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Microscopic structuring can change the effective properties of a material by several orders of magnitude. An example of this is animal bone, which has an effective elastic modulus that is more than 1,000 times larger than that of the constituent proteins. Here, we propose a broadband-enhancement principle of photonic nonlinearity that has a similar mathematical origin as the bone example. The proposed staggered array metamaterials violate the standard Miller's rule in nonlinear optics and candoi:10.1038/s42005-020-0352-0 fatcat:fi6mvogsc5afndxesve4ke42e4