Comment on ‘‘Forbidden nature of multipolar contributions to second-harmonic generation in isotropic fluids’’

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Abstract
Andrews and Blake [Phys. Rev. A 38, 3113 (1988)] have presented an analysis suggesting that no coherent optical second-harmonic radiation is produced to any order in a multipole expansion by a fluid of noninteracting, randomly oriented molecules under excitation by a plane-wave electric field. We demonstrate to all orders of nonlocality that the correct description of any isotropic centrosymmetric medium in the field of a plane wave includes a longitudinal (generalized) nonlinear source polarization, which was not treated by Andrews and Blake. This bulk polarization does not give rise to a second-harmonic wave with a growing intensity in the medium; however, as has been recognized in the literature, it cannot be neglected in measurements of second-harmonic generation from surfaces and interfaces, since a longitudinal polarization is capable of exciting transverse electromagnetic waves at a discontinuity.