Gauge Invariant Formulation of the Semiconductor Bloch Equations.

We derive gauge invariant semiconductor Bloch equations (GI-SBEs) that contain only gauge invariant band structure; shift vectors, and triple phase products. The validity and utility of the GI-SBEs is demonstrated in intense laser driven solids with broken inversion symmetry and nontrivial topology. The GI-SBEs present a useful platform for modeling and interpreting light-matter interactions in solids, in which the gauge freedom of the Bloch basis functions obscures physics and creates numerical obstacles.

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.

Measuring the Kerr nonlinearity via seeded Kerr instability amplification: conceptual analysis.

Whereas the Kerr nonlinearity is well understood in the perturbative limit of nonlinear optics, there is considerable discussion about its functional form and magnitude at extreme intensities, at which point matter starts to ionize. Here, we introduce a concept to answer this question and theoretically analyze its feasibility. We demonstrate that seeded Kerr instability amplification provides clear signatures from which functional form and magnitude of the Kerr nonlinearity can be extracted in the non-perturbative limit of nonlinear optics.

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.

Enhancing High Harmonic Output in Solids through Quantum Confinement.

We investigate theoretically the effect of quantum confinement on high harmonic generation (HHG) in semiconductors by systematically varying the width of a model quantum nanowire. Our analysis reveals a reduction in ionization and a concurrent growth in HHG efficiency with increasing confinement. The drop in ionization results from an increase in the band gap due to stronger confinement. The increase in harmonic efficiency comes as a result of the confinement restricting the spreading of the transverse wave packet. As a result, intense laser driven 1D and 2D nanosystems present a potential pathway to increasing yield and photon energy of HHG in solids.

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.

Theoretical analysis of high-harmonic generation in solids.

We investigate theoretically high-harmonic generation (HHG) in bulk crystals exposed to intense midinfrared lasers with photon energies smaller than the band gap. The two main mechanisms, interband and intraband HHG, are explored. Our analysis indicates that the interband current neglected so far is the dominant mechanism for HHG. Saddle point analysis in the Keldysh limit yields an intuitive picture of interband HHG in solids similar to atomic HHG. Interband and intraband HHG exhibit a fundamentally different wavelength dependence. This signature can be used to experimentally distinguish between the two mechanisms in order to verify their importance.

Tunnel ionization dynamics of bound systems in laser fields: how long does it take for a bound electron to tunnel?

A numerical method is developed by which the tunnel ionization dynamics of bound systems in laser fields can be isolated from the total wave function, as given by the time-dependent Schrödinger equation. The analysis of the numerical data for a step function field reveals the following definition for the tunnel time. It is the time it takes the ground state to develop the underbarrier wave function components necessary for reaching the static field ionization rate. This definition is generalized to time varying laser fields. The tunnel time is found to scale with the Keldysh tunnel time. Our Letter establishes the physical meaning of the tunnel time, its relation to the Keldysh tunnel time, and suggests how it can be measured.

Theory of the quantum breathing mode in harmonic traps and its use as a diagnostic tool.

An analytical expression for the quantum breathing frequency ωb of harmonically trapped quantum particles with inverse power-law repulsion is derived. It is verified by ab initio numerical calculations for electrons confined in a lateral (2D) quantum dot. We show how this relation can be used to express the ground state properties of harmonically trapped quantum particles as functions of the breathing frequency by presenting analytical results for the kinetic, trap, and repulsive energy and for the linear entropy. Measurement of ωb together with these analytical relations represents a tool to characterize the state of harmonically trapped interacting particles--from the Fermi gas to the Wigner crystal regime.

Steplike intensity threshold behavior of extreme ionization in laser-driven xenon clusters.

The generation of highly charged Xe(q+) ions up to q=24 is observed in Xe clusters embedded in helium nanodroplets and exposed to intense femtosecond laser pulses (λ=800 nm). Laser intensity resolved measurements show that the high-q ion generation starts at an unexpectedly low threshold intensity of about 10(14) W/cm2. Above threshold, the Xe ion charge spectrum saturates quickly and changes only weakly for higher laser intensities. Good agreement between these observations and a molecular dynamics analysis allows us to identify the mechanisms responsible for the highly charged ion production and the surprising intensity threshold behavior of the ionization process.

Light amplification by seeded Kerr instability.

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.

Self-phase-matched high harmonic generation

Our theoretical analysis reveals that tunnel ionization significantly modifies the electric field of few-cycle laser pulses within a single oscillation period. This subcycle self-modulation is predicted to result in phase matching, making high harmonic generation in the x-ray regime possible for the first time. Such a radiation source opens novel possibilities in the investigation of matter with x-ray techniques, such as time resolved x-ray diffraction and absorption.

High harmonic generation beyond the electric dipole approximation

A generalization of the analytical theory of high harmonic generation in the long wavelength limit and in the single active electron approximation is developed taking into account the magnetic dipole and electric quadrupole interaction. Quantum mechanical and classical theories are found to be in excellent agreement, which allows one to explain the influence of multipole effects in terms of an intuitive picture. For Ti:S lasers ( 0.8 &mgr;m) multipole contributions are found to be small below an intensity of about 10(17) W/cm(2), at which harmonic radiation with photon energies of several keV is generated. This promises the extension of high harmonic generation well into the sub-nm wavelength regime.

Shakeup excitation during optical tunnel ionization.

Shakeup of a two-electron system is investigated in the strong infrared laser field limit, both theoretically and experimentally. During tunnel ionization the electron shakes up a second electron to an excited bound state. Theoretically, a complete analytical theory of shakeup in intense laser fields is developed. We predict that shakeup produces one excited sigma(u) D(+)(2) state in approximately 10(5) ionization events. Shakeup is measured experimentally by using the molecular clock provided by the internuclear motion. The number of measured events is found to be in excellent agreement with theory.

Theory of self-focusing in a hollow waveguide.

We present a theoretical investigation of self-focusing in a hollow waveguide filled with noble gas. Our analysis was performed for a laser pulse that was predominantly in the fundamental mode and revealed the physical processes involved in self-focusing in a hollow waveguide. A critical power for self-focusing was obtained that was found to be substantially higher than the critical power for self-focusing in a bulk medium. Useful design criteria for pulse-compression systems are presented. We identify the parameter range for which the transverse variation of the pulse phase introduced by the Kerr nonlinearity is small.

Nonlinear source for the generation of high-energy few-cycle optical pulses.

We investigate the evolution of optical pulses in a hollow waveguide filled with noble gas at pulse intensities for which tunnel ionization dominates the nonlinear response of the gas. A numerical analysis reveals that the spectral chirp generated by the plasma nonlinearity is to a good approximation linear over the whole pulse spectrum and can be compensated in a dispersive delay line. Our calculations predict the generation of 3-4-fs optical pulses with energies of a few milijoules. To our knowledge, these energies are an order of magnitude greater than the pulse energies that have been realized to date in hollow-fiber compressors based exclusively on the nonlinear Kerr effect.

Self-starting passive mode locking.

We investigate the evolution of continuous-wave laser oscillation from free-running to mode-locked operation assuming a nonlinear device with an intensity-dependent transmittivity or reflectivity to be the mode-locking element. An intensity threshold for self-starting passive mode locking is predicted and related to the linewidth of the first beat note of the power spectrum of the free-running laser output. Experimental results confirm the predictions of the theory.

Mode locking in solitary lasers.

We present an analysis of passively mode-locked lasers in which pulse formation is dominated by the interplay between self-phase modulation and negative dispersion in separate cavity elements. Steady-state pulse parameters and stability issues are discussed. Stability in these solitary systems relies on some passive amplitude modulation, and the ultimate system performance is found to depend sensitively on the magnitude of amplitude modulation relative to that of phase modulation.

Limits of pulse shortening in solitary lasers.

The influence of dispersive pulse-broadening effects on femtosecond pulse formation in solid-state lasers has been investigated. Empirical formulas are derived from computer simulations, which permits the estimation of the magnitude of performance-limiting effects in practical solid-state systems.