fiber, changes in the refractive index of the fiber due to the applied perturbation can significantly alter the phase of the sensing signal, S. Thus, the intrinsic cavity results in the sensor being sensitive to ambient temperature fluctuations and all states of strain.

The IFPI sensor, like all other interferometric signals, has a nonlinear output that complicates the measurement of large magnitude strain. This can again be overcome by operating the sensor in the linear regime around the Q-point of the sinusoidal transfer function curve. The main limitation of the IFPI strain sensor is that the photoelastic effect-induced change in index of refraction results in a nonlinear relationship between the applied perturbation and the change in cavity length. In fact, for most IFPI sensors, the change in propagation constant of the fundamental mode dominates the change in cavity length. Thus, IFPIs are highly susceptible to temperature changes and transverse strain components [1]. In embedded applications, the sensitivity to all the strain components can result in erroneous outputs. The fabrication process of an IFPI strain sensor is more complicated than that of the EFPI sensor since the sensing cavity must be formed within the optical fiber by some special procedure. The strain resolution of the IFPIs is also expected to be around 1 µε with an operating range greater than 10,000 µε. IFPI sensors also suffer from drift in the output signal due to variations in the polarization state of the input light.

Thus, the preliminary analysis shows that the extrinsic version of the Fabry–Perot optical fiber sensor seems to have an overall advantage over its intrinsic version. The extrinsic sensor has negligible crosssensitivity to temperature and transverse strain. Although the strain sensitivity, dynamic range, and bandwidth of the two sensors are comparable, the IFPIs can be expensive and cumbersome to fabricate due to the intrinsic nature of the sensing cavity.

The extrinsic and intrinsic Fabry–Perot interferometric sensors possess nonlinear sinusoidal outputs that complicate the signal processing at the detection end. Although intensity-based sensors have a simple output variation, they suffer from limited sensitivity to strain or other perturbations of interest. Gratingbased sensors have recently become popular as transducers that provide wavelength-encoded output signals that can typically be easily demodulated to derive information about the perturbation under investigation. The advantages and drawbacks of Bragg grating sensing technology are discussed first. The basic operating mechanism of the Bragg grating-based strain sensor is elucidated and the expressions for strain resolution is obtained. These sensors are then compared to the recently developed long-period gratings in terms of fabrication process, cross-sensitivity to other parameters, and simplicity of signal demodulation.

Fiber Bragg Grating Sensor

The phenomenon of photosensitivity in optical fibers was discovered by Hill and co-workers in 1978 [9]. It was found that permanent refractive index changes could be induced in fibers by exposing the germa- nium-doped core to intense light at 488 or 514 nm. The sinusoidal modulation of index of refraction in the core due to the spatial variation in the writing beam gives rise to a refractive index grating that can be used to couple the energy in the fundamental guided mode to various guided and lossy modes. Later Meltz et al. proposed that photosensitivity is more efficient if the fiber is side-exposed to fringe pattern at wavelengths close to the absorption wavelength (242 nm) of the germanium defects in the fiber [10]. The side-writing process simplified the fabrication of Bragg gratings, and these devices have recently emerged as highly versatile components for communication and sensing systems. Recently, loading the fibers with hydrogen has been reported to result in two orders of magnitude higher index change in germanosilicate fibers [11].

Principle of Operation

Bragg gratings are based on the phase-matching condition between spatial modes propagating in optical fibers. This phase-matching condition is given by:

© 1999 by CRC Press LLC

where, kg , kc, and kB are, respectively, the wave-vectors of the coupled guided mode, the resulting coupling mode, and the grating. For a first-order interaction, kB = 2π/Λ, where Λ is the grating periodicity. Since it is customary to use propagation constants while dealing with optical fiber modes, this condition reduces to the widely used equation for mode coupling due to a periodic perturbation:

where, Δβ is the difference in the propagation constants of the two modes involved in mode coupling (both assumed to travel in the same direction).

Fiber Bragg gratings (FBGs) involve the coupling of the forward-propagating fundamental LP01 optical fiber waveguide propagation mode to the reverse-propagating LP01 mode [12]. Consider a single mode fiber with β01 and –β01 as the propagation constant of the forwardand reverse-propagating fundamental LP01 modes. To satisfy the phase-matching condition,

where, β01 = 2πneff /λ (neff is the effective index of the fundamental mode and λ is the free-space wavelength). Equation 6.121 reduces to [12]:

where λB is termed the Bragg wavelength. The Bragg wavelength is the wavelength at which the forwardpropagating LP01 mode couples to the reverse-propagating LP01 mode. This coupling is wavelength dependent since the propagation constants of the two modes are a function of the wavelength. Hence, if an FBG is interrogated by a broadband optical source, the wavelength at which phase-matching occurs is found to be reflected back. This wavelength is a function of the grating periodicity (Λ) and the effective index (neff ) of the fundamental mode (Equation 6.122). Since strain and temperature effects can modulate both these parameters, the Bragg wavelength shifts with these external perturbations. This spectral shift is utilized to fabricate FBGs for sensing applications.

Figure 6.102 shows the mode coupling mechanism in fiber Bragg gratings using the β-plot. Since the difference in propagation constants (Δβ) between the modes involved in coupling is large, Equation 6.120 reveals that only a small value of periodicity, Λ, is needed to induce this mode coupling. Typically for telecommunication applications, the value of λB is around 1.5 µm. From Equation 6.122, Λ is determined

to be 0.5 µm (for neff = 1.5). Due to the small periodicities (of the order of 1 µm), FBGs are classified as short-period gratings.

Fabrication Techniques

Fiber Bragg gratings have commonly been manufactured using two side-exposure techniques: the interferometric method and the phase mask method. The interferometric method, depicted in Figure 6.103

FIGURE 6.102 Mode coupling mechanism in a fiber Bragg grating.

© 1999 by CRC Press LLC

FIGURE 6.103 The interferometric fiber Bragg grating.

FIGURE 6.104 The novel interferometer technique.

comprises a UV beam at 244 or 248 nm spilt in two equal parts by a beam splitter [10]. The two beams are then focused on a portion of Ge-doped fiber (whose protective coating has been removed) using cylindrical lenses, and the periodicity of the resulting interference pattern and, hence, the Bragg wavelength are varied by altering the mutual angle, θ. The limitation of this method is that any relative vibration of the pairs of mirrors and lenses can lead to the degradation of the quality of the final grating and, hence, the entire system has a stringent stability requirement. To overcome this drawback, Kashyap et al. have proposed the novel interferometer technique where the path difference between the interfering UV beams is produced by the propagation through a right-angled prism (Figure 6.104) [12]. This technique is inherently stable because both beams are perturbed similarly by any prism vibration.

The phase mask technique has recently gained popularity as an efficient holographic side-writing procedure for grating fabrication [13]. In this method, as shown in Figure 6.105, an incident UV beam is diffracted into –1, 0, and +1 orders by a relief grating generated on a silica plate by e-beam exposure and plasma etching. The two first diffraction orders undergo total internal reflection at the glass/air interface of a rectangular prism and interfere on the bare fiber surface placed directly behind the mask. This technique is wavelength specific since the periodicity of the resulting two-beam interference pattern is uniquely determined by the diffraction angle of –1 and +1 orders and, thus, the properties of the phase

© 1999 by CRC Press LLC

FIGURE 6.105 The phase mask technique for grating fabrication.

FIGURE 6.106 Diagram of the setup for monitoring the growth of the grating in transmission during fabrication.

mask. Obviously, different phase masks are required for fabrication of gratings at different Bragg wavelengths. The setup for actively monitoring the growth of the grating in transmission during fabrication is shown in Figure 6.106.

Bragg Grating Sensors

From Equation 6.122 we see that a change in the value of neff and/or Λ can cause the Bragg wavelength, λ, to shift. This fractional change in the resonance wavelength, Δλ/λ, is given by the expression:

© 1999 by CRC Press LLC