VASILEIOS-MARIOS GKORTSAS vasilisg@mit.edu 6.638 Term Paper

Attosecond Pulse Generation

Abstract: The word “attosecond” (1 as = 10-18 sec) entered the vocabulary of physics when sub-femtosecond pulses of UV/XUV light were established. High harmonic generation (HHG) is currently the only experimentally proven method for generating attosecond pulses. Attosecond science has opened the door to real-time observation and time-domain control of atomic-scale electron dynamics. In this work, we review the essentials of the generation of attosecond pulses and we mention the applications of attosecond science in the control of electronic motion.

1. Introduction

The need for finer time resolution and the quest for higher peak power explain the continuous trend towards shorter laser pulses since the invention of the laser. The historical progress of ultra-short technology is summarized in Figure 1. The first pulse lasers had duration of several hundreds of microseconds. The invention of Q-switching (Hellwarth, 1961) reduced the pulse length to 10 ns (four orders of magnitude decrease). The invention of laser mode locking (DiDomenico, 1964; Hargrove et al., 1964; Siegman, 1970) accompanied by broad gain laser media (Shank and Ippen 1974) further reduced the duration to less than 1 ps (another four orders of magnitude decrease). The ring cavity with intra-cavity prism compensation of the group velocity dispersion produced pulses of 6 fs (Fork et al, 1987), causing a further three-order reduction. After that date the progress was marginal. Ti-Sapphire lasers replaced dye lasers and brought considerable changes in the size, performance and ease of operation of ultra-short laser systems. However, the wavelength was shifted to the near infrared (800 nm), where 5 fs long pulses are a few cycles long. By the end of the nineties, the innovations introduced by Kerr-lens modelocking and self-phase modulation spectral broadening, the availability of chirped, ultra-broad band mirrors and pulse compression led to pulse lengths of about two optical cycles (Steinmeyer et al 1999). Since the Ti-Sapphire optical period is 2.7 fs and a pulse of light should be at least one cycle long, the necessary prerequisite for attosecond light pulses was higher carrier frequencies. Attosecond science arises from research of the early nineties into intense ultrashort-pulse atomic physics. In order to break the femtosecond barrier, Hansch (1990), Farkas and Toth (1992) and Harris et al (1993) proposed Fourier Synthesis as a scheme that could possibly generate a pulse of few attoseconds. The basic idea was the production of a comb of equidistant frequencies in the spectral domain with controlled relative phases, mimicking the modelocking of lasers. Farkas and Toth (1992) recognized that High Harmonic Generation (HHG) could easily produce a broad spectral domain in a series of odd harmonics separated by twice the fundamental frequency, while Kaplan (1994) suggested cascaded stimulated Raman scattering (CSRS). Both HHG and CSRS have been proven to be successful and in the case of HHG pulses as short as 130 as have been reported [1]. It is evident that the phase-locking of a periodic spectrum of equidistant frequencies can result in a periodic intensity profile in the time domain (i.e. train of pulses). The most tempting is the production of a single isolated attosecond pulse by harmonic generation with a few-cycle driving pulse. Single pulses approaching 1 fs (Drescher et al 2001), a few hundrends of attoseconds (Hentschel et al 2001), 250 as (Kienberger et al 2004) and 130 as (Sansone et al 2006) are reported. All these numbers give an idea of how fast the field is progressing.

[pic]

Figure 1. Timeline of the laser pulse length evolution. The plot is taken from [2] which includes the progress until 2004. Nowadays the femtosecond barrier has been surpassed and attosecond pulses are produced .

2. Basic Theory

The typical time scale of electron motion in atoms and molecules is a few hundrend attoseconds. Attosecond control of electronic motion is achieved by laser fields that are comparable in strength to the electric field in the atom. In attosecond physics we can separate the dynamics of phenomena in two domains, one “inside” the atom where the atomic forces dominate and one “outside” the atom where the laser force dominates. In order to model attosecond phenomena we can use a simple semiclassical model which describes the essence of these phenomena and quantum mechanical calculations are needed in order to get quantitatively correct results. The laser pulses used have duration from 40 fs down to ~5 fs (which corresponds to about two optical cycles at the wavelength of 800 nm). For pulse durations near or below four optical cycles, in addition to the pulse envelope and the carrier frequency, the carrier envelope phase [pic] is an important parameter that characterizes the pulse. The laser field is defined as

[pic] (1)

where [pic] is the field envelope and ω0 is the carrier frequency. When the pulse is very short the role of [pic] becomes important. For an envelope with its maximum at t=0, a value of [pic]=0 (cosine pulse) means that a single field peak exceeds all other field maxima, while for [pic](sine pulse) two equally strong peaks of opposite sign are reached before and after t=0. The value of the carrier envelope phase is important for the generation of isolated attosecond pulses as we will see later. For the rest of our analysis we will adopt atomic units, where[pic].

A. Ionization

Ionization is the transition form “inside” to “outside” of the atom and plays an important role for attosecond phenomena. A rough distinction of the various regimes of atomic ionization (Figure 2) can be done by the value of the Keldysh parameter[pic][3], where [pic]is the time averaged kinetic energy or ponderomotive energy, E0 is the field amplitude, ω0 is the driving frequency and Ip is the ionization potential For [pic] multiphoton ionization takes place. It is dominant for “small” fields and as a consequence many photons are needed in order to achieve ionization. Note that we consider fields of frequency ω0 such that [pic]and therefore photoionization by a single photon is impossible. For [pic] optical-field ionization takes place and there are two possible ionization regimes, the tunnel ionization and the barrier-suppression ionization. The difference between these two regimes is that in the case of barrier-suppression ionization the field strengths are large enough to allow classical detachment of the electron. In this parameter range, the two last regimes are well described by the quasi-static approximation. That means that the variation of the electric field is so slow that the instantaneous ionization rate coincides with a static one. If [pic]is the static (Stark) ionization rate as function of the electric field, we have

[pic] (2)

where [pic]is the probability amplitude of finding the atom in the ground state. In fact even for [pic] the approximation is satisfactory [4]. Tunnel ionization depends on the electric field strength in a strongly nonlinear way. The static ionization rate [pic]is well described in the tunnel ionization regime by the Ammosov-Delone-Krainov (ADK) formula [5]. The ADK formula is

[pic] (3)

where n*=1/[pic]and l is the total angular momentum quantum number of the valence orbital which is 1 for all noble gases apart from helium (for which it is 0). Γ is the gamma function. We should mention that the magnetic quantum number m is equal to 0 in the above formula. The ADK formula has also been extended to molecules [6]. The formula shows the characteristic exponential dependence of the ionization rate on the inverse of the field strength and due to this nonlinearity in the case of tunneling field strengths most electrons are released at times when the field reaches its peak (Figure 3). When the field approaches the barrier-suppression ionization regime, the ADK formula is no longer valid. In this case somebody should use numerically calculated ionization rates.

[pic]

Figure 2. Regimes of atomic ionization. (Figure taken from [3])
[pic]

Figure 3. Static ionization rate for Argon in a logarithmic scale for sine-shaped driving field with amplitude 0.079 atomic units. We see that the ionization rate is maximum at the peak of the pulse

B. High Harmonic Generation

High Harmonic Generation (HHG) is the only experimentally proven method for generating attosecond pulses in the XUV range. In HHG an intense ultrashort laser pulse is focused into a gas or solid, generating high harmonics that emerge as a coherent, low divergence beam. Modeling HHG in a gas jet involves the calculation of the single-atom dipole response induced by a laser pulse and simulation of co-propagation of the laser and harmonic beams. While the most precise way to calculate the single atom response is by numerically solving the TDSE, this method is time consuming. Instead, we can use a semiclassical model.

i. Three Step model

The individual processes participating in HHG can be interpreted in terms of a semiclassical model introduced by Corkum, Kulander and Lewenstein [7, 8] which is known as Three Step Model (TSM) because of the three-stage description of the HHG process: (1) ionization, (2) electron propagation by the laser field and redirection to the ion, and (3) recombination with the ion (Figure 4). According to this model an electron first tunnels through the barrier formed by the atomic potential and the laser field at an instant tb (birth time) and appears in the continuum with zero velocity. It then propagates in the strong laser field which brings it back to the nucleus approximately an oscillation period later at an instant t (arrival time), where it recombines back to the ground state with some probability upon releasing the energy it gained in the laser field plus the ionization potential Ip, by emitting a high energy photon. In this case a high frequency “burst” of harmonics with photon energy [pic] is generated at the recollision moment. However, there is a chance that the laser field will remove the electron from the ion once for all. Only those electrons that return to the nucleus can emit harmonics by recombining to the ground state. The maximal energy of emitted photons is [pic](harmonic cutoff energy). The dominant contribution to harmonic generation comes from electrons that (i) return to the nucleus, (ii) appear in the continuum with zero velocity, and (iii) have an appropriate kinetic energy to produce a given harmonic at the time of return.
[pic]

Figure 4. Schematic representation of the elementary process responsible for high harmonic generation. (Figure taken from [3])

Step 1: Ionization. When induced by a strong (near-) infrared laser field ([pic]), ionization can be approximated by tunneling; the laser field suppresses the Coulomb potential so strongly that the wave function of the (most weakly bound) electron of energy -Ip penetrates the barrier formed by the atomic potential and the laser field and reaches its outer side within a fraction of the laser oscillation period Tosc (for 800 nm light the oscillation period is 2.7 fs).The intensities are large enough (1014-1015 W/cm2), so that intermediate resonances play no role [8]. The electron leaves the atoms typically when the field reaches its peak value. For 800-nm light, tunneling is most probable during about 300 attoseconds around each field crest near the pulse peak [9]. So, the attosecond timescale arises first during tunneling. Step 2: Electron propagation. The electron leaves the atom when the field reaches its peak value. A typical electron gains a kinetic energy of ~50-1,000 eV (thus tens to hundreds of photons) from the field during its first femtosecond of freedom [9]. So the effects of force due to the potential [pic], is then negligible. The electron undergoes transitions to continuum states which are labeled by the kinetic momentum of the outgoing electron[pic]. As the electron is accelerated by the field, it acquires a high velocity, so that the role of V(x) is less pronounced. Thus, the electron can be treated as a free particle. So the motion of the electron can be described with Classical Mechanics. Tunneling launches electrons on classical trajectories (Figure 5). Each instant of ionization (birth time) is related to a moment of recollision by a trajectory (arrival time). The trajectory which refers to the electron that returns back to the nucleus with the highest kinetic energy is called “most energetic trajectory”. The “most energetic trajectory” (if we assume a perfect sinusoidal electric field) is populated by electrons born at [pic]and recollide with maximum kinetic energy at [pic]. The maximum kinetic energy will determine the maximum photon energy in the emitted attosecond XUV pulse. Step 3: Recombination. When re-encountering the core, the electron recombines back to the ground state with some probability. The recollision electron may give rise to the emission of an attosecond photon burst. The various harmonic frequencies correspond to different field-driven electron trajectories resulting in different kinetic energies at the recombination time. On recombination the free and the bound components of the total wavefunction interfere, producing an oscillating dipole that emits light. During this process, the kinetic energy, amplitude and phase of the recollision electron wavepacket is transferred to the photon pulse. It is of great importance to control the waveform and the shape of the laser driving pulse, since these two magnitudes control the kinetic energy, amplitude and phase of the recollision electron wavepacket and as a result the attosecond pulse that it is produced as we will see later.

ii. Modeling HHG

Given a single atom in a classical electromagnetic field, we can solve the Schrödinger equation using the following approximations [8]: (i) all atomic states except the ground state and the continuum are ignored, (ii) the depletion of the ground state can be neglected, (iii) the electron in the continuum state can be treated as a free particle moving in the electric field with no effect of V(x). Using these assumptions the time dependent wavefunction can be expanded as

[pic] (4)

where [pic]and [pic]are the ground and continuum state amplitudes respectively. We can solve the Schrödinger equation exactly in the length gauge and the time-dependent dipole moment can be evaluated as

[pic] (5)

where [pic]denotes the atomic dipole matrix element for the bound-free transition. The harmonic spectrum is the Fourier transform of the second derivative of [pic]. Another approach would be not to take the second derivative of the dipole moment but using the Ehrenefst theorem (improved TSM) [10].
[pic]

Figure 5. A partial harmonic spectrum from Neon excited by T-Sapphire (800 nm) pulse with duration 50 fsec. (Figure taken from [2])

In the harmonic spectrum (Figure 5), we see that there is a long “plateau” of constant amplitude over a large spectral range, followed by a sudden drop of the harmonic emission which is the cutoff. The cutoff corresponds to the maximum emitted photon energy. Due to the quasiperiodic repetition of the process (ionization, propagation and recombination), the resulting dipole emission spectrum is discrete and because of the central symmetry of the atomic potential, only odd harmonics separated by twice the laser frequency ω0 survive. Introducing the canonical momentum,

[pic] (6)

the dipole can be written as

[pic] (7)

with

[pic] (8)

being the quasiclassical action. Equation (7) has a nice physical interpretation as a sum of probability amplitudes corresponding to the three stages of the TSM [8]: The first term in the integral,[pic], is the probability amplitude for an electron to make a transition to the continuum at time t’(ionization). The electronic wave function is then propagated until the time t and acquires a phase factor equal to[pic]. We assume that the effects of atomic potential are small between t’ and t, so that [pic] actually describes the motion of an electron freely moving in the laser field with a constant momentum p (propagation). The electron recombines at time t with amplitude equal to [pic] (recombination). The major contributions to the integral of equation (7) come from the stationary points of the classical action, i.e. the classical trajectories,

[pic] (9)

The above expression is nothing else than the difference between the position of the free electron at birth and arrival time. So, we conclude that the stationary points of the classical action correspond to those momenta p for which the electron at time t’ (birth time) returns to the same position at time t (arrival time). Thus, the dominant contribution to the harmonic emission originates from the electrons which tunnel away from the nucleus but then reencounter it while oscillating in the laser field. For each harmonic, there is a pair of trajectories which return back to the nucleus with the same velocity and as a result the emitted photons have the same energy. The trajectory with the earlier birth time and as a result the later arrival time is named “long” trajectory, while the trajectory with the later birth time and as a result the earlier arrival time is called “short” trajectory (Figure 6). [pic]

Figure 6. The position of the electron as function of time for different “ionization times”. The driving field (E(t)=E0sin(ω0t)) is presented with blue color. The most energetic trajectory is presented with the cyan color and refers to the solution where the electron encounters the nucleus with the maximal kinetic energy. The time axis is in multiples of period.
C. Attosecond pulses

The time structure of harmonic emission forms the basis of the generation of attosecond pulses. In order to achieve emission in the fraction of a femtsecond, we need to filter a limited band of photon energies near their maximum (cutoff). For many applications, single attosecond pulses (one burst per laser pulse) are preferred. For a few-cycle pulse, the highest harmonic radiation is emitted only during the single laser cycle where the highest electron recollision energies are reached. In this case the harmonic spectrum has a smooth and unmodulated cutoff. In the time domain, the smooth spectrum at the cutoff corresponds to an isolated attosecond burst of radiation. In the case of multi-cycle laser pulses the release and recollision process is repeated periodically and the discrete structure of the harmonic spectrum is pronounced (i.e. pronounced peaks at odd multiples of the fundamental frequency). As a result not a single pulse, but a train of harmonic pulses is generated.

i. Few cycle attosecond pulses

As we have said above the smooth spectrum at the cutoff corresponds to an isolated attosecond burst of radiation. The smoothness of the cutoff and emission of single pulse depend on the carrier-envelope phase[pic].When the laser field is cosine-shaped ([pic]=0) and consists of few oscillation cycles (few cycle pulse), only one electron (“the most energetic one”) with the maximum recollision energy has enough energy to contribute to the filtered high-energy emission. Correspondingly, only a single high frequency attosecond burst of radiation is emitted (Figure 7). By appropriately changing the carrier-envelope phase, the cosine waveform of the driving laser field turns to a sinusoidally shaped one ([pic]) and as a result the attosecond photon emission changes remarkably. Instead of a single pulse, two identical bursts are transmitted to the XUV bandpass filter (Figure 7). The reason is that in this case there are two electrons which have equally high maximum recollision energy. So, two attosecond pulses are generated that are separated by half the laser optical period, because the two electrons that recollide with the maximum harmonic energy have birth and as a consequence arrival times separated by half cycle. In the harmonic frequency spectrum the additional time structure appears as a modulation close to the cutoff. The shortest duration of a single attosecond pulse is limited by the bandwidth within which only the most energetic recollision contributes to the emission. In a 5 fs, 750 nm laser pulse this bandwidth is about 10% [9]. For photon energies of ~100 eV this corresponds to a bandwidth of ~10 eV, so pulses of about 250 attoseconds are generated. For a photon energy of 1 keV, a driver laser field with the above properties will lead to a single pulse emission over a bandwidth of around 100 eV, which corresponds to 25 attoseconds [11]. Taken into account that the atomic unit of time is 24.189 attoseconds, we can say that it is possible to push the frontiers of attosecond technology near the atomic unit of time. [pic]

Figure 7. Generation of single and twin attosecond pulse. The driving wavelength is 750 nm and the laser pulse is 5 fs. a and c show the emited photon energy at each recombination event for each half cycle of the driving field. b, d show the spectra of the emitted XUV photons. By filtering a limited band of photon energies near the cutoff we get a single attosecond pulse in the case of a cosine-shaped driving field EL (a and b) and twin attosecond pulses for a sine-shaped driving field (c and d). Figure taken from [9].

ii. Ways to produce extremely short attosecond pulses

There are various paths that somebody can follow in order to generate as short as possible attosecond pulses. Manipulation of the polarization state (polarization gating) of the driver pulse enables the relative bandwidth of the single pulse emission to be broadened, since we can “switch off“ the recollision before and after the main event [9]. Another way is to control the amplitude and phase of the collected harmonic radiation [12]. The first obstacle to generate short attosecond pulses is that each harmonic can be produced in at least two ways, corresponding to the two different electron trajectories with the same return energy (“long” and “short” trajectories). These two classes of trajectories lead to completely different phase behaviors for the generated fields, so they prevent the formation of bandwidth-limited XUV pulses. Even if we consider just a single class of trajectories, the emitted XUV radiation is intrinsically frequency chirped (Figure 8). External phase compensation is necessary, otherwise the useful bandwidth over which the shortest pulses can be obtained is reduced to only a few harmonics. Implementation of polarization gating with waveform controlled, approximately two-cycle near-infrared pulses has led to a spectacular achievement: the generation of isolated XUV pulses at 36 eV photon energy with a bandwidth of 15 eV. Along with dispersion control and trajectory selection, these isolated pulses resulted in near-single-cycle XUV pulses that had duration of 130 as [1]. In [12], broadband harmonic radiation is first generated by focusing an infrared laser into a gas cell containing argon atoms (Figure 9). The emitted light then goes through a hard aperture and a thin aluminum filter that selects a 30 eV bandwidth around a 30 eV photon energy and synchronizes all the components, enabling the formation of a near-single-cycle 170 attosecond pulses. The thin aperture after the harmonic generation cell is used in order to solve the problem of the multiple trajectories that contribute to each harmonic. Long trajectories lead to spectrally broad and spatially divergent radiation and can be removed by the aperture. The negative group delay dispersion of the thin aluminum foil is used to compensate for the intrinsic chirp across a bandwidth encompassing ten harmonics generated in argon. The onset of transmission of aluminum at lower frequencies and the spectral cutoff of high harmonic emission at higher frequencies act together as a band pass filter. Confining tunnel ionization to a single wave crest at the pulse peak is another way to restrict the number of recollisions to one per laser pulse. A simple, and effective way to achieve that is by superposition of a strong few-cycle near infrared near pulse with its weaker second harmonic [13]. [pic]

Figure 8. Chirp of the trajectories. Long trajectories have negative chirp, while short trajectories have positive one.

[pic]
Figure 9. Principle of the experiment. The generated XUV radiation is compressed in two steps: amplitude and phase control using a 600 nm-thick Al film; spatial filtering with a 1.6 mm iris located 35 cm after the harmonic generation. Picture taken from [12]

3. Applications

Application of attosecond pulses for time-resolved spectroscopy has a broad impact on many areas of science. Attosecond pulses have been used to monitor inner-shell processes in the time domain, for attosecond timing of electron dynamics in HHG with respect to the driving laser field and for the study and for the control of molecular structures and dynamics.

A. Time resolved measurement of Auger decay

Pump/probe experiments are the most direct approach to trace fast dynamics in the time domain. In order to extend time-resolved (pump-probe) spectroscopy to ultrafast electronic processes which take place deep inside atoms, short wavelengths (i.e. high photon energy) and sub-femtosecond pulse duration are required. Also, isolated single pulses are required for the interpretation of the spectroscopic data. With single attosecond pulses and a precisely timed laser pulse, one can observe the atomic inner-shell process with attosecond accuracy. Drescher et al., in 2002 did the experiment [14]. Referring to Figure 10 a 97 eV, 900 attosecond pulse created from a HHG Neon source is used to photoionize a 3d electron in Krypton in a separate target jet. The photoionization process produces a short-lived vacancy in the M-shell (inner shell). This is rapidly filled by an electron from a higher energy level (outer shell). The energy lost by the electron is carried away either by an energetic XUV photon, or by a secondary (Auger) electron. The emission time of the Auger electron corresponds exactly to the lifetime of the inner-shell vacancy. The aim was to measure in real time the Auger lifetime by monitoring the Auger electron’s release time into the continuum after the sub-femtosecond 97 eV photoionizing pulse. This experiment was the first real time measurement of a fast electronic process and represented the beginning of the attophysics era. Extension of the technique to solids will enable direct experimental access to atomic-scale charge-transport phenomena in solids and surfaces for first time. Charge screening, electron-electron scattering, spin-orbit interactions, collective dynamics in metals and semiconductors evolve on a subfemtosecond to a few femtosecond scale. Real-time observation of these phenomena will help explore the limits of current technologies, such as semiconductor optoelectronics, and the potential of new technologies such as spintronics, plasmonics, molecular electronics or optical nanostructuring [9].

[pic]
Figure 10. Schematic and temporal evolution of the Auger process. Figure taken from [15]

B. Attosecond timing of electron dynamics in HHG

The TSM model of HHG that we described previously involves ionization of the electron via tunneling, classical motion under the action of the electric field and recombination with the ion by emitting a high energy photon. This process is repeated periodically at each half cycle giving rise to the discrete harmonic spectrum, where only odd harmonics separated by twice the laser frequency ω0 survive. From the theory, since the tunnel probability grows exponentially with the electric field, the electron is released close to the peak of the electric field. The classical trajectories return to the origin about a half-cycle later. It would be interesting to test experimentally the details of this scenario. This can be done using the RABITT method [2], which determines the timing of the attosecond XUV bursts with respect to the pump cycle in the second atomic jet. We should evaluate carefully all the phase shifts between the ionization and the generation jets to retrieve the timing. Factors such as the Gouy phase shift at focus, the dispersion of the gas medium and the metallic reflection at the mirror can be evaluated with precision. In the experiment [16] the attosecond pulses were found to occur [pic]attoseconds after each maximum of the fundamental electric field. In the TSM model, the kinetic energy gain in the continuum is[pic], where Up is the ponderomotive energy, t’ the birth time and t the arrival time. The photon energy is then Ip+ΔEkin. For the 15th harmonic, which is in the plateau region, the calculation yields a recombination time of the “short” trajectory of 1380 as and a long one of 2320 as. In the experiment the arrival time is [pic]as which is in excellent agreement with the arrival time of the “short” trajectory predicted from the theory and excludes the “long” trajectory. This is a confirmation that the attosecond pulse train arises from the “short” trajectories. This experiment showed that by determining the precisely all the phase delays between the harmonic generation point and the detection apparatus, one can measure the timing of the attosecond pulses in HHG with respect to the pump field cycle. The experiment was important not only because it showed that the “short” trajectory is dominant in the harmonic generation process as the theory predicted, but it was the first application of an attosecond pulse train for clocking electron dynamics in strong field interaction.

C. Study and control of molecular structure and dynamics

Molecular structure and dynamics emerge under the influence of interatomic forces that are created by electrons. The laser pulses that produce attosecond pulses are so intense that their electric fields are of the same order of magnitude with the fields that valence electrons experience in molecules and solids. Attosecond technology is naturally suited to measure molecular structure, since the wavelength of a typical recollision electron (~1-2[pic]) matches almost exactly the interatomic sepration in matter (~1[pic]) and the typical structure size of the valence electron orbitals (~1[pic]). The recollision electron can be used for measuring the molecular structure. The recollision electron wave can diffract from its parent ion and by measuring its 3D electron momentum, we gain information required to reconstruct atomic positions within the molecule. This approach to molecular imaging is called “laser-induced electron diffraction” [9] and makes use of the spatial coherence of the recollision electron. Moreover, the fact that the recollision electron is coherent in ways that an externally generated electron cannot be, opens the opportunity for electron holography. Another opportunity for molecular imaging due to the unique properties of the recollision electron is electron interferometry. The recollision electron wavepacket is split from its parent orbital and when it returns back it interferes with the initial orbital. As we rotate the molecule, the interference changes. Recording the spectrum as a function of molecular alignment, we obtain a tomographic image of the orbital (Figure 11). The technique of molecular orbital tomography uses laser pulses with durations of 25 fs or less [A. Scrinzi, M.Y. Ivanov, R. Kienberger and D. Villeneuve].

[pic]
Figure 11. Measured orbital of N2. Figure taken from [9].

4. Conclusion

Attosecond science is a revolution in technology that became a reality with HHG. It has opened the door to real-time observation and time-domain control of atomic-scale electron dynamics. Imaging the position of both basic ingredients of matter –nuclei and electrons- with sub-atomic resolution simultaneously in time and space is possible using this technology. This will have impact well beyond physics, influencing chemistry, biology and future technologies.

5. References

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Only one electron has the maximum recollision energy

Two electrons have equally high maximum recollision energy

most energetic

long

short