Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials

The optical nonlocality in symmetric metal-dielectric multilayer metamaterials is theoretically and experimentally investigated with respect to transverse-magnetic-polarized incident light. A nonlocal effective medium theory is derived from the transfer-matrix method to determine the nonlocal effective permittivity depending on both the frequency and wave vector in a symmetric metal-dielectric multilayer stack. In contrast to the local effective medium theory, our proposed nonlocal effective medium theory can accurately predict measured incident angle-dependent reflection spectra from a fabricated multilayer stack and provide nonlocal dispersion relations. Moreover, the bulk plasmon polaritons with large wave vectors supported in the multilayer stack are also investigated with the nonlocal effective medium theory through the analysis of the dispersion relation and eigenmode.