## 2 Design of the Plasmonic Sensor  
The operational principle is based on SPR [22; 23]. Figure 1 shows a diagram of the sensor for the measurement of the concentration of CO\({}_{2}\). The experimental set up is schematically illustrated in Figure 1.  
It can be considered that the standard air is a mixture of 78% of N\({}_{2}\), 21% of O\({}_{2}\) and 1% of Ar, CO\({}_{2}\) (0.04%) and H\({}_{2}\)O. As we can measure the concentration of CO\({}_{2}\) both indoors and outdoors, we have to know the variation of the refractive index of the carbon dioxide with atmospheric pressure, temperature, height above the sea level, concentration, etc. A slight variation in humidity of 2 mb may cause a variation of 14% in relative humidity. This affects the eighth-decimal place of the refractive index of CO\({}_{2}\) in concentrations of 200-400 ppm. The difference between the refractive indexes of the CO\({}_{2}\) when the atmospheric pressure varies from 0.5 atm to 1 atm is 1.00025 to 1.0005, respectively, if we consider an atmospheric pressure in the middle, 0.74 atm, the refractive index is 1.000375 [24]. From the Edlen equations, we can calculate the dispersion of the refractive index of the carbonic anhydride for dry air, 1 atm, 15 \({}^{\circ}\)C and 300 ppm in volume. This variation is around 10-8 from 200 nm up to the infrared. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Indoor** & **Outdoor** & **Multigas** & **Only CO\({}_{2}\)** & **Wide Dynamic Range** & **Short Dynamic Range** \\ \hline
[4] & [12; 19] & [20; 21] & [5; 6; 7; 8; 9; 10; 11; 12; 13] & [7; 11; 16] & [5; 6; 8; 13; 15; 18] \\ \hline
**Waveguide/Optical fiber sensor** & **Plasmonic sensor** & **Others** & **Instant response time** & **Fast response time** & **Slow response time** \\ \hline
[10; 11; 12; 16; 20; 21] & [6; 17; 18; 19] & [5; 7; 8; 9] & [6; 17; 18; 19] & [5; 10] & [9; 14; 16] \\ \hline
**High resolution** & **Low resolution** & **High sensitivity** & **Low sensitivity** & & \\ \hline
[17] & [13] & [8; 17; 20] & [12] & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary table with the essential characteristics of the sensors studied. Figure 1: Diagram of the plasmonic sensor. On the left of the hemispherical prism, the optical fiber transports the incident radiation and, on the right, another optical fiber collects the reflected radiation. The SPR are also shown propagating through the LiIO\({}_{3}\)-Au and Au-medium interfaces. Another parameter which provokes variations in the refractive index is the temperature. For 1 atm and 20 \({}^{\circ}\)C, (n \(-\) 1) = 0.000271786 (a variation to the fourth decimal place which we have to take into account). The variation in the refractive index with the water vapour can be calculated with the correction of Birch and Downs [25]. The effects of other gases, such as Ar, N\({}_{2}\) and O\({}_{2}\), have no effect on the change in the refractive index of carbon dioxide. Due to all of the above, our sensor would be able to measure the refractive index for different concentrations of CO\({}_{2}\). As the variation of the refractive index with pressure is very great, these sensors have to be designed taking into account the height above sea level where they are going to be used. The hemispheric prism is made of glass SUMITA (CaFK) (n = 1.4333) [26]. The dielectric layer is lithium iodate (LiIO\({}_{3}\)) with a thickness of 37.26 nm, and the refractive index is 1.8807 [27]. The Au layer has a thickness of 51.48 nm and a refractive index of (n = 0.12517 + 3.3326i) [28]. The hemispherical prism has a radius of 1 cm. The laser used is a continuous emission (to minimize consumption), with polarization \(p\) and a wavelength of 632.8 nm. It strikes the spherical part of the hemiprism with a normal incidence. The light is conducted from the laser to the prism by means of an optical fiber and its endface is glued to the surface of the hemiprism. The incidence angle, compared to the normal, in the LiIO\({}_{3}\) is \(\theta\) (greater than the critical angle) (see Figure 1).