Two-cycle Laser Research Articles

Relativistic effects in photoionizing a circular Rydberg state in the optical regime

We study the photoionization process of a hydrogen atom initially prepared in a circular Rydberg state. The atom is exposed to a two-cycle laser pulse with a central wavelength of 800 nm. Before the atom approaches saturation, at field intensities of the order of ${10}^{17}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$, relativistic corrections to the ionization probability are clearly seen. The ionization is predominantly driven by the radiation pressure in the propagation direction of the laser field, not by the electric field. Direct comparisons with the full numerical solution of the time-dependent Dirac equation demonstrate quantitative agreement with a semirelativistic approximation, which is considerably easier to implement.

Single-shot intense few-cycle pulse interaction with polycrystalline ZnSe.

The interaction of high-intensity few-cycle laser pulses with solids opens a new area of fundamental light-material interaction research. The applied research extends from extreme nonlinearity in solids to the next-generation high laser light damage resistance optical design. In this Letter, 11 fs infrared, carrier-envelope-phase (CEP) stable, two-cycle laser pulses were applied to investigate the process of laser-material interaction on the ZnSe surface. A systematic study of a few-cycle pulse laser-induced damage threshold on ZnSe was performed for a single-pulse regime (1-on-1). Laser damage morphologies were carefully characterized. Our experiment demonstrated the very beginning of laser-induced structures on the ZnSe surface by using the shortest infrared few-cycle laser pulse currently available with a stable CEP.

Entangled trajectories during ionization of an H atom driven by n-cycle laser pulse

We study the ionization of an H atom in a linearly polarized laser field with different optical cycle numbers by calculating the entangled trajectories in phase space. The results indicate that, for a two-cycle laser pulse, the entangled trajectory is simple owing to the simple laser electric distribution. As the number of optical cycles increases, the complexity of the laser electric field distribution, and subsequently, that of the entangled trajectories increase. From these entangled trajectories, re-scattering ionization can be observed. Further, we investigate the effect of quantum force on trajectories by comparing them with classical trajectories. We find that for few-cycle laser pulses (np=2 and 4), the effect of the quantum force is more distinct than classical behavior, whereas for longer laser pulses (np=6 and 8), it is quite similar to the classical behavior. Because of the quantum force, the final kinetic energy is slightly higher than that obtained by classical calculation. The different initial positions have some influence on the individual trajectories, but the individual trajectories still keep similar configuration to the mean trajectories.

Laser waveform control of extreme ultraviolet high harmonics from solids.

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.

In Process Citation

Quantum dynamics of H2+ excited by two-cycle laser pulses with laser carrier frequencies corresponding to the wavelengths λl = 800 and 200 nm (corresponding to the periods τl = 2.667 and 0.667 fs, respectively) and being linearly polarized along the molecular axis have been studied by the numerical solution of the non-Born–Oppenheimer time-dependent Schrödinger equation within a three-dimensional (3D) model, including the internuclear distance R and electron coordinates z and ρ. The amplitudes of the pulses have been chosen such that the energies of H2+ after the ends of the laser pulses, ⟨E⟩ ≈ −0.515 au, were close to the dissociation threshold of H2+. It is found that there exists a certain characteristic oscillation frequency ωosc = 0.2278 au (corresponding to the period τosc = 0.667 fs and the wavelength λosc = 200 nm) that plays the role of a “carrier” frequency of temporally shaped oscillations of the expectation values ⟨−∂V/∂z⟩ emerging after the ends of the laser pulses, both at λl = 800 nm and at λl = 200 nm. Moreover, at λl = 200 nm, the expectation value ⟨z⟩ also demonstrates temporally shaped oscillations after the end of the laser pulse. In contrast, at λl = 800 nm, the characteristic oscillation frequency ωosc = 0.2278 au appears as the frequency of small-amplitude oscillations of the slowly varying expectation value ⟨z⟩ which makes, after the end of the pulse, an excursion with an amplitude of about 4.5 au along the z axis and returns back to ⟨z⟩ ≈ 0 afterward. It is found that the period of the temporally shaped post-field oscillations of ⟨−∂V/∂z⟩ and ⟨z⟩, estimated as τshp ≈ 30 fs, correlates with the nuclear motion. It is also shown that vibrational excitation of H2+ is accompanied by the formation of “hot” and “cold” vibrational ensembles along the R degree of freedom. Power spectra related to the electron motion in H2+ calculated for both the laser-driven z and optically passive ρ degrees of freedom in the acceleration form proved to be very interesting. In particular, both odd and even harmonics can be observed.

Relativistic attosecond electron bunch emission from few-cycle laser irradiated nanoscale droplets

Attosecond electron bunches produced at the surface of nanometer-scale droplets illuminated by a two-cycle laser pulse are investigated for the purpose of determining their optimal emission characteristics. Significant departures from Mie theory are found for electron bunch emission from droplets whose radii satisfy the condition ${\ensuremath{\delta}}_{r}lRl10{\ensuremath{\delta}}_{r}$, where ${\ensuremath{\delta}}_{r}={\ensuremath{\gamma}}^{1/2}c/{\ensuremath{\omega}}_{p}$ is the plasma relativistic skin depth; an effect which can be accounted for by induced transparency. Scattering from such droplets is subject to a transitional regime which is neither accounted for by optical Mie theory valid for $R\ensuremath{\gg}\ensuremath{\delta}$, where $\ensuremath{\delta}$ is the usual plasma skin depth, nor with the Rayleigh regime ($Rl\ensuremath{\delta}\ensuremath{\ll}\ensuremath{\lambda}$). Instead the angular emission of the bunches is to a good approximation described by the nonlinear ponderomotive scattering model. Subsequently, the bunches are subject to further deflection by the ponderomotive pressure of the copropagating laser field in vacuum, depending on the initial droplet parameters. Final emission angles are estimated, together with the energy spectrum of the bunches.

Carrier-Envelope-Phase Dependence of Emission Properties of High-Order Harmonic Generation

The carrier-envelope-phase (CEP) dependence of the emission properties of high-order harmonic generation (HHG) are quantitatively investigated. Calculation shows that a two-cycle laser with CEP of 15° can produce a single energy distribution pulse peaked at 0.94 radian (rad) and spanned 1.29 rad with the cutoff energy 2.9Up+Ip and a bandwidth 0.86Up (where Up is the ponderomotive potential of the laser field and Ip is the atomic ionization potential). The CEP dependence of the energy and temporal localizations of the single distribution pulse show interesting 180° periodic structures. These characteristics may be useful in optimizing attosecond x-ray sources and measurements.

Laser-Duration Dependence of Emission Properties of High-Order Harmonic Generation

Quantitative investigations are made for the laser-duration dependence of the emission properties of high-order harmonic generation (HHG). HHG emission properties produced by few-cycle lasers show some useful characteristics. The cutoff energy is less than that by laser for infinite duration. The single energy distribution pulse decreases much faster than its duration as the laser duration grows. A two-cycle laser with carrier-envelope phase of 0° can produce a single distribution pulse peaked at the laser carrier phase 1.22 rad and spanned 1.18 rad with the cutoff energy 2.9Up + Ip and a bandwidth 0.63Up, where Up is the ponderomotive potential of the laser field and Ip is the atomic ionization potential.

XUV generation with several-cycle laser pulse in barrier-suppression regime

We study XUV generation with several-cycle laser pulses of intensity up to 1015 W cm−2 using numerical solution of the 3D Schrödinger equation for a hydrogen atom. Ionization of the atom mainly takes place in a barrier-suppression regime for such driving intensities. We find that in this regime XUV yield stops growing with the laser intensity and then even essentially decreases. The calculated yield dependence on the laser intensity agrees well with predictions of our theory. The latter shows several factors that lead to the decrease of the XUV yield in the barrier-suppression regime. The calculated cut-off in the XUV spectrum is displaced to slightly lower energies than those predicted by the Ip + 3.17Up law. The change in the cut-off can be due to the non-zero initial velocity of the electron detached under the barrier-suppression ionization. We find that essential population of both the free wave packet returning to the origin and the ground state at the instant of the return is required for effective XUV generation. Rapid ground state depopulation leads to shortening of the attopulse train generated by the two-cycle laser pulse when laser intensity increases. In particular, we find that the cut-off XUV generated under essential barrier-suppression with sine-like laser pulse provides an isolated attopulse, while two attopulses are generated for lower laser intensity.

Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation

The shortest pulses periodically emitted directly from a mode-locked Ti:sapphire laser are approaching the two-optical-cycle range. In this region, the phase of the optical carrier with respect to the pulse envelope becomes important in nonlinear optical processes such as high-harmonic generation. Because there are no locking mechanisms between envelope and carrier inside a laser, their relative phase offset experiences random fluctuations. Here, we propose several novel methods to measure and to stabilize this carrier-envelope offset (CEO) phase with sub-femtosecond uncertainty. The stabilization methods are an important prerequisite for attosecond pulse generation schemes. Short and highly periodic pulses of a two-cycle laser correspond to an extremely wide frequency comb of equally spaced lines, which can be used for absolute frequency measurements. Using the proposed phase-measurement methods, it will be possible to phase-coherently link any unknown optical frequency within the comb spectrum to a primary microwave standard. Experimental studies using a sub-6-fs Ti:sapphire laser suggesting the feasibility of carrier-envelope phase control are presented.