P.B. Corkum and Zenghu Chang
The building block of attosecond pulse generation. An electron wave packet is created from a bound electron by tunneling through the potential barrier jointly formed by the ion and laser field. Components of the wave packet move in a classical-like manner, as illustrated by the orange arrow. Since many photons are involved, classical physics is a valuable guide to intuition. When the electron re-collides, it can produce an XUV photon, represented by the red arrow. Note how closely this process is related to photoelectron spectroscopy, but in reverse.
Extraction of single isolated attosecond pulses with a double optical gating.
Finally, the electron can recombine with its parent ion, producing a photon. This is the origin of attosecond extreme ultraviolet (XUV) pulses. The re-collision electron’s amplitude, phase and energy are transferred to the photon through the oscillating dipole created by the interference of the two parts of the wavefunction—the bound electron wavefunction and the re-collision electron wave packet. In other words, the XUV pulse is a replica of the re-collision electron pulse viewed through the transition moment.
The bottom figure on the right clarifies how, at the single atom level, attosecond XUV radiation arises from the dipole oscillation induced by the interference between the re-collision electron wave packet and the remaining bound state population. The analogy with an interferometer is obvious. Tunneling is the beam splitter. The electron motion in response to the laser field delays one arm of the interferometer—precisely controllable with light. The interference (or time-dependent dipole moment) is read in the emitted attosecond pulse. The amplitude, energy and phase of the re-collision electron are transferred to light through the dipole moment (the transition moment).
Attosecond pulse trains and gating
We have concentrated on the response of a single atom. However, an experiment is a multi-atom measurement aided by phase matching. In a gas jet, cell or hollow fiber, each atom emits identically with all others, synchronized by the fundamental beam. Provided that the fundamental and the XUV propagate with the same phase velocity, a macroscopic signal is produced. Phase matching is as important in attosecond pulse generation as in second harmonic or optical parametric generation.
When atoms are driven by a many-cycle laser pulse, one attosecond XUV pulse is generated every half of a laser period. As the laser approaches a single optical cycle, the cycle-to-cycle laser amplitude variation becomes significant. As a result, the spectrum of the attosecond pulses generated near the peak of the laser pulse envelope extends to a shorter XUV wavelength range compared to the adjacent attosecond pulses when the CEP of the pump laser is set to zero. A single isolated pulse as short as 80 as has been obtained by selecting the cut-off region of the XUV spectrum with a high-pass filter, using less than 4fs pump lasers.
At lower XUV frequencies (the so-called plateau region), single isolated attosecond pulses can be extracted by a scheme called “polarization gating.” This approach uses a laser field with a time-dependent ellipticity. XUV attosecond pulses can only be efficiently generated during the brief interval dtG, when the field is near linearly polarized. So far, the shortest single isolated XUV pulses in the plateau region, 130 as, have been produced this way.
A method called “double optical gating” allows single isolated attosecond pulses to be generated with greater-than-10-fs pump lasers. A second harmonic field is added to the fundamental field to break the symmetry. Ionization only occurs once per cycle and therefore the spacing between the adjacent attosecond pulses to one optical cycle. Then a polarization gate width, δtG, equal to one optical cycle is sufficient to select one isolated XUV pulse.
Measuring attosecond optical pulses
Having produced attosecond optical (and, from the perspective of the ion, electron) pulses, we must confirm their duration. Conventional methods of measuring optical pulses rely upon low-order nonlinear optics. Extending their methods to attosecond pulses has proven difficult.
Therefore, it is natural to look toward extreme nonlinear optics, the method that produced attosecond pulses in the first place. Here, we have an extremely valuable resource. Every attosecond pulse is perfectly synchronized to the time-dependent field of an infrared pulse (as an optical pulse can be synchronized with THz radiation). This is one of the major tools of attosecond science.
Photo-ionization of a simple atom produces a photo-electron replica of the attosecond pulse. If the replica is created in the presence of the phase infrared field, it will be deflected or accelerated by a rapidly varying field. Its final momentum is determined by the spectrum of the attosecond pulse and the moment of birth of a photoelectron into the field.
Thus, the momentum distribution of the photoelectrons contains all the information needed to determine the pulse duration. The concept is very similar to a conventional streak camera. The attosecond streak camera can be generalized to FROG- or SPIDER-like methods. Photoelectron replicas created by atomic ionization in the presence of an infrared field can measure the duration of isolated attosecond pulses and the individual pulses of attosecond trains.
We emphasized earlier that an attosecond pulse was a replica of a pre-existing re-collision electron pulse (as seen through the transition moment). Why, you might ask, is a new photoelectron replica needed for measurement when we already have a pre-existing one? In fact, it is not necessary. Attosecond pulses can be measured in the medium in which they are created.
This is a very un-laser-like idea—generation and measurement are entwined. It opens the exciting prospect that attosecond metrology can be generalized to other high-order nonlinear optical processes such as inelastic scattering. Never before has it seemed possible to find systematic methods of measuring the dynamics of collision-induced processes. To us, both optical scientists, it seems inevitable that optical techniques will be increasingly transferred to collision physics.
Time-resolved experiments
In conventional ultrafast technology, measuring dynamics is very similar to measuring optical pulses. If the pulse is unknown, then one chooses a known phenomenon (for example, frequency doubling) to characterize it. If the pulse is known, one can choose an unknown phenomenon and study its response. It is no different in attosecond science.
It is useful to note a few achievements of attosecond science, some of which rely on the attosecond streak camera:
• Auger recombination has been time-resolved in krypton.
• The time-dependent field of a laser been has been traced.
• Electron photoemission dynamics has been measured in tungsten.