Optimal control theory for selective vibrational excitation in molecules

The design of optimal electromagnetic fields producing selective vibrational excitation in molecules modeled as harmonic physical systems is shown to be equivalent to minimizing a quadratic cost functional balancing the energy distribution in the molecule and the fluence of the optical field. To ensure that a desired final excitation is attained, a terminal constraint is introduced for the state. A physically reasonable controller requires that both the weighting parameter on the fluence in the cost functional and the final time be large. The authors present the asymptotic form of the state and costate for large final time using familiar LQG (linear quadratic Gaussian) technqiues and give an approximation of the modes of the linear chain molecule in the limit in which the weighting parameter becomes large. They conclude with a discussion of the choice of practical design parameters.