# Surface Plasmon Resonance-Based Fiber Optic Sensors Utilizing Molecular Imprinting
## 2 Surface Plasmon Resonance (SPR)  
The phenomenon of SPR has been establishing its potential in its long ambit since 1902, when [PERSON] observed the diffraction of dark and bright bands of light from a grating structure. In 1968, [PERSON] came up with an optical interpretation by considering a setup with an air (dielectric) gap in between prism and metal, where the evanescent wave generated by attenuated total internal reflection at the prism-air interface excites surface plasmons at the air-metal interface. The limitation of the Otto configuration, namely the difficulty in realizing it practically due to the fact the arrangement of air gap thickness needs to be within the penetration depth of the evanescent wave, was overcome by the Kretschmann-Rearther configuration in 1968 [28; 29; 30]. In this configuration, the spacing or gap layer was metal and the evanescent wave generated at the prism-metal interface excites surface plasmons at the metal dielectric interface. The quantum of charge density oscillations supported by a metal-dielectric interface and propagating along the interface are termed a surface plasmons (SPs) while the associated wave is called as surface plasmon wave (SPW) [31; 32; 33]. The electric field of a SPW is maximum at the interface and decays exponentially in dielectric as well as metal media. Further, SPW is a TM-polarized wave and hence to excite SPs a p-polarized light is required [34; 35]. For excitation, the wave vector of excitation light should match with the wave vector of SPs. From [PERSON]'s equations, the general expression for the propagation constant of the surface plasmon wave propagating along the metal-dielectric interface is given by:  
\[k_{SP}=\frac{2\pi}{\lambda}\sqrt{\frac{\epsilon_{m}\epsilon_{d}}{\epsilon_{m} +\epsilon_{d}}} \tag{1}\]  
where \(k_{SP}\) is the propagation constant of surface plasmon wave, \(\lambda\) is the wavelength of the incident light in free space, \(\epsilon_{m}\) and \(\epsilon_{d}\) are the dielectric constants of metal and dielectric medium which are functions of the wavelength. The metals that are generally used include silver, gold, aluminum and copper at optical wavelengths. The surface plasmon wave has its dependency on the real and imaginary parts of the dielectric constant of the metal thin film and dielectric medium, where the real part regulates the periodic appearance and the imaginary part results in the attenuation of the wave [36]. In the case of direct light, SPW holds the momentum/wave vector much higher than that of an incident light and hence cannot excite the SPs. Hence, for the excitation of SPs, the momentum of the excitation light should be increased. Three types of coupling based on gratings, prisms, and waveguides/fibers are used for the excitation of SPs as shown in Figure 1a-c [33]. In grating-based coupling, the diffraction of the light from the grating results in the generation of a diffracted beam in different directions with one of these along the plane of the grating with a wave vector much greater than that of the incident light to match that of the SPs. The period of the grating plays an important role in the excitation of SPs. In the case of prism-based coupling, the attenuated total internal reflection at the prism-metal interface generates an evanescent wave whose propagation constant is given by the following equation:  
\[k_{EV}=\frac{2\pi}{\lambda}n_{p}\sin\theta \tag{2}\]  
where \(n_{p}\) is the refractive index of the material of the prism and \(\theta\) is the angle of incidence of the light. To excite the SPs using a prism-based configuration, the propagation constant of the evanescent wave needs to approach that of the surface plasmons, which idealizes the relation, \(k_{EV}=k_{SP}\), which shows the possibility of increasing \(k_{EV}\) to match \(k_{SP}\) by changing the dielectric constant of the prism. The evanescent wave excites the surface plasmons by its field penetrating through the metal layer.