A sum rule for nonlinear optical susceptibilities

Luciana C. Davila Romero, David L. Andrews

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4 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)59-62
Number of pages4
JournalJournal of Optics B: Quantum and Semiclassical Optics
Issue number1
Publication statusPublished - 3 Nov 2003

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