Plasmonic Metasurfaces with Tunable Gap and Collective SPR Modes

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Plasmonic Metasurfaces with Tunable Gap and Collective SPR Modes Oleg A. Yeshchenko, Viktor V. Kozachenko, Anastasiya V. Tomchuk, Michael Haftel, Randall J. Knize, and Anatoliy O. Pinchuk J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02515 • Publication Date (Web): 29 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019

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The Journal of Physical Chemistry

Plasmonic Metasurfaces with Tunable Gap and Collective SPR Modes Oleg A. Yeshchenko1, Viktor V. Kozachenko1, Anastasiya V. Tomchuk,1 Michael Haftel2, Randall J. Knize4, and Anatoliy O. Pinchuk* 2,3 1Physics

Department, Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska str., 01601 Kyiv, Ukraine

2Department 3Center

of Physics, University of Colorado at Colorado Springs, for Plasmonics, Nanophotonics, and Metamaterials Colorado Springs, Colorado, 80918, USA

4Laser

Optics Research Center, Phys. Dept., US Air Force Academy, CO 80840

Corresponding Author Anatoliy Pinchuk [email protected] Abstract Optical properties of a plasmonic metasurface made of a monolayer of gold nanoparticles in close proximity to an aluminum thin film were studied numerically and experimentally. Extinction spectra of the plasmonic metasurface were studied as functions of the thickness of a dielectric spacer between the monolayer of gold nanoparticles and the aluminum film in the visible wavelength range. The goal was to understand the excitation of a collective surface plasmon resonance (SPR) mode and a gap plasmon mode as well as their dependence on the spacer thickness, nanoparticles spacing and their size. By using finite-difference-time-domain (FDTD) calculations we find that the SPR extinction peak first red-shifts and then splits into two peaks. The first extinction peak is associated with the collective SPR mode of the monolayer and it shifts to shorter wavelengths as the spacer layer decreases. As the spacer layer decreases from 35 nm to 7.5 nm, the second peak gradually appears in the extinction spectra of the metasurface. We assign the second peak to the gap mode. The gap mode first appears at around 620 nm or greater and it shifts to larger wavelength for larger nanoparticle spacing and size. The FDTD simulations are confirmed by an experimental examination of the dispersion curves of a similar multilayer system. The computational results match the experimental results and confirm the excitation of the two modes.

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1. Introduction Metasurfaces are artificially designed nanostructured layers of plasmonic and/or dielectric materials that exhibit unusual and promising optical properties potentially useful for a number of applications in optics, photovoltaics, microscopy, biochemical sensing and surface enhanced spectroscopy.12 When placed in close proximity to a thin metal film, gap modes may be excited between plasmonic nanostructures and the metal film.

3,4,5

The enhanced electromagnetic field

between the plasmonic nanostructures and the film might be used for surface enhanced spectroscopy (e.g. SERS

3,4,5,6 plasmon

enhanced photoluminescence (PL)

7,8,910

plasmon-

driven surface catalysis,11 efficient generation of electron-hole pairs in solar cells,12 and tunable reflection.13 Metasurfaces with tunable optical response are of particular interest since the gap between a monolayer of plasmonic nanoparticles in close proximity to a thin metal film can be used to control the optical response of the metasurface.14 Light emission was recently observed for plasmonic nanoparticles in close proximity to a metal film that potentially can be used in novel photonic devices.15 Though the excitation of gap mode has been recently observed with metasurfaces fabricated of silver and gold nanoparticles,14,16 the possibility of tuning of the wavelength and bandwidth of the gap mode between the nanoparticles and the substrate and collective surface plasmon resonance (SPR) mode in the metasurfaces has not been addressed in details so far. Furthermore, the exact conditions and parameters of the metasurfaces-substrate system, such as the spacing between the nanostructures (or the surface density of nanoparticles), nanoparticle size and the distance between the metasurfaces and the metal thin film remains to be studied. In this work, we show how the surface density of gold nanoparticles and the spacing between the metasurfaces and the thin metal film can be used to tune the collective SPR mode and the gap mode of the metasurface.17 In particular we assess the dependence of the wavelength of the gap mode on the spacer gap, spacing of the Au NPs, and their size. The system under study consists of a monolayer of spherical Au NPs of given diameter and spacing deposited on a glass substrate separated by a dielectric (shellac, n = 1.5) spacer layer varying from 7.5 to 35 nm capped by a 5 nm Al film. Gold nanoparticles exhibit a pronounced localized SPR in the visible spectrum of light. Unlike silver or copper, gold is chemically inert, which makes this metal a number one choice for a variety of plasmonic applications, including this study. The aluminum film was chosen because it develops a self-terminating oxide layer which leads to long-term stability of the film. In addition, aluminum is compatible with complementary metal-oxide semiconductor (CMOS) technology, opening up new possibilities for integration with electronics and on-chip device applications. This

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combination of plasmonic metals is advantageous also for achieving highly tunable optical properties suitable for efficient photonic applications. Using the finite-difference-time-domain (FDTD) method we calculate the extinction spectrum for various combinations of spacer thickness, spacing, and NP diameter to determine the dependence of the frequency (or vacuum wavelength) of the SPR and/or gap plasmon resonance on these parameters. We find that as the spacer gap is decreased below 20 nm the gap mode gradually begins to appear significantly red-shifted from the SPR mode. The red shift usually increases as the spacing is increased from 110 to 320 nm and it is also more pronounced for larger Au NPs. In the next section, we outline the system under study and numerical methods that we use to study the optical response. Section 3 presents the FDTD results for the extinction spectra. Section 4 explains the trends with regards to the gap mode dispersion relations. The near-field calculations of the electromagnetic fields are presented in Section 5. Section 6 provides experimental results and how these confirm the trends mentioned above. Finally, the last section contains concluding remarks. 2. Methods. We consider a monolayer of spherical gold nanoparticles of the radius R located in close proximity to an aluminum thin film as shown in Fig. 1. The distance between the monolayer of nanoparticles and the Al film can be controlled by varying the thickness of the dielectric spacer. The surface coverage or surface density of the AuNPs monolayer can be tuned by varying the spacing between the neighbor nanoparticles. We assume that the spacer layer thickness (d) varies from 7.5 to 35 nm, the spacing (a) from 110 to 320 nm, and we used Au NPs of diameter (D = 2R) of 90 and 110 nm. This is approximately the range of parameters used in the experimental investigations presented in Section 6. The incident plane wave is impinges the Al layer at normal incidence and is polarized linearly along the Al surface as shown in Fig. 1.

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Figure 1. A sketch of a metasurface composed of Au NPs of diameter D and spacing a in close proximity to a thin Al film separated by a spacer layer of thickness d with a glass substrate. The incident light is linearly polarized with the electric field parallel to the monolayer of Au NPs.

To elucidate the dependence of the collective SPR mode and a gap mode we employ FDTD simulations. The simulations are carried out using the HASP code used in similar studies of metallic nanosurfaces.18-20 The HASP code uses a nonstandard variation21,22 of the commonly used Yee algorithm23

but with considerably more accuracy. For homogenous systems this algorithm

achieves about six-place accuracy with a mesh with as few as 20 points per wavelength. For our problem the accuracy-limiting feature is spatial resolution of the spacer layer and resolving the spherical NPs. For this reason we employ a spatial mesh of 2.5 nm spacing and a time step of 0.005 fs. The time step is small enough to assure numerical stability. We estimate the wave amplitudes are accurate to 1-2 %. In our calculations we take the frequency-dependent dielectric constant for Au from the compilation of Johnson and Christy.24 For Al we use the refractive index database compilation given in Ref.(18). For shellac we take the index of refraction n = 1.5 and for glass n = 1.45. The simulations employ periodic boundary conditions in the lateral directions, with the periodicity being equal to the NP spacing, and perfectly-matched-layer (PML) boundary conditions19,20 at the top and bottom of the computational box to virtually eliminate artificial reflections.

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3. Size and spacing dependence of gap and SPR modes Fig. 2 shows the calculated extinction spectra of a monolayer of Au NPS as a function of the distance between the monolayer and the aluminum substrate. The size of Au NPs is D=110 nm and the periodicity of the Au NPs (the density of the particles constituting the monolayer) is 260 nm, which corresponds to the distance between the surfaces of the metal NPs of 150 nm. The thickness of the Al layer is 5 nm. As the distance between the monolayer and the substrate decreases from 20 nm down to 7.5 nm a second peak gradually appears in the extinction spectrum moving from about 620 nm to around 660 nm corresponding to the excitation of the gap mode, as will be demonstrated later when we examine the dispersion relations of the gap mode in the vacuum – Al – shellac – Au – glass multilayer system. Also, the field intensity patterns obtained in the FDTD simulations confirm the gap mode assessment. The numerical calculations also reproduce the experimentally observed trends shown later in Fig. 5.

Figure 2. Extinction spectra of a monolayer of D = 110 nm gold nanoparticles spaced at a = 260 nm for various shellac spacer layer thicknesses (d) between the monolayer and Al film.

Figures 3a and 3b give the extinction spectra for a monolayer of D = 110 nm Au NPs with spacer gaps of 7.5 and 30 nm, respectively, as the periodicity, or spacing, varies from 140 to 320 nm (400 nm in Fig. 3b). Figures 4a and 4b show the corresponding spectra for D = 90 nm with the spacing varying from 110 to 320 nm or 400 nm. In Fig. 3a (7.5 nm spacer) a hump and then a second peak develops as the spacing increases above 200 nm. The SPR peak only very slightly red-shifts with increasing spacing. In Fig. 3b, when there is a 30 nm spacer, there is a single peak that red shifts from 540 nm to 640 nm over the range of periodic spacing. Similar trends with periodicity occur in Figs. 4 a,b (D = 90 nm) but are less dramatic. The second peak for small gaps and larger spacing

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is clear evidence for gap mode. The red-shifting for the 30 nm spacers also give some evidence for a role for gap modes, but here the result is more likely a hybridization of the SPR and gap modes as only a single peak occurs. The gap mode also appears weaker for D = 90 nm than for D = 110 nm, likely due to the smaller lateral extent of this mode relative to the space between the Au NPs. Evidently, even a small change in the size of the NPs can have a large effect on the nature of the excited mode. The source of the above trends is a result of the dispersion relations for the gap modes as a function of gap size and spacing, as we will now discuss. (a)

(b)

Figure 3. (a) Extinction spectra of a monolayer of D = 110 nm gold nanoparticles with spacing a = 140 to 320 nm for shellac spacer layer thicknesses d = 7.5 nm between the monolayer and the Al film. (b) Same for d = 30 nm but with a = 140 to 400 nm. (a)

(b)

Figure 4. (a) Extinction spectra of a monolayer of D = 90 nm gold nanoparticles with spacing a = 140 to 320 nm for shellac spacer layer thicknesses d = 7.5 nm between the monolayer and the Al film. (b) Same for d = 30 nm.

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4. Dispersion for the gap mode To help understand the previous extinction spectra we calculated the dispersion curves for the vacuum – Al (5 nm thick) – shellac (various gaps, n= 1.5) – Au (110 nm thick) – glass (n = 1.45) multilayer system. We calculated analytically the fields from Maxwell’s equations by applying the appropriate boundary conditions at each layer boundary. One looks for “bound” solutions , i.e., solutions that decay exponentially at large positive and negative z , or equivalently, solutions of the light scattering problem that give infinite reflectance. (These occur at ksp> k0 =  / c, i.e., in a region inaccessible to physical scattering experiments on a flat undisturbed surface.) The solution involves finding the zeroes of the determinant of the matrix constructed from the matching conditions, which we carry out by standard conjugate gradient methods. Fig. 5 gives the gap plasmon wavelength sp = 2  Re(ksp) as a function of the vacuum  for various gaps between 7.5 and 50 nm. (The gap plasmon wave number ksp has an imaginary part that determines the width of the resonance and the range of the gap plasmon.) In assigning a gap mode we look for solutions that have large fields especially in the spacer region.17 We exclude modes that correspond to surface plasmons on just the Au or Al surface. We now explain how these curves determine the trends in Figs. 2-4 with regards to gap size and periodicity (or spacing). A metal surface with a periodic array of nanostructures (or “defects”) with a periodicity a can launch surface plasmons, or in our case gap plasmons, according to (in 1D) ksp = 2  n  a

(n is integer),

(1)

or, equivalently

sp = a / n.

(2)

Thus the ordinate label in Fig. 5 can correspond to the spacing divided by an integer. For example, a spacing of a = 260 nm would correspond to in Fig. 5 sp = 260 nm for an n = 1 mode and 130 nm for an n = 2 mode. This allows one to determine, for a given n, the resonant  for a given periodicity and gap. To illustrate this, if we assume a spacing of a = 260 nm, then in Fig. 5 this corresponds to sp = 260 nm for an n = 1 mode and sp = 130 nm for the n = 2 mode. The horizontal dotted lines in Fig. 5 at these values of sp represent the n = 1 and n = 2 gap plasmon modes for a = 260 nm and the abscissa value at which these lines intersect the curve for a given spacer gap determines the resonant . In this case the n = 1 resonant wavelength for a = 260 nm and gap 30 nm is at about 750 nm. For a = 260 nm and gap 10 nm the resonant  is at about 670 nm. In this way we can read off, for any n, the resonant peak for any periodicity for the different gap sizes.

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Figure 5. The real gap plasmon wavelength as a function of vacuum wavelength for various spacer gaps for the system indicated here and in the text. The dotted lines give examples on how to determine the resonant  for a given periodicity and gap, as explained in the text. By the above procedure we see that for > 600 nm for a given spacing the gap plasmon peaks become increasingly red-shifted as the spacer gap becomes smaller. Likewise, for a given gap, the peaks become increasingly red-shifted for increased spacing. Also, for a given periodicity there is a maximum gap above which a gap plasmon mode cannot be supported. These are all trends observed in the FDTD results in Figs. 2-4. The monolayer of Au NP metamaterial is not exactly a plane layered system, so we must expect some deviations between the FDTD (Figs. 2-4) and dispersion peak positions (Fig. 5). Nevertheless, the agreement is almost quantitative, especially for the D = 110 nm results. For example, for a = 260 nm, D = 110 nm, d = 7.5 nm the dispersion curves indicate a (n = 2) peak at about 730 nm whereas the extinction peak in FDTD is at 650 nm. Thus, there would appear to be some disagreement. However, 7.5 nm is the minimum gap. The distance between the nanospheres and the Al surface varies from 7.5 to 62.5 nm. The smaller distances probably play a more important role, so an effective gap of 10 nm may not be an unreasonable estimate. In this case Fig. 5 indicates a peak at 670 nm. (See the top horizontal line in Fig. 5.) For D = 110 nm, d = 30 nm, a = 400 nm

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the n = 2 dispersion peak (sp = 200 nm) is predicted to be at 635 nm whereas the FDTD extinction spectrum gives it at 640 nm. For D = 90 nm, d = 7.5 nm, a = 260 nm the n = 2 dispersion peak (sp = 130 nm) is at 750 nm (albeit for a 110 nm Au layer) whereas the FDTD result is close to 630 nm, so the agreement is not as good for smaller Au NPs. This may be evidence of a mixing of the SPR and gap modes for these smaller NPs. Even for these smaller NPs the trends with respect to spacing and gap is qualitatively predicted by the dispersion curves. 5. Near Field Calculations To confirm that the FDTD results really indicate gap modes implied by the dispersion equation calculations outlined in the previous section, we extracted from the FDTD simulations the nearfield distributions around the gold nanoparticles in close proximity to the aluminum thin film. Figs. 6 (a, b) show the near electromagnetic fields spatial distributions of the SPR mode and gap modes. Fig. 6 (a) shows the magnetic field intensity |Hy|2 in the plane of incidence, i.e., the x-z plane, cutting through the center of the Au NP, for the light incident at 550 nm in the z direction. In this figure z = 150 corresponds to the vacuum-Al interface with a 7.5 nm gap between the Al layer (of thickness 5 nm) and the Au NP of diameter 110 nm. This means the area between z = 155 and z = 272.5 is filled with shellac except for the Au NP which partially fills up the region between z = 162.5 and z = 272.5. The region z > 272.5 is glass. The geometry in Fig. 6 (b) is the same. These figures depict the results of the near-field distribution over a single unit cell of dimensions 260x260 nm2 in the x and y directions, as periodic boundary conditions are employed in these directions in the FDTD simulations. The SPR mode in Fig. 6 (a) is evidenced in the two humps resident on the sides of the nanoparticle surface. There is an increase in the magnetic field strength up to the vacuum-Al interface and a sharp drop off thereafter inside the conductive Al layer. The electric field (not shown) decreases as the vacuum-Al interface is approached and then decreases further inside the conductor, but not as sharply as the magnetic field. Fig. 6 (b) shows the magnetic field intensity for 650 nm incident light for the same geometry as Fig. 6 (a). The behavior near the conductor is similar, but much enhanced fields occur in the gap between the Al and Au NP, especially where the nanoparticle and Al layer is the closest. Any residual evidence of a SPR mode on the nanoparticle surface is very subdued. This is clear evidence of a gap mode identification of the peaks for this geometry and wavelength in the extinction spectra.

(a)

(b)

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Figure. 6 (a) Field intensity |Hy|2 in the plane of incidence, i.e., the x-z plane, cutting through the center of the Au nanosphere, of diameter 110 nm, for light incident at 550 nm in the z direction. (b) The same except for 650 nm incident light. The figure shows the intensities (relative to the incident intensity) over a single 260 nm x 260 nm unit cell in the x and y directions, which can be infinitely repeated. The gap is 7.5 nm, the Al film is 5 nm thick, and z = 150 nm is the position of the Al – vacuum interface.

6. Discussion: distance to the substrate dependence. To validate the numerical calculations presented in the previous section, we carried out experimental measurements of the extinction of a plane wave with the geometry of the sample close to that shown in Fig.1.25 Gold film of the thickness 25 nm was deposited by thermal vacuum deposition on the surface of an optical glass plate following thermal annealing at 370 0C for 30 minutes. The annealing transforms the continuous gold film into gold NPs monolayers. AFM characterization (NT-MDT Ntegra microscope) showed that sample contained an a monolayer of Au NPs with the mean size of 91 nm and a standard deviation of 32 nm. The average distance between the centers of the NPs in the monolayer was 260 nm, which corresponds to the average distance between the surfaces of Au NPs (periodicity) of 150 nm. After annealing, a shellac film was deposited on top the monolayer of Au NPs. The thickness of the shellac film monotonically varied in the range of 7 – 36 nm. Finally a thin aluminum film with the thickness of 5 nm was deposited on top of the shellac film. The optical density spectra of were measured by using Cary 60 UV-VIS spectrophotometer (Agilent Technologies, Inc). The spectra were taken at normal incidence with the light beam normal to the sample plane. The light spot on the sample surface was about 1.5x1.5 mm2, with the shellac film thickness being the same within the area of the light spot. The spectra were measured at room temperature. The experimentally measured spectra are shown in Fig. 7. The figure shows the

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extinction spectra for various spacer gaps whereas the spacing and NP sizes were variable in the sample with the NP sizes averaging 90 nm but ranging from 70 to 130 nm. The average spacing (periodicity) was about 150 nm but portions of the sample had considerably larger spacing.

Figure 7. Extinction spectra of Au NPs in Au NPs monolayer/shellac spacer/Al film nanostructure at various spacer thicknesses l in the range of 7 nm ⩽ l ⩽ 36 nm. The spectra are normalized by SPR peak intensity (the spectra were multiplied by the number indicated at the bottom of spectra). The spectra were shifted vertically for convenience and zero level is indicated for each spectrum by horizontal line to the right of the respective curve. As in the simulations a double-humped spectra begin to appear for d< 23 nm and becomes more pronounced for smaller spacers. Even for spacers larger than this the trend of a red-shifting of the spectrum with decreasing d is similar to the simulations. Generally, the red shifting observed in Fig. 7 is slightly greater than what the simulations predict, at least for the simulations using the “average” size and spacing of the sample. The presence of Au NPs with diameters and spacing considerably more than the average could account for this increased red-shifting. The correspondence between the simulation results in Figs. 2-4 to the dispersion curves in Fig. 5 implies that the n = 2 gap plasmon mode is excited. However, Fig. 5 also indicates that Au NPs spaced at the “average” of 140 nm excite n = 1 modes at wavelengths greater than 700 nm for small enough spacer thicknesses. (For example Fig. 5 indicates an n = 1 gap plasmon peak at 760 nm for a = 140 nm and d = 7.5 nm; also at 700 nm for n = 1, a = 140 nm, d = 10 nm). This mode is likely excited by larger Au NPs in the sample.

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7. Conclusions In conclusion, we studied both numerically and experimentally the extinction of a plane wave by a metasurface composed of a monolayer of gold nanoparticles in close proximity to an aluminum 9 film. The FDTD simulations for spacer layers of less than 35 nm indicate progressively a redshifting of what originally is an SPR peak as the spacer layer thickness is decreased, ultimately resulting in the development of a second peak for spacing less than 15 nm. The explanation is likely a hybridization of the SPR and gap plasmon peaks and then their separation. Larger spacing also produces more red-shifting. The trends with respect to spacer layer thickness and spacing of the Au NPs follow from the dispersion curves in Fig. 5. The coupling between the collective SPR and gape modes might be used to effectively tune the optical response of the metasurface. The results of this investigation can be used to tune the optical response of these types of metamaterials. Acknowledgements This work was partially supported by Ministry of Education and Science of Ukraine (grants

19BF051–04, 19BF037–02), NATO Science for Peace and Security (SPS) Program (grant NUKR.SFPP 984617) and AF SFFP. The theoretical calculations were carried out under the U.S. Department of Defense High Performance Computation Modernization Project.

8. References

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Plasmonic Metasurfaces with Tunable Gap and Collective SPR Modes

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