Excitation of the second harmonic by a periodic sequence of ultrashort light pulses

The problem of the excitation of the second harmonic by a periodic sequence of ultrashort light pulses is considered theoretically. It is shown that, for certain relationships between the period of the amplitude oscillations of the second harmonic and the repetition period of the pumping pulses, me amplitude of the second harmonic can increase linearly with the length of a crystal in the absence of phase matching.