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Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients

The effects of small relativistic corrections to the off-resonant polarizability, hyperpolarizability, and second hyperpolarizability are investigated. Corrections to linear and nonlinear optical coefficients are demonstrated in the three-level ansatz, which includes corrections to the Kuzyk limits when scaled to semi-relativistic energies. It is also shown that the maximum value of the hyperpolarizability is more sensitive than the maximum polarizability or second hyperpolarizability to lowest-order relativistic corrections. These corrections illustrate how the intrinsic nonlinear-optical response is affected at semi-relativistic energies.