# Photonic Crystal-Based Sensors for Detecting Alcohol Concentration
## 3 Results and Discussion
### Ethanol Concentration Examined by PS Opal and TiO\({}_{2}\) Inverse Opal Structures
Consequently, the 600 \({}^{\circ}\)C sintered TiO\({}_{2}\) sensor is the optimal candidate from the studied samples for ethanol concentration detection. From the experiment results, we found that the pore size and incident angle also affect the sensitivity of the sensor [31]:  
\[\lambda_{\text{max}}=1.633D_{\text{inverse opal}}\sqrt{(n_{a}^{2}-sin^{2}\theta)} \tag{3}\]  
\[n_{a}^{2}=(1-f)\times n_{titania}^{2}+f\times n_{ethanol}^{2} \tag{4}\]  
where \(\lambda_{\text{max}}\) is the wavelength of the maximum reflectance peak, \(D_{\text{inverse opal}}\) is the average center-to-center distance between spheres or pores, \(\theta\) is incident angle of light, and \(n_{\text{a}}\) is the average  
Figure 8: The relationship between red shift of reflectance spectra and the ethanol concentration (\(v/v_{0}\)): (**a**) PS opal; (**b**) 500 \({}^{\circ}\)C and (**c**) 600 \({}^{\circ}\)C sintered TiO\({}_{2}\) inverse opal sensors. Error bars represent standard deviation based on data from three measurements. refractive index of the structure. Furthermore, \(n_{\rm titania}\) is the refractive index of titania, \(n_{\rm ethanol}\) is the refractive index of different ethanol concentrations, and \(f\) is the packing factor (=0.74) of the crystal structure, the results indicate that the structure is a well-ordered 3D face centered cubic order structure [10]. From the work of [PERSON]'s group described in [3], the TiO\({}_{2}\) pore size is 210 nm and the incident angle is 90\({}^{\circ}\); however, in our work, the TiO\({}_{2}\) pore size is 200 nm, and the incident angle is 20\({}^{\circ}\). (The refractive index of the 500 \({}^{\circ}\)C sintered TiO\({}_{2}\) inverse opal is 2.50 from [3].) According to Equations (4) and (5), \(\lambda_{\rm max}\) should be 485 nm for the sample in [3] and 670 nm for the sample in our work. Therefore, the ethanol detectability of the TiO\({}_{2}\) inverse opal structure prepared in this study is much better than the one proposed by [PERSON]'s group. Furthermore, as we consider the impact of the refractive index on the sensitivity of the TiO\({}_{2}\) inverse opal, \(\lambda_{\rm max}\) for the 600 \({}^{\circ}\)C sintered TiO\({}_{2}\) inverse opal structure is better than the 500 \({}^{\circ}\)C sintered one. In particular, because the \(\lambda_{\rm max}\) values are 674 nm and 670 nm for the 600 and 500 \({}^{\circ}\)C sintered TiO\({}_{2}\), respectively, the corresponding refractive index are \(n_{600^{\circ}\text{C}}\) = 2.52 [20] and \(n_{500^{\circ}\text{C}}\) = 2.50. A key performance indicator of integrated optical devices for applications in sensing is the ability to detect small refractive index changes. For resonant devices, this ability is expressed in terms of the wavelength change induced by a refractive index change. The sensitivity (\(S\)) can be defined by calculating the shift in wavelength per unit change in refractive index from the following Equation (5) [32; 33]:  
\[S=\frac{\Delta\lambda}{\Delta n_{a}}\ \left(nm/RIU\right) \tag{5}\]  
The wavelength (\(\lambda_{\rm max}\)) is determined with reference to the refractive index of the average refractive index of the structure (\(n_{\rm a}\)). If the refractive index of the structure is altered by \(\Delta n_{\rm a}\), the wavelength of the maximum reflectance peak shifts by \(\Delta\lambda\), the units by nm/RIU (refractive index unit, RIU). As the increasing of ethanol concentration from 10% to 80%, the red shift for the 600 \({}^{\circ}\)C sintered TiO\({}_{2}\) sensor is 130 nm (see Table 2). According to Equations (4) and (5), the sensitivity value of the 600 \({}^{\circ}\)C sintered TiO\({}_{2}\) inverse opal sensors is approximate 9090 nm/RIU, which is higher than that of the LSPR (190 nm/RIU) [34] and the planar SPR technique (3100 to 8800 nm/RIU) [35]. The results show that it is possible to distinguish ethanol concentration in the range between 10% and 80%, if only the peak shift is taken into account.