Theory of laser-molecule interaction: The recursive-residue-generation method

General properties of the semiclassical time propagator are given for molecules in interaction with intense laser fields, i.e., for molecular systems advanced by a periodic time-dependent operator. The operator expression of Floquet's theorem is used to unify various approaches in the literature and to emphasize that the problem can be reduced to a time-independent one with an effective quasienergy operator, if evolution is only considered at multiples of the optical period. The Magnus expansion (through third order) is used to obtain an explicit expression for the quasienergy operator. The recursive-residue-generation method, devised to evaluate transition amplitudes for systems with a very large number of coupled states, is developed in detail and applied to the model problem (with over 3 × ${10}^3$ states) of an anharmonic oscillator, dipole coupled to the laser and also linearly coupled to a multimode harmonic bath.