# Design of Inverted Nano-Cone Arrayed SERS Substrate for Rapid Detection of Pathogens
## 3 Results  
### Nanocone Design and Material Selection for High Field Enhancement  
A 15 nm reflective film is coated on the surface of the PDMS nano-cone, while leaving the top of the cone uncoated. Gold nanorod with 15 nm in diameter, 45 nm in length is used in our simulation, as was previously reported [14]. Si and gold are considered as the reflective film material coated over the PDMS cone, which would have a large enough  
Figure 1: The illustration of nanocone structure designed; (**a**) gold nanorod(s) are located at the top of the transparent PDMS (Polydimethylsiloxane) cones coated with thin Si, (**b**) Internal reflection of incident light from the bottom reaches nanorods, (**c**) Simulations shows electric field enhancement at the tips of the nanorod (one nanorod case). Figure 2: 758 nm power dissipation distribution for cross sections of (**a**) Si-coated (**b**) Au-coated cones without nanorod. 758 nm electric distribution for cross sections of (**c**) Si-coated (**d**) Au-coated cones without nanorod. refractive index difference from that of the PDMS, reflecting most of the incident light to reach the top of the cone and excite nanorods. Our design would have a plane wave light enter the bottom of the PDMS substrate as shown in Figure 1b. The incident light's electric field is then funneled into the cavity and excite the nanorod at the top, resulting LSPR around the nanorod. To elucidate the role of the cavity's photon funneling effect in enhancing a nanorod's LSPR, the case with one nanorod at the top of the inverse cavity is simulated to get the distribution of electromagnetic fields in cross sections of structures along the axis of the nanorods. In order to see the effect of photon funneling of our design, a flat PDMS surface with gold nanorods on top with at least 840 nm separation among them was also simulated. The flat PDMS surface case represents the current common Raman substrates with gold nanorods sprinkled over. To induce cavity resonance for photon funneling, a high internal reflection inside the cavity is required. According to [PERSON]'s equations, a high reflection occurs when the difference of refractive indices of two interface materials is large [24]. Both Si and Au are considered to serve as a coating film for high interreflection, considering the refractive index of PDMS in the visible region is around 1.4, Au with index around 0.3 and Si with index around 4.0. But due to the metallic dissipative nature of Au, the optical loss of Au-coated cavities can be much higher. The power dissipating profile of Si and Au deposited cavities are simulated as shown in Figure 2a,b, across the cross section of the cavity. The power dissipation can be defined as [25], which is directly correlated with the light energy density [26]:  
\[w(x,z)=\frac{1}{2}\varepsilon_{0}\omega\varepsilon^{\prime\prime}(x,z)\left| \overset{\rightarrow}{E}(x,z)\right|^{2} \tag{4}\]  
In Figure 2a,b, photonic energy is mostly dissipated at the film interface for both Si and Au coated cases. But the intensity in the Au-coated film is nearly 750 times larger than that with the Si film coated case. Figure 2c,d show the electric field intensity with a nanorod at the top. In Figure 2c, with a Si coating, the electric field is enhanced by two orders around the top of the cavity. With gradually narrowing cavity upward and low optical loss at the wall interface, the incident photons are concentrated and delivered to the nanorod at the top of the structure. In Figure 2d, when the electric field is enhanced at the side wall of the cavity, the photons are dissipated and scattered at the cavity wall, before arriving the top. Even though photons are concentrated at a similar level in both cases, the dissipation effect at the gold film makes a huge difference. Figure 3a,b show the electric field distribution inside of Si- or Au-coated cones with nanorods at the top: the contours indicate the electric field enhancement, and the green arrows in the cavity show the electric vectors.