Efficiency of high-order optical harmonic generation and of many-quantum processes in a multimode radiation field

An analysis is made of the generation of harmonics and of many-quantum processes (more than three quanta) in a specified field of laser radiation. Different statistics of the mode phases are considered and the absence of saturation effects is assumed. General relationships are derived for the calculation of the efficiency η_k of a nonlinear k-th order process in the case of arbitrary numbers of locked and nonlocked modes. It is shown that mode locking increases considerably the value of η_k. Precise values of η_k are found for third- and fourth-order processes in the case of mode locking and up to sixth order in the absence of such locking.