GENERALIZED FLOQUET THEORETICAL METHODS FOR NONPERTURBATIVE TREATMENTS OF SCHRODINGER AND LIOUVILLE EQUATIONS IN THE PRESENCE OF STRONG FIELDS

We present a brief description of some generalized Floquet formalisms and numerical methods recently developed in our laboratory for nonperturbative treatments of the time-development of wave functions or density matrix operator of quantum systems driven by intense periodic or multi-color (multi-frequency) laser fields. Both the Schrodinger and Liouville equations are considered. In all cases, it is shown that the time-dependent (monochromatic or polychromatic) problems can be exactly transformed into equivalent time-independent infinite-dimensional (Hermitian or non-Hermitian) matrix (or super matrix) eigenvalue problems. These yield numerically stable and computationally efficient techniques for the unified treatment of one- and multiple- photon, resonant and non-resonant, steady-state and transient phenomena in strong fields. Applications of the methods to intense-field multiphoton and nonlinear optical proccesses of current significance are briefly discussed. © 1991, Taylor & Francis Group, LLC. All rights reserved.