# Horizontal Plasmonic Ruler Based on the Scattering Far-Field Pattern

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## Abstract

**:**

## 1. Introduction

## 2. Structure, Specific Mode Profile and Calculation Methods

_{X}= 200 nm, L

_{Y}= 150 nm and a height of 100 nm as shown in Figure 1a. Depending on the direction of the incident light, one of the two plasmonic modes can be independently excited in the air gap. To excite the gap modes, light is linearly polarized along the Z-direction (E

_{Z}). When this light is incident on the nanoblocks along the Y-direction (X-direction), as indicated by the blue (red) arrow in Figure 1a mode 1 (or mode 2) is excited at 890 nm (or at 1100 nm), as observed in the scattering cross-section (σ

_{sc}) spectrum of Figure 1b. Even though the scattering intensity changes are observed at lower and higher wavelengths, the elicited changes are maximized at the resonant peaks of 890 nm and 1100 nm. Therefore, we chose these two wavelengths as the reference wavelengths.

## 3. Novel Method for Measuring 1D Locations

## 4. Expansion to 2D Locations Using Scattering Ratio Maps

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic of the two-metal block assembly when light propagates along the X-axis and the Y-axis with the electric field oriented in the vertical direction. (

**b**) Scattering far-field spectra of the two-metal block assembly using light propagates along the X-axis and Y-axis. Simulated electric field distribution in the YZ, XZ plane and also XY plane with resonance wavelengths of (

**c**) 890 nm and (

**d**) 1100 nm. Additionally, the 3D distribution of the far-field with (

**c**) Y-directional and (

**d**) X-directional incident light propagation. Polar graphs are also plotted to depict the scattering far-field in YZ plane and XZ plane for the wavelengths of (

**e**) 890 nm and (

**f**) 1100 nm, respectively.

**Figure 2.**(

**a**) Indicated by the blue sphere is the numerical calculation domain of the far-field region in the case of upper block shifts in the +Y direction (right side of subfigure). The blue arrow indicates the incident light propagating along the Y-axis with the vertical electric field (E

_{Z}), as shown by the black arrow. (

**b**) Scattering far field intensity plots in the YZ plane as a function of angle for upper block shifts. (

**c**) Plots of far-field values at specific spots along the ±X, ±Y, ±Z directions. All colored dots indicate the respective axes depicted in Figure 2a. (

**d**) Plots of scattering intensity ratios obtained by dividing the value at each positive axis location with the corresponding value at each negative axis location in the YZ plane.

**Figure 3.**(

**a**) Representation of the numerical calculation domain of the far-field region in the case when the upper block is shifted along +X direction (right side of subfigure) by the XZ plane of the red sphere. The red arrow indicates the direction of the incident light along the X-axis with the vertical electric field (E

_{Z}) indicated by the black arrow. (

**b**) Plots of far-field intensity variations of a function of angle in the XZ plane based on the shift of the upper block. (

**c**) Plots of far-field values at specific spots along the ±X, ±Y, ±Z directions. (

**d**) Plots of scattering intensity ratio obtained by dividing the value at each positive axis location with the corresponding value at each negative axis location in the XZ plane.

**Figure 4.**(

**a**) Schematic of the movement of the upper block in the horizontal plane, XY. The purple arrow indicates the direction of the incident light propagation with respect to the blocks at an angle of 40 °. (

**b**) Scattering near-field spectra of all the structures (black line) and the air gap (red line) at an incident light angle of 40°. (

**c**,

**d**) Plots of the scattering field intensities following horizontal and vertical shifts of ΔX = 3.7 nm and ΔY = 9.7 nm, respectively, for mode 1 (or mode 2). (

**e**) Mapping plots showing the combination of the two other modes at the specific shifts of ΔX = 3.7 nm and ΔY = 9.7 nm, as represented by the dotted line and the solid lines.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Shin, E.; Lee, Y.J.; Kim, Y.; Kwon, S.-H.
Horizontal Plasmonic Ruler Based on the Scattering Far-Field Pattern. *Sensors* **2018**, *18*, 3365.
https://doi.org/10.3390/s18103365

**AMA Style**

Shin E, Lee YJ, Kim Y, Kwon S-H.
Horizontal Plasmonic Ruler Based on the Scattering Far-Field Pattern. *Sensors*. 2018; 18(10):3365.
https://doi.org/10.3390/s18103365

**Chicago/Turabian Style**

Shin, Eunso, Young Jin Lee, Youngsoo Kim, and Soon-Hong Kwon.
2018. "Horizontal Plasmonic Ruler Based on the Scattering Far-Field Pattern" *Sensors* 18, no. 10: 3365.
https://doi.org/10.3390/s18103365