  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.
