Accessing the optical nonlinearity of metals with metal–dielectric photonic bandgap structures

Metals typically have very large nonlinear susceptibilities ($\sim {10}^6$ times larger than those of typical dielectrics), but because they are nearly opaque their nonlinear properties are effectively inaccessible. We demonstrate numerically that a multilayer metal–dielectric structure in which the metal is the dominant nonlinear $\left[{\chi }^{\left(3\right)}\right]$ material can have much larger intensity-dependent changes in the complex amplitude of the transmitted beam than a bulk sample containing the same thickness of metal. For 80 nm of copper the magnitude of the nonlinear phase shift is predicted to be as much as 40 times larger for the layered copper–silica sample, and the transmission is also greatly increased. The effective nonlinear refractive-index coefficient $n_2$ of this composite material can be as large as $\left(3+6i\right)\times {10}^{-9} {\mathrm{cm}}^2/\mathrm{W}$, which is among the largest values for known, reasonably transmissive materials.