We fabricate electrically connected gold nanoantenna arrays of homodimers and heterodimers on silica substrates and present a systematic study of their optical properties. Electrically connected arrays of plasmonic nanoantennas make possible the realization of novel photonic devices, including optical sensors and rectifiers. Although the plasmonic response of unconnected arrays has been studied extensively, the present study shows that the inclusion of nanowire connections modifies the device response significantly. After presenting experimental measurements of optical extinction for unconnected dimer arrays, we compare these to measurements of dimers that are interconnected by gold nanowire “busbars.” The connected devices show the familiar dipole response associated with the unconnected dimers but also show a second localized surface plasmon resonance (LSPR) that we refer to as the “coupled-busbar mode.” Our experimental study also demonstrates that the placement of the nanowire along the antenna modifies the LSPR. Using finite-difference time-domain simulations, we confirm the experimental results and investigate the variation of dimer gap and spacing. Changing the dimer gap in connected devices has a significantly smaller effect on the dipole response than it does in unconnected devices. On the other hand, both LSPR modes respond strongly to changing the spacing between devices in the direction along the interconnecting wires. We also give results for the variation of E-field strength in the dimer gap, which will be important for any working sensor or rectenna device.

The Localized Surface Plasmon Resonance (LSPR) of individual metallic nanoantennas has two particularly useful properties: the electric-field (E-field) enhancement at the particle edges and the sensitivity of the particle optical response to the dielectric properties of its surroundings. Both are important for the well-established study of unconnected nanoantennas (monomers, dimers, and arrays) and also the less well-explored study of antennas that are connected to each other, and to an external load, via nanowires.

The study of unconnected nanoparticles has led to the discovery of new plasmonic phenomena and potential applications, including surface-enhanced Raman spectroscopy, optical waveguides, chemical and biomolecule detection, and improved performance of photovoltaic devices.1–4 One particularly important phenomenon is the change in plasmonic response, as observed in the optical extinction, when two or more nanoantennas are brought into close proximity. The results of Rechberger et al. show that when two symmetric particles are brought together along the axis of polarization of incident light, the LSPR extinction peak shifts to longer wavelengths, a redshift. If the particles are understood as two interacting dipoles, then the redshift can be understood as being due to a decrease in the restoring force of the oscillating charge. By contrast, when the particles are brought together along the axis perpendicular to the polarization axis, the extinction peak shifts to smaller wavelengths, a blueshift, due to the strengthening of the effective restoring force.5 In a similar study, Su et al. found a nearly exponential dependence of the redshift with an inter-particle distance for pairs of elliptical Au particles and also noted that the extinction response becomes indistinguishable from that of a single particle once the particle separation exceeds 2.5 times the particle length.6 In a study of gold dimers, Jain et al. developed an empirical equation describing the exponential trend in the LSPR wavelength and making it possible to determine the inter-particle separation.7 However, a simulation study by Ben and Park suggests that the Jain relation is valid only within a fairly small diameter range (from 20 nm to 70 nm).8 

When single nanoantennas of various shapes are placed in arrays, the extinction response is also dependent on spacing. In a study of arrays of Au and Ag monomers, Haynes et al. found that the shift of the LSPR has two regimes. As the spacing is reduced, the LSPR initially blueshifts, until the spacing reaches about 100 nm, when the LSPR begins to redshift.9 In a study of rod-shaped monomers, Smythe et al. use incident light that is polarized along the long axis of the rods and then vary the inter-device spacing for each direction independently. They observe a blueshift as the spacing along the short axis is reduced and a somewhat weaker redshift as the long axis is reduced.10 

To help analyze the often complex plasmon oscillations of individual nanostructures and their interaction, the Halas and Nordlander groups have suggested a “plasmon hybridization model,” developed in analogy with molecular orbital theory. In one study, they understood the plasmon response of arbitrarily shaped structures in terms of the interaction of plasmons arising from simpler or more elementary shapes.11 In a study of nanosphere homodimers, they show that the plasmon response can be understood as a combination of two fundamental modes, which they refer to as “bonding” and “anti-bonding.”12 In a study of heterodimers, Brown et al. found that size asymmetry produces more complex plasmon hybridization. In contrast, symmetric pairs couple more strongly because they share the same dipole resonance mode.13 

The present study takes a step toward understanding interconnected arrays of nanoantennas, in which adjacent devices are connected with nanowires. In this, we are following Miskovsky et al., who suggest the fabrication of large-scale arrays of interconnected heterodimers as a promising approach to energy harvesting. Each device is a “rectenna,” formed by the close proximity of a pointed tip to a flat counter electrode (analogous to the tip in a scanning tunneling microscope). Such asymmetric tunnel junctions should be capable of both receiving and rectifying electromagnetic radiation in the visible regime.14 Three questions immediately come to mind. First, will such arrays be able to rectify signals efficiently? Second, is it possible to fabricate the devices with small-enough gaps? Third, how will the resonant properties of individual devices change when they are interconnected by wires? In partial answer to the first question, Mayer and Cutler have conducted simulations of rectenna devices and found rectification ratios of up to four orders of magnitude when the LSPR is taken into account.15 Another theoretical study by Joshi and Moddel analyzes rectenna devices (not necessarily with pointed tips) using an equivalent circuit for the device and a quantum-mechanical analysis. They found that the internal efficiency of rectenna devices approaches 100% for monochromatic illumination and has a maximum value of about 44% for a continuous, solar source.16 

Before it is possible to fabricate an array of rectenna devices, it is first necessary to fabricate a single device and connect it to an external load. A number of groups have made impressive gains here. The Natelson group relied on electromigration to form single, asymmetric nanogaps. When intense light is incident on an asymmetric tunnel junction, they find a small rectification effect, as confirmed in current-voltage (IV) measurements, which they estimate to correspond to electric field enhancements of 1000 in the gap.17 The Hecht group has also connected individual homodimers to outside test equipment. In a study of individual homodimers with 20 nm gaps, the Hecht group found that connecting nanowires to the node of each nanorod left the dipole response largely undisturbed.18 In a follow-up study, they inserted a gold particle inside the 20 nm gap to produce an effective gap of about 1.3 nm. Biasing of the junction produced tunneling and the emission of visible light by the antenna.19 Two further studies, by Stolz et al.20 and Albee et al.,21 also rely on electromigration to form single junctions and demonstrate stable photocurrents.

Although such results of single devices are promising, the question of how to fabricate large arrays of such tunnel junctions remains. Miskovsky et al. noted that while the initial fabrication of arrays can be accomplished with established lithographic technology, the closing of the heterodimer gaps to the tunneling regime would require a second step. Rather than relying on processes like electromigration (which would not be practical at a large scale) they suggest the use of atomic layer deposition (ALD).14 A study of ours displayed preliminary results using Pd heterodimers and Cu-ALD. By using arrays of unconnected devices, we characterized the redshift introduced to the extinction characteristic as a result of the changes introduced by ALD, including the material modification, the overall lengthening of the devices and, most importantly, the closing of the gaps.22 Although we were able to reduce the gap distance to about 10 nm, this is not small enough to enter the tunneling regime. To accomplish this, further work on ALD is required or the adoption of a different technique.

The present study leaves aside the question of how to reduce the gap distances and investigates the third question noted above: how the extinction response changes when the individual devices of an array are interconnected with nanowires. We find that the extinction response is modified significantly. In addition to the fact that we confirm the Hecht group's conclusion regarding the optimum location of the connecting nanowires, we also note the appearance of a new resonance structure. Numerical simulations strengthen our interpretation of the data and show trends that result from the modification of the dimer gap and device spacing. These trends for connected devices are significantly different than those for unconnected devices. Such considerations will be important in future efforts to design practical sensors or light harvesters, especially in determining resonant frequencies and E-field enhancements.

Electron-beam lithography is used to fabricate device arrays on amorphous SiO2. The process follows the standard procedure of depositing a layer of resist, adding a thin Au layer to deplete charge, followed by the e-beam write. Given the transparency of the silica substrate, reference height markers are included, allowing the beam to maintain its focus across the sample. The e-beam write is followed by removal of the Au layer and an O2 plasma cycle to remove any residuals. Thermal evaporation of a 10 nm Ti adhesion layer is followed by 40 nm of Au. A resist lift-off completes the process.

Drawing on the work of Billaud,23 we subject our samples to a focused beam of white light using a confocal microscopy arrangement (Fig. 1). We focus light from a 250 W quartz-tungsten-halogen (QTH) source filament on a gold-plated tungsten pinhole (typically 200 μm diameter), the image of which determines the focused-beam spot size. Next, the beam is sent through a Glan-Thompson calcite polarizer (axis, vertical), a 70T/30R cube beam-splitter, and into a reflecting 15× objective, where it is focused onto a small spot on the device array. After passing through the array, the light is re-collimated by an equivalent 15× objective. The resulting beam is sent into an f/4.0 converging lens at the entrance of a diffraction-grating monochromator (1/8 m, 600 lines/mm, 750 nm blaze) for the measurement of transmitted light intensity as a function of wavelength. To navigate across the samples, we combine the reflected light from the focused beam and a backlit image of the array area, using the beam splitter, and image these together. One reflection from the cube beam splitter is directed toward a silicon detector via a set of mirrors and a 5° wedge. This detector is monitored by the intensity controller, providing feedback to the lamp power supply. The microscope objectives are mounted on an x-y stage and controlled by two micrometers. The sample holder is mounted on its own stage, which is moved by three piezo-electric actuators that have a range of 12.5 mm and a resolution of 30 nm.

FIG. 1.

Experimental setup for white-light confocal transmission measurements.

FIG. 1.

Experimental setup for white-light confocal transmission measurements.

Close modal

Adjustment of a variable-slit entrance on the monochromator controls the wavelength resolution of the extinction data. For most of our experiments, the slits were set to 375 μm, which provides a resolution of 10 nm (FWHM). Data are typically collected at 10 nm intervals. Mounted after the exit slit of the monochromator, thermoelectrically cooled silicon or germanium detectors register the light intensity. The silicon detector has an effective range from 200 to 1100 nm, while the germanium detector has a range of 700–1800 nm. Each has a pre-amplifier providing a signal gain from 104 to 109 V/A.22 

Data acquisition is controlled using LabVIEW. The voltage output of the Si/Ge detectors is sent to a multimeter that is connected to a computer via a general purpose interface bus (GPIB). The monochromator is connected via a universal serial bus (USB) and is controlled by LabVIEW, which steps through a wavelength range and step interval, reading the voltage at each step. We characterize our devices by determining the optical extinction, E, which is the sum of back-scattered light, S, and absorbed light, A. To measure optical extinction, we first measure the relative transmission of our devices as T=Iλon/Iλoff, where Iλon is the intensity of transmitted light when the beam passes through the devices and Iλoff the intensity when the beam passes through only the transparent substrate. Taking the incident intensity to be unity, along with the definitions T + S + A = 1 and E = S + A, the extinction is given as

E=1T=1IonIoff.
(1)

The extinction characteristic displays one or more resonances that depend on the size, shape, material properties, and density of the devices. Since the extinction measurement is a relative measurement, the data do not need to be normalized to the detector's calibrated response curve. Extinction curves were fit with a Lorentzian-type function to identify dominant peak locations. It should be noted that a confocal microscopy setup collects only light that is transmitted within the cone of acceptance of the objective. Therefore, light scattered outside this region is not measured.

We employ finite-difference time-domain (FDTD) Solutions by Lumerical, making use of the Total Field Scattered Field (TFSF), which features a source box that injects radiation from one face. Any incident light that does not interact with the device is removed by the TFSF as it leaves the region. A monitor box is placed within the TFSF region to determine absorption by the device, while a second monitor, placed outside the TFSF, determines the scattering. Summing the scattered and the absorbed power yields the extinction. We monitor the amount of power left in the system and terminate the simulation when the residual fractional power reaches 10−10. The FDTD region is bounded by a Perfectly Matched Layer (PML), which is placed at a distance of at least half of the maximum wavelength in the simulation spectrum (outside the near-field). We utilize an override mesh (typically 1–3 nm) around the device and, outside of this region, FDTD Solutions' auto-mesh is set to accuracy level 8. We found best results when using FDTD Solutions' conformal variant setting CV0, which does not use the code's conformal mesh technology. For our metals and the frequency range, the dispersion is relatively small, in the range 10%–30%.

Discrepancies between the simulations and experimental data are expected.24 First, the choice of material data has a significant effect on the simulation result. For Au, we used Johnson and Christy data (bulk material properties), included in FDTD Solutions' libraries. However, because we model thin structures with dimensions on the order of the mean free path of electrons, the actual dielectric function of a nanoparticle can deviate from the bulk. Second, the measured arrays are composed of many devices, the dimensions of which vary slightly due to processing variations. The simulations also do not consider morphological factors, such as surface roughness and grain size. Third, while the simulations record scattered light in all directions, including the forward scattered light, our experiment was unable to capture part of the forward-scattered light by the devices. Finally, our simulations of connected devices model small 1×4 arrays and do not use periodic boundary conditions (PBC). The use of a single device and PBC led to time convergence issues using the TFSF with our connected array geometry. Therefore, we simulated 1×n arrays, where n is the number of heterodimers (HDs) or bowties (BTs). The sequence converges remarkably quickly and the difference in the extinction peak wavelength between the n=4 result and the n=5 result is less than 1%. To save on computing time, we used n=4. As noted below, we also performed tests of stacked rows of connected devices. At the y spacings of our fabricated devices (500 nm), adding rows did not result in significant changes to the extinction result. Despite the above issues, agreement between experimental data and simulation results is reasonable (as will be seen in Figs. 7–9). Our objective was not to optimize this agreement but to use simulations as a reliable means of confirming the overall behavior of the data and evaluating the trends due to changes to the gap size and x spacing.

The main objective of our study is to characterize the plasmonic response of arrays of dimers after they have been interconnected by nanowires. To give a firm ground for comparison, we first expanded the results of our recent study of unconnected devices.22 

Figure 2 displays our unconnected gold nanoantenna dimer prototypes. The first is a bowtie (BT) consisting of two opposing triangles, with as-drawn dimensions of 160 nm × 250 nm. The second is a heterodimer (HD) composed of a 160 nm × 250 nm triangle and a 160 nm × 80 nm rectangle. Both are 40 nm-thick gold deposited on a silica substrate using a 10 nm titanium adhesion layer. For the purpose of examining the optical properties of isolated devices, 50 μm × 50 μm arrays of unconnected BT and HD nanoantennas were fabricated with a 1500 nm edge-to-edge spacing, which is beyond the near-field of the isolated antenna (about 1000 nm). Finite-difference time-domain (FDTD) simulations confirmed that such spacing results in minimal coupling between neighboring antennas. We varied the triangle length and the dimer gap to observe the effect on the location of the extinction peak. We found that the wavelength of the peak redshifts linearly with the triangle length: for the HD devices, our data fit the equation of a line y = 3.2x + 330 nm (where x is in nm), while the BT data fit 3.5x + 310 nm. This is similar to the Cu simulation results displayed in our previous study.22 

FIG. 2.

SEM images of (a) gold bowtie, BT, and (b) heterodimer, HD, nanoantenna arrays on SiO2. The edge-to-edge spacing in both directions is 1500 nm.

FIG. 2.

SEM images of (a) gold bowtie, BT, and (b) heterodimer, HD, nanoantenna arrays on SiO2. The edge-to-edge spacing in both directions is 1500 nm.

Close modal

Figure 3 shows that the extinction peak varies inversely with the dimer gap for both prototypes and shows stronger redshifts for the BT than for the HD. For consistency with the experimental data, most of the simulations were performed using wavelength intervals of 10 nm; the one exception is the simulations for Fig. 3(b), which used intervals of 5 nm. The amount of redshift is sensitive to the strength of the coupling between adjacent particles. When particles are brought near to one another along the axis of the incident-beam polarization, the restoring force mechanism for each particle is weakened, resulting in a decrease in the resonant frequency of the dimer. Our measurements are consistent with those of Brown et al., who found that symmetric pairs couple more strongly because they have the same dipole resonance mode.13 Our BT antennas couple more strongly than the HD and therefore show a greater redshift.

FIG. 3.

Variation of the wavelength of the extinction peak with gap for (a) experimental data and (b) simulation results.

FIG. 3.

Variation of the wavelength of the extinction peak with gap for (a) experimental data and (b) simulation results.

Close modal

We also modified the inter-device (i.e., edge-to-edge) spacing of BT arrays. In these measurements, the E-field of the incident beam was polarized along the long-axis of the devices, which we refer to as the y-axis, and the dimensions of the BT devices themselves were kept constant. First, we reduced the y-spacing, but kept the perpendicular x-spacing at 1500 nm. Second, we reduced the x-spacing, but kept the y-spacing at 1500 nm. The results are shown in Fig. 4. In both tests, when the edge-to-edge spacing is 1500 nm for both directions, the arrays resonate near 1030 nm, as indicated by the dotted line in Fig. 4. Reducing the y-spacing below 100 nm produces a strong red shift and reducing the x-spacing below 200 nm produces a blue shift. In both cases, the plasmonic resonance of the antennas is shifted due to interactions with the near-field of adjacent antennas. The fact that the x-coupling is somewhat stronger than the y-coupling contrasts with the studies of nanodisc dimers by Rechberger et al.5 and Jain et al.7 This is not surprising, since these other studies use a different dimer geometry and modify only the dimer gap, while we modify the spacing of arrays.

FIG. 4.

Experimental data showing extinction peak variation for gold BT arrays, as edge-to-edge array spacing is changed in the y-direction (green) and the x-direction (red). The dotted line indicates the value of the extinction peak at 1500 nm edge-to-edge spacing (data not shown).

FIG. 4.

Experimental data showing extinction peak variation for gold BT arrays, as edge-to-edge array spacing is changed in the y-direction (green) and the x-direction (red). The dotted line indicates the value of the extinction peak at 1500 nm edge-to-edge spacing (data not shown).

Close modal

To be of practical use as a photo-sensor or photo-harvesting device, nanoantenna arrays must be electrically connected. We therefore investigate the effects on the plasmonic response due to the addition of nanowire “busbars” that connect rows of antennas in parallel. In a preliminary study, we investigated the effect of busbar position on the extinction resonance. The study of rectangular homodimers by Prangsma et al. found that the optimum placement for the busbar is near the center of each electrode, at the node of the electric field.18 Connected this way, the addition of a busbar has a minimal effect on the dipole response of the antenna. Compared to other busbar placements, the nodal connection ensures that the E-field enhancement within the dimer gap and the associated quality (Q) factor are maximized. (Here, and throughout, the Q-factor is determined by the ratio of the value of the peak wavelength to the full-width at half-maximum of the extinction curve.) To check this last result, we fabricated BT arrays, with the same as-drawn dimensions, and with the same edge-to-edge spacing of 1500 nm. Figure 5 displays the busbar location specified by the distance, d, from the base of the triangle to the bottom edge of the busbar. As fabricated, the busbar widths for these samples averaged about 50 nm, triangle dimensions were 160 nm × 250 nm, and dimer gaps were 80 nm. We moved the connecting busbar from the triangle base, at d = 0 nm, to the tip in 25 nm increments. In our array studies of busbar placement, we found that the optimal position is near the centroid of the triangle. Figure 6 shows a blueshift in the extinction response and a variation in the Q factor of the resonance, with a maximum of 2.0 when the busbar is positioned at d = 99 nm. With the busbar at the centroid, the extinction response is similar to that of an unconnected device, in excellent agreement with Prangsma et al.

FIG. 5.

SEM images of connected dimer arrays for (a) HD connected at the base, (b) HD connected at the centroid, (c) BT connected at the base, and (d) BT connected at the centroid. The S is the edge-to-edge spacing, while d is the distance from the base of the triangle to the bottom of the busbar.

FIG. 5.

SEM images of connected dimer arrays for (a) HD connected at the base, (b) HD connected at the centroid, (c) BT connected at the base, and (d) BT connected at the centroid. The S is the edge-to-edge spacing, while d is the distance from the base of the triangle to the bottom of the busbar.

Close modal
FIG. 6.

(a) Experimental data for optical extinction of gold BT arrays with connecting busbar positioned for d from 0 nm to 124 nm. The maximum Q factor of 2.0 occurs at d = 99 nm.

FIG. 6.

(a) Experimental data for optical extinction of gold BT arrays with connecting busbar positioned for d from 0 nm to 124 nm. The maximum Q factor of 2.0 occurs at d = 99 nm.

Close modal

In our main series of tests, we fabricated BT and HD arrays as displayed in Fig. 5, but now with an edge-to-edge spacing of S = 500 nm. The smaller spacing served to strengthen the extinction signal and achieve better precision for our measurements. In addition, our reason for spacing unconnected devices at 1500 nm (to limit near-field interactions) has no bearing on devices connected by metal wires. For both the BT and HD devices, we positioned the busbar either at the base of the triangle or at the centroid (d value of 0 nm or 100 nm, respectively).

Optical extinction data were taken over the range of 700–1800 nm. In Fig. 7, experimental measurements of the BT and HD devices with the busbar connected at the centroid (blue circles) show the strong dipole mode near 1000 nm and a small, secondary peak near 1500 nm. The fact that the BT and HD curves have nearly identical shapes is not surprising since they use the same triangular electrode. The fact that the extinction levels are similar is a happy accident of the spacing. The fact that both the BT and HD resonate at roughly the same wavelength has a more-subtle explanation. As noted below, simulations show that with the same dimer gap, the BT resonates at slightly longer wavelengths than the HD, due to its stronger coupling. However, because our BT and HD devices were fabricated on the same wafer, and because the BT has two pointed tips, the as-processed gap for the BT is significantly larger (about 80 nm) than that for the HD (about 40 nm). The larger gap for the BT blueshifts its resonance, causing the resonance to occur at nearly the same wavelength as the 40 nm-gap HD.

FIG. 7.

Optical extinction data for connected BT arrays (solid symbols) and HD arrays (open symbols) with the busbar connected at the base (red squares) and the centroid (blue circles).

FIG. 7.

Optical extinction data for connected BT arrays (solid symbols) and HD arrays (open symbols) with the busbar connected at the base (red squares) and the centroid (blue circles).

Close modal

Figure 7 also shows extinction data for devices with the busbar connected to the base (red squares). In their study of busbar location, Prangsma et al. found that the Q factor of the electric field enhancement increases significantly as the busbar is moved from the base to the centroid.18 In agreement with this, we find that the Q factor of the dipole extinction response increases from 1.7 when the busbar is at the base to 2.3 when it is at the centroid. With the busbar at the base, the secondary peak increases greatly and redshifts to 1600 nm, with a Q factor of 4.2. (Note that the long wavelength mode does not appear in Fig. 6. As mentioned below, this is because the mode is pushed to wavelengths above 1800 nm for x-spacings significantly larger than 500 nm.)

To interpret the observed modes, we simulated 1 × 4 arrays of connected HD and BT arrays, using the FDTD method. We used average device dimensions as measured by SEM images: 240 nm and 170 nm for the triangle length and width, and 490 nm for the x-spacing. We used a gap distance of 30 nm, which is smaller than our as-fabricated devices, in order to increase dimer coupling. As mentioned previously, although a detailed comparison between simulations and data is limited, the simulations serve to confirm the general features of our data and extrapolate other trends.

Figures 8 and 9 display the simulated extinction responses, as well as surface charge-density plots (0.5 nm below the incident surface) at the wavelengths of the extinction peaks, (in which red is one polarity, blue the other, and green is zero). Figure 8 displays results when the busbar is connected at the triangle base for both the HD and BT. For the HD device, the dipole mode peaks at 950 nm, while the long-wavelength mode peaks at 1530 nm and shows significantly higher extinction. Because the charge-density plots show that the long-wavelength mode strongly couples the triangular electrode to the busbar, we refer to this as the “coupled-busbar mode.” For the BT device, both modes are redshifted in comparison to the HD, with the dipole at 1020 nm and the coupled-busbar mode at 1650 nm. This is not surprising, since we expected that the stronger coupling of the BT dimers, seen in the unconnected studies, would be evident in the connected. Figure 9 shows simulation results with the busbar connected at the triangle centroid for both the HD and BT. Here, the dipole modes for the HD and the BT (1010 nm and 1100 nm, respectively) have a significantly greater extinction than the coupled-busbar mode (1430 nm and 1550 nm, respectively). This can be understood by the fact that the charge oscillation at the base and the tip of the triangles is not as disturbed by the presence of the busbar. The BT results again show stronger coupling, and both the dipole and coupled-busbar peaks are redshifted relative to the HD. We also see a suggestion of hybridization appearing in the shoulder of the HD. Both of these results for connected devices—the stronger coupling of symmetric dimers and the hybridization of unmatched dimers—are consistent with the findings of Brown et al. for unconnected devices.13 

FIG. 8.

Simulation results when the busbar is at the base. (a) Extinction for HD arrays, with charge density plots (not shown to scale) for the dipole mode at λ1 = 950 nm and the coupled-busbar mode at λ2 = 1530 nm, where red is one polarity, blue the other, and green is zero. (b) Same for BT arrays, where λ1 = 1020 nm and λ2 = 1650 nm.

FIG. 8.

Simulation results when the busbar is at the base. (a) Extinction for HD arrays, with charge density plots (not shown to scale) for the dipole mode at λ1 = 950 nm and the coupled-busbar mode at λ2 = 1530 nm, where red is one polarity, blue the other, and green is zero. (b) Same for BT arrays, where λ1 = 1020 nm and λ2 = 1650 nm.

Close modal
FIG. 9.

Simulation results when the busbar is at the centroid. (a) Extinction for HD arrays, with charge density plots for the dipole mode at λ1 = 1010 nm and the coupled-busbar mode at λ2 = 1430 nm, where red is one polarity, blue the other, and green is zero. (b) Same for BT arrays, where λ1 = 1100 nm and λ2 = 1550 nm.

FIG. 9.

Simulation results when the busbar is at the centroid. (a) Extinction for HD arrays, with charge density plots for the dipole mode at λ1 = 1010 nm and the coupled-busbar mode at λ2 = 1430 nm, where red is one polarity, blue the other, and green is zero. (b) Same for BT arrays, where λ1 = 1100 nm and λ2 = 1550 nm.

Close modal

The purpose of the pointed tips in our devices is to concentrate the electric field. Although any working sensor or energy harvester would need to have gaps significantly smaller than 30 nm, we used the present simulations to compare the maximum field strengths due to the HD and BT designs, the busbar placements, and the two plasmon modes. FDTD Solutions compute the ratio of the local field strength divided by the source strength. Within the uncertainties of the calculation, we found that there is no difference in the electric field maxima for the HD or BT devices. (However, note that while the BT is symmetric, there is the expected E-field difference across the HD.) When the busbar is connected at the base, both devices have a relative field maximum of about 20 for the dipole mode and about 58 for the coupled-busbar mode. When the busbar is connected at the centroid, the devices have a relative field maximum of about 27 for the dipole mode and about 42 for the coupled-busbar mode. These results suggest that the coupled-busbar mode produces higher electric fields than the dipole mode. Also, compared to the base connection, the centroid connection features somewhat higher fields for the dipole mode and lower fields for the coupled-busbar mode. We also ran simulations for busbars only, the results of which are not displayed. The busbars produce an extinction peak near 520 nm, the tail of which decays quickly, reaching values of 0.008 at 700 nm and 0.001 at 1800 nm. (The peak near 520 nm can be easily seen in Figs. 10–13.)

FIG. 10.

Simulation results with the busbar connected at the base for varying gap. (a) Extinction for HD arrays. (b) The peak wavelengths of the two modes. Panels (c) and (d) show the same for BT arrays.

FIG. 10.

Simulation results with the busbar connected at the base for varying gap. (a) Extinction for HD arrays. (b) The peak wavelengths of the two modes. Panels (c) and (d) show the same for BT arrays.

Close modal
FIG. 11.

Simulation results with the busbar connected at the centroid for varying gap. (a) Extinction for HD arrays. (b) The peak wavelengths of the two modes. Panels (c) and (d) show the same for BT arrays.

FIG. 11.

Simulation results with the busbar connected at the centroid for varying gap. (a) Extinction for HD arrays. (b) The peak wavelengths of the two modes. Panels (c) and (d) show the same for BT arrays.

Close modal
FIG. 12.

(a) Simulated extinction data for gold HD arrays with the busbar connected at the base and three different spacings, S. (b) Peak positions for the λ1 and λ2 modes over a range of spacings.

FIG. 12.

(a) Simulated extinction data for gold HD arrays with the busbar connected at the base and three different spacings, S. (b) Peak positions for the λ1 and λ2 modes over a range of spacings.

Close modal
FIG. 13.

(a) Simulated extinction data for gold HD arrays with the busbar connected at the centroid and three different spacings, S. (b) Peak positions for the λ1 and λ2 modes over a range of spacings.

FIG. 13.

(a) Simulated extinction data for gold HD arrays with the busbar connected at the centroid and three different spacings, S. (b) Peak positions for the λ1 and λ2 modes over a range of spacings.

Close modal

In the simulations up to this point, the dimer gap and inter-device spacing were kept constant. We next examine the effect of varying these two parameters. We varied the dimer gaps from 60 nm to 5 nm. Figure 10, panel a, shows that when the HD busbar is positioned at the triangle base, the extinction response of the dipole mode hardly responds to the reduction of the dimer gap, while the coupled-busbar mode grows and red-shifts significantly. The fact that the dipole resonance remains constant is in sharp contrast to the unconnected devices of Fig. 3, which show strong redshifts. (In our recent study of unconnected Pd devices, data and simulations also demonstrated strong redshifts as the device gaps were reduced using Cu ALD.)22 Figure 10, panel b, redisplays these results in terms of peak location, with dotted lines extending from the 60 nm gap serving to guide the eye. As the device gap is reduced, the separation between the two modes increases. The corresponding results for the BT device connected at the base are shown in panels c and d. Now, as the dimer gap gets smaller, there is a small but significant redshift for the dipole mode. Figure 11 summarizes similar results for both HD and BT when the busbar is positioned at the triangle centroid. For the HD, as the gap is reduced, the dipole mode does not redshift, while the coupled-busbar mode does. For the BT, both modes redshift.

Taken together, Figs. 10 and 11 suggest that for the HD, as the gap is reduced, the two modes separate significantly (whether the busbar is connected at the base or the centroid). However, for the BT, because both modes redshift, the two modes do not separate as much. This is likely due to the greater coupling of the BT dimer. Also, note also that hybridization appears on the shoulder of the dipole response for the HD connected at the centroid. Again, our results for connected devices—the greater coupling of the BT and the greater hybridization of unmatched dimers—are consistent with those of Brown et al. for unconnected devices.13 

Simulations also showed the effect of changing the inter-device spacing on the LSPR response. Modifying the x-spacing parameter, S, along the direction of the nanowire connections, has a significant effect on the plasmon response. We kept the dimer dimensions constant (with a gap of 30 nm) and varied the S of Au HD devices from 250 nm to 750 nm. Figure 12 shows the simulated extinction results with the busbar positioned at the triangle base: panel a shows the full extinction response for three specific spacings, while panel b displays the peak locations for all spacings. Both the dipole mode and the coupled-busbar mode redshift linearly with increased spacing, although the net effect slightly increases the separation between the two modes. Figure 13 shows that connecting the busbar at the HD triangle centroid also results in a linear dependence. The splitting between the two modes is somewhat greater here, since the dipole response is less sensitive to the centroid connection. Again, note the presence of hybridization on the shoulder of the dipole response when the HD is connected at the centroid. Though not shown, we performed analogous studies for the BT arrays and observed similar results: stronger coupling of the symmetric structures, leading to larger red-shifts as the spacing is increased. By contrast with the x-spacing parameter, S, modifying the y-spacing has a negligible effect on the LSPR response. Although reducing the y-spacing results in a redshift, it is much less than that seen for unconnected devices. At a y-spacing of 50 nm, the shift in the extinction peak is less than half of what is shown in Fig. 4.

We have demonstrated that experimental measurements of extinction for dimers connected by nanowire busbars give responses that are significantly different from those of unconnected dimers. Whereas the extinction response of the unconnected dimers is dominated by a single dipole mode, the connected devices exhibit a second “coupled-busbar mode.” Experimental data show that when the busbar is connected at the base of the dimer triangles, the coupled-busbar mode has a stronger extinction than the dipole mode. When the busbar is connected at the centroid, however, the coupled-busbar mode is largely suppressed.

Simulation studies bear out these results and extend them. As the device gap is reduced for the HD device, the dipole mode is largely unaffected, while the coupled-busbar mode shows significant redshifts. The lack of a shift for the dipole mode is in strong contrast to studies of unconnected devices. The BT devices, on the other hand, show a significant redshift for the dipole modes. This shows one significant similarity between unconnected and connected devices: both demonstrate stronger coupling in the case of symmetric dimers. Finally, altering the horizontal spacing between connected devices shifts both modes, whether for HD or for BT.

For any practical device, the busbar connection at the centroid is probably preferable, especially if the designer wishes to concentrate on the dipole response. If asymmetric devices are used (as are needed in rectenna applications), then the dipole response will not shift significantly as the device gap is reduced. However, as the inter-device spacing is reduced (perhaps, in an effort to increase array efficiency), the resonant wavelength of the dipole response will blueshift. Finally, although the electric field enhancement for the coupled-busbar mode is higher than that for the dipole mode, this difference is minimized when the busbar is connected at the centroid.

We acknowledge support from the National Science Foundation (NSF/ECCS-EPAS Grant Nos. 1231248 and 1231313), The Pennsylvania State University, Penn State Altoona, and the University of Connecticut. We thank P. H. Cutler, P. B. Lerner, and N. M. Miskovsky for many valuable discussions, particularly with regard to theory and simulations. We are indebted to C. E. Eichfeld and M. I. Labella of NanoFab at Penn State's Materials Research Institute for design suggestions, advances in device fabrication, and for accomplishing the e-beam lithography.

1.
N. J.
Halas
,
S.
Lal
,
W.-S.
Chang
,
S.
Link
, and
P.
Nordlander
,
Chem. Rev.
111
,
3913
(
2011
).
2.
P.
Biagioni
,
J.-S.
Huang
, and
B.
Hecht
,
Rep. Prog. Phys.
75
,
024402
(
2012
).
3.
J. G.
Smith
,
J. A.
Faucheaux
, and
P. K.
Jain
,
Nano Today
10
,
67
(
2015
).
4.
M. B.
Ross
,
C. A.
Mirkin
, and
G. C.
Schatz
,
J. Phys. Chem. C
120
,
816
(
2016
).
5.
W.
Rechberger
,
A.
Hohenau
,
A.
Leitner
,
J. R.
Krenn
,
B.
Lamprecht
, and
F. R.
Aussenegg
,
Opt. Commun.
220
,
137
(
2003
).
6.
K. H.
Su
,
Q. H.
Wei
,
X.
Zhang
,
J. J.
Mock
,
D. R.
Smith
, and
S.
Schultz
,
Nano Lett.
3
,
1087
(
2003
).
7.
P. K.
Jain
,
W. Y.
Huang
, and
M. A.
El-Sayed
,
Nano Lett.
7
,
2080
(
2007
).
8.
X.
Ben
and
H. S.
Park
,
J. Phys. Chem. C
115
,
15915
(
2011
).
9.
C. L.
Haynes
,
A. D.
McFarland
,
L.
Zhao
,
P. R.
Van Duyne
, and
G. C.
Schatz
,
J. Phys. Chem. B
107
,
7337
(
2003
).
10.
E. J.
Smythe
,
E.
Cubukcu
, and
F.
Capasso
,
Opt. Express
15
,
7439
(
2007
).
11.
E.
Prodan
,
C.
Radloff
,
N. J.
Halas
, and
P.
Nordlander
,
Science
302
,
419
(
2003
).
12.
P.
Nordlander
,
C.
Oubre
,
E.
Prodan
,
K.
Li
, and
M. I.
Stockman
,
Nano Lett.
4
,
899
(
2004
).
13.
L. V.
Brown
,
H.
Sobhani
,
J. B.
Lassiter
,
P.
Nordlander
, and
N. J.
Halas
,
ACS Nano
4
,
819
(
2010
).
14.
N. M.
Miskovsky
,
P. H.
Cutler
,
P. B.
Lerner
,
A.
Mayer
,
B. G.
Willis
,
D. T.
Zimmerman
,
G. J.
Weisel
, and
T. E.
Sullivan
, “
Nanoscale rectennas with sharp tips for absorption and rectification of optical radiation
,” in
Rectenna Solar Cells
, edited by
G.
Moddel
and
S.
Grover
(
Springer
,
2013
).
15.
A.
Mayer
and
P. H.
Cutler
,
J. Phys.: Condens. Matter
21
,
395304
(
2009
).
16.
S.
Joshi
and
G.
Moddel
,
Appl. Phys. Lett.
102
,
083901
(
2013
).
17.
D. R.
Ward
,
F.
Huser
,
F.
Pauly
,
J. C.
Cuevas
, and
D.
Natelson
,
Nat. Nanotechnol.
5
,
732
(
2010
).
18.
J. C.
Prangsma
,
J.
Kern
,
A. G.
Knapp
,
S.
Grossmann
,
M.
Emmerling
,
M.
Kamp
, and
B.
Hecht
,
Nano Lett.
12
,
3915
(
2012
).
19.
J.
Kern
,
R.
Kullock
,
J.
Prangsma
,
M.
Emmerling
,
M.
Kamp
, and
B.
Hecht
,
Nat. Photonics
9
,
582
(
2015
).
20.
A.
Stolz
,
J.
Berthelot
,
M. M.
Mennemanteuil
,
G.
Colas des Francs
,
L.
Markey
,
V.
Meunier
, and
A.
Bouhelier
,
Nano Lett.
14
,
2330
(
2014
).
21.
B.
Albee
,
X.
Liu
,
F. T.
Ladani
,
R. K.
Dutta
, and
E. O.
Potma
,
J. Opt.
18
,
054004
(
2016
).
22.
R. A.
Wambold
,
B. D.
Borst
,
J.
Qi
,
G. J.
Weisel
,
B. G.
Willis
, and
D. T.
Zimmerman
,
J. Nanophotonics
10
,
026024
(
2016
).
23.
P. M. S.
Billaud
,
N.
Grillet
,
E.
Cottancin
, and
C.
Bonnet
,
Rev. Sci. Instrum.
81
,
043101
(
2010
).
24.
W. L.
Barnes
,
J. Opt. A: Pure Appl. Opt.
11
,
114002
(
2009
).