Complex modes and effective refractive index in 3D periodic arrays of plasmonic nanospheres

Salvatore Campione, Sergiy Steshenko, Matteo Albani, Filippo Capolino
2011 Optics Express  
We characterize the modes with complex wavenumber for both longitudinal and transverse polarization states (with respect to the mode traveling direction) in three dimensional (3D) periodic arrays of plasmonic nanospheres, including metal losses. The Ewald representation of the required dyadic periodic Green's function to represent the field in 3D periodic arrays is derived from the scalar case, which can be analytically continued into the complex wavenumber space. We observe the presence of one
more » ... the presence of one longitudinal mode and two transverse modes, one forward and one backward. Despite the presence of two modes for transverse polarization, we notice that the forward one is "dominant" (i.e., it contributes most to the field in the array). Therefore, in case of transverse polarization, we describe the composite material in terms of a homogenized effective refractive index, comparing results from (i) modal analysis, (ii) Maxwell Garnett theory, (iii) Nicolson-Ross-Weir retrieval method from scattering parameters for finite thickness structures (considering different thicknesses, showing consistency of results), and (iv) the fitting of the fields obtained through HFSS simulations. The agreement among the different methods justifies the performed homogenization procedure in case of transverse polarization. when 0 z z α β < . By looking at both Figs. 2 and 3, the forward Mode 1 and the backward Mode 2 could be guided in the structure in the lossy case. Note that the presence of two transverse modes with moderately low attenuation constant z α is in agreement with what previously predicted in [9] by using the nano-transmission line network concept, and analytically in [25] for an ideal lossless case. Longitudinal polarization (L-pol) The dispersion diagrams for the Structure I outlined in Table 1 are shown in Fig. 4 for both the real and the imaginary parts of the wavenumber z z z #154629 -$15.00 USD
doi:10.1364/oe.19.026027 pmid:22274192 fatcat:o6wqaxqs3jdtrgf3c52q5lqcmm