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Why experimental hyperpolarizabilities fall short of the fundamental limits and new approaches for breaking this barrier

Sum rules have been shown to impose a fundamental limit on the of nonlinear-optical susceptibility. All of the measured values of the hyperpolarizability and second hyperpolarizability over the last 25+ years, be it on- or off-resonance, fall a factor of 103/2 below these limits. Not only is this result scientifically puzzling on a fundamental level; but, has implications on the kinds of practical devices that can be made. In this work, we discuss molecular engineering techniques that aim to break this bottleneck.