Signature of bulk longitudinal plasmon-polaritons in the transmission/reflection spectra of one-dimensional metamaterial heterostructures

A systematic theoretical study of the transmission and reflection spectra of a 1D metamaterial heterostructure consisting of the finite repetition of a double layer of two different building blocks A (normal non-dispersive layer) and B (dispersive metamaterial) is presented, with the multi-layered system sandwiched between two semi-infinite layers of the A material. For the metamaterial slabs B we have studied two different dielectric/magnetic responses: a first one with both the electric permittivity and magnetic permeability given by a Drude-like metamaterial dispersion response, and a second one with the electric permittivity still given by a Drude-like response, whereas the magnetic permeability is given by a more realistic split-ring resonator metamaterial response. Theoretical calculations are performed within the transfer-matrix formalism, and transmission and reflection coefficients of the metamaterial heterostructure are straightforwardly evaluated. For oblique incidence, a finite projection along the growth direction of the electric or magnetic field of the incident wave associated with the TM or TE modes, respectively, leads to a coupling in each layer of the metamaterial heterostructure of the photon modes with the bulk electric or magnetic metamaterial plasmons, respectively. Such photon-plasmon coupling results in the formation of plasmon-polariton modes and gives rise to signatures of the electric or magnetic longitudinal bulk-plasmon polariton modes in the transmission and reflection spectra of the metamaterial heterostructure. Such features survive even in the case of a single AB double-layer metamaterial heterostructure, and experimental observation should be, therefore, easily achieved.