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Register a new userExtraction of higher-order nonlinear electronic response to strong field excitation in solids using high harmonic generation
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State-of-the-art experiments employ strong ultrafast optical fields to study the nonlinear response of electrons in solids on an attosecond time-scale. Notably, a recent experiment retrieved a 3rd order nonlinear susceptibility by comparing the nonlinear response induced by a strong laser field to a linear response induced by the otherwise identical weak field. In parallel, experiments have demonstrated high harmonic generation (HHG) in solids, a highly nonlinear process that until recently had only been observed in gases. The highly nonlinear nature of HHG has the potential to extract even higher order nonlinear susceptibility terms, and thereby characterize the entire response of the electronic system to strong field excitation. However, up till now, such characterization has been elusive due to a lack of direct correspondence between high harmonics and nonlinear susceptibilities. Here, we demonstrate a regime where such correspondence can be clearly made, extracting nonlinear susceptibilities (7th, 9th, and 11th) from sapphire of the same order as the measured high harmonics. The extracted high order susceptibilities show angular-resolved periodicities arising from variation in the band structure with crystal orientation. Nonlinear susceptibilities are key to ultrafast lightwave driven optoelectronics, allowing petahertz scaling manipulation of the signal. Our results open a door to multi-channel signal processing, controlled by laser polarization.
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High-order harmonic generation (HHG) in isolated atoms and molecules has been widely utilized in extreme ultraviolet (XUV) photonics and attosecond pulse metrology. Recently, HHG has also been observed in solids, which could lead to important applications such as all-optical methods to image valance charge density and reconstruction of electronic band structures, as well as compact XUV light sources. Previous HHG studies are confined on crystalline solids; therefore decoupling the respective roles of long-range periodicity and high density has been challenging. Here, we report the first observation of HHG from amorphous fused silica. We decouple the role of long-range periodicity by comparing with crystal quartz, which contains same atomic constituents but exhibits long-range periodicity. Our results advance current understanding of strong-field processes leading to high harmonic generation in solids with implications in robust and compact coherent XUV light sources.
Various interference effects are known to exist in the process of high harmonic generation (HHG) both at the single atom and macroscopic levels. In particular, the quantum path difference between the long and short trajectories of electron excursion causes the HHG yield to experience interference-based temporal and spectral modulations. In solids, due to additional phenomena such as multi-band superposition and crystal symmetry dependency, the HHG mechanism appears to be more complicated than in gaseous atoms in identifying accompanying interference phenomena. Here, we first report experimental data showing intensity-dependent spectral modulation and broadening of high harmonics observed from bulk sapphire. Then, by adopting theoretical simulation, the extraordinary observation is interpreted as a result of the quantum path interference between the long and short electron/hole trajectories. Specifically, the long trajectory undergoes an intensity-dependent redshift, which coherently combines with the short trajectory to exhibit spectral splitting in an anomalous way of inverse proportion to the driving laser intensity. This quantum interference may be extended to higher harmonics with increasing the laser intensity, underpinning the potential for precise control of the phase matching and modulation even in the extreme ultraviolet and soft X-ray regime. Further, this approach may act as a novel tool for probing arbitrary crystals so as to adjust the electron dynamics of higher harmonics for attosecond spectroscopy.
A promising alternative to Gaussian beams for use in strong field science is Bessel-Gauss (BG or Bessel-like) laser beams as they are easily produced with readily available optics and provide more flexibility of the spot size and working distances. Here we use BG beams produced with a lens-axicon optical system for higher order harmonic generation (HHG) in a thin gas jet. The finite size of the interaction region allows for scans of the HHG yield along the propagation axis. Further, by measuring the ionization yield in unison with the extreme ultraviolet (XUV) we are able to distinguish regions of maximum ionization from regions of optimum XUV generation. This distinction is of great importance for BG fields as the generation of BG beams with axicons often leads to oscillations of the on-axis intensity, which can be exploited for extended phase matching conditions. We observed such oscillations in the ionization and XUV flux along the propagation axis for the first time. As it is the case for Gaussian modes, the harmonic yield is not maximum at the point of highest ionization. Finally, despite Bessel beams having a hole in the center in the far field, the XUV beam is well collimated making BG modes a great alternative when spatial filtering of the fundamental is desired.
We consider several aspects of high-order harmonic generation in solids: the effects of elastic and inelastic scattering; varying pulse characteristics; and inclusion of material-specific parameters through a realistic band structure. We reproduce many observed characteristics of high harmonic generation experiments in solids including the formation of only odd harmonics in inversion-symmetric materials, and the nonlinear formation of high harmonics with increasing field. We find that the harmonic spectra are fairly robust against elastic and inelastic scattering. Furthermore, we find that the pulse characteristics play an important role in determining the harmonic spectra.
We report on efficient nonlinear generation of ultrafast, higher order perfect vortices at the green wavelength. Based on Fourier transformation of the higher order Bessel-Gauss beam generated through the combination of spiral phase plate and axicon we have transformed the Gaussian beam of the ultrafast Yb-fiber laser at 1060 nm into perfect vortices of power 4.4 W and order up to 6. Using single-pass second harmonic generation (SHG) of such vortices in 5-mm long chirped MgO-doped, periodically poled congruent LiNbO$_3$ crystal we have generated perfect vortices at green wavelength with output power of 1.2 W and vortex order up to 12 at single-pass conversion efficiency of 27% independent of its order. This is the highest single-pass SHG efficiency of any optical beams other than Gaussian beams. Unlike the disintegration of higher order vortices in birefringent crystals, here, the use of quasi-phase matching process enables generation of high quality vortices even at higher orders. The green perfect vortices of all orders have temporal and spectral width of 507 fs and 1.9 nm, respectively corresponding to a time-bandwidth product of 1.02.
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