High-order harmonic generation (HHG), a non-perturbative nonlinear light-matter interaction resulting in coherent emission of high-frequency light, has demonstrated promise as an optical probe of carrier dynamics, structural symmetries, and other properties of solids. HHG from bulk solids in transmission geometry, however, is influenced by nonlinear propagation of the driving laser, which leads to spectral skewing and temporal phase variations in the harmonic emission. These effects obscure the microscopic underlying physics, making HHG-based spectroscopy of bulk solids difficult to interpret. HHG in few-to mono-layer materials, however, avoids strong nonlinear propagation effects, and can provide novel material properties for HHG studies. In this work, I compare HHG driven by femtosecond mid-infrared laser pulses in bulk and thin film solids. First, HHG generated from epitaxial ZnO thin films grown using different preparations is compared with HHG from bulk ZnO. I identify spectral signatures that result from nonlinear propagation in bulk samples, while thin films generally yield clean harmonic spectra with features that depend on the crystal growth and preparation. Specifically, I find that as-grown plasma ALD (atomic layer deposition) samples yield monocrystalline polar films, which is modified by annealing. The dependence of the harmonic yield on thickness of the nano-meter scale films was also experimentally measured and found to agree with simulations which incorporated nonlinear conductivity and linear propagation effects. Next, I examine the carrier envelope phase (CEP) dependence of HHG from bulk and thin-film ZnO. I observed a stronger-than-expected sensitivity of the HHG from bulk ZnO to CEP, which results from nonlinear self-compression of the pulse to single-cycle durations. Finally, experimental studies of HHG from novel van der Waals crystals are presented. Together, these results suggest novel frontiers for HHG from few-layer materials.

Doctor of Philosophy / Department of Physics / Chii-Dong Lin / In this thesis, we establish the theoretical tools to investigate high-order harmonic generation (HHG) by intense infrared lasers in a gaseous medium. The macroscopic propagation of both the fundamental and the harmonic fields is taken into account by solving Maxwell’s wave equations, while the single-atom (or single-molecule) response is obtained by quantitative rescattering theory. The initial spatial mode of the fundamental laser is assumed either a Gaussian or a truncated Bessel beam. On the examples of Ar, N[subscript]2 and CO[subscript]2, we demonstrate that the available experimental HHG spectra with isotropic and aligned target media can be accurately reproduced theoretically even though the HHG spectra are sensitive to the experimental conditions. We show that the macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of the target only. The factorization makes it possible to retrieve the single-atom or single-molecule structure information from experimental HHG spectra. As for the multiple molecular orbital contribution in HHG, it causes the disappearance of the minimum in the HHG spectrum of aligned N[subscript]2 with the increase of laser intensity, and the position of minimum in HHG spectrum of aligned CO[subscript]2 depending on many factors is also attributed to it, which could explain why the minima observed in different laboratories may differ. For an important application of HHG as ultrashort light source, we show that measured continuous harmonic spectrum of Xe due to the reshaping of the fundamental laser field can be used to produce an isolated attosecond pulse by spectral and spatial filtering in the far field. For on-going application of using HHG to ionize aligned molecules, we present the photoelectron angular distribution from aligned N[subscript]2 and CO[subscript]2 in the laboratory frame, which can be compared directly with future experiments.

Understanding the electronic structure and dynamics of cyclic organic molecules is becoming increasingly the subject of investigations from different perspectives due to their unique chemical and physical properties. Since they are largely involved in the biochemistry of living organisms, studies on this class of compounds are also valuable to understand biologically relevant complex systems. Compared to other techniques, high-order harmonic generation (HHG) has been increasingly considered as a powerful spectroscopic tool with Angstrom spatial and attosecond temporal resolutions. This thesis demonstrates that high-order harmonic spectroscopy is capable of providing structural and dynamical information on the electronic systems of representative cyclic organic molecules comprising randomly oriented five-membered or six-membered rings. The first part of this thesis shows that the HHG from these molecules is sensitive to their aromatic character, which results from the de-localized pi electrons, and can potentially be a useful qualitative measure of aromaticity. We show that the advantage of utilizing HHG in this direction stems from the result that only pi molecular orbitals, associated with aromatcity, are responsible for the HHG emission in aromatic systems. The capability of HHG to distinguish cyclic isomers is demonstrated in the case of xylene molecules. Supported by numerical calculations, differences in the isomers are attributed to both tunnel ionization and photorecombination, the first and last steps of HHG. These results enable further HHG-based time-resolved studies of the dynamics associated with isomeric effects that these molecules exhibit. The present work also challenges the well-established prediction that strong field ionization from a molecular orbital is suppressed along nodal planes, where the electron density is zero. In fact, our study shows that considerable tunnel ionization in some cyclic molecules can occur near or along nodal planes. This unusual ionization is reported to have its signature on the quantitative and qualitative dependence of harmonic yield on laser ellipticity. The high symmetry displayed by the cyclic molecule, 1,4 cyclohexadiene, is shown to leave its imprints on the HHG in the form of structural interferences even if the target is randomly oriented. Two-color HHG from this molecule also indicates that hole dynamics could be involved in the generation process. A general study on high harmonic spectroscopy of the Cooper minimum in molecules is also reported. The presence of this minimum could affect the interpretation of harmonics spectra in any molecule containing S or Cl atoms. The molecular environment is shown to influence the position of this spectral modulation.

La chiralité est une propriété géométrique caractérisant les objets qui ne sont pas superposables à leur image dans un miroir. Nos mains en sont un exemple emblématique, puisqu’elles existent sous deux formes différentes droite et gauche. Si la chiralité s'observe à toutes les échelles de l'univers, elle joue un rôle particulièrement important en chimie. Une molécule chirale et son image miroir peuvent réagir différemment avec leur environnement et être thérapeutiques ou toxiques. Ces effets ont évidemment d'immenses répercussions sur le règne animal et végétal. Il apparaît alors clairement qu'il est essentiel d’étudier précisément les dynamiques des réactions chimiques chirales.Dans cette thèse, nous avons étudié les dynamiques ultrarapides de molécules chirales par des sources lasers de durée femtosecondes).($10^{-15}$ s). La chiralité moléculaire étant généralement difficile à détecter, nous avons ici utilisé une technique récente, le dichroïsme circulaire de photoélectrons (PECD) qui permet de générer un signal chiral très important. Nous avons ainsi observé des dynamiques moléculaires ultrarapides jusqu'à l'échelle attoseconde ($10^{-18}$ s), et mis en avant des dynamiques de relaxation et d'ionisation encore jamais observées.Parallèlement à ces études résolues en temps, nous avons développé plusieurs expériences employant une nouvelle source laser Yb fibrée à haute cadence et grande puissance moyenne. Nous avons développé une nouvelle méthode, par extension du PECD, qui nous a permis de mesurer la compositions d'échantillons chiraux rapidement avec une grande précision. Enfin, nous avons développé une ligne de lumière XUV ultrabrève de très haute brillance ($sim 2$ mW). Cette source, couplée à un détecteur de photoélectrons et photoions en coïncidence, servira à étudier les mécanismes de reconnaissance chirale. / Chirality is a geometric property that characterizes objects that cannot be superposed on their mirror image. Our hands are an emblematic example of this, since they exist in two different forms, right and left. While chirality is observed at all scales in the universe, it plays a particularly important role in chemistry. A chiral molecule and its mirror image can react differently with their environment and be therapeutic or toxic. These effects obviously have immense repercussions on the animal and plant kingdom. It then becomes clear that it is essential to study precisely the dynamics of chiral chemical reactions.In this thesis, we studied the ultrafast dynamics of chiral molecules by laser sources of femtosecond duration ($10^{-15}$ s). Molecular chirality is generally difficult to detect, so we have used a recent technique, circular photoelectron dichroism (PECD), to generate a very important chiral signal. We have thus observed ultrafast molecular dynamics at the attosecond scale ($10^{-18}$ s), and highlighted relaxation and ionization dynamics never observed before.In parallel to these time-resolved studies, we have developed several experiments using a new high repetition rate, high mean power Yb fiber laser. We have developed a new method, by extending the PECD, that has allowed us to measure the composition of chiral samples quickly and accurately. Finally, we have developed an ultra-short XUV beamline with very high brightness ($sim 2$ mW). This source, coupled with a photoelectron and photoion coincidence detector, will be used to study chiral recognition mechanisms.

No description available.

Mon travail pendant cette thèse a d’abord été le développement d’une source de génération d’harmoniques d’ordre élevé basée sur une chaîne laser femtoseconde amplifiée (Saphir-Titane) fonctionnant à une cadence de 1 kHz (AURORE). Une ligne de lumière construite au CELIA permet de fournir un faisceau focalisé VUV-XUV femtoseconde, monochromatique dans une région spectrale comprise entre 10 nm et 73 nm environ (17 eV à 120 eV). Cette installation expérimentale est en fonctionnement et est parmi les toutes premières lignes à être mise en service pour la communauté scientifique française et étrangère. J’ai également mis en place une installation d'étude des cinétiques de luminescence avec résolution temporelle sub-picoseconde (450 fs) par mélange de fréquences. Le thème général de ce travail est l’étude des processus de relaxation et d'interaction entre les excitations électroniques créées par des impulsions ultra brèves femtosecondes de photons IR, UV et VUV-XUV dans les solides diélectriques massifs et des nano particules. L’observable principale utilisée est la luminescence émise par ces systèmes, résolue spectralement et en temps sur des échelles allant de la µs à des temps sub picosecondes. Ce travail a abouti à une avancée sensible de la description des processus principaux de formation et d’évolution des excitations électroniques. La comparaison et l’interprétation des données expérimentales obtenues pour des nano particules et des cristaux ont permis d’élucider certaines propriétés spécifiques de ces systèmes. / The work during this Ph.D. was a development of a source of high order harmonics generation based on amplified Ti:Sapphire femtosecond laser with repetition rate 1kHz (AURORE). The beam line constructed in CELIA has on its exit a VUV-XUV focalized beam; it may has wide spectrum or monochromatic in spectral range from 10nm up to 73nm (17-120eV). This beam line is in operation and is using for experiments for solid state VUV spectroscopy, photoelectron spectroscopy etc. Also it was installed a system for detection of luminescence with sub-picosecond time resolution (450fs) based on the nonlinear effect – generation of sum of two light frequencies. The main subject of this work was the study of processes of relaxation and interaction of electronic excitations, created by ultra-short pulse of IR, UV or XUV in dielectric crystals and nanoparticles. Out method is based on observation of luminescence with spectral and time resolution up to sub-picosecond temporal resolution. This study has given new experimental results for description of fundamental processes of creation and evolution of electronic excitations. Comparison and interpretation of experimental data of semiconductor nano-particles and monocrystals gave some interpretations of extra-fast luminescence of these systems.

La génération d'harmoniques d'ordre élevé (HHG) est un processus non linéaire extrême qui peut être compris intuitivement par la séquence de trois étapes: i) ionisation tunnel de la cible atome/ molécule et création d'un paquet d'ondes électronique (EWP) dans le continuum, ii) accélération de l'EWP par le champ laser intense et iii) recombinaison avec le cœur ionique et émission d’une impulsion attoseconde de lumière cohérente dans l’extrême UV (XUV). La HHG fournit ainsi une source ultracourte accordable dans l’XUV/ rayons X mous à l'échelle de temps attoseconde pour les applications (schéma «direct»). Dans le même temps, elle encode de manière cohérente dans le rayonnement XUV émis la structure et la dynamique de réarrangement de charge des atomes/molécules qui rayonnent (schéma «auto-sonde» ou Spectroscopie d'harmoniques d'ordre élevé). Cette thèse est consacrée à ces deux schémas d'application en attophysique basés sur une caractérisation et un contrôle avancés de l'émission attoseconde. Dans ce qu'on appelle le schème "auto-sonde", la dernière étape de la HHG, la recombinaison électron-ion peut être considérée comme un procédé de sonde et l'émission peut coder des informations fructueuses sur le système se recombinant, telles que la structure moléculaire et la dynamique. Dans la première partie, nous avons effectué la spectroscopie harmonique de molécules N₂O et CO₂ qui sont alignées par rapport à la polarisation du laser générateur. Nous avons implémenté deux méthodes basées respectivement sur l'interférométrie optique et quantique afin de caractériser l'amplitude et la phase de l'émission attoseconde en fonction à la fois de l'énergie des photons et de l'angle d'alignement. Nous avons découvert de nouveaux effets dans la génération d'harmoniques qui ne peuvent pas être expliqués par la structure de l'orbitale moléculaire la plus haute occupée (HOMO). Au lieu de cela, nous avons trouvé que pendant l'interaction avec le champ laser, deux états électroniques sont excitées de manière cohérente dans l'ion moléculaire, formant un paquet d'ondes de «trou» se déplaçant à une échelle de temps attoseconde dans la molécule après l’ionisation tunnel. Nous nous sommes concentrés sur l'exploration de ce mouvement électronique cohérent à l'intérieur de la molécule, et comparé les mesures de N₂O et CO₂. La différence frappante dans la phase harmonique nous a conduits à l'élaboration d'un modèle multi-canal permettant l'extraction de l’amplitude et de la phase relative des deux canaux impliqués dans l'émission. Un déphasage inattendu de pi/4 entre les deux canaux est obtenu. En outre, nous avons étudié le profil des impulsions attosecondes émises par ces deux molécules, et nous avons proposé un moyen simple mais flexible pour la réalisation de la mise en forme d’impulsions attosecondes. Dans la deuxième partie, la spectroscopie harmonique a été étendue à d'autres systèmes moléculaires, y compris certaines molécules relativement complexes, par exemple, SF₆ et petits hydrocarbures (méthane, éthane, éthylène, acétylène). Elle a révélé de nombreux résultats intéressants tels que des distorsions de phase observées pour la première fois. Dans le schéma «direct», nous avons photoionisé des atomes de gaz rares en utilisant des impulsions attosecondes bien caractérisées combinées avec un laser infrarouge d’habillage avec un délai contrôlé, stabilisé à environ ± 60 as. Nous avons mesuré des différences marquées dans les distributions angulaires des photoélectrons, en fonction du nombre de photons IR échangés. Jointes à notre interprétation théorique, ces observations apportent de nouvelles connaissances sur la dynamique de cette classe de processus de photo-ionisation multi-couleurs qui sont une étape clé vers l'étude de la photo-ionisation dans le domaine temporel avec une résolution attoseconde. / High-order Harmonic Generation (HHG) is an extreme nonlinear process that can be intuitively understood as the sequence of 3 steps: i) tunnel ionization of the target atom/molecule, creating an electronic wave packet (EWP) in the continuum, ii) acceleration of the EWP by the strong laser field and iii) recombination to the core with emission of an attosecond burst of XUV coherent light. HHG thus provides a tunable ultrashort tabletop source of XUV/Soft X-ray radiation on attosecond time scale for applications (‘direct’ scheme). At the same time, it encodes coherently in the XUV radiation the structure and dynamical charge rearrangement of the radiating atoms/molecules (‘self-probing’ scheme or High Harmonic Spectroscopy). This thesis is dedicated to both application schemes in attophysics based on advanced characterization and control of the attosecond emission. In the so-called ‘self-probing’ scheme, the last step of HHG, the electron-ion re-collision can be considered as a probe process and the emission may encode fruitful information on the recombining system, including molecular structure and dynamics. In the first part, we performed high harmonic spectroscopy of N₂O and CO₂ molecules that are (laser-)aligned with respect to the polarization of the driving laser. We implemented two methods based on optical and quantum interferometry respectively in order to characterize the amplitude and phase of the attosecond emission as a function of both photon energy and alignment angle. We discovered new effects in the high harmonic generation, which could not be explained by the structure of the highest occupied molecular orbital (HOMO). Instead, we found that during the interaction with the laser field, two electronic states are coherently excited in the molecular ion and form a hole wave packet moving on an attosecond timescale in the molecule after tunnel ionization. We focused on exploring this coherent electronic motion inside the molecule, and compared the measurements in N₂O and CO₂. The striking difference in the harmonic phase behavior led us to the development of a multi-channel model allowing the extraction of the relative weight and phase of the two channels involved in the emission. An unexpected pi/4 phase shift between the two channels is obtained. Moreover, we studied the attosecond profile of the pulses emitted by these two molecules, and we proposed a simple but flexible way for performing attosecond pulse shaping. In the second part, high harmonic spectroscopy was extended to other molecular systems, including some relatively complex molecules, e.g., SF₆ and small hydrocarbons (methane, ethane, ethylene, acetylene). It revealed many interesting results such as phase distortions not previously reported. For the ‘direct’ scheme, we photoionized rare gas atoms using well characterized attosecond pulses of XUV coherent radiation combined with an infrared (IR) laser ”dressing” field with controlled time delay, stabilized down to about ± 60 as. We evidenced marked differences in the measured angular distributions of the photoelectrons, depending on the number of IR photons exchanged. Joined to a theoretical interpretation, these observations bring new insights into the dynamics of this class of multi-color photoionization processes that are a key step towards studying photoionization in the time domain, with attosecond time resolution.

High-order Harmonic Generation (HHG) is an extreme nonlinear process that can be intuitively understood as the sequence of 3 steps: i) tunnel ionization of the target atom/molecule, creating an electronic wave packet (EWP) in the continuum, ii) acceleration of the EWP by the strong laser field and iii) recombination to the core with emission of an attosecond burst of XUV coherent light. HHG thus provides a tunable ultrashort tabletop source of XUV/Soft X-ray radiation on attosecond time scale for applications ('direct' scheme). At the same time, it encodes coherently in the XUV radiation the structure and dynamical charge rearrangement of the radiating atoms/molecules ('self-probing' scheme or High Harmonic Spectroscopy). This thesis is dedicated to both application schemes in attophysics based on advanced characterization and control of the attosecond emission. In the so-called 'self-probing' scheme, the last step of HHG, the electron-ion re-collision can be considered as a probe process and the emission may encode fruitful information on the recombining system, including molecular structure and dynamics. In the first part, we performed high harmonic spectroscopy of N₂O and CO₂ molecules that are (laser-)aligned with respect to the polarization of the driving laser. We implemented two methods based on optical and quantum interferometry respectively in order to characterize the amplitude and phase of the attosecond emission as a function of both photon energy and alignment angle. We discovered new effects in the high harmonic generation, which could not be explained by the structure of the highest occupied molecular orbital (HOMO). Instead, we found that during the interaction with the laser field, two electronic states are coherently excited in the molecular ion and form a hole wave packet moving on an attosecond timescale in the molecule after tunnel ionization. We focused on exploring this coherent electronic motion inside the molecule, and compared the measurements in N₂O and CO₂. The striking difference in the harmonic phase behavior led us to the development of a multi-channel model allowing the extraction of the relative weight and phase of the two channels involved in the emission. An unexpected pi/4 phase shift between the two channels is obtained. Moreover, we studied the attosecond profile of the pulses emitted by these two molecules, and we proposed a simple but flexible way for performing attosecond pulse shaping. In the second part, high harmonic spectroscopy was extended to other molecular systems, including some relatively complex molecules, e.g., SF₆ and small hydrocarbons (methane, ethane, ethylene, acetylene). It revealed many interesting results such as phase distortions not previously reported. For the 'direct' scheme, we photoionized rare gas atoms using well characterized attosecond pulses of XUV coherent radiation combined with an infrared (IR) laser "dressing" field with controlled time delay, stabilized down to about ± 60 as. We evidenced marked differences in the measured angular distributions of the photoelectrons, depending on the number of IR photons exchanged. Joined to a theoretical interpretation, these observations bring new insights into the dynamics of this class of multi-color photoionization processes that are a key step towards studying photoionization in the time domain, with attosecond time resolution.

Dans ce travail nous présentons nos travaux réalisés sur le contrôle de la générationd’harmoniques d’ordres élevés dans les gaz. Dans un premiers temps nous montronscomment, en générant les harmoniques hors du foyer du faisceau IR, il est possiblede contrôler la phase spatiale des harmoniques dans le milieu générateur permettantd’obtenir un front d’onde divergent, collimaté ou convergent. Par cette méthode nousmontrons qu’il est possible de focaliser les harmoniques à des distances pouvant atteindresix longueur de Rayleigh après le point focal du faisceau IR. Nous avons ensuiteétudié des faisceaux harmoniques XUV présentant des distributions spatio-spectralesen champ lointain structurées. Dans cette étude nous observons l’influence d’un irisde diamètre variable positionné avant la focalisation de l’IR. Dans un troisième tempsnous étudions des méthodes de contrôle du spectre harmonique. Tout d’abord nousavons contrôlé finement la longueur d’onde centrale des harmoniques par modificationdu contenu spectral de l’IR en superposant deux impulsions IR retardées. Puis nousavons utilisé les effets collectifs de la génération d’harmoniques afin de favoriser uneharmonique spécifique ou un groupe d’harmoniques en champ lointain. Enfin, nousprésentons une méthode de caractérisation de la durée d’impulsions attosecondes dansle domaine temporel. Cette méthode, appelée ionisation par paliers, utilise l’ionisationcomme sonde pour mesurer des durée d’impulsions pouvant atteindre la centained’attoseconde. / We present our work on the control of high order harmonic generation in gases.We first show how, by generating the harmonics outside the focus of the IR beam,it is possible to control the spatial phase of the harmonics in the generating mediumallowing to obtain a divergent, collimated or convergent wavefront. With this methodwe show that it is possible to focus the harmonics up to six Rayleigh length after thefocal point of the IR beam. Then we study XUV harmonic beams presenting structuredspacio-spectral distributions in the far field. In this study, we observe the influence ofthe diameter of an iris positioned before the focusing of the IR. In a third step we studymethods for controlling the harmonic spectrum. First, we finely control the harmonicscentral wavelength by modifiying the spectral content of the IR by adding two delayedIR pulses. Then we used the collective effects of the high order harmonic generationin order to foster a specific harmonic or a group of harmonics in the far field. Finally,we present a method for characterizing the duration of attosecond pulses in the timedomain. This method, called ionization ladder, uses ionization as a probe to measurepulse duration of up to hundreds of attosecond.

Dans cette thèse, j'ai étudié théoriquement l'interaction d'atomes et de molécules avec des impulsions laser brèves, intenses et basse-fréquences. En insistant sur la phase spectrale, nous utilisons la génération d'harmoniques d'ordres élevés comme processus auto-sonde pour étudier les dynamiques attoseconde. Nous résolvons l'équation de Schrödinger avec des modèles simples, numériquement ou en utilisant une théorie semi-analytique, nous permettant ainsi d'obtenir des informations approfondies sur les processus physiques mis en jeu, à travers des explications intuitives, tout en gardant une propension prédictive. Avec des outils développés pour analyser nos résultats numériques, nous étudions d'abord la dynamique d'ionisation dans une molécule modèle telle que N2. Puis, en réexaminant les interférences à deux centres, nous mettons au jour un comportement très intéressant, lié à l'habillage de l'état fondamental par le laser, et confirmé par des développements analytiques. Nous prédisons la possibilité d'observer ce phénomène expérimentalement par l'intermédiaire des interférences de chemins quantiques. Enfin, nous étudions les effets de la vibration des noyaux dans les molécules diatomiques en couplant le mouvement des électrons avec celui des noyaux. Nous montrons que pour de telles impulsions laser, l'excitation vibrationnelle de la molécule neutre peut être induite par effet Raman. Nous invalidons alors une théorie non corrélée, nommée Lochfraß, qui base son interprétation sur la dépendance du rendement d'ionisation avec la distance internucléaire. Enfin, nous proposons de prolonger à un modèle analytique standard la notion de potentiel d'ionisation dans les molécules. / In this thesis, I studied theoretically atoms and molecules interacting with a short, low-frequency and intense laser pulse, in the typical regime of high-order harmonic generation (HHG). We use HHG as a self-probe process to examine electronic and nuclear dynamics on the attosecond scale with Ångström resolution, insisting on the spectral phase. By using simple models, we are able to solve extensively the time-dependent Schrödinger equation, either numerically or with the Strong Field Approximation (SFA). Our models give us valuable physical insights on the underlying dynamical processes and intuitive explanations while keeping a predictive propensity. With efficient tools developed to analyze our numerical results, we first investigate the ionization dynamics through a shape resonance in a model molecule such as N2. Secondly, we take another look at two-center interferences, and uncover a very interesting behavior which is linked to the dressing of the electronic ground-state by the laser field. It is indeed confirmed by additional developments of molecular SFA. We predict that this behavior can be observed experimentally using quantum path interferences. Finally, we examine the effect of nuclear vibration in diatomic molecules by coupling consistently electronic and nuclear motions. Our results show that with short pulses, nuclear motion in the neutral molecule can be triggered by Raman effect. Thus, we invalidate an uncorrelated theory, so called Lochfraß, which focuses on the dependence of the ionization yield with internuclear distance as an explanation. Lastly, we question the extension within SFA of the notion of ionization potential in molecules.