**2.1. Fiber Mach-Zehnder interferometer**

A common two-beam fiber-optic interferometer is the fiber Mach-Zehnder interferometer [2, 4]. As shown in **Figure 1(a)**, the optical paths consist of two fiber arms, one to be assigned as *signal* arm with a length *ls* and the other one as *reference* arm with a length *lr*. The light beam from a light source is amplitude-divided by a fiber coupler OC1 into two beams propagating respectively in *signal* and *reference* arms. In general, the *signal* arm is exposed to the external environment to sense disturbances, while the *reference* arm is kept in a relatively constant environment. The phase of the *signal* beam is modified by the external disturbances as a physical measurand when the beam passes through the *signal* arm. It produces a phase difference between two beams, *signal* beam and *reference* beam, which recombine at a second fiber coupler OC2. Two groups of beams output from the two ports of OC2 are then detected by two photodetectors, PD1 and PD2, and converted into a pair of fringe signals in antiphase. If total optical losses in the interferometer are negligible, the two fringe signal intensities, *P*<sup>1</sup> and *P*2, can be expressed as [4]:

$$R\_1 \propto I\_1 + I\_2 + \xi \cdot \gamma \cdot 2\sqrt{I\_1 I\_2} \cos(\Delta\varphi) \tag{1}$$

$$P\_2 \propto I\_1 + I\_2 - \xi \cdot \gamma \cdot 2\sqrt{I\_1 I\_2} \cos(\Delta\phi) \tag{2}$$

where <sup>=</sup> <sup>−</sup> is the phase difference, = 2/λ and = 2/λ are the phases of the *signal* beam and *reference* beam, respectively, and *n* is the refractive index of the fiber core; *I*1 and *I*2 are the intensities of *signal* beam and *reference* beam arose at output ports of OC2, respectively; ξ is a ratio, 0 ≤ ≤ 1, reflecting the matching degree of two beams in their polarization states, which is adjustable by an in-line polarization controller PC, as shown in **Figure 1(a)**; γ is defined as the fringe visibility [2], 0 ≤ ≤ 1, in relation to *I*1 and *I*<sup>2</sup>

$$\gamma = 2\sqrt{I\_1 I\_2} \;/\; (I\_1 + I\_2) \tag{3}$$

Also, γ is a function of the product of the spectral line width Δν of the light source and the optical path difference Δ = <sup>−</sup> , given by

$$
\gamma \left( \Delta \boldsymbol{\nu} \cdot \Delta \boldsymbol{l} \right) \leq 1 \tag{4}
$$

For Δ Δ = 0, 1. In general, for getting a strong contrast on the interference fringe, <sup>γ</sup> Δ Δ <sup>∼</sup> <sup>1</sup> is required. For a known Δν, when <sup>=</sup> −1, Δ*l* corresponds with the coherence length *lc* of the light source [4], having = Δ.

#### **2.2. Fiber Michelson interferometer**

The fiber Michelson interferometer also is a two-beam optical interferometer [4], so its output can be similarly described by Eq. (1) or (2). In the system structure, the fiber Michelson interferometer is very similar to the fiber Mach-Zehnder interferometer. As shown in **Figure 1(b)**, the *signal* and *reference* arms are terminated by two mirrors or Faraday rotator mirrors, so that the *signal* beam and *reference* beam, both are reflected by corresponding mirrors back to the coupler OC where they are recombined to generate the interference signal. It is noted that the phase difference = 2 <sup>−</sup> in the fiber Michelson interferometer is double of that in the fiber Mach-Zehnder interferometer, which, therefore, will effectively double the sensitivity of interferometer.
