transmission reflection absorption

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1 Optical Cages V. Kumar*, J. P. Walker* and H. Grebel The Electronic Imaging Center and the ECE department at NJIT, Newark, NJ * Contributed equally Faraday Cage [], a hollow structure made of knitted metal wires, is capable of shielding its inner domain from external electromagnetic radiation. The openings in the wire mesh ought to be very small compared to the effective radiation wavelength; otherwise, some radiation may penetrate through. Here we explore optical cages where the mesh opening and its overall 3-D size are of the order of the radiation wavelength. Simulations suggest that some electromagnetic energy is trapped within the cage. Resonators are known to store energy. The quality factor Q - the ratio between the stored energy to the dissipated energy per radiation cycle - is large for high-quality resonators that exhibit very narrow band. Resonators may be made of metal enclosures or periodic dielectric structures [2]. Absorption is defined as intensity not transmitted or reflected and we explore metal wire frameworks for which the coefficient is large. Periodic metallo-dielectric structures (also known as screens, or metal meshes) have been studied in the past, and in particular in the wavelength region where the array pitch is of the order of, or smaller than the radiation wavelength [3-5]. This wavelength region is above the diffraction region. Stacked periodic metal screens resemble photonic crystals with a large index of refraction ratio [6]. Metal screens may be divided into two categories: inductive screens (metal films with a periodic array of holes which portray a band) and capacitive screens (the complementary structure where metal structures are embedded in a dielectric and portray a band). The screen's modes are made of local modes within each individual feature and extended propagating modes along the periodic array. At resonance, both local and extended modes form a composite standing wave. The screens exhibit negative index of refraction, or NIR (see SI section). For inductive screens the NIR is exhibited throughout the wavelength band pass. For capacitive screens, the NIR region lies in the longer wavelengths beyond the resonance. Despite large losses in the visible range, metals offer large index of refraction ratio when embedded in common dielectrics. Simulations: In terms of a large coefficient, array of cubic metal meshes (SI section) are not as efficient as icosahedrons. This suggests that there should be some degree of complexity to the knitted framework. Yarn balls, made of azimuthally spaced rings around a common center are more effective than cubes but exhibit large polarization dependency. Single elements are less efficient than when placed in an array. For simplicity, the icosahedrons were constructed of metal wires and were suspended in air. The lattice constant for this square array was micron and the wavelength range of interest was to 2 microns. Complex dielectric constant was selected [7]. The icosahedral edge and wire thickness varied. Periodic boundary

conditions between the icosahedrons and perfect matching layers (PML) on top and bottom of the computation cell were used. A CAD tool (Comsol) was employed in the analysis of the array.

This suggests that the coupling between nearest neighboring frameworks is important. Plots of the intensity coefficients for the, T,, R, and total A (which is defined as, A=-T-R) are provided in Fig.

2 conditions between the icosahedrons and perfect matching layers (PML) on top and bottom of the computation cell were used. A CAD tool (Comsol) was employed in the analysis of the array. There is an optimal icosahedron size, approximately 75% of the lattice constant, with edge length of 0.4 microns and wire thickness of 0.02 microns. This suggests that the coupling between nearest neighboring frameworks is important. Plots of the intensity coefficients for the, T,, R, and total A (which is defined as, A=-T-R) are provided in Fig.. The array of icosahedrons was illuminated by a plane wave along the z-direction with y-polarization (a) (b) (c) Fig.. (a) Copper-made icosahedral array: each edge measures 0.4 microns and the wire thickness was 0.02 microns. (b) Coefficients for the intensity, T, intensity, R, and A (defined as, A=-T-R) as a function of wavelength in microns. (c) Norm of the field distribution near each icosahedron's center. The wavelength is =.62 microns and the light is polarized along the y-direction. The coefficient is almost zero in the wavelength region between to.5 microns since most of the radiation is transmitted through. The intensity coefficient substantially increases beyond that region. Hot spots are situated at the cage edges and "cold spots" at the framework's corners. We identify two peaks, at =.8 and =.58 microns, respectively which vary as a function of the icosahedron size. The peaks are associated with the generation of shielding currents. In order to confirm that we calculate the dissipated electromagnetic intensity through currents in the wires, Q h= dvσ E E; with, the wire conductivity and E, the driving local electric field. The dissipating loss constant is, P=Q h/i 0 where I 0 W is the incident intensity. The difference between the total intensity loss coefficient A and P is practically zero in this wavelength range leading to the conclusion that the electric field has effectively excited resonating currents which may be identified with plasmonic polaritonic modes. The coefficient is quite large; A~0.82 at =.58 microns. Silver is known to be a better conductor than copper. The peak plasmonic loss for a silver-made icosahedral array is smaller than for copper-made frameworks: A~0.72 at =.5 microns. The coefficient is even smaller at =.36 microns: A~0.44. A third peak at =.53 microns exhibits A~0.37. Similar analysis for a cage made of silicon results in P~0.

An aligned, cage-within-cage framework is shown in Fig. 2. Here, the enclosing (larger) icosahedron edge measures 0.44 microns and the enclosed (smaller) icosahedron edge measures 0.22 microns.

(b) Coefficients for the intensity, T, intensity, R, and A (defined as, A=-T-R) as a function of wavelength in microns. (c) Norm of the field distribution near the icosahedron's center at =.

3 An aligned, cage-within-cage framework is shown in Fig. 2. Here, the enclosing (larger) icosahedron edge measures 0.44 microns and the enclosed (smaller) icosahedron edge measures 0.22 microns. The wire thickness is microns (a) (b) (c) Fig. 2. (a) Aligned copper-made cage-within-cage. (b) Coefficients for the intensity, T, intensity, R, and A (defined as, A=-T-R) as a function of wavelength in microns. (c) Norm of the field distribution near the icosahedron's center at =.39 microns. The light was polarized along the y-direction The intensity coefficient for a copper made cage-within-cage has not changed much, A peak~0.83 at =.65 microns, yet, the spectral width has dramatically increased as two peaks merge. The peak internal intensity is concentrated within the enclosed (smaller) icosahedron and is approximately twice the corresponding peak value for a single cage. The peak plasmonic loss for a silver-made cage-within-cage is also smaller than its copper-made counterpart: A~0.72 at =.35 microns. A second peak at =.69 microns exhibits A~0.66. Is icosahedral array the optimal cage structure? This is still an open question. Also puzzling is the smaller effect for silver-made with respect to copper-made framework; this could be explained in part by the lower plasmonic cut-off wavelength for silver. Tuning such structures by means of acoustic waves, extension of these to the far-ir, embedding quantum dots inside them and exploring the nonlinear regime are exciting possibilities. [] S. Jonathan Chapman, David P. Hewett, Lloyd N. Trefethen, "Mathematics of the Faraday Cage", SIAM Review, 57(3), (204). [2] Alexandra Ledermann, Diederik S. Wiersma, Martin Wegener, and Georg von Freymann, "Multiple scattering of light in three-dimensional photonic quasicrystals", OPTICS EXPRESS, 7(3), (2009) [3] R. Ulrich, Interference Filters for the far Infrared, Infrared Phys. 7, 987 (967). [4] O. Sternberg, et al, Square-Shaped Metal Screens in the IR to THz Spectral Region: Resonance Frequency, Band gap and Bandpass Filter Characteristics, J. Appl. Phys., 04(2), art. no (2008)

4 [5] K. D. Moeller, O. Sternberg, H. Grebel and P. Lalanne, "Thick inductive cross shaped metal meshes", J. Appl. Phys., 9, (2002) [6] J. Shah, D. Moeller, H. Grebel, O. Sternberg and J. M. Tobias, "Three-dimensional metallodielectric photonic crystals with cubic symmetry as stacks of two-dimensional screens", J. Opt. Soc. Am. (JOSA) A, 22, (2005) [7] P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals", PRB, 6(2), (972)

5 Transmittance Optical Cages V. Kumar, J. P. Walker and H. Grebel The Electronic Imaging Center and the ECE department at NJIT, Newark, NJ Supplemental Information Capacitive screens: At IR wavelengths, metals may be treated as perfect conductors. Transmission through a capacitive metal screen, with each feature made of a cross-shape is shown in Fig. Sa. The dip in is indicative of a band at the resonance frequency. The equivalent refractive index is shown in Fig. Sb. The array exhibits a NIR beyond the resonance wavelength mm bw=0μm (a) 50μm Lw=42 42 mm 50 50μm mm 0 mm 20 Re{n} 0 Im{n} (b) Fig. S. (a) An example of transmittance through a capacitive grid made of a metal cross on a dielectric at far-ir and (b) its related refractive index (D. Moeller and H. Grebel, unpublished) An array made of thin shell icosahedrons is shown in Fig. S2. The is not as large as for the wire counterpart and little electric field fills the structure. The current is more pronounced at the shadowed portion of the framework (when judged with respect to the incident radiation, along the negative z-direction).

0. (a) 0.0 0.00 (b) (c) Fig. S2. Thin (t=0.

(b) Intensity coefficient for, T,, R, and A (A=-T-R).

6 0. (a) (b) (c) Fig. S2. Thin (t=0.02 microns) hollow icosahedral metal framework. (a) The facet configuration for an edge length of 0.4 microns and a lattice constant of microns. (b) Intensity coefficient for, T,, R, and A (A=-T-R). (c) Norm of the field intensity crosssections at =.08 microns the maximum reflectance wavelength. A framework of cubic metal wires is shown in Fig. S3. The efficiency of the framework as a cage is limited (a) (b)

The peak at =.63 microns is ca 0.4. (c) Norm of the field intensity cross-sections.

7 (c) (d) Fig. S3. Cubic metal framework. (a) The wire configuration for an edge length of 0.9 microns and a lattice constant of microns. (b) Intensity coefficient for, T,, R, and A (A=-T-R). The peak at =.63 microns is ca 0.4. (c) Norm of the field intensity cross-sections. The plane wave illuminates the structure from the top and the polarization is along the y-direction. (d) The distribution of intensity lines at =.63 microns.

Optical cavity modes in gold shell particles

9 Optical cavity modes in gold shell particles Gold (Au) shell particles with dimensions comparable to the wavelength of light exhibit a special resonance, with a tenfold field enhancement over almost