Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles

Arvind Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner

Phys. Rev. B 72, 165409 – Published 7 October 2005

Abstract

The enhancement of the electromagnetic field is described for nanoscale metallic “bowtie” antennas, consisting of two opposing tip-to-tip Au nanotriangles separated by a gap, through simulation and experiment. Currents, field distributions, and scattering efficiencies in the antennas at optical wavelengths are obtained from finite-difference time-domain (FDTD) simulations using realistic wavelength-dependent dielectric constants. The experimentally measured resonant wavelengths and intensity enhancements from individual bowtie antennas are in excellent agreement with the FDTD simulations. A simple physical model based on current distribution in the antennas is presented to understand the variation in resonant wavelength with gap and explain the basis for the field enhancement.

Received 12 May 2005

DOI:https://doi.org/10.1103/PhysRevB.72.165409

Authors & Affiliations

Arvind Sundaramurthy^*, K. B. Crozier^†, and G. S. Kino

E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

D. P. Fromm, P. J. Schuck, and W. E. Moerner

Department of Chemistry, Stanford University, Stanford, California 94305, USA

^*Electronic address: arvisun@stanford.edu
^†Currently with the Division of Engineering and Applied Sciences, Harvard University.

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Vol. 72, Iss. 16 — 15 October 2005

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Images

Figure 1
SEM images of two representative gold bowties on the fused silica-ITO substrate. The polarization of the incident beam and the coordinate system are shown. The simulated structures closely matched the fabricated bowties. The gap width for the bowtie on top is $16 nm$ .Reuse & Permissions
Figure 2
(a) Left, FDTD calculated ${∣ E ∣}^{2}$ enhancement at the top surface of a $16 nm$ gap bowtie antenna, where the two triangles are at the top and bottom of the figure. Right, a 3D surface plot of the peak intensity variation across the bowtie is also shown, with a different color scale and with the triangles at the right and left of the image. The peak value of intensity in both plots is 1645. The illumination is from the substrate side, the illumination wavelength is $856 nm$ , and a node size of $2 nm$ was used for these images. (b) ${∣ E ∣}^{2}$ enhancement vs wavelength and scattering efficiency $(Q_{scat})$ vs wavelength from FDTD simulations for two different gaps. The peak enhancement and scattering efficiency for a bowtie for the $16 nm$ gap width case is 1645 and 4.1, respectively.Reuse & Permissions
Figure 3
The plots (a)–(c) show a comparison of the spectra obtained from FDTD calculations (line with triangles) and experiments (curve with experimental noise) for different gap sizes. $λ_{r T}$ and $λ_{r E}$ are the theoretical and experimental resonant wavelengths. (a) $gap = 32 nm$ , $λ_{r T} = 779 nm$ , $λ_{r E} \sim 776 nm$ ; (b) $gap = 60 nm$ , $λ_{r T} = 706 nm$ , $λ_{r E} \sim 720 nm$ ; (c) $gap = 232 nm$ , $λ_{r T} = 756 nm$ , $λ_{r E} \sim 748 nm$ . (d) shows the variation in resonant length with gap for FDTD calculations (closed triangles) and experimental measurements (open circles).Reuse & Permissions
Figure 4
Vector plot of the instantaneous surface current for two gap widths. (a) $16 nm$ gap width bowtie, instantaneous peak current density in the $metal = 0.1218 μ A ∕ μ m$ , and instantaneous peak displacement current $density = 0.1321 μ A ∕ μ m$ . (b) One triangle in the $500 nm$ gap width bowtie is shown, instantaneous peak current $density = 0.0558 μ A ∕ μ m$ . The node size used in the simulation is $4 nm$ . The incident field, $E$ , on the bowtie is $1 V ∕ m$ . The current is negligible in the portions of the bowtie not shown in the figure. For the $16 nm$ gap width case the current is peaked at the apex of the triangle and is strongly confined. For the $500 nm$ gap width, the current is peaked at the triangle edges and is parallel to the metal and/or air interface.Reuse & Permissions
Figure 5
Plot of total current in one triangle of the bowtie vs the distance along the bowtie from the apex ( $0 nm$ on the abscissa) to the base. The total current is highest at the apex for the $16 nm$ gap bowtie and the peak total current lies within the triangle for the case of a $500 nm$ gap bowtie.Reuse & Permissions
Figure 6
Peak current density variation as a function of distance from the apex of one triangle of the bowtie. Zero on the $x$ -axis refers to the apex of the bowtie. The abscissa values indicate increasing distance into the triangle along a perpendicular line from the apex to the base of the triangle. The peak current $(I_{p})$ and position of peak current density $(y_{p})$ for different gap widths is as follows: (i) $gap = 16 nm$ , $I_{p} = 0.1218 μ A ∕ μ m$ , $y_{p} = 0 nm$ ; (ii) $gap = 32 nm$ , $I_{p} = 0.0993 μ A ∕ μ m$ , $y_{p} = 0 nm$ ; (iii) $gap = 60 nm$ , $I_{p} = 0.0566 μ A ∕ μ m$ , $y_{p} = 4 nm$ ; (iv) $gap = 240 nm$ , $I_{p} = 0.0550 μ A ∕ μ m$ , $y_{p} = 12 nm$ ; (v) $gap = 500 nm$ , $I_{p} = 0.0552 μ A ∕ μ m$ , $y_{p} = 20 nm$ .Reuse & Permissions

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