Abstract: In textbooks, the third-order susceptibility tensor elements in isotropic media are not detailed and intuitive enough to be explained, especially in isotropic chiral media. A analysis method based on cascaded second-order effect is proposed in this paper, to determine whether third-order susceptibility tensor elements in isotropic media are zero. Compared with the symmetry operation method based on group theory, this method can make judgement more quickly, and give intuitive understanding. The limiting conditions of propagation directions of input fields required by the generation of third-order effects in isotropic media are analyzed, and a comparison with the second-order effects is made, where the key is to unify all non-zero third-order polarizations into a vector expression.

Key words: isotropic material, chiral, third-order susceptibility, cascaded second order effect