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Atoms interacting with intense laser fields can emit electrons and photons of very high energies. An intuitive and quantitative explanation of these highly nonlinear processes can be found in terms of a generalization of classical Newtonian particle trajectories, the so-called quantum orbits. Very few quantum orbits are necessary to reproduce the experimental results. These orbits are clearly identified, thus opening the way for an efficient control as well as previously unknown applications of these processes.

An efficient method is investigated for the generation of circularly polarized high-order harmonics by a bichromatic laser field whose two components with frequencies and 2 are circularly polarized in the same plane, but rotate in opposite directions. The generation of intense harmonics by such a driving-field configuration was already confirmed by a previous experiment. With the help of both a semiclassical three-step model as well as a saddle-point analysis, the mechanism of harmonic generation in this case is elucidated and the plateau structure of the harmonic response and their cutoffs are established. The sensitivity of the harmonic yield and the polarization of the harmonics to imperfect circular polarization of the driving fields are investigated. Optimization of both the cutoff frequency and the harmonic efficiency with respect to the intensity ratio of the two components of the driving field is discussed. The electron trajectories responsible for the emission of particular harmonics are identified. Unlike the case of a linearly polarized driving field, they have a nonzero start velocity. By comparison with the driving-field configuration where the two components rotate in the same direction, the mechanism of the intense harmonic emission is further clarified. Depending on the ͑unknown͒ saturation intensity for the bichromatic field with counter-rotating polarizations, this scheme might be of practical interest not only because of the circular polarization of the produced harmonics, but also because of their production efficiency.

A method is proposed for the calculation of the S matrix for many-electron processes in intense-laser atom physics, in close analogy to the strong-field approximation for one-electron processes. Given a scenario of how some process evolves, corresponding approximations to the classical action are made which allow for the evaluation of the quantum-mechanical S matrix. The method is applied to the distribution of the total electronic momentum in nonsequential double ionization, and the results are compared to recent measurements. Good agreement is obtained for neon for a rescattering scenario. There is no comparable agreement for helium and argon, and possible alternative scenarios are discussed.

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