Three-dimensional tomographic reconstruction of ultrashort free electron wave packets

We present a tomographic technique based on Photoelectron Angular Distributions (PADs) measured by Velocity-Map-Imaging (VMI) to reconstruct the three-dimensional shape of ultrashort free electron wave packets obtained from 1+2 Resonance Enhanced Multi-Photon Ionization (REMPI) of potassium atoms. To this end the laser pulse is rotated about its propagation direction and a set of PADs are recorded at different rotation angles. The tomographic reconstruction technique is described and results for linear and elliptical polarization are presented. Results for linearly polarized light producing cylindrically symmetric electron wave packets confirm the validity of our method whereas elliptically polarized light serves as a prototype for polarization-shaped laser pulses.     

Poincaré representation of polarization-shaped femtosecond laser pulses

The usage of Poincaré phase space for the representation of polarization-shaped femtosecond laser pulses is discussed. In these types of light fields the polarization state (i.e. ellipticity and orientation) changes as a function of time within a single laser pulse. Such deliberate variation can be achieved by frequency-domain femtosecond pulse shaping in which two polarization components are manipulated individually. Here it is shown how these light pulses can be represented as temporal trajectories through the ellipticity-orientation (Poincaré) phase space, whereas conventional light (either continuous-wave or pulsed) is determined by only one specific Poincaré location. General properties of parametric Poincaré trajectories are discussed, and their relation to experimentally accessible pulse-manipulation parameters (i.e. amplitudes and phases) determined. Specifically, it is shown how the maximum rate by which a given polarization state can be turned into a different one (at significant intensity levels) is limited by the spectral laser bandwidth. Apart from their direct usage in polarization-shaped pulse representation, Poincaré trajectories also form the basis for intuitive quasi-three-dimensional renderings of the electric field profile. There, the temporal evolution of polarization, intensity, and chirp is directly apparent in a single illustration. Received: 10 December 2002 / Published online: 24 April 2003 RID="*" ID="*"Corresponding author. Fax: +49-931/888-4906, E-mail: brixner@physik.uni-wuerzburg.de     

Frequency doubling and Fourier domain shaping the output of a femtosecond optical parametric amplifier: easy access to tuneable femtosecond pulse shapes in the deep ultraviolet

Tuneable, shaped, ultraviolet (UV) femtosecond laser pulses are produced by shaping and frequency doubling the output of a commercial optical parametric amplifier (OPA). A reflective mode, folded, pulse shaping assembly employing a spatial light modulator (SLM) shapes femtosecond pulses in the visible region of the spectrum. The shaped visible light pulses are frequency doubled to generate phase- and amplitude-shaped, ultrashort light pulses in the deep ultraviolet. This approach benefits from a simple experimental setup and the potential for tuning the central frequency of the shaped ultraviolet waveform. A number of pulse shapes have been synthesised and characterised using cross-correlation frequency resolved optical gating (XFROG). This pulse shaping method can be employed for coherent control experiments in the ultraviolet region of the spectrum where many organic molecules have strong absorption bands. D.S.N. Parker and A.D.G. Nunn contributed equally to this work.     

Effects of the internuclear vector on the photoelectron angular distributions of H<Subscript>2</Subscript><Superscript>+</Superscript>

We study the photoelectron angular distributions (PADs) of diatomic molecule H₂ ⁺ irradiated by intense laser fields using a nonperturbative scattering theory. We find that the internuclear vector may change the PADs. The PADs have qualitative changes with the increasing of the internuclear distance. The molecular orientation affect the symmetry of the PADs. When the internuclear vector is vertical or parallel to the laser polarization vector, the PADs are four-fold symmetric; for other case the PADs are two-fold symmetric. Due to the modulation effect resulting from the molecular multi-core nature, the size of the jet and the main lobe can be enlarged or reduced. The molecular modulation effect become obvious for large internuclear distance.     

Femtosecond shaping of transverse and longitudinal light polarization

Femtosecond laser pulse shaping techniques have been restricted to propagating transverse electromagnetic waves. We present a scheme for pulse shaping of optical near fields based on the excitation of longitudinal electromagnetic fields with polarization-shaped light pulses. By solving Maxwell's equations for a model nanostructure, i.e., a scanning tunneling microscope tip, with help from the boundary-element method, we demonstrate that the electric field vector oscillates in a complex yet controllable fashion in three dimensions. Many applications are envisioned because literally another dimension in the optimal control of light-matter interaction is accessible.     

Extracting generalized multiphoton ionization cross-sections from nonperturbative time-dependent calculations: An application in positronium

Ab initio time-dependent (TD) calculations of the behavior of positronium (Ps) under strong subpicosecond laser pulses are presented. The results are compared with results in H through scaling. It is found that a substantial amount of the population can be found in excited states after the pulse. In the perturbative regime, generalized multiphoton ionization cross-sections are extracted from the results of the time-dependent calculations. The generalized cross-sections are used to predict the response of Ps to nanosecond laser pulses at wavelengths of current experimental interest. Beyond the application to Ps, the generality of the method for extracting generalized cross-sections from TD nonperturbative calculations is discussed. Received 8 June 1999     

Photoelectron angular distributions of molecules in bichromatic laser fields of circular polarization

Photoelectron angular distributions (PADs) from above-threshold ionization of O₂ and N₂ molecules irradiated by a bichromatic laser field of circular polarization are studied. The bichromatic laser field is specially modulated such that it can be used to mimic a sequence of one-cycle laser pulses. The PADs are greatly affected by the molecular alignment, the symmetry of the initial electronic distribution, and the carrier-envelope phase of the laser pulses. Generally, the PADs do not show any symmetry, and become symmetric about an axis only when the symmetric axis of laser field coincides with the symmetric axis of molecules. This study shows that the few-cycle laser pulses can be used to steer the photoelectrons and perform the selective ionization of molecules.     

Generation of polarization-shaped ultraviolet femtosecond pulses

We experimentally demonstrate the generation and characterization of polarization-shaped femtosecond laser pulses in the ultraviolet at a central wavelength of 400 nm. Near-infrared laser pulses are first polarization shaped and then frequency doubled in an interferometrically stable setup that employs two perpendicularly oriented nonlinear crystals. A new pulse shaper design involving volume phase holographic gratings reduces losses and hence leads to an increase in pulse energy.     

Photoelectron angular distributions from two-photon ionization of atoms near ionization threshold

Photoelectron angular distributions(PADs) from two-photon ionization of atoms in linearly polarized strong laser fields are obtained in accordance with the nonperturbative quantum scattering theory.We also study the influence of laser wavelength on PADs.For two-photon ionization very close to the ionization threshold,most of the ionized electrons are vertically ejected to the laser polarization.PADs from twophoton ionization of atoms are determined by the second order generalized phased Bessel function at which the ponderomotive parameter plays a key role.In terms of dependence of PADs on laser wavelength,corresponding variations for the ponderomotive parameter are demonstrated.     

Evolution of photoelectron angular distributions in a train of identical,circularly polarized few-cycle laser pulses

Photoelectron angular distribution (PAD) of atoms irradiated by a train of identical, circularly polarized few-cycle laser pulses is studied in the frame of a nonperturbative scattering theory. Our study shows that the PADs vary with the kinetic energy of photoelectron, the carrier-envelope phase, and the pulse duration. We find that along with increasing of the kinetic energy of photoelectron or with decreasing of the pulse duration or the both, the original one maximum of PAD splits into two maxima; the newly produced two maxima evolve to the opposite pole of the symmetric axis, and finally incorporate as a new maximum located in the symmetric axis.Received: 26 February 2004, Published online: 10 August 2004PACS: 32.80.Rm Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states) - 42.50.Hz Strong-field excitation of optical transitions in quantum systems; multiphoton processes; dynamic Stark shift - 42.65.Re Ultrafast processes; optical pulse generation and pulse compression     

Absorption and ionization of molecular nitrogen by UV femtosecond laser pulses

Mechanisms of non-linear absorption and ionization of molecular nitrogen gas by UV femtosecond laser pulses were studied using photogalvanic and photoacoustic techniques. The effect of the intermediate Rydberg resonance, its dynamic Stark perturbation and ponderomotive upshift of the first ionization potential of nitrogen molecules by the intense laser pulses has been revealed by observing an increase of a power slope of ion yield from three to four at increasing laser intensity.     

Photoelectron angular distributions from above threshold ionization of hydrogen atoms in strong laser fields

We apply a scattering theory of nonperturbative quantum electrodynamics to study the photoelectron angular distributions (PADs) of a hydrogen atom irradiated by linearly polarized laser light. The calculated PADs show main lobes and jetlike structure. Previous experimental studies reveal that in a set of above-threshold-ionization peaks when the absorbed-photon number increases by one, the jet number also increases by one. Our study confirms this experimental observation. Our calculations further predict that in some cases three more jets may appear with just one-more-photon absorption. With consideration of laser-frequency change, one less jet may also appear with one-more-photon absorption. The jetlike structure of PADs is due to the maxima of generalized phased Bessel functions, not an indication of the quantum number of photoelectron angular momentum states.     

Field control in the tight focus of polarization-shaped laser pulses

We show through simulations how to control the spatial field distribution of a tightly focused Gaussian beam of polarization-shaped femtosecond laser pulses. The field in the focus is calculated employing a decomposition into plane-wave components with appropriate incidence angles. Both polarization directions of the shaped pulse are treated separately and then superposed coherently. The incident polarization shape can be used to control the spatial and temporal evolution of the longitudinal field component. PACS 42.25.Ja; 42.30.-d; 42.65.Re     

Jet-like structures in photoelectron angular distributions

The photoelectron angular distributions (PADs) of hydrogen atoms in an intense laser field of linear polarization are studied using the S-matrix theory in the length gauge. The PADs show main lobes along the laser polarization and jet-like structures sticking from the waist of main lobes. Our previous prediction, based on a nonperturbative scattering theory of photoionization developed by Guo et al, showing that the number of jets on one side of PADs may increase by one, three, or other odd numbers and may decrease by one when one more photon is absorbed, is confirmed by this treatment. Within the strong-field approximation, good agreement is obtained between these two quite different treatments. We further study the influence of the Coulomb attraction to PADs, by taking a Coulomb--Volkov state as the continuum state of photoelectrons. We find that under the influence of the Coulomb attraction, the PADs change greatly but the predicted phenomena still appear. This study verifies that the jet-like structures have no relation with the angular momentum of photoelectrons.     

Ultrafast photoionization of ions and molecules by orthogonally polarized intense laser pulses: Effects of the time delay

We present the photoelectron momentum distributions(PMDs) and the photoelectron angular distributions(PADs) of He+ ions, aligned H2+ molecules and N2 molecules by intense orthogonally polarized laser pulses. Simulations are performed by numerically solving the corresponding two-dimensional time-dependent Schr?dinger equations(TDSEs) within the single-electron approximation frame. Photoelectron momentum distributions and photoelectron angular distributions present different patterns with the time delays Td, illustrating the dependences of the PMDs and PADs on the time delays by orthogonally polarized laser pulses. The evolution of the electron wavepackets can be employed to describe the intensity of the PADs from the TDSE simulations for N2 molecules.     

Quantum control by ultrafast polarization shaping

We demonstrate that the use of time-dependent light polarization opens a new level of control over quantum systems. With potassium dimer molecules from a supersonic molecular beam, we show that a polarization-shaped laser pulse increases the ionization yield beyond that obtained with an optimally shaped linearly polarized laser pulse. This is due to the different multiphoton ionization pathways in K2 involving dipole transitions which favor different polarization directions of the exciting laser field. This experiment is a qualitative extension of quantum control mechanisms which opens up new directions giving access to the three-dimensional temporal response of molecular systems.     

Simulations of Sisyphus cooling including multiple excited states

We extend the theory for laser cooling in a near-resonant optical lattice to include multiple excited hyperfine states. Simulations are performed treating the external degrees of freedom of the atom, i.e., position and momentum, classically, while the internal atomic states are treated quantum mechanically, allowing for arbitrary superpositions. Whereas theoretical treatments including only a single excited hyperfine state predict that the temperature should be a function of lattice depth only, except close to resonance, experiments have shown that the minimum temperature achieved depends also on the detuning from resonance of the lattice light. Our results resolve this discrepancy.     

Above-threshold detachment of negative ions by circularly polarized few-cycle laser fields

In accordance with nonperturbative quantum scattering theory,we investigate photoelectron angular distributions(PADs) from above-threshold detachment(ATD) of negative ions irradiated by circularly polarized few-cycle laser fields.Electrons ejected on the polarization plane demonstrate distinct anisotropies in angular distributions which distinctly vary with the carrier-envelope(CE) phase.The anisotropy is caused by interference between transition channels;it also depends strongly on laser frequency,pulse duration,and kinetic energy of photoelectrons.Optimal emission of photoelectrons,which varies with CE phase,makes it possible to control photoelectron motion.     

Stereoscopic flow-tagging velocimetry

A laser-based method for measuring the three components of the velocity in a plane simultaneously and instantaneously without seed particles is presented. This is achieved by combining a laser flow-tagging technique with stereoscopic detection, in which the tagged flow is viewed from two different directions. A single CCD camera is employed for this purpose by using a new optical detection system. The flow tagging is performed by two consecutive laser pulses, i.e., “write” and “read” laser pulses. The write laser creates a grid of tracer molecules (NO) by inducing a photodissociation process. The three-dimensional motion of the tracer molecules is measured by a thick read laser sheet. Received: 22 July 1999 / Revised version: 5 August 1999 / Published online: 30 September 1999     

激光大气成丝中的非线性光频转换

超快强激光在光学介质（如空气）中传播时由于克尔自聚焦效应和等离体散焦效应动态平 衡会发生一种独特的非线性激光成丝现象。激光成丝过程会诱导一些独特的物理现象,如非线性 光频转换产生超连续光谱、等离子体诱导高压放电、锥形辐射等,在大气传感、天气控制等研究 领域具有重要的应用前景。本文针对飞秒激光大气成丝过程中与传输介质相互作用所诱导的非线 性发光过程,介绍了激光大气成丝所产生的超连续光谱（白光）激光、谐波产生和太赫兹波辐射 三种非线性光频转换现象,并着重探讨了太赫兹波辐射的物理机理、研究现状和应用前景。