# Nanoplasmonic Sensor Based on Surface Plasmon-Coupled Emission: Review
## 4 Surface Plasmon Resonance  
According to electromagnetism theory, electrical dipoles can radiate the evanescent wave in the far field. The amplitude of evanescent field decreases in the distance about the wavelength length from the source [12]. The evanescent field is observable in the near field. The evanescent wave can propagate in the medium with the refractive index smaller than that of the source medium. The excitation of evanescent wave occurs from propagation of light beam in the dense medium at the particular angle [12; 13]. For example, if a gold layer is deposited on the surface of prism and the light beam passes through the prism, it can excite the evanescent wave and propagate in the layer that is placed after the gold thin film. Similarly, the evanescent wave will be excited when fluorescence emitted from the layer is placed at the other side of gold thin film. This phenomenon occurs in the layer with finite thickness and is SPCE [14]. For clarification of the mentioned phenomena, a system with three layers is presented in Figure 3, where the electric dipole is accommodated in the medium with unity refractive index. The gold layer with 50 nm thickness (\(n_{Au}\) = 0.15 + 3.27i at the 560 nm wavelength) was coated on the glass slide (\(n_{prism}\) = 1.515) [15]. The size of fluorescence ring is about 150 nm. The electromagnetic waves have two polarization modes, p-polarized and s-polarized, which are perpendicular one respect to the other, and called TM mode and TE mode [16]. In Figure 4, the transmission coefficient of the light amplitude of p-polarized and s-polarized as a function of the angle of emission in the glass medium is illustrated. It can be observed that within a specific angle of the glass medium, a dramatic absorption and emission of p-polarized light occurs, while the transmission and decay of the s-polarized wave occurs in the metal layer. In order for SPCE to occur, there must be a correspondence between the magnitude of incident wave vector and wave number which can get a surface plasmonic wave excited:  
\[k_{spp}=k_{0}\sqrt{\frac{\varepsilon_{1}\cdot\varepsilon_{2}}{\varepsilon_{1}+ \varepsilon_{2}}} \tag{10}\]  
Figure 4: Demonstration of TE and TM mode. Figure 3: Demonstration of surface plasmon-coupled emission (SPCE). where the wave number within the vacuum is denoted by \(k_{0}\) when the wavelength is \(\lambda\) and \(\varepsilon_{1},\varepsilon_{2}\) are the permittivity of the medium where the dipole is embedded and the metal, respectively. Generally \(\varepsilon_{1}<0\) and \(\varepsilon_{2}<|\varepsilon_{1}|\)[12,13], and \(k_{spp}\), the wave number of surface plasma wave, frequently larger than the wave number within the medium where the dipole is immersed, denoted as \(k_{1}\),  
\[k_{1}=k_{0}\sqrt{\varepsilon_{1}} \tag{11}\]  
Based on this principle, the surface plasmonic of the metal can only be excited by the evanescent field is located close to an electric dipole. Therefore, the propagating waves pass under the angle smaller than the evanescent, whereas the passage of evanescent waves occurs under the angles that are larger than the anticortilal angle \(\theta_{c}\); the anti-critical angle can be shown as:  
\[\theta_{c}=\sin^{-1}(\frac{n_{1}}{n_{3}}) \tag{12}\]  
where the refractive index of air and glass are denoted by \(n_{1}\) and \(n_{3}\)[17, 18, 19, 20]. The SPCE is excited by the evanescent field, whereas the propagating field simply passes through the metal layer. Thus, in this situation, the evanescent field will excite SPCE, while the propagating field will simply pass through the metal layer. Therefore, in this case, the combination of the SPCE wave and ordinary propagating waves makes the fluorescence [21,22]. The Fresnel theory can be used to evaluate the SPR signals. Typically, the fluorophore medium is coated on the gold layer and the medium with high refractive index, prism or hemisphere glass is located at the other side of gold layer.