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Quantum theory of scattering of ultrashort electromagnetic field pulses by polyatomic structures

Dmitry N. Makarov

Published Oct 18, 2019• 32 citations
Publisher

Abstract

. Various biomolecules, nanosystems and polyatomic structures can consist of such a number of atoms. This is especially important because experiments are currently being conducted with such structures at the present time using high-power ultrashort laser pulses. It is shown that the developed theory in limiting cases turns into well-known approaches of single-photon and multi-photon theories.

DOI
10.1364/oe.27.031989

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•Jan 1, 2003•2 citations
. Various biomolecules, nanosystems and polyatomic structures can consist of such a number of atoms. This is especially important because experiments are currently being conducted with such structures at the present time using high-power ultrashort laser pulses. It is shown that the developed theory in limiting cases turns into well-known approaches of single-photon and multi-photon theories.
The processes of reemission of ultrashort electromagnetic pulses by arbitrary nanosystems consisted of isolated complex atoms have been considered. The angular distributions of reemission spectra have been obtained for a series of regular nanosystems. It has been shown that the interference of the photon-emission amplitudes leads to the appearance of characteristic “diffraction” maxima. One-, two-, and three-dimensional nanostructures, as well as planar and cylindrical constructions as models of planar nanosystems and nanotubes, were used as examples that allow a simple analytical consideration.
The presentation is devoted to the theoretical investigation of nonlinear scattering of ultrashort electromagnetic pulses (USP) on two-level quantum system. We consider the scattering of several types of USP, namely, so called corrected Gaussian pulse (CGP) and cosine wavelet pulse. Such pulses have no constant component in their spectrum in contrast with traditional Gaussian pulse. It should be noted that the presence of constant component in the limit of ultrashort pulse durations leads to unphysical results. The main purpose of the present work is the investigation of the change of pulse temporal shape after scattering as a function of initial phase at different distances from the target. Numerical calculations are based on the solution of Bloch equations and expression for scattering field strength via dipole moment of two-level system exposed by the action of incident USP. In our calculation we also account for the influence of refracting index of the air on electric field strength in the pulse after scattering.
The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter [1]. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration (τ) [2] as well as the dependence on the carrier phase with respect to the pulse envelope (φ) [3-4]. It should be noted that if the dependence of the probability W on the phase φ manifests itself either only for very short pulses, when ωτ < 1 (ω is carrier frequency of the pulse), or in case of a nonlinear photoprocess [3], the function W(τ) can differ from a linear function in the limit ωτ> 1 too for fields of moderate strength, when the perturbation theory is applicable [2].
Recently, we have proposed two avenues to generating ultrashort (potentially, subfemtosecond) and intense (up to atomic fields) nonoscillating pulses: a high-repetition train of such pulses can be produced in multicomponent stimulated Raman scattering [1], and a single pulse ("electromagnetic bubble" -- EMB) or several of them can result [2,3] from the propagation of an initially broad unipolar pulse (half-cycle pulse -- HCP [4]) in an appropriate nonlinear medium. Such pulses could cause a substantial "shake-up" excitation or ionization of an atomic system within the time much smaller than any characteristic time of the system. These "superpulses" would open a new chapter in nonlinear optics and atomic and molecular physics, both as a new probing tool and a source of new effects. In the present paper, we consider one of them: backward and multi-echo field ionization [5].
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.