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 can

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... hance the third-order nonlinearity by more than a thousand to a billion times, depending on target operation frequencies. This metamaterial principle also enables manipulation of the individual components of the linear and nonlinear susceptibility tensors. Our biomimetic approach overcomes the fundamental speed-efficiency trade-off in current resonant enhancement schemes, making faster and more efficient alloptical devices possible for 1.55 μm wavelength. The principle is also applicable to ionic diffusion, heat conduction, or other transport problems.