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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Plasmonic Properties of Periodic Arrays of Ag Nanocylinders and Dimers, and the Effects of an Underlying Ag Layer Henrique Thadeu MCM Baltar, Krystyna Drozdowicz-Tomsia, and Ewa M. Goldys J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05902 • Publication Date (Web): 05 Sep 2018 Downloaded from http://pubs.acs.org on September 5, 2018

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The Journal of Physical Chemistry

Plasmonic Properties of Periodic Arrays of Ag Nanocylinders and Dimers, and the Effects of an Underlying Ag Layer Henrique T. M. C. M. Baltar*1, Krystyna Drozdowicz-Tomsia1,2, Ewa M. Goldys1,2 1

MQ Photonics Research Centre, Macquarie University, Sydney, Australia 2

ARC Centre of Excellence in Nanoscale BioPhotonics *[email protected]

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Abstract Despite the progress in understanding the properties of plasmonic nanostructures, the design of structures with specific optical characteristics still poses a challenge. In order to better understand how material and various geometrical parameters affect the response of the nanostructures, we analysed, theoretically and experimentally, the optical properties and their tunability in diverse configurations of a two-dimensional periodic array of silver nanocylinders and dimers, with or without an underlying thin silver layer. We show the tuning of the surface plasmon resonances can be approximated by affine equations at the regions we worked on. The controllable parameters that can be used for tuning include nanoparticle-metal layer distance, index of refraction of the surrounding dielectric material, cap layer thickness and cylinder diameter. We also calculated the enhancement of the average square electric field at the top surface, useful for surface-enhanced spectroscopies. Enhanced optical transmission not due to propagating surface plasmon was also observed.

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1 Introduction The intense efforts to understand the properties of nanoscale noble metals in the past decade are driven by the technological demands for new optical devices compatible with electronic technologies for instance, waveguides, photonic circuits, improved solar cells, nanoantennas, as well as biological and chemical sensors.1-3 Several key developments have been important for the understanding and control of the plasmonic properties of nanoparticles (NPs), including advances in chemical and lithographic methods for nanoparticle and nanostructure fabrication, in computational simulations, and in optical characterization.4 Recent progress in colloidal synthesis and the ability to produce NPs of various shapes as well as complex, multilayer geometries led to numerous experimental studies of their plasmonic properties.4-5 These properties can be controlled by using advanced fabrication techniques, such as electron-beam lithography (EBL)4 and deposition methods, such as atomic layer deposition (ALD) and thermal evaporation. Despite progress in understanding the properties of plasmonic nanostructures, the design of structures with specific optical characteristics still remains a challenge. In order to better understand how changes in various parameters affect the properties of nanostructures, we thoroughly investigated the optical properties in structures comprising a two-dimensional (2D) periodic array of single and double (dimers) metallic nanocylinders with an underlying metallic layer. As these arrays of nanocylinders can be constructed by EBL, and the planar layers by ALD or thermal deposition, they are quite reproducible. Plasmonic nanostructures made from gold and silver are preferred due to their stability and their surface plasmon resonances (SPR) at visible frequencies. In this work we chose Ag due to its lower losses and good tunability

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throughout the entire visible range.6-7 The idea of using an underlying metallic layer is inspired by the fact that it reflects the electromagnetic field and produces negative image charges of the localised surface plasmons (LSP) as well as it may provide propagating surface plasmons (PSP). Such metal layers may lead to enhanced optical signals.8 For example annealed thin Ag layer over an Ag mirror were shown to enhance the fluorescence of Alexa Fluor-647 up to 208 times,9 and Au nanodisks over an Au mirror were shown to act as an almost perfect plasmonic absorber at a specific wavelength.10 In this work we determine the tunability of the resonant modes of our selected structures by modifying structure parameters. Moreover, we investigated the enhancement of electromagnetic field in the selected structures, comparing cylinders and dimers, and the effects of the metallic layer.

2 Fabrication of nanostructures Our structures comprise silver cylinders and dimers, with varying diameters in the range of 3080 nm, arranged in a plane with periodicity of 150 nm in both directions, with and without an underlying 45 nm-thick Ag layer. This thickness was selected in order to allow transmission measurements. The structures were covered with a passivating alumina layer in order to protect the metals from oxidation and to improve mechanical stability.8 Furthermore, this layer can also increase the NP thermal stability with CW11 and high-power density-femtosecond laser.12 For the dimers, the distance between centres was kept fixed at 70 nm. The samples without Ag layer were fabricated using a JBX-9600 FX (JEOL) EBL system. A regular 2D array pattern with a fixed period of 150 nm in both directions and varying feature size was

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produced in Ag on fused silica wafers by a lift-off technique using different exposures. The following procedure was employed. Two layers of photoresist: 1) 2% poly(methyl methacrylate) (PMMA) in Anisole followed by 2) 1% of PMMA in methyl isobutyl ketone (MBIK) – were spincoated to a total thickness of 90 nm, and baked at 170°C for 15 min. Further, 10 nm of gold was thermally evaporated to provide a conductive, electron transparent layer to avoid charging during the EBL exposure. The EBL was carried out at 6 different doses varying the beam current in equal steps from 1200 to 2890 C/cm2. As the electron beam has a Gaussian shape, such increasing intensity produces nanostructures with varying feature sizes at the same grid spacing. The gold layer was removed by etching in a solution of KI and I2 in de-ionised (DI) water (Transene). Then, the samples were developed in a solution of 1:3 water and isopropyl alcohol cooled at 4°C with sonication, followed by isopropanol rinse and dried with a N2 gun. After visual inspection under an optical microscope, the samples passed through a 5 s descum process in argon to remove residues of the photoresist using a PlasmaPro RIE (reactive ion etch) 80 (Oxford Instruments). Subsequently, a 40 nm Ag layer was evaporated using 99.999 % Ag in a chemical vapour condensation SC4500 (CVC Products) combination with thermal/e-beam evaporator at 0.05 nm/s. The final lift-off and removal of the PMMA positive resist was carried out by soaking the samples at room temperature in methyl chloride, rinsing with acetone and isopropanol, and drying with the N2 gun. Finally, to prevent degradation of the Ag NPs, a 15 nm alumina cap layer was deposited in a FlexAl ALD system (Oxford Instruments) at a rate of 0.1 nm/min.

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The nanostructures with the Ag layer were produced by the same way only that two steps were introduced before application of the e-beam photoresist: thermal evaporation of a thin Ag layer, followed by ALD of a 15 nm alumina layer. Images of some samples from are presented in Figure 1B. They were imaged using a Zeiss Ultra60 FE-SEM (field-emission SEM) (Carl Zeiss AG), without any sample preparation to prevent contamination.

Figure 1. A) Single cell of the periodic array of nanocylinders. The materials from bottom up are: fused quartz (green), silver (grey) and alumina (blue). B) Electron microscopy images of cylinders and dimers with an underlying Ag layer.

3 Spectral characterisation The experimental optical spectra were obtained by using a 2100 Microspectrophotometer (S.E.E.) in transmission mode, in the range of 360-900 nm, illuminated by a mercury lamp, with a 20× NA 0.40 objective from regions of 8 μm×8 μm at the centre of each pattern.

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4 Theoretical analysis We performed finite element method (FEM) simulations by means of COMSOL Multiphysics 3.5a with the RF Module integrated with MATLAB. We simulated the plasmonic response of the structures from near ultraviolet to near infrared in steps of 10 nm. As lithographic methods are unable to produce sharp 90° edges for such small cylindrical features, and such geometry would produce spurious modes, in our simulations the cylinder edges were considered to be rounded. In our previous work,13 we found out a radius of curvature of 10 nm to present good agreement with experimental results. We studied its variation with diverse parameters, such as presence or absence of the alumina cap layer, and different alumina indices of refraction (1.2-1.9), cylinder heights (25-50 nm), cylinder diameters (40, 50 and 70 nm), separation layer thicknesses (10-25 nm), cap layer thickness (10-20 nm), radius of curvature of the cylinder edges (5-15 nm) and Ag layer thicknesses (35-55 nm). The materials properties were defined by their indices of refraction (Error! Reference source not found.). The excitation was defined as a TEM planar wave, whose fields and Poynting vector are shown in Figure 1A. Dimers were simulated in transverse and longitudinal polarisations. Table 1. Indices of refraction of the materials used in the simulations. The colours in the materials names correspond to the colours presented in Figure 1. When not specified, the refractive index of alumina in the simulations is 1.77.

material

refractive index

alumina (Al2O3)

1.77 for polycrystalline phase (synthetic sapphire at the middle

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of the region of interest, 564 nm),14 1.6 for amorphous phase15 silver (Ag)

= − i , where and were calculated by piecewise cubic interpolation of values acquired by Lynch and Hunter16

fused quartz

approximated to 1.55 (1.54-1.57 in the region of interest, 350700 nm, for the crystalline form)17

We defined a normalised attenuance as the difference of the attenuance18 of a studied structure and the corresponding reference substrate:

≡ − log − − log = − log

(1)

By corresponding reference substrate, we mean a geometry similar to the one being analysed (with or without Ag and alumina layers), but without the cylinders.

5 Results and Discussion 5.1 Cylinders without Ag layer Our simulated and experimental results for cylinders without Ag layer and covered with the alumina layer are presented in Figure 2. The experimental spectra are less than 30 nm blue shifted compared to theoretical calculations. These simulations predict an enhancement of the squared electric field, up to about 1.5-1.8 times, compared with about 0.6 for a substrate without cylinders (Supplementary Information). The normalised attenuances show local minima at around 320 nm. These minima arise from the minimum of the absolute value of Ag

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permittivity.19 The normalised attenuances show clear peaks at wavelengths around 500 nm. The peaks red shift with increasing cylinder diameter. The electric field distribution at these peaks resembles that from an electric dipole.

Figure 2. Results of the simulations of cylinders covered with a 15 nm alumina layer on a substrate without a silver layer. A) Simulated normalised attenuance and B) experimental results for different cylinder diameters (±2 nm). C) Enhancement of the squared electric field. D) Linear fit of the peaks of normalised attenuance. E)

) at 490 nm for a 50 nm cylinder. F) The electric dipole resembles the field Colour map of the electric field ( distribution in dipolar mode (plotted in http://www.falstad.com/emstatic/ on 11/12/2017).

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5.2 Cylinders with Ag layer We considered the case without the cap layer. In such structures, a 45 nm Ag layer sits on top of fused silica. The cylinders are separated from this Ag layer by a 15 nm alumina layer. Due to the cylinders, this structure presents LSP; and due to the silver layer, it may have PSP. We verified the presence of PSPs by using the approach introduced in our earlier Ref.20, as follows. The corresponding reference substrate for this geometry is a 45 nm Ag layer on fused silica, covered with a 15 nm alumina layer. The dispersion relation for this reference substrate was introduced in that Ref. When a periodic array of nanoparticles is added on top of this structure, the particles modify the wave vector of the light. Then, the wave vector parallel to the interface is given by21

!// = !#$%&' sin* ± ,-!. ± -!/

(2)

!#$%&' is the wave vector of the incident light, * is the angle of incidence, -!. and -!/ are Where the Bragg vectors along the two directions of the array, , and are natural numbers. The Bragg vector is given by22

-!.,/ =

22 34 3.,/ .,/

(3)

In which 3.,/ is the period of the grating in the 34. or 34/ directions. Here, the excitation is a TEM planar wave. Besides, the lattice is square (3.,/ = 3 = 150 ,). Therefore,23

!// 8 = 8

22 9,: + : 3

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(4)

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The three solutions with the highest wave vectors of the dispersion relation of the reference substrate are drawn in Figure 3 with the superimposed Bragg vector of order ,, = 0,1 or

1,0. There are two points marked on the graph, P1 (356 nm) and P2 (403 nm), where intersection with the dispersion relation occurs; higher orders do not intersect. P1 is in the region of anomalous dispersion with negative phase velocity, the quasi-bound mode,24 and P2 indicates that the cylinders can excite a Fano surface mode, a PSP at the interface. Studies with Au metal layers and grating or array of nanoparticles reported propagating surface plasmon resonances at 670-900 nm.23, 25-26 Another study using Ag,27 showed a PSP due to an array with

400 nm of period at about 490 nm. Ag structures are expected to produce blue shifted features compared to Au structures due to its Drude parameters. Besides, the shorter grating period can explain the further shift.

Figure 3. Dispersion relation of surface modes on a reference substrate composed of fused quartz surmounted by a 45 nm Ag layer and a 15 nm alumina layer (< = =. ??). Solutions 1-3 refer to the solutions with the highest wave vectors. It also shows the light lines in the dielectric materials (air, alumina and quartz) and the Bragg vector superimposing the dispersion relation.

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Normalised attenuances for the geometry with cylinders of different diameters without the cap layer are presented in Figure 4d. This figure shows two peaks: at 360-370 nm, and at 440540 nm. The long wavelength peak has a strong dependence on the size of the nanoparticle; therefore, it is assigned to LSP. The short wavelength peak is close to the theoretical position of the PSP; nevertheless, this peak was also presented in a simulation performed with a single cylinder instead of a periodic array (see Supplementary Information). Also, the electric field distribution around the NPs shows a quadrupole resonance (next paragraph). Hence, quadrupolar LSP resonance has a stronger effect here than a PSP resonance.

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Figure 4. Effect of different parameters on the normalized attenuances: a) silver layer thickness (without cap layer); b) NPs-Ag layer separation thickness (without cap layer); c) cylinder height (without cap layer); d) and e) cylinder diameter (without and with cap layer); f) refractive index of the alumina (with cap layer); g) cap layer thickness; h) radius of curvature of the cylinder edges (with cap layer); i) experimental data for different nominal diameters (with ±3 nm accuracy).

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In Figure 2, we showed a clear peak in the normalised attenuance for a cylinder without Ag layer and with a cap layer representing a dipolar resonant mode. The presence of the Ag layer shifts this dipolar peak from 470-510 nm to 510-610 nm (Figure 4e). This shift is due to the interaction of the mode with its own image at the surface.28 Their related experimental counterpart is in Figure 4i. Besides this red shift, there is a clear new peak at 460 nm, irrespective of the cylinder diameter. The red shift due to particle-surface interaction makes it possible for this mode to appear, as it gets farther from the region where the absolute value of the permittivity of the metal is close to a minimum, as well as the particle efficiencies.19 This peak is the red-shifted replica of the one at 360-370 nm discussed in the previous paragraph for the geometry without cap layer. Figure 5 presents the colour map of the electric field for both attenuance peaks. As it can be seen from the field distribution, that new peak is associated with a quadrupolar resonance in the cylinder (see comparison to the field lines in an electric quadrupole, Figure 5B).

) for a Figure 5. A) Cross section of the electric field distributions in the direction of the incident wave ( nanostructure with 50 nm cylinders over a 45 nm silver layer: dipolar and quadrupolar resonances at 550 and 460 nm, respectively. B) The electric quadrupole resembles the field distribution in quadrupolar mode (plotted in http://www.falstad.com/emstatic/ on 11/12/2017).

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Figure 4 also presents normalised attenuances in function of other parameters. In Figure 4a, the variation of the Ag layer thickness does not change significantly the shape of normalised attenuance, except by the higher attenuance for thicker layers, with its two peaks situated at 360 nm and at about 470-480 nm. We also performed simulations with other cylinder diameters (40 and 70 nm, data not shown) leading to similar results concerning the Ag layer thickness. Figure 4b presents the normalized attenuances for different thicknesses of the separation layer. This geometry is similar to the previous one except that the alumina separation layer was varied from 10 to 25 nm. In these structures, the attenuance peak at lower wavelength changed only from 360 to 370 nm with increasing NP-Ag layer distance. This weak effect is due to the permittivity region with high imaginary part and small absolute value of the real part.19 The second peak, however, blue shifts with increasing distance, from 500 nm down to 450 nm, reflecting a weaker influence of the near-field of the silver layer on the NPs. In order to study the effect of the cylinder height, this parameter was varied from 25 to 50 nm. The results (Figure 4c) show that the cylinder height does not change the position of the attenuance maxima, remaining at 360 nm and 470-480 nm. Nevertheless, the higher is the cylinder, the more accentuated is the quadrupolar peak. We propose that this is related to opposite charges concentrating on the corners of the cylinder. The shorter is the cylinder, the closer are its bottom and top edges, increasing attractive forces on the charges and reducing charge density.

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By varying the cylinder diameter (Figure 4d), the position of the quadrupolar resonance slightly moved from 360 to 370 nm; while the dipolar peak shifted from 440 to 540 nm, indicating the tunability of the optical properties for this nanostructure. Similar behaviour can be seen comparing the Mie scattering of spheres with different diameters: the dipolar resonance shifts faster than the quadrupolar. It is worth to note that the peaks are more discernible for larger diameters. The effect of the alumina cap layer can be seen comparing the Figure 4d (without cap layer) with Figure 4e (with cap layer). It is clear that a dielectric over the structure red shifts both attenuance maxima. The quadrupolar peak, which in all previous simulations was around 360370 nm, with the cap layer shifts to 460 nm. The other peak shifted from 440-540 to 510610 nm in the presence of the cap. We also simulated alternative structures where, instead of alumina, we used other dielectrics with varying refractive indices. The result of these variations (for 50 nm cylinder) is presented in Figure 4f for the index of refraction varying from 1.3 to 1.9. We also performed simulations with other indices of refraction from 1.2 to 2, which we omitted for easiness of visualisation. The graph shows that the attenuance peaks red shift with the refractive index of the cap layer. The red shift discussed above varies with the refractive index of the environment surrounding the structure in accordance with the Fröhlich condition for the dipole surface plasmon of spherical metallic NPs29 and of metallic thin wires with perpendicular polarisation30. However, we cannot quantitatively predict this shift by using the same equations, due to different geometry.

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Furthermore, we varied the cap layer thickness (Figure 4g) and the radius of curvature of the cylinders edges in conjunction with the radius of curvature of the upper edge of the cap layer around the cylinder (Figure 4h). It is possible to tune both attenuance peaks with these two parameters. The edges radius of curvature directly affect the modes whose charges are known to concentrate on the own edges and sides;13,

31

and thicker cap layers means that there is

larger volume of high-refractive-index material in the near-field region, leading to a further red shift. In summary, we established the tunability of the SPR by varying parameters for an array of cylinders over an Ag layer. Figure 6 summarises those tuning parameters and presents linear fits of the spectral positions of the attenuance features. The fits are good enough to be able to estimate the resonances wavelengths by affine equations in the entire parameter space under investigation. The dipolar resonance can be tuned throughout almost the entire visible spectrum. These strong and tuneable plasmon resonances are suitable for surface-enhanced spectroscopies.32-35 Besides, the tunability in function of the refractive index of the cap layer makes it useful for chemical/biological sensing by resonant wavelength interrogation.33, 36-38

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Figure 6. Linear fits of the tuning parameters versus position of the attenuance peaks in function of: a) NP-Ag layer separation thickness (no cap layer); b) alumina index of refraction (with cap layer); c) cap layer thickness; d) radius of curvature of the cylinder edges; e) cylinder diameter – the simulations with cap layer and amorphous (< = =. @) or polycrystalline alumina (< = =. ??), and the experimental data.

The alumina is known to have a refractive index of about 1.6 to 1.77 depending on growth conditions (Table 1). With these indices, Error! Reference source not found.e shows a 40 to 60 nm blue shift in the experimental data compared to the simulated positions of the quadrupolar resonance. In addition, the slope of the experimental linear fit for the dipolar resonance position as a function of cylinder diameter is about half of the theoretical value. These discrepancies can be explained by differences between samples and simulated geometries, imperfections in the measurements and manufacturing process, which are subject to significant errors on the scale of these structures, besides the indices of refraction used to

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model the simulations. The fabricated structures show the cylinders are not perfect (Figure 1Error! Reference source not found.B), and tolerances on the cylinder diameters were up to ±3 nm. The layers thicknesses and cylinder heights are subject to a tolerance of ±5 nm, and there was some degree of granularity in the thin metallic layers. Although there is some disagreement between the peak positions obtained from the simulations and real samples, the shapes of their attenuances and the trends for varying cylinder diameters are in good agreement. Returning to Figure 5, we draw attention to the hot spots on the sides of the cylinder on the plane crossing the centre and along the direction of the polarisation (A ). More specifically, the fields are higher at the edges of the cylinders, although these edges are curved (electric field tends to concentrate mainly at sharp edges13, 31). For the dipolar resonance, the bottom edge is characterised by a higher field; for the quadrupolar resonance, the highest field shifts to the upper edge. Note also that the field decreases away from the metal. In order to apply plasmonic structures for applications such as surface-enhanced Raman spectroscopy (SERS), it is necessary the metal to be uncoated, as SERS signal has an approximated dependence on the fourth power of the electric field.5 For surface-enhanced fluorescence (SEF), a fluorochromemetal distance up to tens of nanometres is necessary to avoid metal quenching, but this distance causes a significant reduction of the square of the electric field. The electric field and its second power averaged over the whole top surface are plotted in Figure 7A and B. The average of the field is only slightly enhanced (2.05-2.45 times for 50 nm cylinder), but the hot spots increase the average square of the electric field by a factor ranging from 5.4 to 8 times.

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Figure 7. A) Squared electric field and B) electric field enhancements averaged over structures composed of 15 nm capped cylinders over 45 nm Ag layer and cylinders with 40, 50 or 70 nm. C) Positions of the peaks of the squared electric field and normalised attenuance for a 50 nm cylinder.

Comparing Figure 4e and Figure 7A, it is clear that the electric field maxima (near field) are red shifted in comparison to the attenuance maxima (far field). A plot of these peak positions is shown in Figure 7C. Ref.39 tries to explain this shift by assuming the plasmon to be a damped harmonic oscillator driven by an external field. In this way, the system is characterised by a natural frequency and a red shifted frequency of higher-amplitude oscillation dependent on the damping. Nevertheless, comparing the observed shift of more than 100 nm for the 70 nm particles with the ones obtained in another study,40 we cannot say this harmonic oscillator model can explain the effect. Further study is required.

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Figure 8 presents colour maps of the magnetic field enhancement in the dipolar and quadrupolar resonances. In the quadrupolar mode, the electric field concentrates at the top edges of the NP (Figure 5A); while the magnetic field concentrates at the bottom, but not at the edges. In the dipolar mode, the electric field concentrates at the bottom edges of the NP; and the magnetic field, on the top of the NP. The Poynting vector and the power dissipation by resistive heating are shown at the bottom of Figure 8. In the same fashion, the dissipation occurs mainly on top or on bottom of the NP according to the mode. In the dipolar resonance, the closer the NP is to the silver layer, the higher the dissipation is on the silver layer right under the NP. Kie et al.41 applied this concentrated heating on a metallic layer as a near-field optical lithographic method.

Figure 8. Colour maps and vectors quadrupolar (470 nm, left) and dipolar resonances (610 nm, right). Top: 3

magnetic flux density enhancement. Bottom: power loss (colour map in W/m ) and Poynting vector (arrows).

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5.3 Dimers We also simulated 40 and 50 nm cylinders with and without Ag layer. It is important to note that the NPs coupling depends on the near field, which for dipolar interaction has a dependence on the inverse cube distance.30, 42-43 Therefore, we expect little difference between small isolated cylinders and small double cylinders, where the inter-particle distance is of tens of nanometres. For the 40 nm cylinders, the cap layers touch each other. For the 50 nm cylinders, the metallic NPs are separated, but the cap layers merge. Their normalised attenuances are plotted in Figure 9 in transverse (TP) and longitudinal (LP) polarisations along with the ones of single cylinders. Our simulations with 70 nm dimers spaced by 70 nm did not converge, due to the sharp features where they touch each other. Besides, this geometry would be lithographically unfeasible. We did not simulate larger cylinders, as they merge turning into a single nanostructure. The experimental results are not shown, as the signal-to-noise ratio was very low with the available polariser.

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Figure 9. Normalised attenuances of dimers with or without the underlying Ag layer and cap layer. The dimers are composed of cylinders with 40 or 50 nm. TP and LP stand for transverse and longitudinal polarisations, according to the inset. The attenuances of single cylinders are also plotted for comparison.

For structures without Ag layer, dimers have twice the filling factor of single cylinders. In principle, this factor would be responsible for twice more light being reflected and absorbed by the NPs, but that does not account for interactions between them. Both far- and near-field interactions can modify the extinction cross section of the NPs.44 In all simulations, with and without Ag layer, LP led to higher attenuances than TP. For LP, the metallic edges, where the field is highly enhanced, have the closest position to the edges of the next NP: 30 nm (40 nm cylinders) or 20 nm (50 nm cylinders). It means that, in LP, the proximity of the cylinders has a more significant effect than in TP. Without the Ag layer (Figure 9a and b), the attenuance peaks in TP are blue shifted in relation to the ones of single

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cylinders, while in LP the peaks are red shifted. The structures with an Ag layer (Figure 9c) showed the opposite effect: red shift the attenuance in TP, and blue shift in LP, except on the case (50 nm particles) where the near field created a new resonance. We now discuss the general structure of the electromagnetic modes. In the hybridisation model,45 we would expect four distinct modes split from the interaction of two close NPs without the metal layer: Two modes – bounding (parity of moments) and anti-bounding (negative parity of moments) – for each resonance of individual NP: quadrupolar and dipolar modes. We did not achieve such a split of surface plasmon resonances, probably because of the not so small distance between the NPs, 30 or 20 nm. However the weak near-field coupling was weak, for the 50 nm NPs with Ag and cap layers at LP (Figure 9d) there was a new attenuance peak between the quadrupolar and dipolar resonant modes. This peak is clearer in the plot of the squared electric field enhancement (close to 550 nm in Figure 10b). The electric field distributions at the three peaks for this geometry are plotted in Figure 10c, d and e. The field distributions at 500 and 600 nm clearly show the bonding modes for quadrupolar and dipolar modes at LP, respectively. In LP, the anti-bonding mode is at higher energy.45 Therefore, we would expect the 570 nm to be the anti-bonding dipolar resonance, but the field distribution is not fully clear, possibly due to a comparatively large NPs separation.

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Figure 10. Squared electric field enhancement over structures composed of dimers with (a) or without (b) the Ag layer. The dimers are composed of cylinders with 40 or 50 nm. And resonant modes of dimers with Ag layer: c) quadrupolar, d) the intermediate and e) dipolar modes.

Without the Ag layer, the maximum squared field enhancement was 1.2 times for TP and 1.92.4 times for LP (Error! Reference source not found.a and b). With the presence of an Ag layer, the maximum enhancement increased to 4.9-5.6 times for TP and 12.3-13.4 times for LP. 5.4 Enhanced transmission It could be anticipated that, when a NPs array is added to the geometry, more light is scattered and absorbed by resistive heating, compared to the reference substrate. This is correct at short wavelengths. However, at long wavelengths, the interaction of the NPs and the thin metal layer leads to a higher transmittance than just with the layer, as can be verified by the negative normalised attenuances in Figure 4 and Figure 9. This effect was observed in both theoretical

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and experimental data. The value of the theoretical normalised attenuance decreased down to about -0.35 (Figure 9), what represents a transmittance enhanced more than twice in relation to a reference substrate with Ag layer (eq. 3). Earlier literature on enhanced or extraordinary transmission usually refers to structures such as periodic array of sub-wavelength apertures or nanoparticles,21,

27, 46-48

single aperture

surrounded by a circular grating or by a 2D array of dimples49-50 and periodically corrugated metal surface.51-52 There is still a debate on the causes of such enhanced transmission. This phenomenon is usually attributed to PSPs, which can transport electromagnetic energy to the other side of a metallic film. According to our calculations, PSPs can be excited in our structures, but only at short wavelengths, not at left of the dipolar mode (red shifted, >500 nm). For the case of uncapped cylinders, the PSP is at 403 nm (P2 in Figure 3). The enhanced transmission is not present in the ‘local normalised attenuance’ caused by single cylinders (see Supplementary Information Figure S3). Therefore, the extraordinary transmission was caused by the periodic array of NPs. Alternative explanations of enhanced transmission include interference of diffracted waves53 or diffracted evanescent waves.54 Another possibility would be the same reason for which metal NPs have been used to enhance the efficiency of photovoltaic devices, such as photodetectors and solar cells.55-57 According to Yu et al.,56 for particles with sizes for which the scattering efficiency dominates in relation to the absorption efficiency, there is a strong forward scattering that improves the transmission into the semiconductor under the NPs, working as an anti-reflecting coating. Nevertheless, these structures are different from the IIMI geometry with

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NPs. Hence, their findings are not directly applicable here. Zhou et al. suggested that LSP can lead to extraordinary transmission.27 As in their work, the position of the transmittance peak changes with the NP-metal layer distance (Figure 4b); however, the transmission improvement was not obtained for a sole cylinder. Further studies are required to establish the reason for the enhanced transmission of this periodic NPs array over the thin metal layer.

6 Conclusions We theoretically studied the optical properties of a periodic array of single and double cylinders and the effects of an underlying thin metal layer. Some well-controllable parameters can be used for tuning the SPRs, including NP-silver layer distance, index of refraction, cap layer thickness and cylinder diameter. The proximity of the array of cylinders to the silver layer improved the transmission at long wavelengths, but we showed this effect is neither due to PSP nor LSP. The reason for this extraordinary transmission is still unclear. The presence of an underlying Ag layer red shifts the resonant modes, and makes it possible the appearance of new resonances, such as quadrupolar and an intermediate mode that appeared in dimers 20 nm apart in LP. The electric field is maximised along the direction of polarisation around the edges of the cylinders. We estimated the enhancement of the electric field to the second power over the top surface of the whole structure. The highest enhancement, obtained for a dimer with 50 nm in diameter and in LP, represents a gain of 21.8 times in relation to a simple dielectric substrate.

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The periodic array of cylinders over an Ag layer, with its tuneable SPRs, has potential applications in SES. As the SPRs are sensitive to changes in the refractive index of the cap layer, other potential application is SPR sensing by wavelength interrogation.

7 Associated content Supporting Information Available: results of simulations of references substrates, sole Ag cylinder over Ag layer and simulation convergence. This material is available free of charge via the Internet at http://pubs.acs.org.

8 Acknowledgements H.B. acknowledges the support of the International Macquarie Research Excellence Scholarship. This work was partially supported by the awards DP140104458 and CE140100003 from the Australian Research Council.

9 References 1. Catchpole, K. R.; Pillai, S., Surface plasmons for enhanced silicon light-emitting diodes and solar cells. J. Lumin. 2006, 121 (2), 315-318. 2. Ebbesen, T. W.; Genet, C.; Bozhevolnyi, S. I., Surface-plasmon circuitry. Phys. Today 2008, 61 (5), 44-50. 3. Lal, S.; Link, S.; Halas, N. J., Nano-optics from sensing to waveguiding. Nat. Photon. 2007, 1 (11), 641-648. 4. Pelton, M.; Aizpurua, J.; Bryant, G., Metal-nanoparticle plasmonics. Laser Photon. Rev. 2008, 2 (3), 136-159.

28/35


Page 28 of 36

Page 29 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5. Le Ru, E. C.; Etchegoin, P. G., Surface-enhanced Raman scattering (SERS) and surfaceenhanced fluorescence (SEF) in the context of modified spontaneous emission. ArXiv eprints 2008. 6. Naik, G. V.; Shalaev, V. M.; Boltasseva, A., Alternative plasmonic materials: beyond gold and silver. Adv. Mater. 2013, 25 (24), 3264-3294. 7. West, P. R.; Ishii, S.; Naik, G. V.; Emani, N. K.; Shalaev, V. M.; Boltasseva, A., Searching for better plasmonic materials. Laser Photon. Rev. 2010, 4 (6), 795-808. 8. D'Agostino, S.; Della Sala, F., Active role of oxide layers on the polarization of plasmonic nanostructures. Acs Nano 2010, 4 (7), 4117-4125. 9. Szmacinski, H.; Badugu, R.; Lakowicz, J. R., Fabrication and characterization of planar plasmonic substrates with high fluorescence enhancement. J. Phys. Chem. C 2010, 114 (49), 21142-21149. 10. Liu, N.; Mesch, M.; Weiss, T.; Hentschel, M.; Giessen, H., Infrared perfect absorber and its application as plasmonic sensor. Nano Lett. 2010, 10 (7), 2342-2348. 11. Whitney, A. V.; Elam, J. W.; Stair, P. C.; Van Duyne, R. P., Toward a thermally robust operando surface-enhanced Raman spectroscopy substrate. J. Phys. Chem. C 2007, 111 (45), 16827-16832. 12. Sung, J.; Kosuda, K. M.; Zhao, J.; Elam, J. W.; Spears, K. G.; Van Duyne, R. P., Stability of silver nanoparticles fabricated by nanosphere lithography and atomic layer deposition to femtosecond laser excitation. J. Phys. Chem. C 2008, 112 (15), 5707-5714.

29/35



13. Goldys, E. M.; Calander, N.; Drozdowicz-Tomsia, K., Extreme sensitivity of the optical properties of metal nanostructures to minor variations in geometry is due to highly localized electromagnetic field modes. J. Phys. Chem. C 2010, 115 (3), 676-682. 14. Malitson, I. H., Refraction and dispersion of synthetic sapphire. Journal of the Optical Society of America 1962, 52 (12), 1377-1379. 15. Groner, M. D.; Fabreguette, F. H.; Elam, J. W.; George, S. M., Low-temperature Al2O3 atomic layer deposition. Chem. Mater. 2004, 16 (4), 639-645. 16. Lynch, D. W.; Hunter, W. R., Comments on the optical constants of metals and an introduction to the data for several metals. In Handbook of optical constants of solids, Palik, E. D., Ed. Academic Press: Orlando, 1985. 17. Philipp, H. R., Silicon dioxide (SiO2), type alpha (crystalline). In Handbook of optical constants of solids, Palik, E. D., Ed. Academic Press: Orlando, 1985; p 804. 18. IUPAC, Compendium of chemical terminology. 2 ed.; Blackwell Scientific Publications: 1997. 19. Noguez, C., Optical properties of isolated and supported metal nanoparticles. Optical Materials 2005, 27 (7), 1204-1211. 20. Baltar, H. T. M. C. M.; Drozdowicz-Tomsia, K.; Goldys, E. M., Propagating surface plasmons and dispersion relations for nanoscale multilayer metallic-dielectric films. In Plasmonics Principles and Applications, Kim, K. Y., Ed. InTech: 2012. 21. Barnes, W. L.; Murray, W. A.; Dintinger, J.; Devaux, E.; Ebbesen, T. W., Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film. Phys. Rev. Lett. 2004, 92 (10), 107401.

30/35


Page 30 of 36

Page 31 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


22. Akarca-Biyikli, S. S.; Bulu, I.; Ozbay, E., Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture. Appl. Phys. Lett. 2004, 85 (7), 1098-1100. 23. Chu, Y.; Crozier, K. B., Experimental study of the interaction between localized and propagating surface plasmons. Opt. Lett. 2009, 34 (3), 244-246. 24. Dionne, J. A.; Sweatlock, L. A.; Atwater, H. A.; Polman, A., Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model. Phys. Rev. B 2005, 72 (7), 75405. 25. Félidj, N.; Aubard, J.; Lévi, G.; Krenn, J. R.; Schider, G.; Leitner, A.; Aussenegg, F. R., Enhanced substrate-induced coupling in two-dimensional gold nanoparticle arrays. Phys. Rev. B 2002, 66 (24), 245407. 26. Raymond, G.; Mitradeep, S.; Jean-François, B.; Ryohei, Y.; Julien, M.; Mondher, B.; Grégory, B.; Bernard, B.; Michael, C.; Marc Lamy de la, C., Directional surface enhanced Raman scattering on gold nano-gratings. Nanotechnology 2016, 27 (11), 115202. 27. Zhou, Y.; Zhao, Y.; Zou, S., Different Transmission Enhancement Mechanisms in a Sandwiched Nanofilm. Particle & Particle Systems Characterization 2017, 34 (8), 1600327. 28. Holland, W. R.; Hall, D. G., Frequency Shifts of an Electric-Dipole Resonance near a Conducting Surface. Phys. Rev. Lett. 1984, 52 (12), 1041-1044. 29. Maier, S. A., Plasmonics: fundamentals and applications. Springer: 2007; p 223. 30. Novotny, L.; Hecht, B., Principles of nano-optics. 2 ed.; Cambridge: 2012; p 564.

31/35



31. Beck, F. J.; Verhagen, E.; Mokkapati, S.; Polman, A.; Catchpole, K. R., Resonant SPP modes supported by discrete metal nanoparticles on high-index substrates. Opt Express 2011, 19 (S2), A146-A156. 32. Hao, F.; Nordlander, P.; Burnett, M. T.; Maier, S. A., Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities. Phys. Rev. B 2007, 76 (24), 245417. 33. Haynes, C. L.; Haes, A. J.; McFarland, A. D.; Van Duyne, R. P., Nanoparticles with tunable localized surface plasmon resonances. In Radiative Decay Engineering, Geddes, C. D.; Lakowicz, J. R., Eds. Springer US: 2005; Vol. 8, pp 47-99. 34. Jensen, T. R.; Malinsky, M. D.; Haynes, C. L.; Van Duyne, R. P., Nanosphere lithography: tunable localized surface plasmon resonance spectra of silver nanoparticles. J. Phys. Chem. B 2000, 104 (45), 10549-10556. 35. Lal, S.; Grady, N. K.; Kundu, J.; Levin, C. S.; Lassiter, J. B.; Halas, N. J., Tailoring plasmonic substrates for surface enhanced spectroscopies. Chem Soc Rev 2008, 37 (5), 898-911. 36. Enoch, S.; Quidant, R.; Badenes, G., Optical sensing based on plasmon coupling in nanoparticle arrays. Opt Express 2004, 12 (15), 3422-3427. 37. Homola, J.; Koudela, I.; Yee, S. S., Surface plasmon resonance sensors based on diffraction gratings and prism couplers: sensitivity comparison. Sensors and Actuators B: Chemical 1999, 54 (1–2), 16-24. 38. Homola, J.; Yee, S. S.; Gauglitz, G., Surface plasmon resonance sensors: review. Sensors and Actuators B: Chemical 1999, 54 (1–2), 3-15.

32/35


Page 32 of 36

Page 33 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


39. Zuloaga, J.; Nordlander, P., On the energy shift between near-field and far-field peak intensities in localized plasmon systems. Nano Lett. 2011, 11 (3), 1280-1283. 40. Colas, F. J.; Cottat, M.; Gillibert, R.; Guillot, N.; Djaker, N.; Lidgi-Guigui, N.; Toury, T.; Barchiesi, D.; Toma, A.; Di Fabrizio, E.; Gucciardi, P. G.; de la Chapelle, M. L., Red-Shift Effects in Surface Enhanced Raman Spectroscopy: Spectral or Intensity Dependence of the Near-Field? J. Phys. Chem. C 2016, 120 (25), 13675-13683. 41. Kik, P. G.; Martin, A. L.; Maier, S. A.; Atwater, H. A. In Metal nanoparticle arrays for nearfield optical lithography, Properties of metal nanostructures, Seattle, WA, SPIE: Seattle, WA, 2002; pp 7-13. 42. Jain, P. K.; El-Sayed, M. A., Universal scaling of plasmon coupling in metal nanostructures: extension from particle pairs to nanoshells. Nano Lett. 2007, 7 (9), 28542858. 43. Jain, P. K.; Huang, W.; El-Sayed, M. A., On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: a plasmon ruler equation. Nano Lett. 2007, 7 (7), 2080-2088. 44. Pinchuk, A. O.; Schatz, G. C., Nanoparticle optical properties: far- and near-field electrodynamic coupling in a chain of silver spherical nanoparticles. Materials Science and Engineering: B 2008, 149 (3), 251-258. 45. Nordlander, P.; Oubre, C.; Prodan, E.; Li, K.; Stockman, M. I., Plasmon hybridization in nanoparticle dimers. Nano Lett. 2004, 4 (5), 899-903. 46. García de Abajo, F. J., Colloquium: light scattering by particle and hole arrays. Reviews of Modern Physics 2007, 79 (4), 1267-1290.

33/35



47. Heer, J. M.; Coe, J. V., 3{D-FDTD} modeling of angular spread for the extraordinary transmission spectra of metal films with arrays of subwavelength holes. Plasmonics 2012, 7 (1), 71-75. 48. Miyamaru, F.; Kamijyo, M.; Hanaoka, N.; Takeda, M. W., Controlling extraordinary transmission characteristics of metal hole arrays with spoof surface plasmons. Appl. Phys. Lett. 2012, 100 (8), 081112-4. 49. Lezec, H. J.; Degiron, A.; Devaux, E.; Linke, R. A.; Martín-Moreno, L.; García-Vidal, F. J.; Ebbesen, T. W., Beaming light from a subwavelength aperture. Science 2002, 297 (5582), 820-822. 50. Thio, T.; Pellerin, K. M.; Linke, R. A.; Lezec, H. J.; Ebbesen, T. W., Enhanced light transmission through a single subwavelength aperture. Opt. Lett. 2001, 26 (24), 1972-1974. 51. Fiala, J.; Richter, I. In Theory and simulations of enhanced transmission through plasmonic sub-wavelength structures, Optical Society of America: 2009; p FWC7. 52. Gurel, K.; Kaplan, B.; Guner, H.; Bayindir, M.; Dana, A., Resonant transmission of light through surface plasmon structures. Appl. Phys. Lett. 2009, 94 (23), 233102. 53. Schwarz, I.; Livneh, N.; Rapaport, R., General closed-form condition for enhanced transmission in subwavelength metallic gratings in both TE and TM polarizations. Opt Express 2012, 20 (1), 426-439. 54. Lezec, H. J.; Thio, T., Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays. Opt Express 2004, 12 (16), 36293651.

34/35


Page 34 of 36

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55. Stuart, H. R.; Hall, D. G., Island size effects in nanoparticle-enhanced photodetectors. Appl. Phys. Lett. 1998, 73 (26), 3815-3817. 56. Yu, E. T.; Derkacs, D.; Matheu, P.; Schaadt, D. M. In Plasmonic nanoparticle scattering for enhanced performance of photovoltaic and photodetector devices, 2008; pp 70331V70331V-9. 57. Zhang, Y.; Ouyang, Z.; Stokes, N.; Jia, B.; Shi, Z.; Gu, M., Low cost and high performance Al nanoparticles for broadband light trapping in Si wafer solar cells. Appl. Phys. Lett. 2012, 100 (15), 151101.

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Plasmonic Properties of Periodic Arrays of Ag ... - ACS Publications

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