ab-initio description of optical nonlinearities in femtosecond filaments

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Femtosecond filaments are self-organized strings of light and free electric charges. The electric field strength in these filaments comes closeto the atomic field strength.Therefore, laser filamentation, together with high-harmonic generation, is oneof the most extreme scenarios in nonlinear optics, with a largenumber of effects acting simultaneously in the spatial as well as inthe temporal domain. While numerical modeling is quite advanced,recently, the commonly accepted picture of filamentation has beenchallenged by experimental reports that indicate a previouslyunderestimated effect resulting from higher-order electronicnonlinearities which may overrule plasma effects. While this reporthas given rise to vivid discussions, a rigorous theoreticalunderstanding going all the way back to the quantum mechanicalroots, i.e., the Schr\"odinger Equation is still outstanding. Herewe propose a suite of theoretical tests for the role of high-orderharmonics in nonlinear optics. These tests start with the simplestcase of atomic hydrogen or helium, using non-perturbativetechniques. For more complex and experimentally more relevantscenarios, we plan to use time-dependent density functional theoryto calculate the induced dipole moment. Such rigorous theoreticalinvestigations appear to be the only way to decide whether we reallyhave a new paradigm in Nonlinear Optics or whether old pictures ofplasma effects balancing Kerr effects actually prevail.