The damping factors that occur in nonlinear-optical response tensors are commonly assigned signs that depend upon the temporal ordering of the associated photon interactions. However, time-reversal symmetry is satisfied only if all these signs are identical. For example, only then is there a formal equivalence between the amplitudes for second-harmonic generation and parametric down-conversion and only then is electro-optic rotation forbidden in fluids. This correction reflects deficiencies in certain commonly employed semiclassical approaches to nonlinear optics.
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Andrews et al. (1998) studied this question.
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