Cherenkov second harmonic generation of femtosecond laser pulses in a homogeneous nonlinear crystal

In experiments on second harmonic (SH) generation (SHG), a conical structure of radiation has been observed. In the present study, a non-stationary theory of SH excitation of ultrashort laser pulses with phase modulation has been developed, which explains the properties of such a structure as Cherenkov radiation. Under phase-mismatched interactions, a maximum of the SH spectrum is observed at the Cherenkov angle, which is determined by the ratio of the SH and laser radiation phase velocities. It is shown that tightly focused laser beams are preferred to observe Cherenkov SHG. The SH spectral width depends on the group velocity mismatch and is more complicated on the excited radiation spectrum. The SH energy can be proportional to the crystal length or group delay length depending on their ratio. We also demonstrate that a complex angular distribution of spectral components (an angular chirp) appears within the SH cross-section.