3.1.

Single Nanowire Width Dependence

First, the dependence of enhancement on the width of the nanowire was determined. The enhancement spectra for various widths are plotted in the waterfall plot of Fig. 1(a). These are the maximum optical enhancement values of a single gold nanowire as a function of the wavelength of the light incident on the structure. Each line on the plot represents a different simulation for a particular width. The nanowire thickness remains fixed at 15 nm and the width ranges from 40 to 140 nm, with a step size of 5 nm between each width. Figure 1(a) shows that the enhancement peak shifts toward the red as nanowire width increases. Figure 1(b) is a cross-sectional view of the EFDs to demonstrate the enhancement patterns as a function of width for a constant wavelength of 700 nm.

Figure 2(a) plots the incident wavelength that provides the maximum optical enhancement for a particular nanowire width. The values in Fig. 2(a) are obtained from Fig. 1(a). The simulation results in Fig. 1(a) were fitted with a first-order Gaussian function. The coefficients for the best-fit Gaussian function were then used to determine the peak enhancement wavelength. The results show a linearly increasing relationship. This corresponds to the fact that the transversely polarized incident light excites the transverse plasmonic mode, which oscillates across the horizontal surfaces of the cross section. As the nanowire width increases, the transverse plasmon couples efficiently with larger wavelengths. Figure 2(b) plots the full width at half maximum of the broadening in the enhancement spectrum as nanowire width increases. As can be seen from the plot, the broadening exhibits a quadratic proportionality to the width of the nanowire. The enhancement spectral peak broadens as the width increases because the plasmon resonance also broadens as size increases for structures that are greater than 40 nm. This is due to the larger structures having multipolar plasmons that can couple with a broader range of wavelengths and due to additional electron damping caused by secondary radiation from accelerated electrons.^23,24

Fig. 2

(a) Wavelength that gives maximum enhancement as a function of nanowire width and (b) full width at half maximum of enhancement spectrum for each width.

3.2.

Triple Nanowire Array

The next simulations model the three nanowires in parallel separated by nanogaps. The geometry is motivated by nanogap plasmonic structures that can be fabricated by the nanomasking technique.²⁵ Figure 3(a) identifies the geometric parameters that were investigated for the triple nanowire array. The outer two nanowires have the same width, denoted $w_{\mathrm{s}}$, which is shorter than the width of the center nanowire, denoted $w_{\mathrm{L}}$. Figures 3(b)–3(d) are EFDs for several unique simulations. For the three simulations shown, the incident wavelength, gap width, and nanowire thickness remain constant at values of 700, 5, and 15 nm, respectively. The difference between each simulation is the width of the nanowires, indicated at the top of each EFD. This figure shows that the optical enhancement is concentrated in the gaps between the nanowires and also at the corners of each nanowire. Another observation of significance is the substantial difference in gap enhancement for varying nanowire widths, such as seen between Figs. 3(b) and 3(d). In this case, a substantial increase [from Figs. 3(d) to 3(b)] in optical enhancement is seen for a difference in $w_{\mathrm{s}}$ of only 20 nm.

Fig. 3

(a) Triple nanowire array cross-section geometry showing the incident light direction and polarization (b–d) EFDs of triple nanowire arrays with various geometries. The maximum EFD achieved in these simulations was approximately 37.24.

Figures 4(a)–4(d) plot the maximum optical enhancement for each unique $w_{\mathrm{s}}$ and $w_{\mathrm{L}}$ combination for incident wavelengths of 600, 700, 800, and 900 nm. The width $w_{\mathrm{s}}$ ranges from 10 to 90 nm while $w_{\mathrm{L}}$ ranges from 40 to 140 nm, both with a step size of 10 nm. The intensity profile follows a roughly negative linear pattern for all wavelengths. The negative linear relationship shown in Fig. 4 [and also Fig. 5(b)] could be due to a plasmonic coupling between the nanowires resulting in an effective overall width of the array structure.

Fig. 4

Maximum enhancement of triple nanowire array as a function of $w_{\mathrm{s}}$ and $w_{\mathrm{L}}$ for four different wavelengths. The maximum enhancement achieved in these simulations was approximately 1387.

Fig. 5

(a) Maximum enhancement at optimal $w_{\mathrm{L}}$ as a function of $w_{\mathrm{s}}$. (b) $w_{\mathrm{L}}$ that gives maximum enhancement as a function of $w_{\mathrm{s}}$ for triple nanowire array. Data points are individual simulation results, and the line is fitting obtained from Eq. (3).

Figure 5(a) plots the maximum optical enhancement that was obtained as a function of $w_{\mathrm{s}}$. The peak of the optical enhancement curves strongly shifts to higher $w_{\mathrm{s}}$ for increasing wavelength and reaches a maximum value of approximately 1387 for a wavelength of 700 nm. Figure 5(b) plots the $w_{\mathrm{L}}$ that provides the maximum optical enhancement as a function of $w_{\mathrm{s}}$, which shows a linear relationship. The range of points plotted differs for each wavelength due to shifts in the enhancement patterns that can be shown in Figs. 4(a)–4(d). The slope values obtained for 600, 700, 800, and 900 nm wavelengths are $-0.900$, $-0.982$, $-0.976$, and $-0.867$ with vertical intercept ($b_i$) 72, 113, 147, and 173 nm, respectively. In order to develop a general equation to determine the optimal $w_{\mathrm{L}}$ for maximum enhancement based on wavelength and $w_{\mathrm{s}}$, a general function

The solid lines in Fig. 5(b) are plots of Eq. (3) for each wavelength. Equation (3) is a useful result that can be used to design a structure with appropriate parameters ($w_{\mathrm{L}}$, $w_{\mathrm{s}}$, or $\lambda$) to maximize the optical enhancement of a gold nanowire array if the other two variables are defined. As can be shown in Fig. 5(b), Eq. (3) is a good estimation of the optimum value of $w_{\mathrm{L}}$ for the plotted data.

3.3.

Thickness Dependence

Next, the effects of nanowire thickness were investigated. Figure 6 displays simulation results in the form of EFDs, each corresponding to a different nanowire thickness. For each simulation, the wavelength and nanowire width remain constant: $\lambda =700\mathrm{nm}$ and $w=100\mathrm{nm}$. These plots show that there is a significant difference in the optical enhancement as the thickness changes, as can most clearly be seen between the EFDs for nanowire thicknesses of 5 and 11 nm. This is potentially due to effects of vertical plasmonic modes²⁶ that oscillate vertically along the side surfaces of the cross section of the nanowire.

Fig. 6

EFDs of single nanowires of varying thickness. The maximum EFD achieved in these simulations was approximately 78.4.

Figures 7(a)–7(d) correspond to simulations of a single nanowire, and plot the maximum optical enhancement as a function of nanowire thickness and width for incident wavelengths of 600, 700, 800, and 900 nm. The slope of the maximum enhancement line changes between each wavelength, though it remains positive in each case. Additionally, as wavelength increases, the maximum enhancement at lower nanowire thickness shifts toward larger widths.

Fig. 7

Maximum optical enhancement as a function of width and thickness for a single nanowire for four different wavelengths. The maximum enhancement achieved in these simulations was approximately 6147.

Figure 8(a) plots the thickness that provides the maximum enhancement as a function of width, similar to how Fig. 5(b) demonstrated this for widths. Again, the range of points on each line is limited by the range that was calculated and due to shifts in the enhancement pattern that can be shown in Figs. 7(a)–7(d). Figure 8(a) more clearly demonstrates the shift in the slope of the enhancement pattern between each wavelength. The slope values obtained for 600, 700, 800, and 900 nm wavelengths are 0.285, 0.167, 0.099, and 0.079, respectively. Using the same method as for the first equation, the first step in developing a general equation is

Fig. 8

(a) Thickness that produces maximum enhancement as a function of width. (b) Maximum enhancement at the optimal thickness as a function of width.