Fig. 1. Principle of terahertz field modulated quasi-phase-matched high-order harmonic generation (an intense femtosecond pump laser with a central wavelength of λ₁ is focused into the gas target from the forward direction to generate high-order harmonics; another relatively weak quasi-CW terahertz field with a wavelength of λ₂ counter propagates in the gas target, which interferes with the pump laser and causes the pump intensity to produce a periodic sinusoidal modu

Fig. 2. High-order harmonic spectra of argon near the cutoff region. The terahertz modulation field with a wavelength of λ₂=100 μm and with a modulation field ratio of r=0.05 is used in the simulation. In the figure, the black solid line represents the harmonic spectrum E

Fig. 3. Quasi-phase-matched high-order harmonic spectra E_HHG(ω,λ₂) with different terahertz modulation wavelengths λ₂ under a modulation field ratio r=0.07, corresponding to a terahertz field intensity of 2.45×10¹² W/cm². The black solid line is the result of fitting the quasi-phase-matched photon energies E_q with the wavelengths of the terahertz light field λ₂ by inverse

Fig. 4. Quasi-phase-matched high-order harmonic spectra E_HHG(ω,r) with different terahertz modulation field ratios r under a modulation wavelength λ₂=100 μm. The range of terahertz field intensity in the figure is from 4.5×10¹¹ to 5.0×10¹² W/cm². The black solid line with a slope of 0.0018 is obtained by linearly fitting the quasi-phase-matched photon energies E_q and the modulation field ratios

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