The electromagnetic near fields and the angular distributions of scattered light were preferentially calculated with 3D FEM simulations. Whereas Mie theory is a fast calculation method, it cannot handle nanoparticles at an interface which we will address in our last chapter. The comparison of the two calculation approaches for the simple case of a Saracatinib mw nanoparticle in vacuum (air) gives us confidence about the conformity of the two methods where possible. Apoptosis inhibitor If not stated otherwise, a spherical nanoparticle in air is investigated and cross sections are always the normalized values. Dielectric function of materials

For the above mentioned calculation methods along with the particular geometry, the optical constants of the materials, i.e., the dielectric functions, are the fundamental input parameters. Therefore, we now bring together the essentials of describing the dielectric mTOR inhibitor function of a material which we will use in the following. The dielectric function ∈ = ∈ 1 + i ∈ 2 relates to the refractive index ñ = n + ik as (10) The dielectric function of a material strongly depends on its electronic states: metals are dominated by free electrons whereas dielectrics have no free movable charges and semiconductors

are characterized by a band gap plus possibly free charge carriers. The corresponding dielectric functions are often times described by models of which the most common ones are summarized below: Metals – Drude formula

(11) With the damping γ and the plasma frequency ω P related to the free charge carrier concentration n e and the effective mass m * by ℏ (12) Whereas the plasma frequency relates to a property of a bulk material, for a spherical nanoparticle with radius r made from a material that can be described by the Drude formula, the resonance conditions for Benzatropine particle plasmons given by ∈ = −2 may be fulfilled. This condition results from the polarizability α which is derived for small particles [21] as (13) Metals may also show significant interband transitions and related absorption which can be described by a Lorentz oscillator compare also the semiconductors. Dielectrics – Cauchy equations (14) With the Sellmeier coefficients B 1, 2, 3 and C 1, 2, 3. The Cauchy equation can be approximated by a constant refractive index value for longer wavelengths. Semiconductors – Tauc-Lorentz model Combine the Tauc joint density of states with the Lorentz oscillator model for ∈ 2: (15) and ∈ 1 is defined according to the Kramers-Kronig relation (16) For the presence of significant free charge carriers in the semiconductor, the Tauc-Lorentz model can be combined with the Drude formula.