**2.3. Fiber Sagnac interferometer**

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>

2 cos 1 2 (

2 cos 1 2 (

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

12 1 2

Also, γ is a function of the product of the spectral line width Δν of the light source and the

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

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

j

j

is the phase difference, = 2/λ and = 2/λ are the phases of

= 2 /( ) *II I I* + (3)

× £ *l*) (4)

) (1)

) (2)

*P I I II* 1 12 µ + +×× D x g

*P I I II* 2 12 µ + -×× D x g

**Figure 1(a)**; γ is defined as the fringe visibility [2], 0 ≤ ≤ 1, in relation to *I*1 and *I*<sup>2</sup>

, given by

γΔ Δ 1 ( n

= Δ.

g

<sup>−</sup>

and *P*2, can be expressed as [4]:

optical path difference Δ =

length *lc* of the light source [4], having

**2.2. Fiber Michelson interferometer**

sensitivity of interferometer.

where <sup>=</sup> <sup>−</sup>

146 Optical Interferometry

The fiber Sagnac interferometer is a special and important two-beam, common-path interferometer system [2, 4], in which, as shown in **Figure 1(c)**, two beams from the coupler OC traverse the same fiber loop in opposite directions, usually referred to as the clockwise (CW) and the counter-clockwise (CCW) directions, respectively. The interference fringe is generated when CW and CCW beams, after traveling the whole fiber loop, recombine at OC. Since the optical paths traversed by two beams are very nearly equal, at first sight, the optical phase difference between two beams would always be zero, which represents a static state. However, when the external measurand, such as the acoustic wave, disturbs the fiber close to one end of the loop, an instant phase shift arises. This property makes the Sagnac interferometer be particularly well suited for sensing rapidly varying environmental perturbations. In the early years, the fiber Sagnac interferometer had been developed principally for the purpose of measuring the angle velocity [15], as a fiber gyroscope [4, 16]. Now it has become an important sensor used in the electric power industry for sensing of various physical parameters, such as currents, voltages, electric and magnetic fields, and vibrations as well as acoustic emissions from the partial discharges occurring inside the high-voltage power equipment [17–19].

Similarly, as a two-beam interferometer, the two outputs of fiber Sagnac interferometer also can be expressed by Eqs. (1) and (2). It should be noted that since the optical path difference in the Sagnac interferometer is almost zero, any type of the light source with low or high coherence can be employed.
