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We experimentally demonstrate coherent control of the nonlinear response ofoptical second harmonic generation in resonant nanostructures beyond theweak-field regime. Contrary to common perception, we show that maximizing theintensity of the pulse does not yield the strongest nonlinear power-lawresponse. We show this effect emerges from the temporally asymmetricphoto-induced response in a resonant mediated non-instantaneous interaction. Wedevelop a novel theoretical approach which captures the photoinducednonlinearities in resonant nanostructures beyond the two photon description andgive an intuitive picture to the observed non-instantaneous phenomena.

Coherent Control of the Non-instantaneous Nonlinear Power-law Response in Resonant Nanostructures