Analysis of homogeneous layer approximations in the modeling of localized surface plasmon resonance biosensors

We analyze theoretically the effectiveness of homogeneous layer approximations in modeling localized surface plasmon resonance biosensors made of spherical metal nanoparticles coated with biomolecular layers that have radially variable refractive indices. Using an extended Mie theory, we compute the extinction spectrum and peak wavelength of the system and compare them with when effective medium approximations are applied to treat the biomolecular layer as homogeneous. We investigate how the accuracies of the approximations depend on the geometric parameters of the system and the material of the metal nanoparticle. We also derive expressions that can be used to predict if the approximations would accurately predict the spectral position of the peak wavelength.