Nonadiabatic redshifts in high-order harmonic generation from solids

Abstract

We studied the multi-plateau high-order harmonic generation (HHG) from solids numerically. It is found that the HHG spectrum in the second or higher plateau is redshifted in short laser pulses due to the nonadiabatic effect. The corresponding FWHMs also increase, suggesting the step-by-step excitation process of higher conduction bands in the HHG process. Even order harmonics in the higher plateaus of HHG are present due to the break of symmetry in the k space. It may stimulate related experimental work. High-order harmonic generation (HHG) from gases has been well studied. It has been used to generate attosecond laser pulses [1,2]. It is described by the three-step model [3]. The cutoff energy of HHG is around Ip+3.17Up (Ip is the ionization potential, and Up=A0 2 /4 is the ponderomotive energy). The HHG from bulk crystals has been reported recently [4,5] as the development of long-wavelength lasers. It is quite different from the HHG from gases. The cutoff energy of solid HHG depends on the amplitude of the laser field linearly [4]. It also exhibits multi-plateau structure [6]. However, the mechanisms of HHG from solids are much debated. Inter-and intra-band transitions [4,7,8] are proposed. Three-step model in the coordinate space [9] and vector k space [10] are investigated. Recently, multi-plateau HHG from solids are studied theoretically [7,8,11] and experimentally. Our theoretical model [10] propose that the multi-plateau structure reflects the population of higher conduction bands which are pumped step by step.In the solid systems, even-order harmonics are measured experimentally. They may come from the interference of HHG trajectories in the different valence bands [12]. It may also come from the Berry phase [13]. In this work, we will present a new mechanism for even-order harmonic generation in symmetric periodic potentials.Redshifts of HHG spectra were predicted in the HHG from gases and plasmas [14][15][16][17][18][19][20]. They originate from delayed emission times of HHG from the excited state, resonate state, or dissociation of molecules. It is a nonadiabatic effect. The feature is that most of the HHG signals are generated from the trailing edge of the laser pulse, where dI/dt<0. The driving force from the laser fields is weaker than the previous cycle. The electrons obtain less energy compared to the previous cycle and redshifts of HHG occur. They have been experimentally confirmed [18,[21][22][23]. It was reported that redshift was observed in the optical absorption of crystals in the presence of an intense mid-infrared laser field [24]. In this letter, we find that redshift also exists in emission of HHG from solids. It is universal. The higher conduction bands are excited step by step. As a result, the HHG process in the higher plateau is delayed compared to ultrafast process in the lower conduction bands. As will be shown next, even the system is symmetric in the coordinate space, the electron motion is not symmetric in the k space. Consequently, redshifts of HHG and even-order harmonics ar...

High-order harmonic generation from 2D periodic potentials in circularly and bichromatic circularly polarized laser fields

“…To check if it is from the asymmetry introduced by the finite laser pulses, we have increased the pulse duration to 20 cycles. The weak even harmonics remain, which suggests that they are from the influence of interband transitions, similar to the case of interband-transition-induced even-order HHG in linearly polarized laser fields [25]. The cutoff energy is determined by the maximum energy band gap between the first conduction band and the valence band at all possible wave vector k(t) from our proposed model [24] in the momentum space.…”

“…Inter-and intra-band transition models [18][19][20][21][22][23] are proposed. Three-step model in coordinate space [22] and step-by-step model in vector k space [24][25][26][27] are investigated. The drawback of the solid HHG is the low damage threshold of solid materials.…”

Spectral control of high order harmonics through non-linear propagation effects

“…This effect is attributed to the delayed emission of HHG from excited states or resonant states 30 or dislocation of molecules 31 . In solids, numerically computed HHG spectra have shown redshifts in the "higher plateaus" due to higher band transitions 32 . In sapphire, intensity-dependent redshifts and blueshifts were observed in the spectrum of harmonics and attributed to the long and short electron/hole tra-FIG.…”

Enhancement of High-Order Harmonic Generation due to the Large Gradient of the Electric Field Amplitude

“…The rapid development of attosecond physics, including the subject of high-order harmonic generation [1][2][3][4][5], ionization [6][7][8][9][10], target excitation [11][12][13], etc., has allowed us to probe ultrafast dynamics in atoms and molecules with unprecedented temporal and spatial resolutions. Recently, high-order harmonic (HH) generation driven by circularly polarized laser fields has been a hot topic due to its potential application in the generation of circularly polarized attosecond pulses [14][15][16][17], which is a new tool for controlling and imaging ultrafast dynamics, such as charge transfer and migration and the generation of attosecond quantum electron currents for ultrafast magneto-optics.…”