Universal theory of third-order nonlinear polarization in isotropic media
Vector expression of third-order nonlinear polarization in isotropic media is derived,which is suitable for multiple beams incidence with different frequencies.This expression is applied to elucidate multiple well-known and distinct nonlinear optical phenomena,thereby validating its universality and accuracy.This offers a unified description of third-order nonlinear optical effects in isotropic media.By extending its application to hexagonal materials,this expression offers straightforward solutions to a variety of complex cases.This study is crucial for a systematic understanding of third-order nonlinear optical effects in both isotropic media and hexagonal materials,with the potential to enhance application of nonlinear optics in fields such as frequency conversion,polarization detection,and quantum information.