Macroscopic scaling of high-order harmonics generated by two-color optimized waveforms in a hollow waveguide

Abstract

We present the macroscopic scaling of high harmonics generated by two-color laser pulses interacting with Ne gas in a hollow waveguide. We demonstrate that the divergence of harmonics is inversely proportional to the waveguide radius and harmonic yields are proportional to the square of the waveguide radius when the gas pressure and waveguide length are chosen to meet the phase-matching condition. We also show that harmonic yields are inversely proportional to the ionization level of the optimized two-color waveform with proper gas pressure if waveguide radius and length are fixed. These scaling relations would help experimentalists find phase-matching conditions to efficiently generate tabletop high-flux coherent soft x rays for applications.

Spectral splitting and phase matching of the macroscopic high-order harmonic generation in intense laser fields

“…As we know, there are potential models and ionization rates much more accurate than a hydrogen-like model in Ar or Ne atoms, such as quantitative rescattering theory [18,29,30]. However, the hydrogenlike model has been employed extensively for the dipole matrix element of the source term in propagation, such as [15,28].…”

“…The laser-field and the harmonic-field propagation in a macroscopic medium are described by three-dimensional (3D) Maxwell's equations [29,30,36,37] in cylindrical coordinate separately, which have the following forms: ) is the nonlinear polarization of the medium. Both equations (8) and (9) are solved by using the Crank-Nicholson routine in the frequency domain.…”

Harmonic Analysis in Gaseous Helium by Coherent Schrödinger-Maxwell Method

“…Fang et al [20] established a full hydrodynamic model to simulate nonlinear harmonic response and distribution in metallic metamaterials. For high-order harmonics, Jin et al [21] investigated medium propagation effects in Ar and N 2 , with an approximate nonlinear polarization source based on quantitative rescattering (QRS) theory [22]. Besides, many efforts have been made on IAP propagation effects of beam quality and spatial profile due to its crucial role for experimental measurement [23], [24].…”

Control of soft X-ray high harmonic spectrum by using two-color laser pulses

“…In recent years, it has become possible to control optical waveform of the driving lasers by synthesizing multi-color laser pulses [42][43][44][45] to optimize the yields of high harmonics (see the review [46]). In our recent works we have focused on the optimization of multi-color laser waveform for the enhancement of harmonic yields [47], the improvement of two-color harmonic divergence in soft X-rays [48,49], as well as the macroscopic scaling of HHG generated by a two-color laser in a hollow waveguide [50]. In this article, we address whether the optimized multi-color waveform can be employed to control the spectral structure of HHG by adjusting macroscopic phasematching conditions.…”