Centrosymmetry is a property of a geometric or physical system that indicates symmetry with respect to a central point. In a centrosymmetric structure, for every point in the structure, there is an identical point located at an equal distance in the opposite direction from a central origin.
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A crystal has centrosymmetry when its crystallographic point group contains spatial inversion. Its bulk electric-dipole polarization law must then satisfy . Substituting a power expansion in E makes every even-order coefficient vanish, including the second-order nonlinear optical susceptibility. A surface, an external symmetry-breaking field or a response beyond the electric-dipole approximation can change the conclusion.