The thesis deals with the development and characterization of new light sources, which are mandatory for applications in atomic and molecular spectroscopy, medical and biological imaging or industrial production. For that purpose, the employment of interactions of high intensity ultra-short laser pulses with gaseous media offers a rich variety of physical effects which can be exploited. The effects are characterized by a nonlinear dependency on the present light fields. Therefore, accurate modeling of the nonlinearities of the gas is crucial. In general, the nonlinearities are due to the electronic response of the gas atoms to the light field and one distinguishes between the response of bound and ionized electrons. The first part investigates laser pulse self compression, where the consideration of a purely bound electron response is sufficient. We apply an exotic setup with an negative Kerr nonlinearity in order to avoid spatial collapse of the beam on the cost of dealing with an highly dispersive nonlinearity. Analytical analysis and numerical simulations prove the possibility of laser pulse compression in such setups and reveals a new compression scheme, where the usually disturbing dispersion of the nonlinaerity is responsible for compression. Dealing with tera-Hertz generation by focusing an ionizing two-color laser pulse into gas, the second part exploits a medium nonlinearity caused by ionized electrons. We reveal in a mixed analytical and numerical analysis the underlying physical mechanism for THz generation: ionized electrons build up a current, which radiates. Thereby, the the two-color nature of the input laser is crucial for the emitted radiation to be in the tera-Hertz range. Combining this physical model with a pulse propagation equation allows us to achieve remarkable agreement with experimental measurements. Finally, the third part deals with nonlinearities from bound as well from ionized electrons on a fundamental level. We advance beyond phenomenological models for responses of bound and ionized electrons and quantum mechanically model the interaction of an ultra-short laser pulse with a gas. Already the simplest case of one dimensional hydrogen reveals basic features. For low intensities, the Kerr nonlinearity excellently describes the response of bound electrons. For increasing intensity, ionization becomes important and the response from ionized electrons is the governing one for high intensities. This quantum mechanical correct modeling allows us to explain saturation and change of sing of the nonlinear refractive index and to deduce suited approximate models for optical nonlinearities.

The thesis deals with the development and characterization of new light sources, which are mandatory for applications in atomic and molecular spectroscopy, medical and biological imaging or industrial production. For that purpose, the employment of interactions of high intensity ultra-short laser pulses with gaseous media offers a rich variety of physical effects which can be exploited. The effects are characterized by a nonlinear dependency on the present light fields. Therefore, accurate modeling of the nonlinearities of the gas is crucial. In general, the nonlinearities are due to the electronic response of the gas atoms to the light field and one distinguishes between the response of bound and ionized electrons. The first part investigates laser pulse self compression, where the consideration of a purely bound electron response is sufficient. We apply an exotic setup with an negative Kerr nonlinearity in order to avoid spatial collapse of the beam on the cost of dealing with an highly dispersive nonlinearity. Analytical analysis and numerical simulations prove the possibility of laser pulse compression in such setups and reveals a new compression scheme, where the usually disturbing dispersion of the nonlinaerity is responsible for compression. Dealing with tera-Hertz generation by focusing an ionizing two-color laser pulse into gas, the second part exploits a medium nonlinearity caused by ionized electrons. We reveal in a mixed analytical and numerical analysis the underlying physical mechanism for THz generation: ionized electrons build up a current, which radiates. Thereby, the the two-color nature of the input laser is crucial for the emitted radiation to be in the tera-Hertz range. Combining this physical model with a pulse propagation equation allows us to achieve remarkable agreement with experimental measurements. Finally, the third part deals with nonlinearities from bound as well from ionized electrons on a fundamental level. We advance beyond phenomenological models for responses of bound and ionized electrons and quantum mechanically model the interaction of an ultra-short laser pulse with a gas. Already the simplest case of one dimensional hydrogen reveals basic features. For low intensities, the Kerr nonlinearity excellently describes the response of bound electrons. For increasing intensity, ionization becomes important and the response from ionized electrons is the governing one for high intensities. This quantum mechanical correct modeling allows us to explain saturation and change of sing of the nonlinear refractive index and to deduce suited approximate models for optical nonlinearities.

Die vorliegende Arbeit beschäftigt sich mit dem Konzept der radial nicht-oszillierenden, zeitlich stabilen ultrakurzen Bessel ähnlichen Strahlen oder "Nadelstrahlen" ("needle beams"), die zu einer Klasse von optischen hochlokalisierten Wellenpaketen generalisiert werden. Hierbei wird die Theorie über das räumlich-zeitlichen Ausbreitungsverhaltens von nicht auseinanderdriftenden Nadelstrahlen mit Pulsdauern von kleiner als 10 fs näher diskutiert. Dies wird durch eine systematische Darstellung der Methoden zur Generierung und Detektierung von lokalisierten Wellen komplettiert, die ein optischen Drehmoment tragen. Für die Erzeugung von HLWs kommen räumliche Lichtmodulatoren zum Einsatz, die ein flexibles Zuschneiden von Wellenpaketen mit der Dauer weniger Zyklen des EM-Feldes erlauben. Es wird gezeigt, dass solche optischen Pulse sich über beträchtliche Entfernungen ausbreiten, ohne dass sich dabei signifikant der Strahldurchmesser vergrößert oder der Puls zeitlich verbreitert. In variabler Weise werden verschiedene geometrische (z.B. ringförmige) Lichtverteilungen erzeugt. Anwendungspotential findet sich insbesondere in den Techniken der räumlichen Pulsformung und Diagnostik. Als besonders wichtiger Ansatz ist der Zeit-Wellenfront-Sensor zu erwähnen, welcher die nichtlineare, mehrkanalige Autokorrelation, die Wellenfrontdetektion mittels nichtdiffraktiver Teilstrahlen nach dem Shack-Hartmann-Prinzip und eine adaptive Funktionalität miteinander vorteilhaft verbindet. Das enorme Potential solcher Ansätze wird durch die hohe Genauigkeit orts-, winkel- und zeitabhängiger Rekonstruktionen der Wellenpakete nachgewiesen. Darüber hinaus ermöglicht das räumliche Kodieren und anschließende Verfolgen der Teilstrahlen eine wesentliche Verbesserung der Identifikation relevanter Parameter von Verteilungsfunktionen. Schließlich werden erste Schritte zur experimentellen Generation von optischen "light bullets" mit ganzzahligen und fraktalen orbitalen Drehmomenten präsentiert. / This thesis deals with the concept of radially non-oscillating, temporally stable ultrashort-pulsed Bessel-like beams or "needle pulses", which are an example of a highly localized wave packet (HLW). HLWs are the closest approximation of linear-optical light bullets and provide specific benefits compared to conventional Gaussian-like light bullets. The spatio-temporally nonspreading propagation behavior of few-cycle needle beams of less than 10 fs duration will be theoretically discussed in detail. An overview of the generation and detection of localized waves carrying an orbital angular momentum is also given. High fidelity spatial light modulators are used for the generation of HLWs. The flexible tailoring of few-cycle wave packets at near-infrared wavelengths is reported. It is shown that such pulses propagate over a huge depth of focus, neither significantly changing their spot size or nor the pulse duration. Variable geometrical distributions like circular disks, rings, or bars of light are shaped and exploited as building blocks for structures of higher complexity. Another section of the thesis emphasizes the numerous potential applications of related techniques for an optimized two-dimensional spatial pulse shaping and diagnostics (reduce ambiguities) based on localized waves. As a particularly important example, time-wavefront sensing is used to combine nonlinear multichannel autocorrelation with Shack-Hartmann wavefront sensing by means of localized sub-beams and adaptive functionality. The capabilities of such devices are illustrated by the results of angular and temporal mapping of few-cycle wave packets. Moreover, spatial encoding and subsequent tracking of individual sub-beams, even at incident angles of up to 50°, enables to significantly improve the spot recognition. Finally, first steps towards the generation of optical light bullets carrying integer or non-integer orbital angular momenta are presented.