Giulio Vampa

Linking high harmonics from gases and solids

When intense light interacts with an atomic gas, recollision between an ionizing electron and its parent ion creates high-order harmonics of the fundamental laser frequency. This sub-cycle effect generates coherent soft X-rays and attosecond pulses, and provides a means to image molecular orbitals. Recently, high harmonics have been generated from bulk crystals, but what mechanism dominates the emission remains uncertain. To resolve this issue, we adapt measurement methods from gas-phase research to solid zinc oxide driven by mid-infrared laser fields of 0.25 volts per ångström. We find that when we alter the generation process with a second-harmonic beam, the modified harmonic spectrum bears the signature of a generalized recollision between an electron and its associated hole. In addition, we find that solid-state high harmonics are perturbed by fields so weak that they are present in conventional electronic circuits, thus opening a route to integrate electronics with attosecond and high-harmonic technology. Future experiments will permit the band structure of a solid to be tomographically reconstructed.

All-Optical Reconstruction of Crystal Band Structure

The band structure of matter determines its properties. In solids, it is typically mapped with angle-resolved photoemission spectroscopy, in which the momentum and the energy of incoherent electrons are independently measured. Sometimes, however, photoelectrons are difficult or impossible to detect. Here we demonstrate an all-optical technique to reconstruct momentum-dependent band gaps by exploiting the coherent motion of electron-hole pairs driven by intense midinfrared femtosecond laser pulses. Applying the method to experimental data for a semiconductor ZnO crystal, we identify the split-off valence band as making the greatest contribution to tunneling to the conduction band. Our new band structure measurement technique is intrinsically bulk sensitive, does not require a vacuum, and has high temporal resolution, making it suitable to study reactions at ambient conditions, matter under extreme pressures, and ultrafast transient modifications to band structures.

Tailored semiconductors for high-harmonic optoelectronics

Hitting the highs in solid state The ability to generate high harmonics of optical frequencies through the nonlinear interaction between intense light pulses and gas atoms has opened up the area of ultrafast optics and spectroscopy. Sivis et al. now show that high harmonics can also be generated with a solid-state sample. They used nanofabricated structured targets of ZnO and varied the chemical composition of the sample to demonstrate that (modest) high harmonics can be generated as the light interacts with the target materials. The results present the possibility of developing solid-state ultrafast optical devices. Science, this issue p. 303 Nanofabricated structures and chemical composition can tune the generation of high harmonics from solid-state targets. The advent of high-harmonic generation in gases 30 years ago set the foundation for attosecond science and facilitated ultrafast spectroscopy in atoms, molecules, and solids. We explore high-harmonic generation in the solid state by means of nanostructured and ion-implanted semiconductors. We use wavelength-selective microscopic imaging to map enhanced harmonic emission and show that the generation medium and the driving field can be locally tailored in solids by modifying the chemical composition and morphology. This enables the control of high-harmonic technology within precisely engineered solid targets. We demonstrate customized high-harmonic wave fields with wavelengths down to 225 nanometers (ninth-harmonic order of 2-micrometer laser pulses) and present an integrated Fresnel zone plate target in silicon, which leads to diffraction-limited self-focusing of the generated harmonics down to 1-micrometer spot sizes.

Intense-Laser Solid State Physics: Unraveling the Difference between Semiconductors and Dielectrics

Experiments on intense laser driven dielectrics have revealed population transfer to the conduction band to be oscillatory in time. This is in stark contrast to ionization in semiconductors and is currently unexplained. Current ionization theories neglect coupling between the valence and conduction band and therewith, the dynamic Stark shift. Our single-particle analysis identifies this as a potential reason for the different ionization behavior. The dynamic Stark shift increases the band gap with increasing laser intensities, thus suppressing ionization to an extent where virtual population oscillations become dominant. The dynamic Stark shift plays a role dominantly in dielectrics which, due to the larger band gap, can be exposed to significantly higher laser intensities.

Tunnelling time, what does it mean?

In a seminal paper, Keldysh published a theory of ionization of atoms and solids in intense sinusoidally varying laser fields. In this paper the Keldysh parameter was introduced, which separates optical field ionization into tunnel ionization and multi-photon ionization for and , respectively. Keldysh showed that the Keldysh parameter can be written as a product of laser frequency ω and of the Keldysh tunnel time , i.e. . Over the past 50 years there has been much debate about the meaning and the significance of the Keldysh tunnel time and of the tunnel time in general. This debate has been rekindled by recent attosecond experiment measurements of the tunnel time that are in contradiction with the Keldysh tunnel time and with other definitions of the tunnel time. This paper focuses on an analytical and numerical investigation of the Keldysh tunnel time. It is proven that the tunnel time in atoms represents a response time needed for the groundstate wavefunction to react to the laser field and to develop into the quasi-static resonance state, where full tunnel ionization occurs. Based on this definition, methods to measure the tunnel time of atoms in intense fields are discussed.

Harmonic generation in solids with direct fiber laser pumping

High harmonic generation in solids presents the possibility for bringing attosecond techniques to semiconductors and a simple source for frequency comb spectroscopy in the vacuum ultraviolet. We generate up to the seventh harmonic of a Tm fiber laser by focusing in silicon or zinc oxide. The harmonics are strong and stable, with no indication of material damage. Calculations show the potential for generating nineteenth harmonic photons at 12 eV photons of energy.

High-Harmonic Generation in Solids: Bridging the Gap Between Attosecond Science and Condensed Matter Physics

We review recent progress in understanding the dominant mechanism driving high-harmonic generation in solids. Three-dimensional two-band single active electron calculations predict that the major emission arises from the recombination of electron-hole pairs upon their creation and acceleration in the laser field, in analogy to atomic high-harmonic generation. The main goal of this study is to review a simple quasi-classical trajectory formalism and use it to better understand the fundamental properties of high-harmonic generation in solids and how they compare to high-harmonic generation in atomic and molecular gases. The simple formalism presents a valuable tool for extending attosecond science from the gas to the condensed matter phase. This is demonstrated by discussing the potential synthesis of attosecond pulses from solids.

Theory of high-harmonic generation in solids

High-harmonic generation (HHG) in bulk crystals exposed to intense mid-infrared lasers with photon energies below the bandgap is investigated theoretically. A three dimensional, two-band model that considers both interband and intraband currents is used. It is shown that the interband current is the dominant mechanism for HHG in solids. A physical interpretation of interband HHG – similar to atomic HHG – is provided by saddle point analysis. The effects of dephasing time and driving field wavelength on the harmonic specrum are investigated.

Light amplification by seeded Kerr instability

Seeding a laser amplifier Amplification of femtosecond laser pulses requires a lasing medium or a nonlinear crystal. The chemical properties of the lasing medium or adherence to momentum conservation rules in the nonlinear crystal constrain the frequency and the bandwidth of the amplified pulses. Vampa et al. seeded modulation instability in a laser crystal pumped with femtosecond near-infrared pulses. This provided a method for the high gain amplification of broadband and short laser pulses up to intensities of 1 terawatt per square centimeter. The method avoids constraints related to doping and phase matching and can be expected to be applied to a wide pool of glasses and crystals. Science, this issue p. 673 Seeding optical instability in a laser crystal provides a flexible method of amplifying laser pulses. Amplification of femtosecond laser pulses typically requires a lasing medium or a nonlinear crystal. In either case, the chemical properties of the lasing medium or the momentum conservation in the nonlinear crystal constrain the frequency and the bandwidth of the amplified pulses. We demonstrate high gain amplification (greater than 1000) of widely tunable (0.5 to 2.2 micrometers) and short (less than 60 femtosecond) laser pulses, up to intensities of 1 terawatt per square centimeter, by seeding the modulation instability in an Y3Al5O12 crystal pumped by femtosecond near-infrared pulses. Our method avoids constraints related to doping and phase matching and therefore can occur in a wider pool of glasses and crystals even at far-infrared frequencies and for single-cycle pulses. Such amplified pulses are ideal to study strong-field processes in solids and highly excited states in gases.

Tailored high-harmonic generation in nanostructured semiconductors

High harmonic generation (HHG) [1, 2] in gas-phase atomic or molecular targets has been extensively studied and developed over the past few decades, enabling attosecond spectroscopy [3] and tomographic imaging of molecular orbitals [4]. Recently, HHG could also been demonstrated in solid-state systems [5-8], which allows for applying attosecond spectroscopy techniques to condensed matter in an all-optical fashion as well as utilizing a solids electrons as a probe to investigate structural anisotropies [9]. Here, we extend these novel approaches by nanoscale engineering of the solid targets and demonstrate that HHG in semiconductors can be tailored and controlled by modification of the local chemical composition or the microstructure.