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Hierarchical Semiconductor, Metal and Hybrid Nanostructures and the Study of their Light-Matter
Interactions
By
Anna Lee
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy
Graduate Department of Chemistry University of Toronto
Materials and Methods....................................................................................................................................48
A1.2. The Yee algorithm…………………………………………………………………………191
A1.3. Finite difference expressions for Maxwell’s Equations…………….………193
A2. The Drude Model………………………………………………………………………..………………195
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Tables of Figures
Chapter1 Introduction
Figure 1.1. Energy band gap diagram for (A) conductors whose conduction band (CB) and valence band (VB) overlap slightly, (B) in semiconductors CB and VB are spaced and (C) in insulatorsCB and VB are widely separated…………………………………….....………………………………2
Figure 1.2. Volume plasmon-the collective longitudinal oscillations of the conduction electrons of a metal…………………………………………………………………………………………………...……5
Figure 1.3. Schematic illustration of a surface plasmon polariton (SPP) propagating along the x direction. Electric field lines of a SPP wave on a single interface where the structure is invariant with respect to the y axis……………………………………………………………………….…………6
Figure 1.4. Schematic illustration of a non-propagating localized surface plasmon..................7
Figure1.5. Schematic illustration of an isotropic sphere placed into an electrostatic field….8
Figure 1.6. Schematic illustration of near-field coupling between metal nanoparticles (MNPs). Two different polarizations (parallel and perpendicular to the MNP axis) are shown……………………………………………………………………………………………………….………………….13
Figure 1.7. (A) SEM image of arrays of gold nanoparticle (B) Dependence of the plasmon peak position on the interparticle spacing d for both the transverse and longitudinal excitation of the collective mode. The dotted line shows a fit to the d-3 dependence of coupling predicted by a point dipole interaction model………………………………..…………………14
Figure 1.8. Extinction spectra of gold nanoparticles (height 14 nm, diameter 150 nm). Reprinted with permission from Reference 35. Copyright 2000, American Physical Society ........................................................................................................................................................................................15
Figure 1.9. Schematic illustration of (A) a bulk semiconductor: continuous conduction band (CB) and valence band (VB) which are separated by an energy gap (Egap) (B) a semiconductor nanocrystal (NC): with discrete atomic-like energy states and size-dependent Egap………………………………………………………………………………...…………….……………..16
Figure 1.10. (A) Allowed optical transitions from hole quantized states resulting from mixing between valence sub-bands to CB for the case of CdSe QDs. (B) Absorption spectra of size-dependent as-synthesized CdSe QDs showing well-resolved optical transitions..................................................................................................................................................................18
Figure 1.11. Schematic illustration of fine-structure splitting of the lowest exciton state for CdSe QDs with wurzite crystal structure. The band-edge 1S(e)-1S3/2(h) transition is
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induced by a strong electron and hole exchange interaction and shape and crystal field anisotropy..................................................................................................................................................................19
Figure 1.12. Electric polarization in dielectrics showing ionic (or molecular) and electronic polarization……………………………………………………………………………………………...…………………..21
Figure 1.13. Schematic of the self-assembly of nanoparticles into a variety of hierarchical structures: chains, bi-layer, ring, and hexagonal arrays……………………………....………………….24
Figure 1.14. TEM images of (A) Self-assembly of magnetic dipole–dipole interactions by using 20 nm cobalt nanoparticles in the absence of an external magnetic field. Reprinted with permission from Reference 32. Copyright 1966, American Institute of Physics. (B) Formation of “ring” conformation under an applied magnetic field of 0.225 T. Inset shows a ring with almost single-particle thickness. (Inset Scale bar is 100 nm). Reprinted with permission from Reference 51. Copyright 2008, American Chemical Society………..….…..….25 Figure 1.15. (A) Schematic illustration of a charged gold NP interacting with a gold nanorod via electrostatic interactions. (B) Ratio of the interaction energies for the end and side configurations as a function of screening length. Reprinted with permission from Reference 24. Reprinted with permission from Reference 48. Copyright 2009, Small.......................29
Figure 1.16. Fluorescence confocal microscope images of varying sizes of water droplets in toluene in which CdSe NPs show self-assembly at the liquid-liquid interface. Optical cross-sectional images at various depths are shown on the left. Reprinted with permission from Reference 81. Copyright 2003, Science……………………………………………....……………………….….32
Figure1.17. (A) Naturally occurring conventional material with its atoms (B) Metamaterial artificially structured “atoms” Figure is adapted from reference 87………..……………………….34
Figure 1.18. Permittivity(ε)/Permeability(µ) Diagram. The first quadrant, second, third and fourth quadrant are assigned as double- positive (DPS), epsilon-negative (ENG), double-negative (DNG) and mu- negative (MNG) respectively……………………...…………………35
Figure 1.19. Schematic illustration of the proposed structure for making a double-negative (DNG) material showing arrays of paired nanorods. The arrows show the direction of current flow. Figure is adapted from reference 106……………………………....………………………..37
Figure 1.20. The idea of a perfect lens with sub-wavelength resolution (A) A conventional lens only collecting the propagating waves: kt < k0 (B) The loss of the evanescent waves in a conventional imaging system (solid line represents propagating modes whereas dashed lines represents evanescent modes) (C) The focusing ability of a DNG slab (D) The growth of evanescent waves in the DNG slab and the restoration of both the propagating and evanescent waves. Figure was adapted from Reference 91……………………………………………..39
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Chapter 2 Materials and Methods
Figure 2.1. Cross-sectional sample preparation for internal structure investigation of lamellae by STEM. (A) CdSe QD and nanorod lamellae were prepared on separate carbon coated indexed TEM grids. STEM was used to identify the locations of individual lamellae. (B) the indexed grids were then coated with approx. 10nm of carbon via evaporation to secure the structure. (C) Grids were then sputtered with a 20-30nm layer of Au which was used as a visual marker in imaging. (D) The indexed grids were then embedded in epoxy resin and 30nm cross-sections through individual lamellae were prepared by ultramicrotomy…………………………………………………………………………………...………………………..54
Figure 2.2. Optical transmission setup using super-continuum (SC) laser source along with an acousto-optic tunable filter (AOTF) for monochromatic illumination of the cloak sample.........................................................................................................................................................................57
Chapter 3 Results: Probing Dynamic Generation of Hot-Spots in Self-Assembled Chains of Gold Nanorods by Surface-Enhanced Raman Scattering
Figure 3.1. Schematic of the generation of hot-spots via end-to-end self-assembly of gold NRs into chains. (a) Gold NRs stabilized with CTAB. (b) Ligand exchange of CTAB with SH-PS at the ends of the NRs. (c) End-to-end assembly of NRs triggered by adding water to the solution of NRs in DMF, in the presence of Raman reporter OX. The volume fraction of water in the DMF/water mixture is 20 vol %. Hot-spots are generated between the ends of adjacent NRs. The distance between the adjacent NRs in the chain is maintained constant. Schematic is not drawn to scale………………………………..………………………………………..…………..65
Figure 3.2. (a) Representative STEM images of the self-assembled chains of NRs. Diffuse grey regions between adjacent NRs indicate the presence of SH-PS globules forming in a poor solvent. Scale bar is 40 nm. (b) Variation in extinction properties of NRs in the course of their self-assembly in chains. The spectral position of LSPR shifts from 754 nm to 812 nm
with the aggregation number of the NR chains changing from =1 at t < 5 min to = 8 at t =18 hr. Transverse LSPR is located at 514 nm. The peak at 660 nm corresponds to OX......66
Figure 3.3. (a) Evolution of normalized ensemble averaged SERS spectra in self-assembled
NR chains. The average aggregation number of NR assemblies changes from =1 at t < 5
min (bright-red spectrum) to = 8 at t =18 hr (black spectrum). The SERS peaks at 563 and 604 cm-1 are normalized against the SERS peak of DMF at 659 cm-1 (indicated with astericks). (b) Variation in the normalized SERS peak intensity measured at 563 cm-1
plotted as a function of the average aggregation number of the NR chains. SERS variation (y error) is based on three measurements taken within 15 min. Approximately 1000 NRs
(including individual species) were used in the calculations of number (x error). Laser excitation wavelength was 785 nm…………………………………………………………................................68
Figure 3.4. SER spectra of oxazine 4 5M adsorbed on roughened gold substrate as a function of solvent environment (a) H2O, (b) DMF and (c) DMF/ H2O mixture containing 20 vol. % of H2O………………………………………………………………………..………………………………….70
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Figure 3.5. Correlation of the normalized intensity of SERS peak at 563 cm-1 (red circles) and the product of extinctions measured at 785 and 821 nm (blue circles), plotted as a
function of the aggregation number of the NR chains. Top: y errors of the intensity of SERS peak (red squares) and the product of extinctions (blue squares) were calculated based on three measurements………………………………………………………………………………………72
Figure 3.6. Three-dimensional finite-difference time-domain (3D-FDTD) simulation of the end-to-end assembly of gold NRs. Electric field profile was calculated at the resonance wavelength of the co-linear NR chain at (a) 760 nm, (b) 782 nm, and (c) 802 nm. Polarization of the incident light is parallel to the long axes of the NRs (i.e., to the z-coordinate). Hot-spots between adjacent NRs show a maximum electric field intensity 4000 times greater than the incident field………………………………………………………………………………74
Figure 3.7. FDTD simulation showing (a) Electric field intensity squared obtained from incorporating average NR aggregation number, as a function of wavelength (factoring in experimentally determined statistical data) (b) Normalized sum of electric field intensity squared over a small volume enclosing the NR chain, for ideal NR chain lengths (Standard deviation is equal to zero) ranging from 1 to 9 NRs as a function of wavelength. (c) Sum of electric field intensity squared over a small volume enclosing NRs, chain lengths (number of NRs ranging from 1 to 9) as a function of wavelength (not normalized). (d) Peak electric field intensity squared values plotted against their corresponding resonant wavelengths. Number of NRs increases from 1 to 9 (left to right)……………………………………………………….. 75
Figure 3.8. Three-dimensional finite-difference time-domain (3D-FDTD) simulation showing examples of electric field profiles for end-to-end assembled gold NR dimmers and trimers. Polarization of the incident light is parallel to z-coordinate. Angular variance of (a) 0 degrees (b) 20 degrees (c) 40 degrees (d) 60 degrees (e) 90 degrees (f - i) Calculated absorption, scattering, extinction cross sections and electric field intensity squared respectively of various angled NR dimmers and trimers as a function of wavelength. Electric field strength between adjacent NRs decreases as angle between adjacent NRs increases……………………………………………………………………………………………………………………..78
Figure 3.9. Calculated absorption, scattering and extinction cross sections as a function of wavelength for various NR chain lengths ((a) to (c) respectively) and average NR aggregation number ((d) to (f) respectively). A total-field scattered field (TFSF) source is utilized for calculating the scattering and absorption cross-sections. Incident field polarization is parallel to the major rod axis (i.e. z), the bandwidth of source is from 600 nm to 1000 nm. Simulation domain is terminated with perfectly matched layer (PML). A mesh override region of (1 nm x 1nm x 1nm) mesh size is defined for better modeling of the circular rods in Cartesian coordinates. A 3-D time domain monitor is utilized for recording the field strengths as a function of time and a Fourier transform provides the frequency domain results. Extinction cross-section were calculated for different NR chain lengths and a certain factor (see main text) from each curve was added according to the experimental statistical data to lead figure (f). The heterogenity of NR chain size at each stage of the assembly is one of the contributing factors to variations in the observed amplitude………..79
Figure 4.1. Schematic illustration of gold nanorods (NRs) assembled in a side-by-side manner showing a reduction of electric field as the number of NRs increases in NR ensembles…………………………………….………………………………………………………………………………92
Figure 4.2. Calculated normalized absorption (a), scattering (b) and extinction cross section (c), all plotted as a function of wavelength for NR assemblies containing from 1 to 8 NRs. Simulations were carried out using three-dimensional finite-difference time-domain (3D-FDTD) simulation……………………………………………………………………………………………….….94
Figure 4.3. Modes supported by side-by-side assembly of NRs. Mode shapes of surface plasmons of 1 to 3 NRs from left to right. The resulting effective index values are used for the calculation of propagation constant of surface wave in the different geometries. Fields are normalized to their maximum intensities……………………………………………………………..….96
Figure 4.4. (a-d) Examples of electric field profiles produced via 3D-FDTD simulation for ensembles of side-by-side assembled NRs. Polarization of the incident light is at 45 degrees to the long axis (z-coordinate) of NRs. (e) Sum of electric field intensity squared of ensembles containing a different number of NRs. ………...………………………….….…………………97
Figure 4.5. Schematic illustration of side-by-side NR assembly. A thiolated polystyrene (SH-PS) is attached to the ends of cetyltrimethylammonium bromide (CTAB) coated gold NRs in THF via site-specific ligand functionalization. After the addition of the Raman reporter, side-by-side assembly was triggered by the addition of water (10 vol. %)............98
Figure 4.6. (a) A photograph showing the typical change in color of self-assembling NRs in solution as a function of time (Top left). Representative scanning transmission electron microscopy (STEM) images of NRs in various stages of self-assembly. Scale bar is 15 nm (b) Variation in extinction properties of NR ensembles over time............……………………………..100
Figure 4.7. FDTD simulations showing absorption, scattering, and extinction of 2NRs per stack for y and z directions of propagation of incident radiation. When wave vector
inck is
parallel to the NR axis, a peak at 520 nm is observed corresponding to the transverse SPR……………………………………………………………………………………………………………………………103
Figure 4.8. Representative scanning transmission electron microscopy (STEM) images of NRs in various stages of side-by-side assembly. Recorded on a Hitachi S-5200 scanning electron microscope operating in STEM mode. Note: as-synthesized NRs contain a small population of spheroids (~5%)…………………………………………………………………….…………….102
Figure 4.9. (a) Representative ensemble-averaged SERS spectra of Cresyl violet (CV), measured in the course of side-by-side assembly of the NRs as a function of time. The band
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at 900 cm-1 corresponds to THF which is used as an internal standard to normalize the SERS of CV at 535, 595 cm-1. (b) Normalized SERS intensity at 535 (red circle), 595 cm-1 (blue triangle) and control experiments without the assembly (black square, for SERS of CV at 595 cm-1 ) as a function of time. (c, d) SERS of CV on a roughened gold substrate in THF and water respectively. A 785 nm laser excitation was used...........................................................106
Figure 4.10. A sum over volume of the electric field intensity squared via FDTD simulations for various NR assemblies (number of NRs from 1 to 8) as a function of wave length (nm) (right figure). The total volume of the sum of E field intensity squared for the ends of NR ensembles show a decrease with increasing number of NRs. Blue: 1 NR, green: 2 NRs, Red: 3 NRs, light blue: 4 NRs, pink: 5 NRs, black: 6 NRs, dotted blue: 7 NRs, and dotted green: 8 NRs...........................................................................................................................................................107
Chapter 5 Results: Surface-Enhanced Raman Spectroscopy in Hollow Core Photonic Crystal Fibers: a tool for exploring the surface chemistry of gold nanoparticles
Figure 5.1. Schematic illustration of experimental set-up. A hollow core photonic crystal fiber (HCPCF) filled with gold nanorod (NRs) solution……………………………..…………………..116
Figure 5.2. (A) SERS spectra of CTAB coated gold NRs detected through direct sampling in a cuvette and core-filled HCPCF. (B) Variation in the normalized SERS peak intensity measured at 178 cm-1 plotted as a function of concentration of CTAB coated gold NRs (the concentration of the NRs were determined by extinction measurements).21 SERS variation (y error) is based on 3 measurements………………………………………………………………………….118
Figure 5.3. SERS spectra of 3 µM Congo Red molecules by using (A) core-filled HCPCF (B) direct sampling from a cuvette. (C) Ordinary Raman spectrum of Congo Red molecules at the concentration of 560 µM. The spectra have been separated vertically for clarity………………………………………………………………………………………………………………………..119
Figure 5.4. Normalized SERS spectra of CTAB coated gold NRs as a function of SH-mPEG concentration (A) CTAB coated NRs as a control system (B) 20 µM of PEG (C) 50 µM of PEG (D) 100 µM of PEG. The peak at 103 cm-1 was used to normalize the peaks. The spectra have been separated vertically for clarity. 0.54 nM of NRs were used…………...……………….122
Chapter 6 Results: Lamellar Envelopes of Semiconductor Quantum Dots
Figure 6.1. (A and B) Scanning transmission electron microscopy (STEM) images of colloidal CdSe QDs and CdSe bullet-shaped nanorods as controls, deposited from toluene solution onto carbon coated TEM grids, exhibiting the typical short range order produced by evaporation……………………………………………………………………………………………………………129
Figure 6.2. (A) Liquid state confocal fluorescence microscopy image of CdSe NC lamellae formed by the addition of 10% (v/v) water with subsequent 20 sec sonication. (B) Confocal image of the same preparation as (A) at less than 10 s sonication time. Confocal images were recorded using an oil immersion lens (excitation at 364 nm, detection 550 to 600
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nm). (C) Solution state “Wet cell” BSE image showing the existence of large lamellar structures (see 1) in solution along with small droplets (see 2) whose greatest signal exists at its periphery. (D) Solution state “Wet cell” BSE image overview of large lamellae along with disordered aggregates. (E) Image intensity profiling of a lamella (inset) showing uniform intensity consistent with a disk- or sheetlike structure……………………………………130
Figure 6.3. (A) Bright field STEM low magnification overview of NC pancake shaped lamellae created by the addition of nonsolvent (water) and subsequent sonication. (B) Dark field STEM image of an individual nanorod pancake shaped lamella created by a similar procedure, mounted on a TEM grid with a combination ultrathin/lacy carbon film….……133
Figure 6.4. (A) STEM image of a NC lamella. Inset 1 shows NC ovelap indicated by linear structures. Fourier transform (inset 2) indicates hexagonal symmetry. (B) STEM image of a nanorod lamella inset 1 shows nanorod ovelap indicated by fine lines subdividing individual NCs. A region of ordered hexagonal packing is confirmed by Fourier transform (inset 2). (C) SEM image of a lamella (see 1) mounted on an uncoated Cu TEM grid. The lamella (∼15nm thick) spans the dark void (∼15 μm) (see 2) in the grid without support. (D) Examples of folds and tears present in lamellae indicating their structural integrity. (E and F) Cross-sectional STEM images of NC tri- and bilayers. For all cross sections, the thickness is ∼30 nm. The capping Au overlayer is used as a location marker……………..….135
Figure 6.5. EDS line scan of a cross-sectioned QD lamellar tri-layer. A line scan showing the presence of Cd (solid line), Se (dot dot dash) and P (dot dash). Ti (dot), which has no spectral overlap with the elements of interest, is included as a background control. Cd, Se and P are all significantly above background. Coincidence of P with Cd and Se indicates the presence of TOPO…………………………………………………………………..……………………………………136
Figure 6.6. (A) Liquid state confocal fluorescence microscopy images of NC lamellae formed in the presence of the water-soluble dye fluorescein isothiocyanate (FITC), water 10% (v/v). Both FITC and NCs were excited using the 488 nm line of an argon ion laser. Note the coincidence between FITC (green) (collection range 490-530 nm) and NCs (yellow) (collection range 550-600 nm) indicating that the water-soluble dye is associated with the lamellar structure. (B) Energy dispersive X-ray spectroscopic (EDS) line scans for CoCl2 ·6H2O incroporated into CdSe lamellae. The inset shows an HAADF STEM image with the line scan (yellow line) across the lamellar structure (scale bar: 10 μm). (C) EDS line scan of a cross-sectioned (∼70 nm thick) Co incorporated NC lamellar bilayer showing the presnce of Co within the structure. The inset shows corresponding HAADF STEM image (scale bar: 35 nm). (D)EDS data for ferritin incorporated into the lamellae. The inset shows a corresponding HAADF STEM image (scale bar: 500 nm). Note: Ti Kα or V Kα lines were used as backgrounds since they have no spectral overlap with the elements of interest…139
Figure 6.7. (A to D) EDS maps of Cd, Se, Au and Ti (background) respectively, corresponding to the structure presented in Figure 6.8.A showing that distribution of Au NPs is fully contained within the structure……………………………………………………………..……140
Figure 6.8. (A) Incorporation of Au NPs into CdSe NC lamellae. In the HAADF STEM image shown, the bright “dots” are individual Au NPs. (B) Crosssectional (∼30 nm thickness)
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STEM image confirming the encapsulation of Au NPs inside the NC bilayer (as previously, an evaporated Au layer, upper portion of the image, is used as a marker). (C and D) Simultaneously recorded SEM and TEM images, respectively, confirming encapsualtion of Au NPs within the NC lamellae. (E) SEM image of control sample with Au NPs added after the NC lamellae formation. (F) Histogram showing 10 maximum photoluminescense intensity measurements for both NC lamellae and Au encapsulated NC lamellae. (G and H) Representative fluorescence confocal microscope images of CdSe NC lamellae and Au encapsulated NC lamellae, respectively………………………………………………………………………..143
Chapter 7 Results: Towards Experimental Demonstration of ‘2D’ Visible Range Cloaking via a Bottom-up Approach
Figure 7.1. Schematic illustration of a three-dimensional view showing the wave trajectories of a spherical cloaking system. Reprinted with permission from Reference 14. Copyright 2006, Science………………………………………………………….…………………………………..150
Figure 7.2. (A) Straight field line through a homogeneous medium against a Cartesian coordinate system (B) distorted field line travelling through a heterogeneous medium produced by varying the spatial distribution of permittivity and permeability. Reprinted with permission from Reference 14. Copyright 2006, Science……………………………………….151
Figure 7.3. A two-dimensional cross-sectional view of wave trajectories of a spherical cloaking system where light is deviated around the object to be cloaked (radius a) within the annular cloak region (radius b – a) and return to its original path. Reprinted with permission from Reference 14. Copyright 2006, Science………………….………………………….. 152
Figure 7.4. The coordinate transformation of a cylindrical shell model. A cylindrical region r<b into a concentric cylindrical shell a <r < b. There is no variation along the z direction. Reprinted with permission from Reference 13. Copyright 2007, Nature……………..…………153
Figure 7.5. Calculated plot of radial component of electric permittivity (εradial) as a function of cloak dimensions (A) a = 0.7 µm and b = 2 µm (B) a = 1.2 µm and b = 3.5µm. Both parameters result in the effective permittivity at operating wavelength of 500 nm. Silver nanoparticles with a radius of 10 nm were used for the calculations……………….…………….156
Figure 7. 6. Schematic illustration of the non-magnetic cloak structure. Inner core (dark grey) is the cloak area surrounded by metal nanowires (NWs) in a dielectric host. A Radial array of NWs is perpendicular to the z-axis and must satisfy the filling factor such that the radial component of electric permittivity varies from 0 at a to 1 at the exterior surface. Spatial positions of NWs do not need to be periodic……………………………………..………………158
Figure 7. 7. Summary of explored routes for the fabrication of a non-magnetic optical cloak device………………………………………………………………………………………………………………..……….159
Figure 7.8. Schematic showing two possible routes to produce the optical cloak. Route I: vertical assembly of gold nanorods on silica then subsequently embedded via silica
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deposition. Route II: radial assembly of binary metal NWs (eg, gold/nickel) around a cylindrical host directed by a controlled magnetic field…………………………………………...……160
Figure 7.9. Representative TEM image of vertical assembly of gold nanorods onto synthesized silica particles. The ends of gold nanorods were functionalized by the introduction of 3-mercaptopropyl trimethoxysilane………………………….…………………………162
Figure 7.10. Schematic illustration of the electrochemical method used to produce binary nanowires (NWs) composed of nickel and gold……………………………………………………………163
Figure 7.11. (A) Backscattered SEM images of binary NWs showing various lengths of each component. Note: silver is used to fill the bifurcated pores to provide even deposition of gold and nickel (B) EDS mapping showing atomic composition of NWs…………….…………..164
Figure 7.12. Magnetic field line simulations analogous to (A) Helmholtz and (B) anti-Helmholtz configurations……..……………………………………………………………………………………. 165
Figure 7.13. (A) Example of experimental set-up using annular magnets in an anti-Helmholtz arrangement producing a radial magnetic field in the central zone between magnets (B) Optical micrographs showing top-views of NW assemblies via the two different configurations, showing a radial alignment of NWs in the anti-Helmholtz arrangement..……………………………………………………………………………………………………………..166
Figure 7.14. Schematic of the proposed route to the fabrication of radial porous alumina as a dielectric host via anodization of aluminum (Al) wire. The cross-sectional view shows a metallic Al core surrounded by a porous alumina coating with a radial distribution of pores………………………………………...………………………………………………………………………………..168
Figure 7.15. SEM images of (A) Bare Aluminum wire after electropolishing. (B) Anodized aluminum oxide (AAO) grown as a cylindrical dielectric shell around an Al wire core. (C) Surface morphology of AAO shell showing a uniform pore structure (D) A cross-sectional view of radial porous AAO grown using 3 % Oxalic acid (nb, surface roughness shown is due to fracturing artifact)……………………………………...……………………………………………………170
Figure 7.16. (A) Variations of average pore diameter (blue circle) and average cell size (red square) as a function of applied potential. (B) Calculated pore volume fraction as a function of applied voltage. The oxide layer was electrochemically grown over 105 minutes using 3 wt. % of Oxalic acid in water as an electrolyte solution……………………………….…….171
Figure 7.17. (A-B) Low and high magnification backscattered SEM images of the surface of AAO structures containing silver NWs. Inset shows superficial deposition of larger silver particles which were subsequently removed by diamond paste washing. (C) Backscattered SEM image of a silver NW loaded radial AAO structure. This example shows both the desired radial silver NW distribution in a dielectric host along with the required structural dimensions. (D) Calculated plot based on (C) showing r response for a = 0.6 µm and b = 1.75 µm. Operating wavelength is 500 nm. Radius is variable ranging from a to b………..175
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Figure 7.18. Optical images captured by CCD camera at a wavelength of 540nm for transverse electric (TE) and transverse magnetic (TM) polarization. Quantification of the intensity across the fabricated structure was carried out by a series of sequential diagonal scans over the wavelength range of 450 to 750 nm……………………………………………..………..177 Figure 7.19. Polarization-dependent normalized field intensity plotted as a function of wavelength via transmission measurement. Transverse electric illumination (TE) and Transverse magnetic illumination (TM) on the fabricated structure. Field intensity of TM shows enhanced transmission (blue) in the range 540 to 550nm…………….…………....………179 Table 1.1. Van der Waals interaction energy and force between macroscopic bodies of different geometries with surfaces a distance of D apart where D<<R. R is the radius and A is the Hamaker constant………………………………………………………………………………………………………………………….……..….28
Table. 7.1. Summary of required parameters for the fabrication of a non-magnetic optical cloak device………………………………………………………………………………………………………………..158
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List of Appendices
Figure A1.1. The Yee mesh , the Yee’s algorithm centers its E and H components in three dimensional space so that every E component is surrounded by four circulating H components and vice versa. Figure A1.2. Space and time distribution of E and H fields based on Yee mesh and the leap frog algorithm.
1
Chapter 1
Introduction
The work presented in this thesis explores and utilizes a variety of building blocks
including conducting, semiconducting and insulating materials both in isolation and
combination to exploit the optical properties of designed, hierarchically assembled
nanoscale structures. In this chapter, optoelectronic properties of the constituent
materials used as “building-blocks” are described. This chapter concludes with a brief
discussion of various examples of the self-assembly of nanomaterials and an overview of
metamaterials.
1.1. Overview of Metals, Semiconductors and Insulators
Within atoms, the energy of bound electrons is quantized and as such only discrete
values of electron energy are permitted. The overlapping wave functions of electrons
results in discrete, quantized energy level splitting. As the number of atoms increases (i.e.,
in a crystalline solid) the allowed energies form two distinct energy bands – the valence
band (VB) and the conduction band (CB). The VB consists of closely spaced levels which are
mostly filled with electrons whereas the CB represents mostly unoccupied electronic levels
at higher energies. At particular interatomic distances, CB and VB can be separated by a
zone where electron energies are not permitted. These forbidden energies represent the
band gap of a material.1 Energy band gap is a core property which influences a material’s
2
characteristics from optical and electronic to mechanical properties. Simplified energy
band gap diagrams for conductors, semiconductors and insulators are shown in Figure 1.1.
A conductor (e.g., a metal) contains a free electron gas which is mobile when an electric
potential difference is applied to the system. Metals are opaque and highly reflective. These
optical properties are governed by the collective behavior of electrons in metals. Unlike
metals whose electrons are loosely held together due to partly filled energy bands, most
semiconducting materials have their energy bands filled. In an insulator (i.e., a dielectric),
allowed energy bands are either completely filled or empty. As such, electrons are not
mobile in an electric field and dielectrics are characterized by a wide energy band gap
(usually larger than 5 eV). Therefore, thermal generation of free carriers in dielectric
materials is extremely weak and requires a large amount of energy to generate a minute
amount of current.
Figure 1.1. Energy band gap diagram for (A) conductors whose conduction band (CB) and valence band (VB) overlap slightly, (B) in semiconductors CB and VB are spaced and (C) in insulators CB and VB are widely separated.
3
In the following sections, concise summaries of the optical and electronic properties
of conducting, semiconducting and dielectric materials and their unique behavior on the
nano-scale are provided.
1.1.1. Optical Properties of Metals
1.1.1.1. The Dielectric Function of the Free Electron Gas
Optical properties of metals can be explained by a plasma model where a free
electron gas moves against fixed positive ion cores. Metals have frequency-dependent
optical responses. For example, at the low frequency region of the electromagnetic
spectrum (i.e., microwave and far-infrared), metals are reflective and electromagnetic
waves are unable to penetrate. At higher frequencies (i.e., near-infrared and the visible
region), the field penetration increases significantly which results in increased dissipation.
In the case of ultraviolet frequencies, fields can propagate into the metal resulting in a
dielectric character which is dependent on the electronic band structures of the specific
metal. For noble metals such as gold and silver, the transition between electronic bands
results in strong absorption. The dispersive nature of metals can be described via a
complex frequency dependent dielectric function ε(ω) of the Drude model (the Drude
model is explained in Appendix A2):
( )
( )
where p
n
is the plasma frequency at which the density of the free electron gas
oscillates. The real and imaginary parts of the dielectric function ( ) ( )
( ) are given by:
4
( )
( )
( )
( ) ( )
Although the behavior of noble metals is predominantly governed by free electron
responses, details of lattice potential and bound state electrons are not taken into
consideration in Equation (1). Instead, it is assumed that the effective optical mass m of
electrons in the band structure oscillate under an electromagnetic (EM) field and their
motions are damped via collisions with a characteristic collision frequency (damping
constant and is the mean electron collision time). In the case of noble metals
(e.g., gold and silver), the applicability of Equation (2) breaks down due to interband
transitions resulting in an increase of at visible frequencies.2 Therefore, the dielectric
function of the metal should contain the Drude term for both free electrons and bound
electrons3 ( ( )
):
( ) ( ) ( ) ( )
( )
1.1.1.2. Volume Plasmons, Surface Plasmon Polaritons and Localized Surface Plasmons
Figure1.2 is a schematic illustration of collective displacement of the electron cloud
which results in surface charge density ±σ at the metal slab boundaries. As a consequence,
an electric (E) field is produced inside the metal and displaced electrons experience a
restoring force. Volume plasmon is the quanta of these charge oscillations.
5
Figure 1.2. Volume plasmon - the collective longitudinal oscillations of the conduction electrons of
a metal.2
In 1957, Ritchie predicted a special kind of surface wave that can exist at a
metal/dielectric interface.4 Surface plasmon polaritons (SPPs) are electromagnetic modes
propagating at the interface between a dielectric and a metal with dielectric constants
and respectively (Figure 1.3). The energy in this type of wave is shared between the
electron charge density of the metal (plasmon) and the electromagnetic wave (photon) and
is confined to the surface. SPPs are transverse magnetic plane waves which propagate
along the x direction, that is, the structure is invariant with respect to the y direction (i.e.,
). Thus, SPPs are evanescently confined in the direction normal to the interface.
These electromagnetic surface waves arise via the coupling of EM fields to coherent surface
oscillations of free electrons in the metal.2,4-7 The EM field intensity reaches its maximum at
the metal surface and decays exponentially away from the interface. The specific mode,
shape and decay rate are dependent on the material involved and the geometry of the
structures. The reason for the existence of such waves is the opposing signs of the dielectric
constants of the two media involved (i.e., metal and dielectric).
6
Figure 1.3. Schematic illustration of a surface plasmon polariton (SPP) propagating along the x
direction. Electric field lines of a SPP wave on a single interface where the structure is invariant
with respect to the y axis.8
By using Maxwell’s equations and applying the necessary boundary conditions, the
dispersion relation for a single interface is given as:2,5,8
√
( )
where is the free space wave vector, and are the dielectric constants of metal and
dielectric respectively. Equation (1) shows that the propagation constant reaches
infinity as approaches . This results in the confinement of the wave at the surface
and the wave decays exponentially on both sides of the interface.9,10 Using a Drude fit for
the dielectric constant of the metal results in a surface plasmon frequency in which the
propagation constant approaches infinity:
7
√
( )
where is the bulk plasmon frequency of the metal. Unlike SPPs, localized surface
plasmons are non-propagating excitations of the conduction electrons of metal
nanoparticles (MNPs) coupled to the EM field (Figure 1.4).8,11 These modes arise from the
scattering of sub-wavelength conductive MNPs as a result of excitation of the conduction
electrons which experience a restoring force due to the surface curvature of these particles.
Therefore, resonance can arise leading to field amplification in both the inside and outside
(near-field) of MNPs. This resonance condition is called localized surface plasmon
resonance (LSPR). The spectral positions of the LSPRs for gold and silver MNPs are in the
visible range.
Figure 1.4. Schematic illustration of a non-propagating localized surface plasmon.12
Interaction of a particle with an EM field can be analyzed by a quasi-static
approximation (i.e., size of the particle is much smaller than the wavelength of light). In this
condition, the phase of the harmonically oscillating EM field is constant over the volume of
8
the particle and as such, spatial field distribution can be obtained based on the assumption
that the particle is in an electrostatic field.2,3,10 Figure 1.5 shows a schematic illustration of
a homogenous, isotropic sphere in an electrostatic field.13
Figure 1.5. Schematic illustration of an isotropic sphere placed into an electrostatic field.
In the electrostatic approximation, the fields can be derived using the Laplace equation,
, where is the electric potential and the E field can then be obtained from the
gradient of the potential as - .13 This results in the following relationship for the field
inside (Ein) and outside (Eout) of the sphere:
( )
where and are the permittivity of the surrounding medium and metal respectively
and is the magnitude of the incident field:
9
( )
(4)
where r is the radial distance for the point of observation from the center of the particle
and the dipole moment is given by:13
( )
where a is the radius of the MNPs. Equation (5) shows that there is a resonant
enhancement in the dipolar moment for the wavelength range where approaches .
This resonant enhancement, in turn, enhances the fields both inside and outside of the
particle. This field enhancement at the plasmon resonance is the phenomenon on which
numerous optical applications such as surface enhanced Raman scattering (SERS) rely.
1.1.1.3. Absorbing and Scattering of Light by Metal Nanoparticles
One of the important results of the resonantly enhanced polarization α is the greatly
improved efficiency with which MNPs are able to scatter and absorb light.14 Absorption
and scattering cross sections, Cabs and Csca are given by:15
[ ] [
] ( )
| |
|
|
( )
10
Equations (1 and 2) show that for small MNPs (i.e., a≪λ),16 the contribution of absorption
is relatively large as compared to scattering. The absorption efficiency is scaling with a3,
whereas scattering efficiency scales with a6. The equations also show that scattering and
absorption of a MNP are resonantly enhanced at its plasmon resonance (based on dipole
approximation and Frӧlich condition Re[ ( )] ).17 The expression for the
extinction cross section which is the sum of absorption (transfer to heat) and scattering
(re-radiation), Cext = Cabs +Csca is:
[ ] ( )
1.1.1.4. Anisotropic Metal Nanoparticles
It should be noted that to date, no analytical solution exists for the scattering and
absorption cross sections of nanorods (NRs). However, a very similar geometry that has
been analysed in the electrostatic approximation is that of an ellipsoid. Consider an
ellipsoid with three perpendicular principal axes ai (i=1,2,3). The polarizabilities along
the three principal axes are given as:15
( ) ( )
where and are the permittivities of metal and surrounding medium respectively and
depolarization factor is a geometry dependant factor given by:
∫
( )((
) ( ) (
) )
( )
11
For the case of a prolate spheroid where the two minor axes are equal ( ) further, if
( ), and as , therefore . The denominator of
Equation (1) predicts two separate resonances in the polarizability for the prolate
spheroid, depending on the incident E field polarization. The resonant condition is:
(
) ( )
It can be seen that for the incident polarization along the major axis the resonance is red
shifted due to a small value of . It can also be noted that for the case of a sphere where all
three principal axes are equal resulting in , the resonant condition acquires the
familiar form of .
The scattering and absorption cross sections can easily be extracted from Equations
(1 and 2 from Section 1.1.1.3) using Equations (1 and 2 described above) for an ellipsoid.
We can analytically predict the two different resonant peaks corresponding to the
longitudinal and transverse surface plasmons (SPs) in absorption and scattering of a NR,
assuming that its response can be approximated by that of an ellipsoid. Consider a NR with
dimensions nm and nm. From Equation (2) these dimensions results
in and . By inserting these values in Equation (3) we expect the
following two resonant conditions for E field polarized along the long axis of
the NR corresponding to the longitudinal SP and for E field polarized along
the short axis of the NR, that is the transverse SP. It can be seen that polarization along the
long axis of the NR results in SP resonance at longer wavelengths. Assuming gold NRs are
immersed in H2O (i.e., ), the two resonant wavelengths are 761 nm and 490 nm.
12
1.1.1.5. Interactions between Metal Nanoparticles
Optical properties of metal nanoparticle (MNP) ensembles exhibit unique surface
plasmon resonance (SPR) shifts as compared to the SPR of individual MNPs. This is due to
electromagnetic interactions between the localized plasmon modes. The interaction effect
between plasmonic nanostructures have been investigated experimentally and
theoretically for a variety of arrangements and shapes of MNPs. Specifically, studies of the
coupling effect of dimers (e.g., ellipsoids,18 spheres,19,20 nanodisks,21 nanorods,22-24 or
nanoantennas25,26), and also many-nanoparticle systems such as nanorod assemblies,27
linear arrays of nanocylinders,28 and two- or three-dimensional MNP arrays29-32 have been
the subject of studies.
For MNPs, SP interactions are of a dipolar nature and MNP ensembles can be treated
as an ensemble of interacting dipoles in a first approximation. Let us consider an ordered
array of MNPs. The optical response depends on the size of MNPs a and the interparticle
distances d between adjacent MNPs. There are two regimes based on the magnitude of d:
(i) for closely spaced MNPs where d≪λ, the arrays of interacting MNPs can be
described as dipolar near-field interactions with a distance dependence of d-3. In this case, a
strong localized field enhancement occurs in the gap between MNPs33 and thus can serve as
a “hot spot” for surface-enhanced Raman scattering. These interparticle interactions shift
the spectral position of the SPR. The direction of the SPR shifts can be determined by the
Coulomb forces associated with the polarization of MNPs. As shown in Figure 1.6, the
restoring forces acting on the coherent oscillation of electrons of each MNP can be either
increased or decreased by the charge distribution of adjacent MNPs. Depending on the
13
direction of the polarization of incident light, the SPR wavelength of MNP ensembles can
either be red-shifted or blue-shifted. For example, if the incident light is polarized parallel
to the MNP axis, a red-shift of SPR can be observed. On the other hand, when the incident
light is perpendicular, a blue-shift of SPR is seen. In the case of end-to-end NR dimers, if d
between the ends of NRs is reduced, a red-shift of the longitudinal SPR occurs while a
decrease of d perpendicular to the long axis of NRs results in a small blue-shift of the
resonance.23,24
Figure 1.6. Schematic illustration of near-field coupling between metal nanoparticles (MNPs). Two
different polarizations (parallel and perpendicular to the MNP axis) are shown.
Figure 1.7(A) shows arrays of 50 nm gold MNPs with varying interparticle distances. The
dependence of the spectral position of the SPR on interparticle distance for both
longitudinal and transverse polarization is shown in Figure 1.7(B).34 These experimental
results showed that when d>150 nm, the SPR of the arrays of the MNPs showed spectral
14
features similar to individual MNPs. This is due to the strong coupling strength with d-3
dependence. The spectral position of SPR via near-field coupling is also dependent on the
chain length of MNPs.
Figure 1.7. (A) SEM image of arrays of gold nanoparticle (B) Dependence of the plasmon peak
position on the interparticle spacing d for both the transverse and longitudinal excitation of the
collective mode. The dotted line shows a fit to the d-3 dependence of coupling predicted by a point
dipole interaction model. Reprinted with permission from Reference 34. Copyright 2002, American
Physical Society.
(ii) For large particle separation, the arrays of interacting MNPs can be described as
a dipolar far-field interaction with a distance dependence of d-1. These coupling effects have
been investigated for both two-dimensional arrays31 and one-dimensional chains.28 For
example, Figure 1.8 shows extinction spectra of two-dimensional gold MNPs with a
diameter of 150 nm and height of 14 nm.35 Far-field coupling of these MNPs shows
influences on both spectral position of the SPR wavelength and spectral peak width. This
15
observed spectral peak width is due to the decay time of the plasmon oscillations
(43) Hagfeldt, A.; Gratzel, M. Chem. ReV. 1995, 95, 49–68.
(44) Kamat, P. V. J. Phys. Chem. C 2008, 112, 18737–18753.
148
Chapter 7
Towards an Experimental Demonstration
of ‘2D’ Visible Range Cloaking via a
Bottom-up Approach
This chapter explores a bottom-up method to produce a metamaterial which can
potentially function as an optical cloak in the visible range. A composite material
consisting of an array of silver nanowires (NWs) in a dielectric host has been produced
based on the theory of a non-magnetic optical cloak.1 The required radial array of silver
NWs was achieved by electroless deposition of the metal into the channels of a porous
alumina structure grown perpendicularly from the curved surface of a micrometer scale
aluminum wire. While the required architecture and dimensions may require further
adjustment, the functionality of the cloak in the visible range has been demonstrated.
Fundamentally this metamaterial structure represents an important step forward in the
production of tunable, optically functional, complex three dimensional architectures
through the bottom-up approach.
149
7.1. Introduction
7.1.1. Metamaterials and Optical Cloaking via Transformation
Optics
Metamaterials are artificially constructed composite materials which exhibit
ensemble electromagnetic (EM) properties not present in the constituent materials.2-8 The
heterogeneity of these materials exists on a length scale smaller than the wavelength of
interest. Thus, the EM response of the material is a function of the collective behavior of a
material’s components (an overview of metamaterials is provided in Chapter 1).
As a consequence of their tunable EM properties, metamaterials have become a
focus in the area of transformation optics.4,7,9-12 Transformation optics explores the control
of light paths via manipulation of the spatial distribution of permittivity (ε) and
permeability (μ)13 within metamaterials. In effect, transformation optics7,12 describes the
conditions necessary to ‘warp’ light space in a manner analogous to warping space-time in
general relativity.
Within the realm of transformation optics, the possibility of optical cloaking (i.e.,
invisibility) has sparked scientific curiosity in recent years.1,14-19 In a perfect optical cloak,
the object to be rendered invisible will create no reflection, scattering or absorption.
Figure 7.1 illustrates an optical cloak in a spherical coordinate system where light is bent
around an object and redirected to its original trajectory. The object being cloaked is to be
placed within the inner sphere whereas the region between the inner and outer sphere
constitutes the cloaking device.
150
Figure 7.1. Schematic illustration of a three-dimensional view showing the wave trajectories of a
spherical cloaking system. Reprinted with permission from Reference 14. Copyright 2006, Science.
In any naturally occurring material, light rays will bend toward the center of the
sphere due to the material’s higher refractive index in accordance with Snell’s law.20 To
diffract light rays away from the center, a material whose refractive index is less than 1 is
required. For example, one way to achieve this is by employing thin metallic wires in a
dielectric host which acts to ‘dilute’ the metal and thus reduce the plasma frequency to
obtain ε less then unity, for a desired wavelength.21
One exploitation of this notion, is the design of an optical cloak which was
introduced by Pendry18 and Leonhardt et al.7,18 In this model, the path of the EM wave was
controlled by using a specific spatial profile of ε and μ to make light avoid a particular
region in space. Figure 7.2 shows an example of the transformed media using ε and μ
tensors. In a homogenous medium where ε and μ are constant, a straight field line is
produced. However, by varying the spatial distribution of ε and μ, a distorted field line
results as it travels through the heterogeneous medium.
151
Figure 7.2. (A) Straight field line through a homogeneous medium against a Cartesian coordinate
system (B) distorted field line travelling through a heterogeneous medium produced by varying the
spatial distribution of permittivity and permeability. Reprinted with permission from Reference
14. Copyright 2006, Science.
For the design of an optical cloak, in the case of a cylindrical coordinate system, the region
0 < r < b is transformed into < r’ < b by using the following transformation:
( )
where a and b are the radius of the core (i.e., region of invisibility) and the distance from
the center of the core to the outer diameter (i.e., perimeter of the cloak) respectively. r and
r’ are the radial coordinates in the original and transformed system respectively z’ and θ’
are the coordinates of the transformed system respectively.
The transformed region extends from a to b only, shown in Figure 7.3. The
transformation can be obtained by the following space profiles of ε and μ for the case of a z-
polarized incident field:
(
)
(
)
( )
152
It should be noted that only has a gradient as a function of radius and thus this type of
transformation is known as a magnetic cloak. However, this type of transformation still
suffers from non-zero scattering. The first practical demonstration of a cloak based on the
above mentioned transformation was performed by Schurig et al at microwave frequencies
in 2006.19
Figure 7.3. A two-dimensional cross-sectional view of wave trajectories of a spherical cloaking
system where light is deviated around the object to be cloaked (radius a) within the annular cloak
region (radius b – a) and return to its original path. Reprinted with permission from Reference 14.
Copyright 2006, Science.
7.1.2. Theoretical Design of a Non-magnetic Optical Cloak
The magnetic cloak discussed above cannot be practically scaled down in
dimensions for the development of a cloak in the visible spectrum range as indicated by
Klein et al.22 An alternative theoretical solution for a non-magnetic cloak which can operate
at optical frequencies (390 to 750 nm) was proposed by Cai and Shalaev et al.1 Our bottom-
up approach for the production of the cloaking structure illustrated in the following
sections is based on this model. In the model, ε has a gradient as a function of radius. Figure
7.4 illustrates a coordinate transformation of this cylindrical shell model. The proposed
153
design should meet the following space profile for transverse magnetic (TM) illumination
(i.e., the magnetic field polarized along the z-axis):
(
)
(
)
(
)
( )
where , and are the azimuthal and the radial dielectric permittivity and the z-axis
magnetic permeability respectively.
Figure 7.4. The coordinate transformation of a cylindrical shell model. A cylindrical region r<b into
a concentric cylindrical shell a <r < b. There is no variation along the z direction. Reprinted with
permission from Reference 13. Copyright 2007, Nature.
It should be pointed out that although this design can produce the desired trajectory of
light, impedance mismatch at the outer boundary of the cloak occurs. This results in a
certain amount of scattering determined by the ratio of a to b. The main advantage of this
theoretical design is its ease of fabrication due to the fact that no magnetic resonance is
required. Further is a constant and is larger than unity which can be easily achieved
through a variety of dielectric materials. The largest design challenge is the choice and
control of an appropriate metamaterial where the profile of varies from 1 to 0 as the
wave propagates from the outer boundary of the cloak b to the inner a.
154
The space profile of εr and εθ dictates an interaction between the media and applied
field in the radial direction only, whereas negligible interaction in the azimuthal direction is
desirable to provide a constant εθ. The choice of metallic rod-like structures (e.g., arrays of
nanowires or nanoparticles) is well-suited for this purpose since it lends itself to predictive
modeling via the effective medium theory.23,24
Let us consider a metal ellipsoid with three perpendicular semiaxes ai (i=1,2,3). The
depolarization factor q1 for incident field polarized along a1 is given as:
∫
( ) (
) ( )
( )
Similar expressions for q2 and q3 can be obtained with cyclic changes. In the case of a long
elliptical cylinder, a2=a3 and a1 >> a2 which will result in q1≈0 and as q1+q2+q3=1, therefore
q2=q3=0.5. The screening factor k which indicates the strength of interaction between the
wire and the applied field is given by:
( )
(7.5)
Equation (7.5) shows that k1 will achieve a very large value whereas k2= k3=1. Therefore, if
the long axis of the metal nanowires or rods (i.e., a1) is in the radial direction, we will
observe a strong interaction in the radial direction whereas the interaction in the
transverse direction will be negligible. The effective permittivity of such a composite media
in a given direction is:
[ ̅ √ ̅ ] ( )
155
where ̅ [( ) ] [ ( ) ] . As we expect no interaction in the
azimuthal direction:
(
)
( )
where is the permittivity of the dielectric host. Thus the ratio of inner to outer radius of
the cloak (R=a/b) is governed by :
( )
where and are the filling factors for the metal nanowires at the inner and outer
surfaces of the cloak respectively and their ratio should satisfy the above relation.
Considering the possible dimensions of the cylindrical shell i.e., a and b that can be
achieved by the bottom-up approach, we have utilized radial arrays of silver nanowires
(and nanoparticles). From a practical, experimental point of view, it is important to note
that as long as the Equations from (7.4) to (7.8) are satisfied, the key parameters i.e., a, b
and filling factors may be varied considerably. Given the complexity of the components
involved in generating the necessary architecture, such flexibility is critical in producing
the necessary structure. Based on these equations, examples of the design possibilities are
presented in Figure 7.5 which shows the calculated variation of r as a function of design
parameters e.g., a and b at the operating wavelength of 500 nm. For these examples, we
used silver nanowires (NWs) in a dielectric host, alumina (See Route III, Section 7.2.3). The
required variation of r from 0 to 1 for the interior and exterior surfaces of the cloak
respectively are achieved by a = 0.7 µm and b = 2 µm (Figure 7.5 A) and a = 1.2 µm and b =
3.5 µm (Figure 7.5 B). In order to satisfy the equations, the corresponding filling factors are
156
f0 =24.4 % and f1 =9.4 % and values of R calculated from Equation (7.8) is 0.35 at the
operating wavelength of 500 nm.
Figure 7.5. Calculated plot of radial component of electric permittivity (εradial) as a function of cloak
dimensions (A) a = 0.7 µm and b = 2 µm (B) a = 1.2 µm and b = 3.5µm. Both parameters result in
the effective permittivity at operating wavelength of 500 nm. Silver nanoparticles with a radius of
10 nm were used for the calculations.
157
7.2. Results and Discussions
7.2.1. Experimental Rationale
The model proposed by Cai and Shalaev et al1 represents a significant fabrication
challenge for both top-down and bottom-up approaches. Figure 7.6 and Table 7.1.
summarize the required parameters for the bottom-up approach of a ‘2D’ cloaking material
at a visible frequency. Based on this model the target dimensions for our experiment for
the object to be cloaked is approximately 1 µm in diameter surrounded by a cylindrical
cloak with a wall thickness of approximately 1.5 µm. In addition, the metamaterial cloak
consists of a radial array of metal NWs in an appropriate dielectric host. Since the
refractive index of the cloak is required to be 0 at the interior and 1 at the exterior, it is
critical that the filling factor of the metal within the dielectric host varies accordingly. For
example, if the specific cloak dimensions described above are used, a filling factor of metal
NWs (or a radial array of nanoparticles (NPs)) of 4% at the exterior and 12% at the interior
of the cloak is needed. While structures in this dimensional range are relatively simple to
achieve via top down methods, the most significant challenge is the formation of a radial
array of metal NWs organized within the dielectric host. The NWs are required to be less
than 1/10 in width of the incoming optical wavelength. For example, this would require a
NW width of less than approximately 40 nm for blue light and less than 70 nm for red light.
While the formation of metal NWs in this size range is possible using focused ion beam
technology,25 the device is required to be three-dimensional. Specifically, using top-down
strategies, only one layer could be deposited at a time and multiple individual layers of
158
dielectric and subsequent radial metal deposition would need to be manufactured. The
time and cost of this process rules it out as a practical approach.
Figure 7. 6. Schematic illustration of the non-magnetic cloak structure. Inner core (dark grey) is the
cloak area surrounded by metal nanowires (NWs) in a dielectric host. A Radial array of NWs is
perpendicular to the z-axis and must satisfy the filling factor such that the radial component of
electric permittivity varies from 0 at a to 1 at the exterior surface. Spatial positions of NWs do not
need to be periodic.
Table. 7.1. Summary of required parameters for the fabrication of a non-magnetic optical cloak
device.
Material Arrays of metal nanowires or nanoparticles (eg, gold or silver)
Host for metal Dielectric (e.g., SiO2, Al2O3) Shape of host Cylindrical Metal orientation Radial Metal width 40-70 nm or less Filling factors of metal Must satisfy εrad 0 at inner boundary to εrad = 1 at outer
boundary. The filling factor varies depending on dimensions of host and metal (eg, for a = 1.4 µm, b = 4 µm and metal width ~10 nm, f0=18.6% and f1 =6.6%).
Additional practical notes (1) Diameter of object to be cloaked is ~ 30% of total diameter of cloaking device.
159
(2) Variations in metal length may not be important as long as filling factor is satisfied (i.e.,averaging effect). (3) System must be robust, processible, temporally stable and needs to be responsive and allow for fine tuning.
Using a bottom-up approach, the general rationale would be to produce a NW (or
NP) array which is stabilized by a dielectric host. A porous dielectric host with tunable
dimensions can be realized and subsequently, the pores can be populated with appropriate
metal NWs (See details in Section 7.2.3, Route III).
Figure 7.7 is a summary of three possible routes which were explored for the
fabrication of the optical cloak via bottom-up approaches.
Figure 7. 7. Summary of explored routes for the fabrication of a non-magnetic optical cloak device.
160
7.2.2. Routes I and II
Of the three approaches outlined in Figure 7.7, Route III (Section 7.2.3) allowed for the
production of structures falling within the range of the desired parameters while Route I
and II, failed to produce effective architectures. The preliminary experimental data for
Routes I and II (Figure 7.8) will be discussed concisely in this section.
Figure 7.8. Schematic showing two possible routes to produce the optical cloak. Route I: vertical
assembly of gold nanorods on silica then subsequently embedded via silica deposition. Route II:
radial assembly of binary metal NWs (eg, gold/nickel) around a cylindrical host directed by a
controlled magnetic field.
161
In preliminary experiments via Route I, the concept is to produce a radial array of
NWs or NRs which project vertically from the surface of dielectric spheres with subsequent
‘embedding’ of the NWs through the deposition of an additional layer of dielectric. By
repeating this process in a stepwise manner, multiple layers of radially arranged NWs in a
dielectric host could be produced. The vertical assembly of NWs can be realized, in
principle, by functionalizing their ends. However, one of the foreseen challenges of this
approach is that since both ends of the NWs are functionalized, there is the possibility of
undesired ‘bridging’ of adjacent spheres by NWs or attachment of both ends of a single NW
to the substrate.
Silica spheres (and hollow silica spheres)26 were chosen as the dielectric host and
substrate for assembling metal NW arrays. Monodisperse colloidal silica (SiO2) particles
were prepared by controlled hydrolysis and condensation of tetraethylorthosilicate (TEOS)
in ethanol to which water and ammonia were added (the Stöber method).27 We produced
highly monodisperse spherical SiO2 particles with dimensions ranging from 300 to 500 nm.
Gold nanorods (NRs) (L NRs = 40 ± 4 nm, H NRs= 13 ± 1 nm) were synthesized and the ends of
NRs were functionalized with 3-mercaptopropyl trimethoxysilane to facilitate their vertical
assembly on the surface of the SiO2 spheres. Figure 7.9 shows the results of vertical gold
NR assembly on the silica particles. Although the majority of NRs observed were close to
vertical alignment, the number density of NRs on the surface of the spheres was
consistently too low to move on to the next step of multiple layer formation. In addition,
direct ‘seed’ deposition of gold on the surface of SiO2 particles was explored. In this
approach, gold seed nanoparticles were obtained by the reduction of HAuCl4 by NaBH4.
These seeds were then deposited and grown on the surface of the SiO2 spheres. In both
162
cases, the required control of NR vertical assembly necessary for this hybrid structure to be
effective as a cloak was not achieved.
Figure 7.9. Representative TEM image of vertical assembly of gold nanorods onto synthesized silica
particles. The ends of gold nanorods were functionalized by the introduction of 3-mercaptopropyl
trimethoxysilane.
As an alternate approach (Route II) an attempt was made to create a radial array of
nickel-tipped gold NWs by the use of a magnetic field in an “anti-Helmholtz” configuration.
Figure 7.10 illustrates an electrochemical method28-30 for the production of binary NW
structures consisting of gold and magnetically responsive nickel. A thin film of silver (~400
nm) was evaporated on a commercially available aluminum oxide filter (AnodiscTM, USA)
and used as the cathode. A platinum wire served as an anode. A silver “buffer layer” was
deposited first to fill the pores evenly, followed by gold and nickel deposition. The
optimized plating conditions were 0.5 mA/cm2 for deposition times of 10 to 60 min,
depending on the desired length of each segment. Figure 7.10 shows examples of
163
representative SEM images of the resultant binary structures with varying lengths. Energy
dispersive X-Ray spectroscopy (EDS) mapping confirms the composition.
Figure 7.10. Schematic illustration of the electrochemical method used to produce binary
nanowires (NWs) composed of nickel and gold.
164
Figure 7.11. (A) Backscattered SEM images of binary NWs showing various lengths of each
component. Note: silver is used to fill the bifurcated pores to provide even deposition of gold and
nickel (B) EDS mapping showing atomic composition of NWs.
For the magnetic radial assembly, as synthesized binary Ni-Au NWs described above
were used as a building-block. Figure 7.12 (A) shows the simulation of the magnetic field
lines analogous to the Helmholtz configuration. In this configuration, the opposing poles of
cylindrical annular magnets are facing each other such that a homogenous magnetic field
can be produced within the central region between the magnets. However, when their
dipole moments are aligned in the anti-Helmholtz configuration i.e., the same poles are
facing each other, the magnetic fields from two poles flow in opposite directions. This
165
results in a zero net magnetic field at the center surrounded by a radial field as indicated in
Figure 7.12 (B).
Figure 7.12. Magnetic field line simulations analogous to (A) Helmholtz and (B) anti-Helmholtz
configurations.
By exploiting the anti-Helmholtz configuration, we hypothesized that radial
assembly of the binary NWs could be achieved in this region where the radial magnetic
field lines are compressed along the horizontal axis between two magnets due to the
resulting pressure in the field by repulsion. Figure 7.13 (A) shows a photograph of our
general experimental set-up. Annular magnets were arranged in an anti-Helmholtz
configuration and placed on a capillary tube (or a glass vial) containing binary NWs in an
aqueous solution. This set-up should produce a radial magnetic field line in the central
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zone between the magnets such that the magnetically responsive component, Ni, of the
binary NWs should align within this field. Figure 7.13 (B) shows the top-views of NW
assembly in the Helmholtz and anti-Helmholtz configurations respectively. In the case of
the Helmholtz configuration, most of the NWs were aligned parallel to the field and thus
from the top view, we are looking down the long axis of the NWs. For the anti-Helmholtz
configuration, a distinctly different radial distribution of NWs was observed. Although the
radial alignment of NWs was successful on the millimeter scale, there was insufficient
control once the process was miniaturized to the micrometer scale. Further, while radial
arrangement of NWs was possible, achieving precise radial control of the volume fraction
via magnetic fields was problematic.
Figure 7.13. (A) Example of experimental set-up using annular magnets in an anti-Helmholtz
arrangement producing a radial magnetic field in the central zone between magnets (B) Optical
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micrographs showing top-views of NW assemblies via the two different configurations, showing a
radial alignment of NWs in the anti-Helmholtz arrangement.
7.2.3. Route III
7.2.3.1. Fabrication of a Cylindrical Shaped Dielectric Host
Our third approach (Route III) was to use a porous host as a template for creating
radial metal arrays. While the model proposed by Cai and Shalaev et al 1 (see section 7.1.2)
considers silica as a dielectric host and silver NWs, a combination of other dielectrics and
metals is possible. Of the available materials, porous alumina is particularly attractive since
the band gap energy of alumina (Al2O3) is approximately 9 eV and its critical wavelength
(see Chapter 1) at room temperature is approximately 0.14 µm which makes alumina
transparent in the visible range (note, band gap energy and critical wavelength of SiO2 ≃
8.5 eV and ≃ 0.15 µm respectively).31,32 Dimensions of porous alumina can be controlled by
the appropriate selection of applied voltage during anodization.33 Further, since the
starting material, aluminum, can be readily fabricated into wires with a diameter smaller
than 20 µm, this metal offers a unique opportunity for a structure to produce its own cloak.
Figure 7.14 is a schematic illustration of the method for the production of a radial porous
alumina template as a dielectric host for the optical cloak.
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Figure 7.14. Schematic of the proposed route to the fabrication of radial porous alumina as a
dielectric host via anodization of aluminum (Al) wire. The cross-sectional view shows a metallic Al
core surrounded by a porous alumina coating with a radial distribution of pores.
Anodized aluminum oxide (AAO) is a material whose thickness, pore size and pore
volume fraction can be readily manipulated through chemistry and applied potential
during oxide growth.34-36 Porous AAO as a dielectric host should provide: (1) radial arrays
of pores for metal deposition and (2) appropriate pore size and template dimensions to
potentially satisfy the filling fraction of metal required by the theoretical model.1
In our work, the anodization process was carried out on an aluminum wire (Al,
99.999%, purchased from Alfa Aesar) electropolished to be less than 5 µm in diameter. An
Al wire should in principle, provide radial arrays of pores, since it is known that pores grow
perpendicular to the Al metal surface. This is because there is an equilibrium of oxide
dissolution and oxide growth at the interface between oxide/electrolyte and metal/oxide
respectively.37 The net reaction during anodization is:
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2Al + 3H2O → Al2O3 +3H2
Oxide growth is electrochemically driven by the movement of oxygen containing ions (e.g.,
O2-/OH-) at the metal/oxide interface from the electrolyte through the oxide layer at the
bottom of the pore where the following reaction takes place:
2Al +3O2- → Al2O3 +6e-
By the hydration reaction, the dissolution of the oxide layer results. Al3+ ions migrate through
the oxide layer and eject into the electrolyte solution at the oxide/electrolyte interface.
This loss of Al3+ ions into the electrolyte is necessary for growth of the porous oxide:
Al2O3 +6H+→2Al3+ +3H2O
At the cathode, hydrogen gas evolution can occur by the ejection of electrons into the
electrolyte solution:
6H+ + 6e– → 3H2
This balance between the growth of Al2O3 and the loss of Al3+ ions, is key to producing
alumina’s porous columnar structure.37,38
We explored growth rate, pore density, pore regularity and overall integrity of the
oxide layer by using a number of acids e.g., sulfuric, phosphoric and oxalic acids33,34 to
determine optimal conditions for radial oxide growth. In the case of sulfuric acid (15 v %
in an aqueous solution at 10 °C), the AAO growth rate was rapid (>1 µm in 5 min) and it
produced a high pore volume fraction. Therefore, the commensurate pore diameter was
too small to satisfy the model.1 Phosphoric acid had a significantly slower growth yielding
controllable pore size but suffered from bifurcation, that is, branching during the
anodization process which suggested that control over pore volume by varying applied
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potential would be impossible. Ultimately, oxalic acid (3 wt %, in aqueous solution at 21
°C), was chosen because it formed straight, well defined pores with dimensions in broad
compliance with those required by the model. Figure 7.15 shows representative SEM
images of the AAO host formed in the presence of oxalic acid. A cylindrical oxide shell was
grown with pores perpendicular to the Al wire surface. Relatively straight porous channels
without bifurcation were formed.
Figure 7.15. SEM images of (A) Bare Aluminum wire after electropolishing. (B) Anodized
aluminum oxide (AAO) grown as a cylindrical dielectric shell around an Al wire core. (C) Surface
morphology of AAO shell showing a uniform pore structure (D) A cross-sectional view of radial
porous AAO grown using 3 % Oxalic acid (nb, surface roughness shown is due to fracturing
artifact).
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Although the theoretical model requires a filling factor for silver NWs of 12 % for
the interior and 4 % for the exterior of the cloak,1 for the dimensions and wavelength of a ≈
0.5 µm, b ≈ 2 µm and 633 nm respectively, the model affords significant flexibility. This is
because the required filling factor varies with the dimensions of the host and the object to
be cloaked. Therefore, we investigated the effect of oxide growth and subsequent pore
size, volume, and density by applying various potentials to the electrolyte.33 Assuming a 2D
dense packing of the pores, applied voltage dependent average pore size and cell size (that
is the distance between adjacent pores) were measured by analyzing SEM micrographs.
Figure 7.16 (A) shows the variations of average pore size and average cell size plotted as a
function of applied potential. In the voltage range 30 – 18 V, the AAO pore diameter
showed only a modest decrease while a significant decrease of the average cell size was
observed. This feature is critical in providing the template for the required filling factor
control.
Figure 7.16. (A) Variations of average pore diameter (blue circle) and average cell size (red
square) as a function of applied potential. (B) Calculated pore volume fraction as a function of
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applied voltage. The oxide layer was electrochemically grown over 105 minutes using 3 wt. % of
Oxalic acid in water as an electrolyte solution.
Figure 7.16 (B) shows the variation in the pore volume fraction as a function of applied
voltage. The volume fraction was calculated as V = 78.5P2/C2 from the pore diameter (P)
and the cell size (C) based on the assumption that the cross-section of pores is cylindrical
and constant.33 As can been seen from Figure 7.16 (B), by choosing the appropriate applied
voltage, it is possible to alter the volume fraction of the pores from greater than 15 % to
less than 5 %. It is important to note that during the growth process of approximately 100
min the voltage has to be changed gradually to prevent bifurcation or the formation of
steps which could influence subsequent metal loading.
During preliminary studies with thicker wires of 10-15 µm in diameter, severe
cracking of the AAO was observed. The reason for cracking is unclear however based on
our observations, it appeared to be related to the thickness of the AAO layer. This may be
due to the fact that AAO occupies a measurably larger volume than the aluminum substrate
from which it grows. Since significant compressive stresses are induced during the growth
process36 these are likely exacerbated by the high radius of curvature of our cylindrical-
shaped system. However, as we approached the target dimensions required for cloaking
(e.g., a = 0.6 µm and b = 1.75 µm), cracking routinely terminated at a wire diameter of
approximately 5 µm, with an uninterrupted porous radial array below this diameter.
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7.2.3.2. Electroless Deposition of Ag NPs and Ag NWs into AAO
pores
Initially, a pulsed electrochemical approach using silver nitrate (AgNO3) was
employed. However, it typically produced polydisperse silver NWs with incomplete pore
filling. Consequently, we focused on electroless deposition via polyol reduction of Ag+ ions.
In a typical polyol synthesis, ethylene glycol reduces AgNO3 to produce Ag atoms by the
following mechanism:39
2HOCH2CH2OH ⟶ 2CH3CHO + 2H2O
2Ag+ +2CH3CHO ⟶ CH3CO—OCCH3 + 2Ag +2H+
Similar to the synthesis of quantum dots, nucleation and growth of silver nanostructures
can be initiated once the concentration of silver atoms reaches the supersaturation point.40-
42 In order to enhance the rate of silver NW growth, a trace amount of sodium sulfide
(Na2S) was added.43
One of the challenges of this method was that the NW density was greater at the
surface of the AAO, tapering off towards the interior – the opposite of that required for the
model. To overcome this challenge, first, a solvothermal reduction was used to deposit
seeds of Ag at the base of the AAO pores. In order to produce a higher concentration of
seeds at the base, the AAO was dipped in AgNO3 solution then briefly rinsed in 1:1
ethanol/acetone solution prior to solvothermal reduction of the silver followed by polyol
reduction. The resulting structure showed a much more uniform distribution throughout
the AAO layer.
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Even with uniform loading, another challenge originated from the excess silver
present as large particles on the surface of the AAO. The formation of these undesired
particles occurred during electroless deposition (Figure 7.17 (A) inset). This was resolved
by sonicating the structure in a diamond paste slurry which led to uniformly clean surfaces
(Figure 7.17 (B)) without disruption of the silver NWs deposited in the pores. We found
that the optimal silver loading was achieved by using a 12 wt % solution of AgNO3 in
ethylene glycol. Figure 7.17 (C) shows silver NWs loaded in the AAO structure whose inner
and outer diameters were 1.2 µm and 3.5 µm respectively (i.e., a =0.6 µm and b =1.75 µm).
For this system, the calculated response of r as a function of the structure’s dimensions
(radius/a) is shown in Figure 7.17 (D). As an example, at an operating wavelength of 500
nm, the value of r exhibited the required variation from 0 to 1 for the experimentally
produced cloak with the following parameters; filling factor of f0 =24.4 % and f1 =9.4 % and
calculated R = 0.35.
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Figure 7.17. (A-B) Low and high magnification backscattered SEM images of the surface of AAO
structures containing silver NWs. Inset shows superficial deposition of larger silver particles which
were subsequently removed by diamond paste washing. (C) Backscattered SEM image of a silver
NW loaded radial AAO structure. This example shows both the desired radial silver NW
distribution in a dielectric host along with the required structural dimensions. (D) Calculated plot
based on (C) showing r response for a = 0.6 µm and b = 1.75 µm. Operating wavelength is 500 nm.
Radius is variable ranging from a to b.
7.2.3.3. Optical Transmission Measurements
To validate the performance of the experimentally produced non-magnetic cloak
structure, we used the optical transmission setup (shown in Figure 2.2, Chapter 2) where a
super-continuum (SC) laser source was used which allowed us to cover a wide range of
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wavelengths from 450 nm to 1100 nm. An acousto-optic tunable filter was used to select a
specific wavelength from the broad spectrum of the SC source for the illumination of the
cloak sample. The sample was illuminated by TM polarized monochromatic light (i.e.,
transverse magnetic illumination) and the transmitted light was collected and displayed on
a CCD camera. At the chosen wavelength, with TM polarization, the cloak is expected to
bend the rays of light around the object, in this case the Al wire core.1 Ideally, the
wavefront should be completely recovered behind the sample. In reality, this is not
possible due to the fact that the cloak is not impedance matched to free space and thus a
finite amount of scattering is inevitable which is determined by the ratio of a to b. The
reflected power due to this mismatch can be given as [ ( )] where .
Therefore we expect only partial recovery of the wavefront after passing through the
cloak.1
Figure 7.18 (A-B) shows examples of transmission optical images at a wavelength of
540 nm recorded on a CCD camera for the TE and TM polarizations respectively. Similar
images are shown at wavelengths ranging from 450 to 750 nm in increments of 5 nm. In
order to quantify the transmission through the fabricated structure, as a function of
wavelength, we collected sequential intensity data across the structure in a diagonal
manner at each chosen wavelength.
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Figure 7.18. Optical images captured by CCD camera at a wavelength of 540nm for transverse
electric (TE) and transverse magnetic (TM) polarization. Quantification of the intensity across
the fabricated structure was carried out by a series of sequential diagonal scans over the
wavelength range of 450 to 750 nm.
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Figure 7.19 shows the intensity data as a function of wavelength across a specific
location of the fabricated structure. Transmission results for two polarizations are shown.
As the cloak is active for TM polarization only, we expect measurable transmission in the
geometric shadow of the structure on the CCD whereas TE polarization which was used as
a control experiment should result in negligible transmission. Our preliminary results
showed a measureable transmission when the field intensity collected for the TM
polarization. Specifically, an approximately 100 % higher transmission for the TM
polarization at the wavelength range from 540 nm was observed.
Although this result demonstrates the functionality of the fabricated device, a
number of factors for optimization of the structure need to be considered: (1) the
optimization of the loading of the silver NWs may be necessary. (2) the SC setup allows for
the examination of a single small region at a time and as such, any local structural
imperfections or silver surface contamination could result in ineffective cloaking.
Therefore, automation in data collection would be beneficial. (3) time-dependent oxidation
of the silver NWs is possible which would negatively affect the properties of the resultant
metamaterial. A solution to this may be the replacement of the silver NWs with gold NWs.
One route to achieve this is via galvanic displacement of silver NWs by gold.
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Figure 7.19. Polarization-dependent normalized field intensity plotted as a function of wavelength
via transmission measurement. Transverse electric illumination (TE) and Transverse magnetic
illumination (TM) on the fabricated structure. Field intensity of TM shows enhanced transmission
(blue) in the range 540 to 550nm.
7.3. Summary and Conclusions Building on the theory of a non-magnetic cloak based on transformation optics
proposed by Cai and Shalaev et al,1 we have demonstrated a method for the production of a
complex structure consisting of a metal core surrounded by a metamaterial shell (a radial
array of metal nanowires in a dielectric host). A bottom-up approach was used to produce
a radial dielectric host by anodization of aluminum wire and subsequent electroless silver
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NW deposition. This structure provides tunability with respect to both required filling
factor and overall dimensions. The functionality of the structure was tested by optical
transmission measurements and demonstrated partial cloaking in the visible range.
More fundamentally, this composite structure provides the basis for a new level of
design complexity through the bottom-up approach and opens up the possibilities for
functionality not available through top-down methods at this length scale. Further, careful
control of dimensions and filling factor may be possible offering potential tunability of
optical behavior of the metamaterial at a chosen operating wavelength.
Structures of this kind are limited to potentially cloak at one specific wavelength.
While this may be of limited practical use as a cloak, it may offer the potential for