Singularities of the second-harmonic light field polarisation arising upon reflection of normally incident elliptically polarised Gaussian beam from the surface of an isotropic chiral medium

We have analysed the conditions for the appearance of polarisation singularities in the second-harmonic beam cross section arising in the case of reflection of a uniformly elliptically polarised Gaussian beam at the fundamental frequency from the surface of an isotropic gyrotropic medium. It is shown that there are elliptical polarisation states of the incident light at which the cross section of the second-harmonic reflected beam contains either one or two C lines and either two, or one, or none L lines [the loci of the points where the propagating radiation is circularly (C) or linearly (L) polarised].The formulas determining the conditions for the occurrence of L and C lines and specifying their orientation in the plane of the cross-section of the second-harmonic beam are obtained.