• Research
• A Perfect Image from a...
• Timing of Femtosecond ...
• Soft X-ray Spectroscop...
• Multiphoton Ionization

Multiphoton Ionization – New Opportunities at FLASH

Multiphoton processes cover areas as diverse as precision measurements, studies of ultrafast dynamics, laser acceleration of charged particles, laser machining of solid-state materials and medical applications. FLASH allows for the extension of these efforts from the infrared and visible part of the spectrum into the soft X-ray regime.

With the advent of lasers the nonlinear, or multiphoton, interactions between radiation and matter have become a key area in basic and applied research. In nonlinear processes the response of matter to intense radiation is no longer proportional to the intensity of the radiation but depends on a higher power of the intensity, giving rise to dramatic new effects which have been studied extensively using infrared or visible lasers.

Free-electron lasers like FLASH and the planned European facility XFEL will extend these studies towards the much shorter wavelengths of soft and hard X-rays, respectively. This new opportunity will greatly improve our knowledge of the fundamental interactions between radiation and matter, because a number of effects characterizing nonlinear processes at longer wavelengths vanish or diminish in the X-ray regime. Especially for atoms this considerably simplifies the situation and allows for stringent tests of the most advanced theoretical approaches. In addition, however, novel phenomena not present in the visible will emerge at X-ray energies like e.g. nonlinear Compton processes or simultaneous photon scattering (elastic and inelastic) and absorption.

Infrared and Visible Lasers

The investigation of nonlinear interactions of intense laser radiation with atoms and molecules has already granted deep insights into the fundamental multiphoton processes. Exposing atoms to intense laser beams can result in multiple ionization, the generation of photoelectron sidebands in the Above-Threshold Ionization (ATI) process, the launch of rotational or vibrational wavepackets in ground, excited or ionized states of molecules, and in the emission of higher harmonics of the fundamental laser frequency at much shorter wavelengths (High Harmonic Generation, HHG) and attosecond pulse durations.

Since the ionization potential of atoms is greater than the photon energy in the infrared and visible parts of the spectrum, the atom has to absorb several photons to be ionized, and hence this process is called multiphoton ionization. However, at very high intensities the radiation field deforms the ionic potential so strongly that bound electrons can tunnel through the remaining potential barrier in a process called tunneling ionization. A third mechanism called rescattering also contributes to the ionization. In this process an emitted electron is accelerated and driven back to the atomic core by the laser field. In the encounter with the nucleus it can k­ick out further electrons. Close to the atomic core, conserving energy and momentum, the electron can also absorb further laser photons (ATI) or emit higher harmonics of the fundamental laser frequency (HHG). At high intensities all these processes result in multiple ionization removing several electrons from the atom. A central parameter, called the Keldysh parameter, roughly determines which process dominates.

At FLASH, nonlinear interactions between light and matter can be studied at the higher photon energies in the vacuum- ultraviolet, extreme-ultraviolet and soft X-ray regimes. Here the rescattering ionization, the above-threshold ionization and the higher harmonics all vanish, and the contribution from tunneling ionization decreases. Thus, multiphoton ionization is expected to dominate the multiple ionization processes. This is why the nonlinear interactions, which can be explored using the intense FEL pulses, are much simpler than the processes hitherto studied using infrared and visible lasers.

---

The Keldysh Parameter

The Keldysh parameter determines whether multiphoton or tunneling ionization dominates the nonlinear ionization processes, where the ponderomotive energy U_p

denotes the mean energy transferred to an electron in its oscillatory motion caused by the electromagnetic laser field. For >1 multiphoton ionization dominates, whereas for < 0.5 tunneling ionization takes over. Rescattering ionization contributes to the ionization for U_P larger than the atom’s Ionization Potential IP.

Since the ponderomotive energy scales with the inverse square root (hν)^-2 of the photon energy, the rescattering ionization, the above-threshold ionization and the higher harmonic generation all vanish at higher photon energies and not exceedingly large intensities. The contribution of tunneling ionization also decreases because the Keldysh parameter increases with increasing photon energy.

For example at an intensity of 10¹⁶ Wcm^-2, achievable with FLASH at a photon energy of 92.5 eV corresponding to a wavelength of 13.4 nm, the ponderomotive energy amounts to 0.16 eV. A similar intensity at 1.55 eV photon energy, corresponding to a wavelength of 800 nm in the infrared, generates a ponderomotive energy of 600 eV. For the rare gas xenon with an ionization potential equal to 12.1 eV, the above-mentioned FLASH parameters result in a Keldysh parameter = 8.7.

---

---

Doubly and Triply Charged Argon Ions

Perturbation theory predicts that the ionization yield Y should be proportional to the n^th power of the intensity Y ~ Iⁿ, where n is the number of photons needed for ionization. In the double ionization of argon atoms non-sequential ionization and sequential ionization both require two photons. This is consistent with the exponent n = 2.0 + 0.1 extracted from the data displayed in (a). The exponent of n = 3.5 + 0.2 obtained by the analysis of the Ar³⁺ data given in (b) indicates that both non-sequential ionization and sequential ionization comparably contribute to the creation of Ar³⁺ ions.

---

Few-Photon Multiple Ionization at FLASH

The interaction of two or three photons with the valence electrons of an atom represents one of the most fundamental nonlinear processes, and detailed studies of these processes are of decisive importance to advance nonlinear theories.

At FLASH such nonlinear interactions have been studied by a group of scientists from MPI Heidelberg, University of Frank­furt, Stockholm University, University of Crete, and DESY as a function of the intensity in a series of experiments where argon atoms were multiply ionized with focused, approximately 30-femtosecond pulses at a photon energy of 38.8 eV corresponding to a wavelength of 32 nm. At the lower intensities studied the yield of doubly charged argon ions Ar²⁺ dominates, whereas the yield of triply charged argon ions Ar³⁺ increases with increasing intensity.

The first three ionization potentials of argon are 15.8 eV, 27.7 eV and 40.7 eV, respectively. Thus, a minimum energy of 43.5 eV is required to doubly ionize argon, and 84.2 eV are needed for the removal of three electrons. Two basic dynamical processes contribute to the multiple ionization. In sequential ionization the argon atom is ionized step by step “by one photon at a time”, while in non-sequential ionization several photons act simultaneously. Double ionization of argon by the non-sequential pathway requires the ejection of two electrons by simultaneous absorption of two photons, and simultaneous absorption of three photons is needed for triple ionization.

In the sequential process double ionization occurs in two steps. First the argon atom gets singly ionized by the absorption of one photon and then, in the second step, another electron is removed from the ion within the same FEL pulse. Here triple ionization requires the absorption of four photons. The first photon ionizes the atom to Ar⁺. In the second step one additional photon ionizes the singly charged ion to Ar²⁺, and in the third step two photons further ionizes the doubly charged ion to Ar³⁺. All these steps are induced by the same pulse.

According to theory, double ionization of argon requires two photons by both of the two ionization processes, which is consistent with the experimental results. The analysis of the Ar³⁺ data indicates that both non-sequential ionization and sequential ionization comparably contribute to the creation of the triply charged argon ions. Similar data on the multiple ionization of neon atoms corroborate the growing importance of sequential ionization with increasing intensity.

All these first experimental results show that FLASH already opens up new vistas in science and technology.