Time-dependent multiphoton

Time-dependent multiphoton dissociation above and below the threshold of diatomic volcanic states [50, 51]... 

Th. Mercouris, l.D. Petsalakis, P. Valtazanos, C.A. Nicolaides, Time-dependent multiphoton absorption by NO++. Above and below threshold dissociation and the effect of the first excited surface, J. Phys. B 27 (1994) L519. 

Similar transient signals were obtained from time-dependent quantum mechanical calculations performed by Meier and Engel, which well reproduce the observed behavior [49]. They show that for different laser field strengths the electronic states involved in the multiphoton ionization (MPI) are differently populated in Rabi-type processes. In Fig. 13 the population in the neutral electronic states is calculated during interaction of the molecule with 60-fs pulses at 618 nm. For lower intensities the A state is preferentially populated by the pump pulse, and the A state wavepacket dominates the transient Na2+ signal. However, for the higher intensities used in the... 

In summary, the photon has been modeled as a doublet in rotation in the preferred frame E. Spin and energy have been obtained from a semiclassical analysis. Polarization corresponds to a fixed direction of vector L in E. In a nonpolarized photon vector L has a time-dependent direction. A particular case of nonpolarization is the ellipsoid, as in Hunter and Wadlinger [37]. Our Eq. (96) allows for the existence of multiphotons that vary in steps of half the ground-state photon energy such prediction differs of the prediction of Hunter and Wadlinger [37]. Photons in motion with respect to E will be considered elsewhere. The photon is the source of the electromagnetic field, as explained next. 

For the special case of non relativistic Hydrogen, the multiphoton transition rate can be obtained exactly using methods based on Green function techniques, which avoid summations over intermediate states. This approach was introduced in order to treat time independent problems, and later extended to time dependent ones [2]. In the Green function method, the evaluation of the infinite sums over intermediate states is reduced to the solution of a linear differential equation. For systems other than Hydrogen, this method can also be used, but the associated differential equation has to be integrated numerically. The two-photon transition rate can also be evaluated exactly by performing explicitly the summation over the intermediate states. 

The nonlinear phenomena in intense magnetic and laser fields are given some prominence in this volume. Two chapters deal with multiphoton processes and time-dependent phenomena in atoms. In another chapter it is emphasized that the process of multi-electron dissociative ionization of molecules offers considerable challenges both for modeling and for the study of first-principles. The dynamics of molecules in such intense laser fields is an area of great interest, both at the time of writing and for future studies. In all these chapters the interplay between theory and experiment is demonstrated. 

For very small field amplitudes, the multiphoton resonances can be treated by time-dependent perturbation theory combined with the rotating wave approximation (RWA) [10]. In a strong field, all types of resonances can be treated by the concept of the rotating wave transformation, combined with an additional stationary perturbation theory (such as the KAM techniques explained above). It will allow us to construct an effective Hamiltonian in a subspace spanned by the resonant dressed states, degenerate at zero field. 

The first term on the right side of Eq. 8 describes the avalanche ionization and the second one the multiphoton ionization. 7(f) is the time-dependent intensity of the laser and a the avalanche coefficient, denotes the /c-pho-ton absorption cross section and k is equal to the smallest number of photons needed to overcome the optical bandgap of the material. Equation 8 demonstrates that the bandgap of a dielectric has a major influence on its ablation efficiency. For an increasing bandgap, the relative weight of the avalanche process is greater than that of MPI. Yet, MPI provides a deterministic seed electron production for the subsequent avalanche process. Therefore, for shorter pulses, the statistical character of the ablation is reduced [42, 43],... 

Time-dependent quantum treatment of two-colour multiphoton ionization using a strong laser pulse and high-order harmonic radiation... 

Time-Dependent Quantum Treatment of Multiphoton Ionization... 

Multiphoton processes taking place in atoms in strong laser fields can be investigated by the non-Hermitian Floquet formalism (69-71,12). This time-independent theory is based on the equivalence of the time-dependent Schrodin-ger description to a time-independent field-dressed-atom picture, under assumption of monochromaticity, periodicity and adiabaticity (69,72). Implementation of complex coordinates within the Floquet formalism allows direct determination of the complex energy associated with the decaying state. The... 

Finally, HHG can be studied by Fourier transforming the induced time-dependent dipole moment, D(f) = ( F(r,f) D vl/( ,f)), where D is the dipole operator in the polarization of the EMF [33]. For the one-electron hydrogen atom, our choice of the form of the dipole operator has been the acceleration form since, in this case, the computation of the free-free matrix elements is both efficient and accurate [119]. However, in later work on the multiphoton ionization from the two-electron metastable excited state of He, the ls2s S, we stressed that for many-electron systems, "calculations of harmonic spectra based on the use of the acceleration form of the dipole operator will produce, in general, unreliable results even when some correlations are accounted for" [120]. 

K.G. Kulander, Multiphoton ionization of hydrogen A time-dependent theory, Phys. Rev. A 35 (1987) 445. 

Certain ion sources are not continuous, as with ESI and Ni, and instead are intermittent, requiring electrical pnlses, snch as with CDs or optical pulsing like that with multiphoton ionization to make ions from a sample. Ion injection with such sources can be coincident with ion formation, and ion injection may be arranged without ion shutters. In this instance, an ion shntter may be seen as optional or unnecessary. While a pulsed ion sonrce conld be attractive for reduced costs of drift tube manufacture and simplicity of design, pnlsed sources can introduce time-dependent chemistry or ion intensity into a mobility measurement, and neither of these is easily controlled or desirable. 

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