Tomography reconstruction
Written by: Constant Schouder
December 6, 2017
Introduction
Strong-field physics has attracted much interest over the last decade [[1][2]] thanks to the development of optical sources (e.g. lasers) with intense electromagnetic fields. These fields are able to compete against the ‘Coulombic interaction’, the force acting between charged particles.The development and improvement of new laser sources, such as free-electron lasers and synchrotrons has allowed scientists significant control over both the accessible wavelengths and pulse durations of the optical source. Fine control of these two parameters has made the study of ‘ultrafast’ dynamic processes possible [[3]], such as electron density change and nuclear dynamics, on the attosecond (10−18s) and femtosecond (10−15s) scale, respectively. Importantly, achieving an understanding of the inner-relaxation behaviour of electronic populations and the correlation between electronic states provides information on photo-electrons. Photo-electrons are precious ‘reporters’ as they can contain valuable information on the system being studied. For example photo-electrons can help answer questions such as: Which orbitals can be ionized? What is the interaction between the electron and its cation? Is the cation a meta-stable state? How does the system relax?
In the strong-field description, two ‘limiting’ cases are usually defined by the use of a dimensionless parameter, the Keldysh parameter [[4]], a bench- mark to discriminate the two regimes (equation 1).
(1)
The two parameters in the Keldysh parameter are the ionization potential (Ip), the lowest energy needed for a system to lose an electron, and Up, the ponderomotive energy, which is the mean kinetic energy that an electron acquires in an electric field. Up is the most important parameter since it depends on both the laser intensity (I) and the wavelength (λ) which are two parameters that scientists can control as seen in equation 2.
(2)
The Keldysh parameter separates the multiphoton-regime (γ >> 1) from the tunnelling regime (γ << 1), sometimes called the quasi-static regime. However it should be noted that recent studies show that a value of γ << 1 alone is not sufficient to claim that the tunnelling regime is the most favourable state since high photon energy (low λ) and high intensity (I) can keep γ constant even when the tunnelling regime should not be accessible. [[5]] In light of this, some voices in the community have highlighted the need for another parameter to be considered to differentiate those two regimes. This parameter is the ratio between the classical frequency of an orbital electron (Ωe) and the frequency of the field (ω) [[6]]. Equation 3 explains this model wherein it is possible for the tunnelling regime to dominate the multiphoton regime.
(3)
In this area of research many tools have recently been developed to control what is commonly referred to as the ‘molecular frame’. Usually when a measurement is taken on a system, the measurement is related to the ‘laboratory frame’ meaning the results do not necessarily coincide with those expected for system under study. However, it is now possible to fix this disconnect thanks to intense laser using second-order interaction between the induced dipole and the electric field or using a ‘kick’ experiment. A ‘kick’ experiment is where a short laser ‘kick’ (of the order of hundred of femtoseconds) is used to start rotating the system being studied over a picoseconds (10−12s) time frame. This allows us to probe the test species for any differences e.g. between the ‘molecular frame’, and the ‘laboratory frame’ [[7]]. It is also possible to numerically simulate these processes for linear pulses thanks to the distribution of a number of free ‘calculators’ such as the one developed in our group [[8]].
My area of research aims to resolve different regimes of strong-field physics which are not well understood. Strong-field physics is usually examined in a semi-classical way using classical-field approaches, due to the high intensity of the laser source used in the Hamiltonian of the system. However, the electronic description of atomic/molecular systems requires quantum treatment which is still too computationally expensive for complex molecules. Moreover, the Born-Oppenheimer approximation used in strong-field physics is less reliable for light atoms which have motions on the femtosecond timescale making crossing between electronic states unavoidable [[9],[10]]. If we can gain an understanding of these mechanics it would be a significant breakthrough and would allow us to access the “femto-atto” chemistry realm where one could create new molecules, or visualise electronic density dynamics [[11]].
Our experiment
Our experiment uses a circular pulse with a duration of 30 fs and a central wave- length of 1850 nm. We studied three different systems, anthracene, naphthalene and biphenyl which all have ionization potentials of 8 eV. In these experiments, the used intensities range from 10 to 100 TW/cm2, which is equivalent to a Keldysh parameter of (0.4 and 0.6), with a ratio R ≈ 75.
A second pulse is then used to 3D-align the system. This pulse has an elliptical polarization represented by the ratio ε between the two orthogonal components of the electric field. It should be noted that ε = 0 and ε = 1 represents linear polarization and circular polarization, respectively. We used ε = 1/3 in our experiment.
The aim of this experiment is to reconstruct the 3D-photoelectron momentum distribution of the test species. To do this, we must collect the photoelectron momentum data from 0 to 180 degrees for the species as shown in the figure above. We then use velocity map imaging [[12]] to collect the 2D-photoelectron momentum (multichannel plate + CCD camera). The final dimension is extracted by using an Inverse Radon transform [[13]].
Personal experience as an Early Stage Researcher (ESR)
The great advantage of being an ASPIRE ESR is the opportunity to meet a lot of people working in a similar field of science. It is of great importance to follow the evolution of research connected to your field, and if you are not vigilant it is easy to only focus on your specific domain. The ASPIRE network has allowed me to access to a broad range of colleagues where I get to discuss and understand the problems encountered by others in their research. Moreover, as an ASPIRE ESR I get a unique insight into how Academic and Industrial partners’ needs often overlap and how both sectors require equipment capable of delivering high accuracy, stability and control.
References
[1] Benjamin Wolter, Michael G. Pullen, Matthias Baudisch, Michele Sclafani, Micha ̈el Hemmer, Arne Senftleben, Claus Dieter Schr ̈oter, Joachim Ullrich, Robert Moshammer, and Jens Biegert. Strong-field physics with Mid-IR Fields. Phys. Rev. X, 5:021034, Jun 2015.
[2] Louis DiMauro, Mikhail Frolov, Kenichi L Ishikawa, and Misha Ivanov. 50 years of optical tunneling. Journal of Physics B: Atomic, Molecular and Optical Physics, 47(20):200301, 2014.
[3] Franck L ́epine, Misha Y. Ivanov, and Marc J. J. Vrakking. Attosecond molecular dynamics: fact or fiction? Nature Photonics, 8:195 EP –, Feb 2014. Review Article.
[4] L. V. Keldysh. Iionization in the field of a strong electromagnetic wave. SOVIET PHYSICS JETP, 20, May 1965.
[5] H. R. Reiss. Unsuitability of the keldysh parameter for laser fields. Phys. Rev. A, 82:023418, Aug 2010.
[6] Turker Topcu and Francis Robicheaux. Dichotomy between tunneling and multiphoton ionization in atomic photoionization: Keldysh parameter γ versus scaled frequency Ω. Phys. Rev. A, 86:053407, Nov 2012.
[7] Claude Marceau, Varun Makhija, Dominique Platzer, A. Yu. Naumov, P. B. Corkum, Albert Stolow, D. M. Villeneuve, and Paul Hockett. Molecu- lar frame reconstruction using time-domain photoionization interferometry. Phys. Rev. Lett., 119:083401, Aug 2017.
[8] Anders Aspegren Søndergaard, Benjamin Shepperson, and Henrik Stapelfeldt. Nonadiabatic laser-induced alignment of molecules: Recon- structing ⟨cos2 θ⟩ directly from ⟨cos2 θ2D⟩ by fourier analysis. The Journal of Chemical Physics, 147(1):013905, 2017.
[9] Laurie J. Butler. Chemical reaction dynamics beyond the born- oppenheimer approximation. Annual Review of Physical Chemistry, 49(1):125–171, 1998. PMID: 15012427.
[10] Wolfgang Domcke and David R. Yarkony. Role of conical intersections in molecular spectroscopy and photoinduced chemical dynamics. Annual Review of Physical Chemistry, 63(1):325–352, 2012. PMID: 22475338.
[11] G. Sansone, F. Kelkensberg, J. F. P ́erez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. L ́epine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Yu Ivanov, M. Nisoli, F. Mart ́ın, and M. J. J. Vrakking. Electron lo- calization following attosecond molecular photoionization. Nature, 465:763 EP –, Jun 2010.
[12] A. T. J. B. Eppink and D. H. Parker. Velocity map imaging of ions and electrons using electrostatic lenses: Application in photoelectron and photofragment ion imaging of molecular oxygen. Review of Scientific In- struments, 68:3477–3484, September 1997.
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[13] Dudgeon and Mersereau. Multidimensional digital signal processing. Prentice-Hall, 1984