Optical properties based on simplifying approximations. For Drude model nanoparticles in the quasistatic limit, analytic expressions are available for the induced dipole polarizability α eff (ω), resonant frequency ω res , and extinction cross-section σ(ω) in limiting cases (Table ). Cases of particular interest here include a single isolated nanoparticle, a many-body configuration where each particle experiences only the mean field generated by the other particles (i.e., the Maxwell Garnett effective medium approximation), and an isolated pair of particles oriented parallel or perpendicular to E 0 truncated at the dipole level. The dipole moments are written in terms of the effective polarizability α eff ,