Optical responses under lateral compression

5 FBG under lateral compression. The length of FBG and compressed length of fibre are 1 cm and 1.8cm, respectively. 

The case that an uncoated silica optical fibre is laminated by two rigid plates is considered, as shown in Fig. 9.5. Since the silica optical fibre is a rigid medium, this contact problem can be simplified to line force loading. Then the close form of the stress solutions can be obtained with the help of the plane stress assumption. Since the electric field in a single mode fibre is concentrated in the core region, the solution in the centre is approximately selected to represent the stress of a single mode fibre under lateral compression. The stress in the core can be expressed as  

6 Polarization signals of FBG under lateral compression. The normal compression is shown in (a), and slant compression with 45° in ib) the angle of ellipticity is 0. The orientations are 0, tt/12, tl6 and n/A, respectively. 

In the case of lateral compression, the propagated fundamental mode perfectly degenerates into x- and y-polarized modes with different propagation constants. According to the photoelastic effect and the stress strain relationship, the effective index changes of the two polarized modes ean be expressed as  

Using the stress-strain relationship and Eq. (9.17), the relative shifts of the Bragg wavelength of two polarized modes at any point of the FBG due to lateral compression are then obtained by  

---

This chapter has given the optical responses of FBG sensors under different modes of deformation. Both the polarization behaviour and optical spectrum of FBGs have been used to analyse the deformation perturbations. In the case of an FBG under tension, the wavelength sensitivity to tension is significant. In the case of torsion, the wavelength sensitivity is very small, and the polarization behaviour is sensitive to it. In the case of lateral compression, the wavelength sensitivity is much smaller than that under tension, but the deformation induced birefringence can broaden and split the reflection peaks. 

The lateral compression can be sensed by the spectrum behaviour in some sensing schemes. Both the polarization behaviour and the optical spectrum of FBGs can be used to analyse lateral eompression. Bending of FBGs can be analysed for both the polarization behaviour and the optical spectrum, but it is difficult to measure the polarization evolution of fibre under bending. The optical responses of normal germanosilicate FBG under different individual modes of deformations are summarized in Table 9.1. 

---