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.

<p>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.</p><p>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.</p><p>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.</p>