Gradient effective medium model for inhomogenous nanoparticle layers

Czajkowski K. M., Świtlik D., Antosiewicz T. J.

Engineered Materials Platforms for Novel Wave Phenomena (Metamaterials), 2017 11th International Congress on

2017, 10.1109/MetaMaterials.2017.8107840

Electromagnetic modeling of sensing of stochastic distributions of nanometer-sized particles usually requires a large number of calculations to correctly obtain the average response of a sensor. Here, we present an alternative method, which utilizes a gradient effective permittivity model based on the classical Maxwell-Garnett mixing formula. In our model the nanoparticle layer is homogenized into several effective sublayers, whose permittivities depend on the spatial distribution of nanoparticles (and consequently volume fraction) in the direction normal to the substrate. The presented approach enables more accurate prediction of the properties of inhomogenous nanoparticle layers in a simpler way than by simulating actual particle distributions. The model is applied to simulate a plasmonic sensor covered by a Pd nanoparticle layer which undergoes sintering. The results of finite-difference-time-domain and transfer-matrix simulations with effective gradient layers are consistent with rigorous simulations and are more precise than analogous simulations with a single Maxwell-Garnett effective layer.