Retrieving the Effective Permittivity of an Optical Metamaterial Structured with Metallic Cylindrical Nanorods - An Analytical Approach Based on the Calculation of the Depolarization Field

The optical properties displayed by materials nanostructured with metallic inclusions are mainly driven by the excitation of surface plasmon-polaritons. With this in mind, a valid homogenization procedure must be able to describe appropriately the relationship between the geometry of the inclusions and the nature of local field modes. In this paper, we derive a corrected version of the Maxwell-Garnett model for the homogenization of nonmagnetic materials structured with cylindrical nanorod inclusions. The analytical formulation combines the Meier-Wokaun approach with the Green's function method for source regions to rigorously depict the impact of shape and size of the inclusions on the effective permittivity of those media. From the comparison to the respective results obtained by the Maxwell-Garnett formalism corrected for spheres and prolate spheroids, we show that our deduction provides further reliability in describing the spectral variation of the effective permittivity, particularly at the resonance regions. Moreover, we perform a comparison to the results given by the Bruggeman model in order to evidence that the nature of local field modes is also crucial in regarding the Maxwell-Garnett approach as a suitable choice to retrieve the effective resonance characteristics.