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A Sum Rule for Nonlinear Optical Susceptibilities

Luciana C. Davila Romero·David L. Andrews
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Abstract

It is explicitly shown, for optical processes arbitrarily comprising two-, three- or four-photon interactions, that the sum over all matter states of any optical susceptibility is exactly zero. The result remains true even in frequency regions where damping is prominent. Using a quantum electrodynamical framework to render the photonic nature of the fundamental interactions, the result emerges in the form of a traceless operator in Hilbert space. The generality of the sum rule and its significance as a thermodynamic limit are discussed, and the applicability to real systems is assessed.

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Luciana C. Davila Romero, David L. Andrews. 2003-05-30. A Sum Rule for Nonlinear Optical Susceptibilities. https://doi.org/10.1088/1464-4266/6/1/010

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