We analyze the control of molecular orientation by nonresonant and quasiresonant two-color laser pulses (2+1 process). The laser pulses are assumed to be short with respect to the rotational period. In the nonresonant case, we show that the efficiency of this strategy crucially depends on the polarizability and the hyperpolarizability of the molecule. In the quasiresonant case, i.e., if the 2 omega frequency is in quasiresonance with a vibrational frequency, one can improve the orientation by adjusting the detuning. The best orientation is obtained for an optimal value of the detuning, which is different from zero.
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