The high-harmonic conversion efficiencies in optimized two-color laser pulses

Abstract

High-order harmonic generation (HHG) is a remarkable frequency up-conversion process in which an ultrafast femtosecond laser pulse at high intensity (>10 14 W/cm 2 ) interacts with a gaseous target to generate coherent extreme ultraviolet radiation. High-order harmonics, due to their high repetition rate operation, tunable wavelength and high coherence degree, have been widely used in many fields. HHG is currently a cornerstone of attosecond pulse, and promises to be a valuable tabletop light source. Their main drawback, however, is the low conversion efficiency, which limits many applications. In this work we present a promising way to increase harmonic yield by using the synthesized two-color field, whose validity is demonstrated both on single-atom and macroscopic levels. The single-atom harmonic spectrum is calculated by the strong field approximation method. The macroscopic propagation of the fundamental and harmonic fields in an ionizing medium is obtained by solving Maxwell equations, which involves the dispersion, absorption, Kerr and plasma effects. The waveform of two-color laser field is determined by using a genetic algorithm to optimize the maximum single-atom Ne harmonic yield, for the lasers with fundamental wavelengths of 800 nm to 3000 nm. Optimizations are performed on condition that the cutoff and total laser power for the single-color field and the optimized wave are the same. The optimizations show that the optimal wavelengths and intensities meet the conditions of λ 1 / λ 2 ≈ 3 , I 1 / I 2 ≈ 5 for two component fields, and carrier-envelop phases are f 1 =0, f 2 =1.6 p . Our analysis show that the spreading of the electron wavepacket is almost the same in the optimized and single-color field. But the ionization level and yields of harmonics emitted from short-trajectory returning electrons are enhanced in the optimized field. Thus, the harmonic conversion efficiency generated by the optimized laser field can be increased by at least one order without increasing total laser power even after considering macroscopic propagation effects. We also compare the wavelength scaling laws of harmonic yield generated by the single- and optimized two-color fields. For the single atom, the present wavelength scaling in the single-color field agrees with the previous results, which scales as l - 5 ~ l - 8 . In the two-color field, the scaling law is slightly worse than that in the homochromous field mainly due to different contributions of short and long trajectories. While for the macroscopic high harmonic generation, its efficiency falls more dramatically with increasing wavelength because of the unfavourable phase-matching and dominant contribution of harmonics from short-trajectory electrons, with a very unfavorable scaling law of l - 8 ~ l - 13 . Although we can not obtain a much better wavelength scaling of harmonic yield in the two-color fields, the conversion efficiency can be enhanced more than one order. Further analysis shows that the stability of optimized waveform is maintained in consideration of relative intensity, wavelength and phase fluctuations of ±10%, ±40 nm and ±0.05 p , respectively. Due to the great advent of the ultrafast lasers technology, such as waveform synthesizing, optical parametric amplification and optical parametric chirped-pulse amplification, this work gives helpful guidance for intense harmonic generation.