We develop a theoretical formalism that provides a powerful tool for the detailed numerical analysis of the interaction of three-dimensional (as well as one-dimensional model) hydrogen atoms with an intense radiation field. A combination of Floquet theory and complex dilation, together with a representation of the atomic degrees of freedom in a Sturmian basis, allows us to treat this problem in its entire complexity. The application of this approach to the microwave ionization of Rydberg states of hydrogen provides the most advanced numerical experiments in this area to date, to our knowledge, with maximum control of the individual physical parameters involved. Special emphasis is given to a discussion of the effect of some of these parameters on the numerical results.

© 1995 Optical Society of America

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