Optimization of high-order harmonic generation by optimal control theory: Ascending a functional landscape in extreme conditions

A theoretical optimization method of high-order harmonic generation (HHG) is developed in the framework of optimal control theory (OCT). The target of optimization is the emission radiation of a particular frequency. The OCT formulation includes restrictions on the frequency band of the driving pulse, the permanent ionization probability, and the total energy of the driving pulse. The optimization task requires a highly accurate simulation of the dynamics. Absorbing boundary conditions are employed, where a complex absorbing potential is constructed by an optimization scheme for maximization of the absorption. A highly accurate propagation scheme is employed, which can address explicit time dependence of the driving as well as a non-Hermitian Hamiltonian. The optimization process is performed by a second-order gradient scheme. The method is applied to a simple one-dimensional model system. The results demonstrate a significant enhancement of selected harmonics, with minimized total energy of the driving pulse and controlled permanent ionization probability. A successful enhancement of an even harmonic emission is also demonstrated.