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As discussed in Chapter 1, the propagating modes of a single-mode optical fiber can be expressed as a combination of linearly polarized (LP) modes with the fundamental mode designated as the LP01. Also highlighted was the concept of describing the light energy as a combination of two degenerate modes possessing orthogonal linear polarizations. The polarization evolution of light in an optical fiber has been studied quite extensively. Typical eigenmode analysis can be applied, and, in most cases, linear polarization states are used as the basis vectors. However, it is important to note that any two orthogonal basis vectors are sufficient to completely describe all polarization states in the waveguide. In fact, as will be discussed later in this chapter, for Faraday rotation it is more mathematically convenient to use circular states (left and right) as the basis vectors to describe the process. Polarization-based fiber optic sensors typically involve an extrinsic birefringent component to perform the actual polarization modulation. Intrinsic types of sensors include Faraday rotation and some Bragg gratings, which are written in polarizing-maintaining (PM) type fibers. Other components required for the system including polarizers and analyzers can also be implemented in fiber and are described in further detail in Section 7.2. The sensitivity of optical components to polarization has been known and studied for a very long time. Most of the effects studied manifest themselves as operations on linear coordinate systems. Again, these are systems that possess linear eigenvectors. Detailed in Fig. 7.1 is a general component in a linear right-handed coordinate system. The angle of the light vector θ is defined as being positive when measured from the vertical coordinate y as observed while looking into the light source.
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