion; harmonic generation, including higher-order harmonic generation)  
  42.65.Re (Ultrafast processes; optical pulse generation and pulse compression)  
  31.70.Hq (Time-dependent phenomena: excitation and relaxation processes, and reaction rates)  
  32.90.+a (Other topics in atomic properties and interactions of atoms with photons)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 91950102, 12274230, and 11834004) and the Funding of Nanjing University of Science and Technology (Grant No. TSXK2022D005).
Corresponding Authors:  Cheng Jin     E-mail:

Cite this article: 

Yanbo Chen(陈炎波), Baochang Li(李保昌), Xuhong Li(李胥红), Xiangyu Tang(唐翔宇), Chi Zhang(张弛), and Cheng Jin(金成) Effect of laser focus in two-color synthesized waveform on generation of soft x-ray high harmonics 2023 Chin. Phys. B 32 014203

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