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Multi-Photon Interactions with a Time Structure

Alexander S. Baev

Published Jan 1, 2003• 2 citations
OpenAlex

Abstract

The present thesis concerns aspects of the interaction ofmatter in gas, liquid and solid phases, with electromagneticradiation, ranging from the optical to the X-ray region. Overthe last decade the availability of ultrashort strong laserpulses as well as of high power synchrotron sources of tunableX-ray radiation has stimulated a rapid development of newexperimental techniques which makes it possible to analysedifferent physical, chemical and biological processes inunprecedented detail. All of this urges a concomitantdevelopment of adequate theoretical language and methodscombined with simulation techniques. The first part of the thesis addresses nonlinear propagationof strong optical pulses. This study is motivated by thebreakthrough in synthesis of novel organic materials possessingprespecified nonlinear optical properties and which has led toa multitude of potential applications such as, for example, 3Dimaging and data storage, optical limiting and photodynamiccancer therapy. In order to clarify the underlying physics, astrict solution has been derived of the density matrixequations of a material aiming at an explicit treatment of itsnonlinear polarization without addressing a conventional Taylorexpansion over field amplitudes. Such a formalism is developedfor many-level molecules, allowing to solve the coupledMaxwell's and density matrix equations for the propagation of afew interacting laser pulses through a nonlinear molecularmedium. The theory presented is capable to account formulti-photon processes of an arbitrary order and for differentsaturation effects. The theory is applied to simulations oftwo- and three-photon absorption as well as to upconvertedstimulated emission of organic molecules in solvents. The second part of the thesis is devoted to resonant X-rayRaman scattering from free molecules, solutions and polymerfilms. The temporal analysis of the spectral profiles isperformed using the technique of scattering duration whichallows to select physical processes with different time scales.The slowing-down/speeding-up of the scattering by frequencydetuning provides insight in the formation of the differentparts of the scattering profile like atomic and molecularbands, resonant and vertical scattering channels, anomalousenhancement of the Stokes doubling effect. The lifetimevibrational interference (LVI), playing a crucial role inresonant scattering, is found to strongly influence thedispersion of the Auger resonances of polymers in agreementwith experiment. An almost complete quenching of the scatteringcross section by LVI is observed for the N2molecule. It is found that the interferenceelimination of the scattering amplitude gives valuableinformation on molecular geometry. The electron Doppler effectis minutely studied making use of a wave packet technique. Thesimulations show an "interference burning" of a narrow hole onthe top of the Doppler broadened profile of the Auger spectraof molecular oxygen. For the SF6molecule the Auger Doppler effect is found to besensitive to the detuning due to the scattering anisotropy. Inall of these studies the temporal language was foundconstructive and enormously helpful for understanding theunderlying physical processes. Most theoretical predictionsmade have been verified by experiments.

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The present thesis concerns aspects of the interaction ofmatter in gas, liquid and solid phases, with electromagneticradiation, ranging from the optical to the X-ray region. Overthe last decade the availability of ultrashort strong laserpulses as well as of high power synchrotron sources of tunableX-ray radiation has stimulated a rapid development of newexperimental techniques which makes it possible to analysedifferent physical, chemical and biological processes inunprecedented detail. All of this urges a concomitantdevelopment of adequate theoretical language and methodscombined with simulation techniques. The first part of the thesis addresses nonlinear propagationof strong optical pulses. This study is motivated by thebreakthrough in synthesis of novel organic materials possessingprespecified nonlinear optical properties and which has led toa multitude of potential applications such as, for example, 3Dimaging and data storage, optical limiting and photodynamiccancer therapy. In order to clarify the underlying physics, astrict solution has been derived of the density matrixequations of a material aiming at an explicit treatment of itsnonlinear polarization without addressing a conventional Taylorexpansion over field amplitudes. Such a formalism is developedfor many-level molecules, allowing to solve the coupledMaxwell's and density matrix equations for the propagation of afew interacting laser pulses through a nonlinear molecularmedium. The theory presented is capable to account formulti-photon processes of an arbitrary order and for differentsaturation effects. The theory is applied to simulations oftwo- and three-photon absorption as well as to upconvertedstimulated emission of organic molecules in solvents. The second part of the thesis is devoted to resonant X-rayRaman scattering from free molecules, solutions and polymerfilms. The temporal analysis of the spectral profiles isperformed using the technique of scattering duration whichallows to select physical processes with different time scales.The slowing-down/speeding-up of the scattering by frequencydetuning provides insight in the formation of the differentparts of the scattering profile like atomic and molecularbands, resonant and vertical scattering channels, anomalousenhancement of the Stokes doubling effect. The lifetimevibrational interference (LVI), playing a crucial role inresonant scattering, is found to strongly influence thedispersion of the Auger resonances of polymers in agreementwith experiment. An almost complete quenching of the scatteringcross section by LVI is observed for the N2molecule. It is found that the interferenceelimination of the scattering amplitude gives valuableinformation on molecular geometry. The electron Doppler effectis minutely studied making use of a wave packet technique. Thesimulations show an "interference burning" of a narrow hole onthe top of the Doppler broadened profile of the Auger spectraof molecular oxygen. For the SF6molecule the Auger Doppler effect is found to besensitive to the detuning due to the scattering anisotropy. Inall of these studies the temporal language was foundconstructive and enormously helpful for understanding theunderlying physical processes. Most theoretical predictionsmade have been verified by experiments.
New generations of ultrashort and intense laser pulses as well ashigh power synchrotron radiation sources and x-ray free electronlasers have promoted fast developments in nonlinear optics andx-ray spectroscopy.The new experimental achievements and the appearance of varieties of novelnonlinear phenomena call for further development of theories. The objective of this thesis is to develop and apply thetheories to explain existing experimental data and to suggest new experiments. The first part of the thesis is devoted to nonlinear propagation of optical pulses. It is shown that the vibrational levels can be selectively populated by varying the duration, shape and intensity of the pump pulse. We obtained a strict analytical solution for the resonant two-photon interaction in a multilevel system beyond rotating wave approximation. Simulations show that the polarization anisotropy of the two-photon excitation affects strongly the anisotropy of photobleaching.The two-photon area theorem is reformulated with taking into account the dynamical Stark shift and the contribution from the permanent dipole moments. In general the dynamical Stark shift does not allow complete population of the excited state, but it can be compensated by detunings in atoms. A dynamical theory of the sequential two-photon absorption of microsecond pulses is developed to explore the role of transverse inhomogeneity of the light beam on optical limiting properties. The propagation of ultrashort laser pulses in nondipolar and dipolar media is investigated with special attention to the generation of superfluorescence and supercontinuum and the formation of attosecond pulses. The second part of the thesis addresses the interaction of molecules with x-ray radiation. We explore here the role of nuclear dynamics in resonant Auger scattering. Multimode simulations of the Auger spectra of ethylene molecule explain the main spectral features of the experimental spectra and show that the spectral profiles are formed mainly due to six vibrational modes. We predict the Doppler splitting of the atomic peak in resonant Auger scattering from SF6 molecule for circularly polarized x-rays. This effect is confirmed by the recent experiment. A new scheme of x-ray pump-probe spectroscopy, namely, resonant inelastic x-ray scattering accompanied by core-hole hopping induced by strong laser fields is suggested. The laser-induced promotion of core holes opens the symmetry forbidden scattering channels and gives rise to new spectral lines in the x-ray scattering spectrum. The strength of the symmetry forbidden lines becomes strong when the time of Rabi flopping is shorter than the lifetime of the core-excited state. We study the role of propagation of femtosecond x-ray free-electron pulses on the Auger process. Simulations show that there exists a strong competition between Auger decay and stimulated emission. The Auger yield and Auger branching ratio are strongly suppressed in the course of pulse propagation.
The present thesis is devoted to theoretical studies of pulse propagation of light through linear and nonlinear media, and of light-induced nuclear dynamics. The first part of the thesis addresses propagation of light pulses in linear periodical media - photonic crystals. The main accent was put on studies of the angular properties of two qualitatively different types of photonic crystals: holographic photonic crystals, and impurity band based photonic crystals. The anisotropy of band structure, group velocity and pulse delay with respect to the light polarization are analyzed. In the second part of the thesis a strict theory of nonlinear propagation of a few strong interacting light beams is presented. The key idea of this approach is a self-consistent solution of the nonlinear wave equation and the density matrix equations of the material. This technique is applied to studies of dynamics of cavityless lasing generated by ultra-fast multi-photon excitation. It is shown that interaction of co- and counter-propagating pulses of amplified spontaneous emission (ASE) affects the dynamics and efficiency of nonlinear conversion. Our dynamical theory allows to explain the asymmetric spectral properties of the forward and backward ASE pulses, which were observed in recent experiment with different dye molecules. It is shown that the ASE spectral profile changes drastically when the pump intensity approaches the threshold level. The effect of the temporal self-pulsation of ASE is studied in detail. The third part of the thesis is devoted to light-induced nuclear dynamics. Time- and frequency-resolved X-ray spectroscopy of molecules driven by strong and coherent infrared (IR) pulses shows that the phase of the IR field strongly influences the trajectory of the nuclear wave packet, and hence, the X-ray spectrum. Such a dependence arises due to the interference of one (X-ray) and two-photon (X-ray + IR) excitation channels. The phase of the light influences the dynamics also when the Rabi frequency approaches the vibrational frequency, breaking down the rotating-wave approximation. The probe X-ray spectra are also sensitive to the delay time, the duration, and the shape of the pulses. The evolution of the nuclear wave packets in the dissociative core-excited state affects the dynamics of resonant Auger scattering from fixed-in-space molecules. One of the important dynamical effects is the atomic-like resonance which experiences electronic Doppler shift. We predict that the scattering of the Auger electrons by nearby atoms leads to new Doppler shifted resonances. These extra resonances show sharp maxima in the bond directions, which makes them very promising as probes for local molecular structure using energy and angular resolved electron-ion coincidence techniques. Our theory provides prediction of several new effects, but also results that are in good agreement with the available experimental data.
The present thesis is devoted to theoretical studies of light pulse propagation through different linear and nonlinear media. One dimensional holographic photonic crystals and one dimensional impurity band based photonic crystals are investigated as linear media. The effects of angular dependence of the band structures and pulse delay with respect to the light polarization are analyzed. A strict theory of nonlinear propagation of a few strong interacting light beams is presented and applied in the field of nonlinear optics. The key idea of this approach is a self-consistent solution of the nonlinear wave equation and the density matrix equations of the material beyond the so-called rotating wave approximation. The results of numerical studies led to a successful interpretation of recent experimental data [Nature, 415:767, 2002]. A theoretical study of the NO molecule by means of two-color infrared -- X-ray pump probe spectroscopy is presented. It was found that the phase of the infrared field strongly influences the trajectory of the nuclear wave packet, and hence, the X-ray spectrum. The dependence of the X-ray spectra on the delay time, the duration and the shape of the pulses are studied.
In this thesis we discuss a theoretical description of ultrafast and non-linear spectroscopy. Due to the high intensities and ultrashort pulse durations involved in such experiments, it is necessary to use an explicitly time-dependent formalism. In addition, many of the systems we have considered exhibit strong interactions between the constituent particles, such as electron-electron, electron-nuclear and electron-photon interactions. To properly account for such interactions we have made extensive use of effective models, designed to capture the qualitative aspects of the systems.The thesis is based on six papers, that can be broadly categorized as follows: In Papers III and VI we study the non-linear interaction of light and matter. In Paper III we look at the multi-photon photo-emission from InAs nanowires, and in particular at the polarization dependence of the photo-emission signal on the crystal structure. In Paper VI we discuss second harmonic generation in a two-level system, and compare the fluorescence spectra from a quantum and semi-classical treatment of radiation.The remaining four papers are concerned with ultrafast dynamical processes: In Papers I and II we study atomic desorption from a surface, resulting from strong electron-nuclear interactions. To account for these interactions we consider a finite system that can be solved using exact diagonalization. We show that the desorption yield can be controlled by using a protocol with two ultrashort pulses and varying their delay. To assess finite size effects we compare the exact solution of the finite system to an approximate solution of a semi-infinite system based on non-equilibrium Green's functions and Ehrenfest dynamics. In Paper V we study Auger decay in a real-time description, and propose a protocol to induce the quantum Zeno effect by driving the system during decay. The Zeno effect leads to an increase in the Auger lifetime, that is experimentally measurable and can be controlled by varying the intensity of the driving field. In Paper IV we discuss the role of electron-electron interactions for charge-separation in donor-acceptor systems. We identify a regime where the charge-separation is driven solely by electronic correlations, that are captured by treating interactions to first order beyond a mean-field description.
This work aims at development of new dynamical methods to control a resonant light-matter interaction as well as at their application for producing new sources of coherent intense sub-fs radiation in x-ray range. The dynamical control is based on modulation in time and in space of the parameters of the atomic transition (coupled to the resonant high-frequency field) by means of sufficiently strong off-resonant low-frequency control field. In particular, it may result in efficient transfer of quasi-monochromatic VUV or XUV radiation into ultrashort pulses via its resonant interaction with atomic hydrogen gas or plasma of hydrogen-like ions respectively by means of two different techniques: time and space dependent linear Stark effect or interruption of resonant interaction by the tunneling ionization, as shown in previous works of our group. \n\nIn this thesis, I further develop these ideas and demonstrate their important potential applications. First of all, both techniques are extended to arbitrary (non-hydrogen-like) atomic medium. Furthermore, advanced analytical and numerical solutions describing a process of pulses formation are found and shown to be in excellent agreement with each other. A deep physical analogy between the processes of coherent forward scattering of γ-ray radiation in the vibrated quasi-resonant nuclear absorber and the XUV field propagation in the quasi-resonant atomic medium in the presence of the moderately strong IR field is established. \n\nFinally, the application of the developed techniques for production of intense coherent attosecond sources of soft X-ray radiation, including so-called “water window” range (2.2-4.3nm) (especially promising for dynamical imaging of the proteins in a living cell) is proposed. Two different paths towards production of intense coherent attosecond pulses in a soft X-ray range are suggested: (i) via efficient transformation of the picosecond radiation of the high energy pulses of the existing x-ray plasma lasers into the trains of attosecond pulses in the resonant passive plasma, and (ii) via amplification of the low energy pulses of the existing high harmonic sources in the resonant active plasma of x-ray lasers.
Until recently, the nonlinear interaction between light and matter has been restricted to only low photon energies produced by optical lasers. However, about a decade ago, the rise of free-electron laser facilities revolutionized the field of nonlinear light-matter interaction by delivering intense high-energy light pulses. Today, such lasers are used for research in materials science, chemical technology, biophysical science, solid state physics as well as fundamental research. It is the new experimental possibilities provided by free-electron lasers that motivated the work presented in this thesis. Two-photon ionization process is one of the simplest nonlinear interactions in which absorption of two photons by an atom (or a molecule) leads to promoting one of its bound electrons to continuum. This work presents studies of two-photon ionization of neutral atoms. After a brief historical introduction to the topic of nonlinear light-matter interaction, the density matrix describing the state of an atom and a photoelectron following two-photon ionization is derived. In each successive chapter, part of this density matrix is used to obtain characteristic quantities such as total two-photon ionization cross section, photoelectron angular distributions, ion polarization or degree of polarization of fluorescence photon produced by subsequent decay of the photoion. Physical properties of these quantities are studied and intriguing phenomena, such as elliptical dichroism, polarization transfer as well as relativistic and screening effects are investigated.