Analysis of nonlocal effective permittivity and permeability in symmetric metal–dielectric multilayer metamaterials

A generalized nonlocal effective medium theory is derived based on the transfer-matrix method to determine the nonlocal effective permittivity and permeability for the symmetric and periodic metal–dielectric multilayer metamaterials, with respect to both transverse-electric and transverse-magnetic polarized light at arbitrary angle of incidence. The nonlocal effective permittivity and permeability tensors are analyzed in detail as functions of the wavelength, the angle of incidence, and the multilayer period. Our generalized nonlocal effective medium theory in consideration of both permittivity and permeability can accurately predict the dispersion relation, the transmission and reflection spectra, and the optical field distributions of symmetric metal–dielectric multilayer stacks with either subwavelength or wavelength-scale period of the unit cell.