Limitation on the efficiency of frequency doublers of picosecond light pulses

A theoretical analysis is made of the influence of the phase modulation of the fundamental-frequency radiation on the second-harmonic generation. The phase modulation must be allowed for in the calculations of the field intensities from known values of the energy of a pulse and the width of its frequency spectrum. Moreover, in the case of a mismatch between the group velocities the phase modulation results in deviation from the optimal phase relationships (loss of the coherence of the interaction between pulses) and then the harmonic energy is pumped back to the fundamental-frequency radiation. This mechanism imposes basic limitations on the doubler efficiency. The results are given of numerical calculations of the excitation of the second harmonic of Gaussian pulses with a linear variation of the instantaneous frequency; the width of the frequency spectrum and the peak amplitude are fixed in one series of calculations and the energy in another series.