The spectrum broadening of a single-cycle terahertz pulse caused by phase self-modulation in a nonlinear medium and the spectrum of radiation generated in its field at tripled frequencies

When the number of oscillations in an optical pulse decreases, the emission spectrum generated at triple frequencies and the spectrum of the fundamental pulse, broadened due to phase self-modulation during propagation in a medium with cubic nonlinearity, begin to overlap. This work demonstrates that the overlap magnitude of the spectrum broadening for a single-period terahertz pulse, caused by the emission of triple frequencies and phase self-modulation of the fundamental pulse, is $|s|=0.85$. The complex spectra are phase-shifted by $pi$, which mutually weakens these nonlinear effects. For a single-period pulse, the attenuation coefficient is 7.7. The frequency-dependent inhomogeneity of mutual attenuation of nonlinear effects results in the absence of radiation at the triple frequency relative to the frequency of the maximum spectrum of the single-period wave in the nonlinear medium, while the maximum spectrum of the generated high-frequency radiation shifts to quadrupled frequencies. Thus, for terahertz waves with a small number of oscillations, new possibilities for controlling their parameters during nonlinear processes in optical media open up.