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HHG: Frontier in High-order Harmonic Generation

Principal investigator: Shambhu Ghimire

Our research interests are in understanding and using condensed phase attosecond (billionths of a billionth of a second) electron dynamics for extreme ultraviolet photonics. We use intense infrared laser pulses to create extremely fast electron oscillations in bulk crystals. These oscillations correspond to extremely nonlinear electrical current, which subsequently radiates high-energy photons in the form of high order harmonics of the laser. Because these oscillations take place in the sub-cycle time scale the pulse duration of harmonic radiation could also be in the sub-cycle range. Therefore we envision attosecond pulse metrology that is based on high harmonic generation in solid targets. Also, controlling electrical currents in materials on attosecond time scale may lead to the development of devices that are million times faster than those possible with current technology.

Interferometry of dipole phase in high harmonics from solids

Nature Photonics, 13, 96–100 (2019)
Jian Lu, Eric F. Cunningham, Yong Sing You, David A. Reis & Shambhu Ghimire

We performed self-referenced interferometry of high harmonics from  bulk crystals subjected to intense near infrared laser fields. We found that the role of laser induced dipole phase depends strongly on the electronic structure of the source material. This is intriguing because  in the gas phase high harmonics the dipole phase is largely independent of the target atom. In dilute gas medium, the tunnel-ionized electron spends much of its travel time in the continuum—far from the parent ion, where it accumulates the dipole phase. In the solid-state high-harmonic generation process the driven electron experiences a periodic potential during the entire travel time therefore the dipole phase  depends strongly on the electronic structures of source materials.The material-dependent dipole phase can provide a robust platform for high-harmonic spectroscopy of solids.

Image courtesy: Greg Stewart, SLAC National Accelerator Laboratory

Crystal orientation-dependent polarization state of high-order harmonics

Optics Letters, 44, 3, 530-533  (2019)
Yong Sing You, Jian Lu, Eric F. Cunningham, Christian Roedel & Shambhu Ghimire

Figure 1. Experimental setup to analyze polarization state of XUV harmonics.


Review: High-harmonic generation from solids

Nature Physics, 15, 10-16, (2019)
Shambhu Ghimire & David A. Reis

a, The real-space picture of HHG with several possibilities; the driven electron could scatter from the periodic Coulomb potential termed as Bloch oscillations, recombine with the associated hole (ion) and recollide with the first- and second-nearest holes (ions) because of closely packed atoms. b, The momentum-space version of a using simple cosine bands, showing intraband Bloch oscillations in the conduction band and interband coupling between the valance band and the conduction band, both emitting high-frequency radiation in the forward direction. c, Schematic diagram of the three-step recollision model comprising tunnel ionization, free-acceleration and recombination. d, The momentum-space version of c, where the electron tunnels from the bound state to the continuum state, accelerates in the parabolic continuum band and then recombines to the bound state (parent ion) emitting high-frequency radiation.

Locking the waveform with a quartz crystal

Nature Photonics 12, 256-257, (2018)
Shambhu Ghimire

High-order harmonics in the extreme-ultraviolet regime can be produced and a stable waveform-locked attosecond pulse can be formed when quartz is excited by a strong short-pulsed laser, providing a robust path towards attosecond photonics.

The nonlinear optical response of the crystal produces high-order harmonics, whose spectrum extends to the extreme ultraviolet (XUV) wavelength range. In the time domain, the duration of the XUV pulse is on the attosecond timescale and its waveform remains locked to the phase of the pump laser field despite fluctuations in the pump laser’s amplitude (shown by dashed lines). See details in Nature Photonics 12, 291-296, (2018) by Goulielmakis team.

High-harmonic generation in amorphous solids

Nature Communications 8, 724 (2017); doi:10.1038/s41467-017-00989-4
Yong Sing You, Yanchun Yin, Yi Wu, Andrew Chew, Xiaoming Ren, Fengjiang Zhuang, Shima Gholam-Mirzaei, Michael Chini, Zenghu Chang & Shambhu Ghimire
High-harmonic generation (HHG) was originally discovered in gas medium (using Ar, Kr, Ne etc.), and more recently in bulk crystals (ZnO, MgO, frozen Ar crystals, etc.). Here, we observe high-harmonics from amorphous glass (SiO2) pumped by strong, few-cycle, near infrared laser pulses. The photon energy of high-harmonic spectrum extended to about 25 eV.
We compare amorphous and crystalline SiO2 such that important underlying microscopic differences can be explored. Our comparison involve carrier-envelope phase (CEP) dependence and pump laser wavelength dependence. We find that, in amorphous SiO2, the photon-energy of harmonic peaks shift significantly as a function of the CEP, indicating that high harmonics are delayed to each other in the sub-cycle time-scale. The CEP dependence in crystalline SiO2 is different, which contains monotonic change with 2 pi modulation, consistent to the non-centrosymmetric crystal structure. 
The observation of coherent extreme ultraviolet (XUV) light from common glass is particularly attractive because now it seems feasible to produce and manipulate XUV light directly in optical fibers. Advantages of the use of optical fibers for XUV light generation include the possibility to further scale photon flux to a new level and to deliver light to the inspection tools essentially without much loss.

Figure a, b are experimental data for carrier-envelope-phase (CEP) dependence of high-harmonic spectrum from fused silica and crystalline quartz respectively, at a peak laser field of 2 V/Å. The dotted black lines trace the change in photon energy of harmonic peaks with CEP. The amplitude of CEP slope is ~3 eV/π. The spectrum of fused silica repeats every π (horizontal axis) while there is a dominant 2π periodicity for crystalline quartz. The spectral minimum of crystalline quartz persists for all CEP settings. c, d show the calculated high-harmonic spectrum from a quantum mechanical simulation of multi-level models. The insets show the respective energy levels and the couplings used in the simulations. The simulation results reproduce the periodicity and CEP slope of the experimental results.

Laser waveform control of extreme ultraviolet high harmonics from solids

Optics Letters, 42, 9, 1816-1819 (2017)
Yong Sing You, Mengxi Wu, Yanchun Yin, Andrew Chew, Xiaoming Ren, Shima Gholam-Mirzaei, Dana A. Browne, Michael Chini, Zenghu Chang, Kenneth J. Schafer, Mette B. Gaarde, and Shambhu Ghimire
Solid-state high-harmonic sources offer the possibility of compact, high-repetition-rate attosecond light emitters. However, the time structure of high harmonics must be characterized at the sub-cycle level. We use strong two-cycle laser pulses to directly control the time-dependent nonlinear current in single-crystal MgO, leading to the generation of extreme ultraviolet harmonics. We find that harmonics are delayed with respect to each other, yielding an atto-chirp, the value of which depends on the laser field strength. Our results provide the foundation for attosecond pulse metrology based on solid-state harmonics and a new approach to studying sub-cycle dynamics in solids.
Top row shows the measured CEP dependence of HHG from MgO with peak laser fields of (a) 1.2 V/Å, (b) 1.7 V/Å, and (c) 2.1 V/Å, respectively. The bottom row shows calculation results from the three-level model, at similar field strengths of (d) 1.0 V/Å, (e) 1.3 V/Å, and (f) 1.8 V/Å, respectively. The dashed black lines trace the change in photon energy of the harmonic peak around 18 eV. The slope of this line for a given plateau harmonic decreases with an increasing peak field. In the calculations, which show a larger range of photon energies, this behavior can also be recognized in the CEP dependence for each intensity: the slope is largest for the highest photon energies close to the cutoff and decreases with harmonic order.

Anisotropic high-harmonic generation in bulk crystals

Nature Physics, doi:10.1038/nphys3955 (2016) 

Yong Sing You, David A. Reis & Shambhu Ghimire

We demonstrate that high-harmonic generation in bulk crystals is sensitive to the interatomic bonding. We measure highly anisotropic high-harmonic generation in bulk MgO crystals, which we describe by using real-space semi-classical electron trajectories. Generation is enhanced (diminished) for electron trajectories that connect (avoid) neighboring atomic sites in the crystal. Therefore our results indicate the possibility of using materials own electrons for retrieving the interatomic potential and thus the valence electron density, and perhaps even wavefunctions, in an all-optical setting.


High-harmonic generation from an atomically thin semiconductor 

Nature Physics, doi:10.1038/nphys3946 (2016)

Hanzhe Liu, Yilei Li, Yong Sing You, Shambhu Ghimire, Tony F. Heinz & David A. Reis

Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the electron dynamics responsible for high order harmonic generation. We demonstrate non-perturbative HHG from a monolayer MoS2 crystal, with even and odd harmonics extending to the 13th order. The even orders are predominantly polarized perpendicular to the pump and are compatible with the anomalous transverse intraband current arising from the material’s Berry curvature, while the weak parallel component suggests the importance of interband transitions. The odd harmonics exhibit a significant enhancement in efficiency per layer compared to the bulk, which is attributed to correlation effects. The combination of strong many-body Coulomb interactions and widely tunable electronic properties in two-dimensional materials offers a new platform for attosecond physics.

Solid-state harmonics beyond the atomic limit

Nature 534, 520–523 (2016)

Georges Ndabashimiye, Shambhu Ghimire, Mengxi Wu, Dana A. Browne, Kenneth J. Schafer, Mette B. Gaarde & David A. Reis

High harmonic generation in bulk solids is a new research topic while the atomic HHG has been studied for about 30 years now. Therefore it would be desirable to compare the generation process in solid and gas phase same atomic constituents. We compared high harmonic generation in the solid and gas phases of argon and krypton. Owing to the weak van der Waals interaction, rare (noble)-gas solids are a near-ideal medium in which to study the role of high density and periodicity in the generation process. We find that the high harmonic generation spectra from the rare-gas solids exhibit multiple plateaus extending well beyond the atomic limit of the corresponding gas-phase harmonics measured under similar conditions. The appearance of multiple plateaus indicates strong interband couplings involving multiple single-particle bands. We also compare the dependence of the solid and gas harmonic yield on laser ellipticity and find that they are similar, suggesting the importance of electron–hole recollision in these solids. This implies that gas-phase methods such as polarization gating for attosecond pulse generation and orbital tomography could be realized in solids.