What Is a Strong Laser

Before discussing the behavior of atoms and molecules in strong laser fields, we have to specify what the adjective strong means in this context. The electric field that an electron feels in a hydrogen atom, at the distance of one Bohr from the nucleus, is 

The laser intensity that corresponds to this field is given by 

We can clearly consider a laser to be strong when its intensity becomes comparable to (4.113). In this regime, perturbation theory is no longer applicable, and the theorist has to resort to non-perturbative methods. When approaching these high intensities, a wealth of non-linear phenomena appear, like multi-photon ionization, above threshold ionization (ATI), high harmonic generation, etc. 

TDDFT is a tool particularly suited for the study of systems under the influence of strong lasers. We recall that the time-dependent Kohn-Sham equations yield the exact density of the system, including all non-linear effects. To simulate laser induced phenomena it is customary to start from the ground-state of the system, which is then propagated imder the influence of the potential 

Other observables, such as the total ionization yield or the ATI spectrum, are much harder to calculate within TDDFT. Even though these observables (as all others) are functionals of the density by virtue of the Runge-Gross theorem, the explicit functional dependence is miknown and has to be approximated. 

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