Abstract

Classical Cherenkov radiation appears when a small object moves in a medium with a velocity exceeding the phase velocity of the waves in the given medium^[1]. It is assumed that the source has dimensions much smaller that the wavelength. The source of radiation does not necessarily have to be a real particle, but can be, for example, waves of polarisation induced in a nonlinear medium by external fields. If the size of the source is finite and comparable with the wavelength at least in one direction, then the radiation is defined in this direction by the 'Cherenkov conditions' rather than full phase-matching conditions. In nonlinear optics, the concept of Cherenkov radiation was introduced by Tien et al. in 1970 ^[2]. Their experiment shows that a thin-film pump beam can generate a second-harmonic (SH) beam in the substrate below the film. The phase velocity of the induced nonlinear polarization is higher than the phase velocity of the waves in the substrate, or the effective wavenumber of the polarization in the film must be shorter than the wavenumber of the waves in the substrate at the SH frequency. The emerging SH-beam is therefore tilted with respect to the longitudinal direction of the pump, due to the longitudinal phase-matching of the wave vectors. This is an example of Cherenkov radiation with longitudinal phase-matching, but without transverse phase-matching.

© 1995 Optical Society of America