# FBG-Based Monitoring of Geohazards: Current Status and Trends
## 2 Basics of Fiber Bragg Grating (FBG)  
### Sensing Principle  
The use of optical fibers for digital data communications was proposed by [PERSON] in 1966, and later on he won the 2009 Nobel Prize for Physics. An optical fiber, normally made of glass, is designed to guide light along its length by total internal reflection. With the rapid development of fiber optics, the optical fiber is now dominant in telecommunication, which permits data transmission over longer distances and at higher data rates in comparison with electronic communication. More importantly, the optical fiber can form different types of sensors, which presents unique advantages that have no match in conventional optical, mechanical or electrical-based sensors. When strain or temperature variations occur in an optical fiber, the wavelength or intensity of the scattered, reflected, or transmitted light will change accordingly, which can be measured by an optoelectronic instrument [7]. Depending on the sensor distribution form, the FOS technologies are divided into three types: point sensing, quasi-distributed sensing, and fully-distributed sensing. The sensors can be further categorized into several types in terms of sensing principle, e.g., intensity based, reflection based, interferometry based, and scattering based. FBG is a popular quasi-distributed FOS technology, which makes use of a special phenomenon of the reflected light due to Bragg grating in an optical fiber. The physical fundamentals for FBG were set by [PERSON] and his son [PERSON], for which they both won the 1915 Nobel Prize. The first FBG sensor was fabricated by [PERSON] et al., a scientist at the Communications Research Centre in Ottawa, Canada [8], who discovered for the first time the photosensitivity phenomenon in Ge-doped silica fibers. The Bragg grating can be written into a segment of Ge-doped single-mode optical fiber using a spatial pattern of ultraviolet (UV) light. Figure 1 illustrates the working principle of an FBG sensor. According to [PERSON]'s law, when a broadband source of light has been injected into the fiber, FBG reflects a narrow spectral part of light at a certain wavelength [9]:  
\[\lambda_{B}=2n_{eff}\Lambda \tag{1}\]  
where \(\lambda_{B}\) is called the Bragg wavelength; \(n_{eff}\) is the effective core index of refraction; \(\Lambda\) is the periodicity of the index modulation. The Bragg wavelength is strain- and temperature-dependent through physical elongation or thermal change of the sensor and through the change in the fiber refractive index due to photo-elastic and thermo-optic effects. Considering a standard single mode silica fiber, a change in strain \(\Delta\varepsilon\) or temperature \(\Delta T\) will alter the Bragg wavelength \(\lambda_{B}\) as follows [10]:  
\[\Delta\lambda_{B}=2n_{eff}\Lambda\left[\left(1-\frac{n_{eff}}{2}\right)[p_{12 }-\
u(p_{11}-p_{12})]\Delta\varepsilon+\left(\alpha+\frac{\frac{dn_{eff}}{d \Delta T}}{n_{eff}}\right)\Delta T\right] \tag{2}\]  
where \(\Delta\lambda_{B}\) is the change in Bragg wavelength due to applied strain and temperature change; \(p_{ij}\left(i,j=1\text{ or }2\right)\) are the Pockel's coefficients of the stress-optic tensor; \(\
u\) is Poisson's ratio; \(\alpha\) is the coefficient of thermal expansion of the fiber. Equation (2) can be simplified as:  
\[\frac{\Delta\lambda_{B}}{\lambda_{B0}}=\Big{(}1-p_{eff}\Big{)}\Delta \varepsilon+(\alpha+\xi)\Delta T=c_{\varepsilon}\Delta\varepsilon+c_{T}\Delta T \tag{3}\]  
Figure 1: Generic concept of the FBG sensor. where \(\lambda_{B0}\) is the original Bragg wavelength under strain free and 0 \({}^{\circ}\)C condition; \(\xi\) is the thermo-optic coefficient; \(c_{\varepsilon}\) and \(c_{T}\) are the calibration coefficients of strain and temperature; \(p_{eff}\) is the photo-elastic parameter defined by the following equation:  
\[p_{eff}=\frac{{{n_{eff}}^{2}}}{2}[p_{12}-\
u(p_{11}-p_{12})] \tag{4}\]  
In 1993, [PERSON] et al. proposed a cost-effective method for fabricating FBG using the phase mask, which makes mass production possible [11].