Optical Properties of a Silver Nanodisk for Application to Optical Frequency Selective Surfaces Chiya Saeidi and Daniel van der Weide Electrical and Computer Engineering Department University of Wisconsin-Madison, Madison, Wisconsin 53706 Email: saeidi@wisc.edu Abstract—Depolarization factor of a silver nanodisk for use with Gans theory is derived from numerically extracted ex- tinction spectra. Results are adapted for nanodisk arrays using interaction constant, and validated through a frequency selective surface design. I. I NTRODUCTION Here, we examine the optical properties of a nanodisk (ND) as an important structures in nanophotonics, providing a useful geometry for optical frequency selective surfaces (OFSSs). Nanoparticles (NPs) of different morphologies have different extinction spectra. Computationally expensive calculation and optimization of extinction spectra of nanostructures makes it reasonable to derive a closed-form solution for rapid ap- proximation of the most important feature of the spectra, the resonance f max location. Although the Gans ellipsoid model quantitatively predicts the peak in the absorption spectra depending only on the aspect ratio, recent works have shown that f max also depends on the size of the cylindrical NP [1], [2]. In [2] the DDA method is used to determine the evolution of the optical properties of silver NDs with various parameters and for limited aspect ratios and sizes of a ND. Conversely, we derive the geometrical parameter of silver ND for use in Gans theory, namely depolarization factor L. Results are extracted from the numerically calculated extinction spectra for tens of ND sizes and aspect ratios. Results from the individual NP studies are adapted for array structure design considering appropriate interaction constant between particles. II. GEOMETRICAL FACTOR EXTRACTION The polarization-dependent response of the NDs can be discussed with the help of a static solution for the polarizability α. For a subwavelength ellipsoid-shaped NP of permittivity ε when a uniform field is applied along the l i axis, α is [3] α = V L i + ε h /(ε − ε h ) (1) where V is the volume of the NP, ε h is the permittivity of the host medium, and L i is is the depolarization factor in the i direction defined in [3] (subscript i dropped for simplicity from here on). The localized surface plasmon resonance (LSPR) is induced when the real part of the denominator is zero [3] Re[ε(ω)]| ωmax = −ε h 1 − L i L i (2) which is the exact condition under which the expression for extinction efficiency Q ext experiences a maximum [1]. Here ε is described by modified Drude model (ignoring loss) as ε (ω)= ε a − (εb-εa)ω 2 p ω 2 , with the high-frequency ε a , static dielectric constant ε b , and plasmon resonance frequency ω p . Values ε a =5.45, ε b =6.18, and ω p =1.7 × 10 16 rad/s are extracted from fitting with experimental data for silver in the optical frequency range [4]. So by substituting this model into (2), and by calculating the extinction spectra maximum of various aspect ratios and sizes with the finite element solver of CST MWS, an appropriate L for each of these spectra is determined. Fig 1.a shows f max for a range of aspect ratios k (k = 2r t where r is the radius and t is the thickness of the ND shown in Fig. 2) for 0.5 steps. It is seen that the ND radius affects the position of the peak. However, before excitation of higher plasmon modes, for ND of diameter smaller than 50 nm with dominating dipole resonance [5], the curves are only slightly different which is also clear from extinction spectra (Fig 1.c). This rule stands true for extracted depolarization factor L shown in Fig 1.b. Therefore, an average exponential fitting curve, which only depends on k, can be derived that essentially determines the resonance position with equation: L =0.22e -0.175k +0.038. (3) For more accuracy and bigger radii, parameters to fit L for various radii in ae -bk + c are also provided in Table I. Figures 1.a and 1.b also show that the analytical solution for oblate spheroid fails to predict the optical behavior of the ND. III. APPLICATION TO OPTICAL FSS DESIGN In order to design an nanoparticle array (NPA) acting as an OFSS, we need to determine its resonance frequency. If the NP is a part of 2-D periodic structure as shown in Fig. 2, the interaction between NPs changes the frequency of the resonance. Note that the collective plasmon resonance (CPR) of an NPA can be far away from the LSPR of an isolated NP. In this case an interaction polarizability is defined which is given by ( α -1 − β ) -1 where β is the interaction constant [6]. Thus, the induced moment on each NP in NPA experiences an extremum at frequency for which Re[α -1 (ω)] = Re[β (ω)]. (4) The real part of β can be found in [6] which for a dense square lattice of NPs excited by a normally-incident transverse plane 629 ThD1.2 (Contributed) 8:45 AM – 11:00 AM 978-1-4577-1507-5/13/$26.00 ©2013 IEEE