# Nanometric Plasmonic Rulers Based on Orthogonal Plasmonic Gap Modes in Metal Nanoblocks
## 4 Conclusions  
We propose a simple 3D plasmonic ruler consisting of three silver nanoblocks: two small blocks (200 nm \(\times\) 150 nm \(\times\) 100 nm) and one large block (260 nm \(\times\) 210 nm \(\times\) 100 nm), placed with 10 nm-thick air gaps. Because of the different size of the \(x\)- and \(y\)-directions of the block, two orthogonal plasmonic modes are excited in the air gaps. By measuring the wavelengths of the absorption peaks corresponding to the modes, one can determine the lateral displacement and the vertical movement of the center large block relative to the two small reference blocks due to the distinctive dependences of the two orthogonal modes on \(x\)- and \(y\)-direction displacement and the strong dependences on air gap size. The proposed structure can be fabricated by direct self-assembly methods [17; 18], or high-precision electron beam lithography and layer-by-layer stacking techniques [10; 11]. In comparison with previous complex structures [10], this structure can be a blueprint for innovative plasmonic rulers that are easily fabricated and ultrasensitive to small distance changes on the nanometer-scale in 3D space.  
Figure 8: **(a)** 3D surface mapping of absorption cross-section peak wavelengths of mode 1 and mode 2 for the upper air gap and the lower air gap for the movement of the central block, \(\Delta x\) = 30 nm, \(\Delta y\) = 0 nm, and \(\Delta z\) = 2 nm. The surfaces indicate the positions of the center block, where the absorption wavelength is maintained as constant. Mode 1 (P1, 852.1 nm) and mode 2 (P3, 1017.5 nm) for the lower gap of 12 nm are represented by red and cyan, respectively. Mode 1 (P2, 953.3 nm) and mode 2 (P4, 1148.3 nm) for the upper gap of 8 nm are indicated by yellow and blue, respectively. Red and blue lines represent the line of the intersection of the two surfaces, P2 and P4, P1 and P3, respectively, which are projected on an x–y plane. **(b)** The projection of the two red and blue lines on the x–\(y\) plane. The black circle indicates the cross-sectional point.  
In order to apply this plasmonic ruler to biological particles, two small upper and lower reference blocks are attached at the pre-fabricated frame structure so that total gap size from the upper and lower air gaps are maintained as constant, like in the proposed structure. Between the reference blocks, one biological particle is fixed by chemical treatments and the center block is attached at a certain position of the biological particle where one wants to observe the dynamic interactions of the biological particle. In this wavelength range, the Drude-Lorentz model can give a more realistic model of silver. However, the operation of the proposed 3D plasmonic ruler is maintained regardless of the material models, except for the larger loss in the Drude-Lorentz model. Higher losses of the structure decrease the sensitivity due to the large linewidth of the resonant peaks. In addition, in terms of chemical stability in biological applications, gold may be a more appropriate plasmonic material.  
In principle, the theoretically calculated wavelength 2D and 3D maps can be directly applied to an experimental system. However, some fabrication differences between the theoretical and experimental systems (i.e., the rounded block edges and thin oxide layers on the surfaces of silver) should be calibrated. The calibration can be accomplished by observing the absorption peaks of several fabricated samples and comparing with the theoretically expected wavelengths. Such calibrations can be performed in 2D plasmonic rulers and applied into 3D wavelength maps.  
This work was supported in part by the National Research Foundation of Korea through the Korean Government under Grants NRF-2016R1C1B2007007, and NRF-2013M3C1A3065051.  
[PERSON] performed simulations and wrote the manuscript. [PERSON] and [PERSON] analyzed the simulation results. [PERSON] supervised all simulations and revised the manuscript.  
The authors declare no conflict of interest.