Development of Fiber Bragg Gratings for the Optical Sensor Solutions in Structural Health Monitoring

Abstract

Fiber optical sensors (FOS) have been widely used to ensure physical parameter monitoring such as strain, temperature, vibration, etc. Fiber Bragg grating (FBG) sensors are of interest mainly as they offer relatively easy integration, multiplexing capabilities, and other advantages. A topical area of investigation for FOS integration is structural health monitoring (SHM) and perimeter-security monitoring. Different objects and infrastructures have certain needs, such as long-distance (40+ km) placement and monitoring solutions, lack of active power supply availability on the site, etc. It is vital to study and develop specific FBG profiles to ensure optimal operation of FBG in security, perimeter, and SHM solutions. In this research, we have evaluated the areas and categories in which such FOS and FBGs, in particular, have been used regarding SHM and perimeter monitoring solutions. Authors have also studied, simulated, and experimentally tested various FBGs that can be implemented for the perimeter—security applications and in SHM solutions.

1. Introduction

The number of sites and territories in Latvia and worldwide that need different kinds of real-time health monitoring (roads, barrages, bridges, pipelines, dams, railways, buildings, and other structures) is constantly growing. Over the last decade, monitoring of various processes and sites and sensor-based safety control of the public infrastructure has extensively increased [1, 2]. Since monitoring often should be conducted simultaneously at long distances across many locations, in corrosive environments under electromagnetic interference, or in environments without power supply, FBG optical sensors can be applied in such types of monitoring [3, 4, 5].

Nowadays, the infrastructure of optical networks has not been exploited and utilized to its full capacity. The authors see high potential in extending the infrastructure applications using optical fiber sensors. Considering that the optical network infrastructure is located at/near roads, bridges, tunnels, railways, dams, etc., it can be used as a transmission medium for monitoring those infrastructure objects. “Dark” optical fiber lines can be applied in such monitoring solutions or working lines can be used, utilizing their free frequency ranges. In order to promote further development of such solutions, it is essential to develop high-value optical FBG sensor networks for long-distance monitoring (40+ km) solutions, to provide interoperability of communication and sensor solutions, and to ensure integration of high-quality sensors in various infrastructure objects for monitoring purposes.

To observe and more comprehensively evaluate the topic’s importance and objective topicality, we have analyzed FBG optical sensor-based number of published articles that have been indexed in the SCOPUS database (see Figure 1). For our search, we used article abstracts, their titles, and keywords for finding references regarding “fiber optical sensors,” “fiber Bragg grating sensors,” and “distributed fiber optical sensors.” As observable from Figure 1, all of our mentioned “search parameters” show clear increased interest, reaching more than 3000 articles per year consisting of keywords related to “fiber optical sensors,” more than 1000 articles per year for “fiber Bragg grating sensors” and more than 500 – for “distributed fiber optical sensors.” The available data shows a stable increase in interest in optical sensor-based solutions in the upcoming years as well. Therefore, this research field also fosters the development of additional binding technologies, such as SHM and perimeter-security solutions.

Figure 1.

Amount of research articles regarding FBG-based optical sensors indexed by SCOPUS database.

Nowadays, most of the population understands the meaning of the term “optical internet.” Optical fiber is used as a medium for the transmission of information to provide such a service to customers. Along with technology development, the number of applications of such optical fibers is increasing, and fiber-optic sensors are among these solutions.

The application of optical fibers in sensor designs was reported already in 1970. That became possible due to the invention of the laser in 1960 and the development of low-attenuation optical fibers in 1966 [6]. In the early 1990s, optical sensors, which could measure temperature, strain, pressure, and other parameters, were put into use. In turn, the beginning of the twenty-first century was characterized by the wide application of optical sensors, which measured temperature over the entire fiber length and allowed oil and gas companies to monitor their networks and timely repair damages. In the building construction sector, optical fiber sensors were used to monitor critical areas of the buildings and to plan timely repair works. In the meantime, process efficiency has been considered a growingly important issue, and optical fiber sensors have started playing an ever-increasing role.

Given the topicality of such FBG optical sensor utilization in various SHM applications in the next section of this work, an analysis of the most topical FOS FBG types and SHM applications is made, particularly discussing extrinsic and intrinsic optical fiber sensors. Fiber optical sensor classification is then made, as well as FBG sensor application category segregation is developed and evaluated. Further, descriptive analysis and design of FBG for the FOS solutions in SHM applications are shown. For this, potential FBG apodizations are studied and bandwidth, reflectivity, and side-lobe suppressions versus grating lengths are analyzed. Comparison analysis of such apodization profiles is then evaluated. Lastly, conclusions regarding the gained results are made.

2. Analysis of the most topical FOS FBG types and SHM applications

A lot of progress has been made since, and today, optical fiber sensors allow measuring changes in a wide range of parameters such as strain, pressure, temperature, movement, vibration, acceleration, rotation, moisture level, humidity, amperage, chemical composition, and many other parameters [6]. Development of those sensors was, to a great extent, promoted by the advantages optical fibers have over other kinds of sensors, for example, high sensitivity, immunity against electromagnetic interference, passive sensors, lightweight and compact size, chemical resistance, multiplexing opportunities, suitability for long-distance change monitoring, low-level induced attenuation [6], and wide range of measured chemical and physical parameters [7].

Optical fiber sensors can be classified into two large groups: intrinsic and extrinsic optical fiber sensors.

2.1 Extrinsic optical fiber sensors

In the scenario of extrinsic optical fiber sensors, optical signals are propagated outside the optical fiber, and a sensing element is needed at the end of the fiber. Materials that change their optical parameters, such as refraction index, absorption, fluorescence, reflection, etc., enable the production of a wide range of sensors depending on the monitored parameters. Nowadays, extrinsic optical fiber sensors still play an essential role in the general range of optical fiber sensors. Extrinsic optical fiber sensors use dual fiber connector sensors and Fabry–Pérot interferometers [8].

The dual fiber connector sensor is based on the principle in which the light beam of the transmitted optical signal interacts with a specific environment. The light beam is reflected from the said environment, and the receiver block analyzes how it affects the beam of light, factoring in observed parameters. Depending upon the observed parameter, the reflected signal can be further transmitted through the same or other fiber. The sensors of this variety can be utilized for monitoring temperature, displacement, pressure, and vibration [9].

Because of the relatively low manufacturing costs and compact size, the Fabry-Perrot interferometer is one of the first and most widely used extrinsic optical fiber sensors. The operational principle of the Fabry-Perrot interferometer is based upon two parallel reflective surfaces with a predetermined spacing between the two that is mainly filled with air, creating a cavity structure [10]. Drawbacks of this type of sensor are associated with coupling efficiency and calibration of the sensor [11]. Sensors of this kind are being deployed to detect pressure (e.g., gas, constructions from concrete and composites), single-point temperature points, and ultrasound monitoring [12, 13].

2.2 Intrinsic optical fiber sensors

Alternatively, intrinsic optical fiber sensors use optical fiber as a sensing element. Intrinsic optical fiber sensors can be classified into macrobending and microbending sensors, FBG sensors, as well as Rayleigh, Raman, and Brillouin scattering-based sensors. In the scenario of optical fiber scattering sensors (Rayleigh, Raman, and Brillouin), optical fiber is used both as a transmission medium and as a sensitive component. In sensors of such kind, optical fiber works as a sensor over the whole length.

Macrobending and micro-bending sensors are intensity-modulated sensors based on optical fiber bending. The micro-bending optical fiber sensor fundamentally consists of optical fiber inserted between two saw tooth structure deformation plates. Depending on the deformation plate, it can be modified to enable measurements of different parameters such as deformation, pressure, velocity, acceleration, weight, etc. The most substantial drawback of microlending sensors is high insertion loss (around 20 dB), which prevents them from being used in sensor network solutions where measurements are carried out at multiple points [9, 14].

For the macrobending sensor, the bending radius is many times larger than that of the microlending sensor, reaching 10–30 mm (depending on the utilized wavelength range). Macrobending sensors operate based on the principle of one or more bending loops. The attenuation increases with a reduction in the diameter of the optical fiber loop. Such sensors can be used as displacement (for monitoring buildings, railways, dams, embankments, and other objects), airflow, and temperature sensors. Given the fact that the attenuation of these sensors is many times lower than that of micro-bending sensors, it allows them to be multiplexed and deployed in an optical sensor network [15, 16].

In the use of optical fiber scattering (Rayleigh, Raman, Brillouin) based sensors, the optical fiber is used as both a transmission medium and a sensor. The whole length of the fiber acts as a sensor in this scenario. Scattering-based sensors do not require any modifications to their design to operate as sensors, but high-quality and high-sensitivity equipment is needed.

The power of the reflected signal due to the Rayleigh scattering is proportional to the optical power of the transmitted signal, which is approximately equal to λ⁻⁴ [17]. Energy is not transferred to the fiber during Rayleigh scattering. Furthermore, signal frequency is not altered as an effect of scattering, so it is considered elastic scattering, which is relative to the transmitted signal. The disadvantage of the mentioned sensors is introduced due to Rayleigh’s scattered signal, which has low power (several dozen dB lower than the input signal) [17]. Regardless of the mentioned deficiency, such sensors are employed for monitoring temperature, deformations, vibrations [18], humidity [19], radiation [20], etc. It is important to note that the optical time domain reflectometer (OTDR) technology used to monitor optical lines (for monitoring insertion loss and impairments detection of optical lines) is based on Rayleigh scattering. If micro-bending and macrobending sensors are deployed in sensor network solutions, OTDR is also used to enable monitoring. Incorporating several fiber-optic sensor technologies and solutions into one (e.g., OTDR and FBG [21]) also seems interesting as this potentially provides an even more comprehensive range of monitoring services.

Optical fiber sensors based on stimulated Brillouin scattering (SBS) are used for temperature and deformation monitoring throughout the entire fiber length. Optical fiber Brillouin scattering sensors are based on inelastic scattering in which scattered waves experience frequency/wavelength shifts [22]. SBS-based sensors, depending on the realization principle and placement of continuous wave (CW) laser, can be further segregated into Brillouin optical time domain reflectometer (BOTDR) and Brillouin optical time domain analyzer (BOTDA) [17, 22, 23]. For BOTDA, the CW lasers and impulse signals propagate in different directions [17, 23]. This wavelength shift depends on temperature and deformation changes, allowing these devices to be used in sensor solutions. For BOTDR, the sensor’s operational monitoring range is between 20 and 50 km. For BOTDA, it is possible to reach up to 200 km [17]. The spatial resolution for BOTDR is approximately 1 m (depending on the monitoring range), but for BOTDA, spatial resolution is 2 cm (for a monitoring range of 2 km) [24] and 2 m (for 150 km) [23].

Optical fiber sensors based on Raman’s scattering are used to monitor temperature throughout the entire fiber length. The technological solution is broadly used for monitoring concrete structures, gas pipelines, and water supply systems [17, 25]. The operational monitoring range distance of the sensor can reach up to 37 km. Spatial resolution is closely dependent on monitoring distance, for example, at 1 km, spatial resolution is 1 cm, but at 37 km, spatial resolution is 17 m [23, 26, 27]. Studies indicate that optical fiber Raman scattering-based sensors can be used for temperature monitoring at distances 26 km away using SMF with a precision of 3 C and spatial resolution of 1 m [28]. Using graded-index few-mode fibers (GI-FMF), monitoring can be conducted for distances up to 25 km with a precision of 1°C and spatial resolution of 1,13 m [28, 29, 30].

The discovery of FBG significantly promoted the development of the optical fiber sensor and telecommunications industry. FBG is produced by modifying the refractive index within the core of an optical fiber (along the longitudinal axis). FBG has a wide range of applications, for example, in dispersion compensation, optical filters, optical fiber amplifiers, lasers, multiplexors, demultiplexers, sensors, and other solutions [31]. The reflected Bragg wavelength is sensitive to various physical parameters, so FBG can be used as an optical sensor to monitor and determine changes in physical parameters over time. FBG sensors as in quasi-distributed architecture, allow for simple multiplexing – using them in sensor network solutions (typically, approximately 100 sensors, but using CDM-WDM allows achieving the array of up to 1000 sensors) [32]. The spatial resolution of FBG sensors is equal to the grating length (typically, 2–10 mm, in rare configurations reaching up to 20 mm). The sampling frequency for standard optical sensors signal interrogation unit is up to 1 kHz; in rare cases, it reaches 5 kHz. FBG sensors can be used in various industries to measure and monitor temperature, strain, movement, pressure, vibration, and other physical parameters. FBG sensors tend to be most commonly used (2/3 of cases) in structural health monitoring (e.g., bridges, dams, roads, buildings, pipelines, etc.) [10, 23, 33].

2.3 Fiber optical sensor classification

To recognize the role and impact the optical sensors have on the monitoring and telecommunication sector, it is essential to classify them according to operational principle, spatial position, and field of application [6, 34, 35].

Based on operational principle or modulation type, sensors can be classified as [36, 37, 38]:

• Intensity-modulated sensors: Change of measured parameter is determined by intensity;

• Phase-modulated or interferometric sensors: Change of measured parameter is determined by the phase of signal;

• Polarization-modulated or polarimetric sensors: Change of measured parameter is determined by polarization change;

• Wavelength or spectrometric sensors: Change of measured parameter is determined by wavelength [6].

Based on the response to the measurement point sensors can be classified [36, 37, 38, 39]:

• Point sensors: Measurement is performed at one point;

• Quasi-distributed scattered sensors: Measurements are performed at multiple points (sensor network);

• Distributed scattered sensors: The entire length of fiber operates as a sensor network.

Based on specific applications, field sensors can be classified as [36, 37, 38]:

• Physical (temperature, pressure, deformation, velocity, etc.);

• Chemical (pH level, gas analysis, spectroscopy, etc.);

• Biomedicine (blood flow, glucose level, etc.).

2.4 The application of FBG sensors

The application flowchart of FBG sensors, based on the parameters monitored by the sensors, is shown below in Figure 2. Most commonly, FBG sensors are used for strain and temperature monitoring of various roads [40, 41, 42, 43], railways [44, 45], buildings [46, 47, 48], composite materials [49, 50], and healthcare facilities [51, 52].

Figure 2.

Developed FBG FOS category model based on the main measured parameters and SHM, as well as security applications.

For instance, when FBG FOS are applied for monitoring needs of the railways, motorways, buildings, and composite materials, commonly deformation sensors are mainly used for object’s/infrastructure’s structural monitoring [45, 46, 47, 50], whereas in medicine [52, 53] for physiological monitoring of as well as monitoring of the respiratory and cardiac [51] related aspects.

Optical FBG temperature sensors can also compensate for induced temperature changes and their influence on the measurements of other physical parameters being monitored with such technology such as FBG strain, movement, vibration, pressure, etc. sensors. Temperature [54, 55] as a primary measurement can also be monitored with the FBGs, and such an approach can be utilized for structural health monitoring (SHM) and security [47, 54] solutions.

As for the FBG vibration sensors, such are used mainly in the oil and gas industry [56], SHM [57, 58], as well as in 2D and 3D vibration monitoring solutions [57, 59, 60].

In turn, FBG pressure sensors are used in pipeline [61], tank [62], and borehole [63] monitoring. Research results often report on additional types of developed pressure (2D and 3D) sensors [64, 65] for monitoring purposes.

FBG displacement sensors are classified by the range into micro-displacement (l = 0–10 mm) and movement (l > 10 mm) sensors. Micro-displacement sensors are less common as they monitor structure [66, 67] and soil [68] movement. In turn, movement sensors are used in industrial applications [69, 70], railway [71], and health care [61] solutions, as well as in the monitoring of building structures [72, 73] and ground movement [67, 74].

From our analysis, it is possible to evaluate that the FBG technology is a topical part of the FOS solutions within a variety of modern and industrial applications and monitoring solutions; therefore, it is important to address core component grating profile research and development to further improve and advance their applications within the SHM and perimeter monitoring solutions.

3. Analysis and design of FBG for the FOS solutions in SHM applications

By using optiwave system’s “OptiGrating” software, the properties of the FBG were examined in the simulation environment. This software provides a variety of alternatives for the analysis and design of common grating-aided fibers and waveguides. Apodization type, index modulation, grating length, grating form, and period chirp are all adjusted during the construction of a Bragg fiber grating. The application can be used to do numerical simulations after such a device configuration is carried out. Solving coupled-mode equations, which explain how guided modes interact, is the foundation of these simulations. The transfer matrix method (TMM) is utilized to solve the coupled-mode equations. An overview of coupled-mode theory (CMT) for optical waveguides is presented by focusing on coupled optical waveguide analysis. It is applied to understand and examine the interplay of various light modes inside a waveguide. When there are many modes present in a waveguide, the waveguide’s shape or refractive index variation may have an impact on how the modes interact. CMT uses mathematical formulas to depict the amplitudes of these various modes as they go through the waveguide. The energy transfer between modes and the amplitude changes with distance [75].

This concept makes the research of near resonance directed mode interaction possible. Furthermore, the coupled-mode equation may be solved using the TMM if the application has numerous gratings plus phase shifts. The study of nearly periodic gratings may also be done with TMM. The whole structure of the transfer matrix may be obtained by multiplying all the separate transfer matrixes, as shown by our researchers [76].

While FBG sensors have been widely employed for many applications, their implementation to enhance the performance of optical transmission links has transformed the communications sector. Researchers are using cascaded FBG (CFBG) structures to improve optical communication systems’ performance by lowering the laser source’s spectrum breadth and, therefore, the dispersion [77]. Because apodized grating offers excellent side-lobe suppression and improved filtering efficiency, apodized FBGs have been created and used extensively in optical fiber technology. An apodized periodic grating’s reflection spectrum closely resembles the applied apodization profile’s Fourier transform. Therefore, improved side-lobe suppression and higher grating performance are the outcomes of smooth and tight apodization [78].

Due to FBG’s technological capabilities allowing for a certain reference wavelength inscription, light propagation in fiber is reflected in accordance with the Bragg wavelength. The combination of its component parts forms the entire reflected light, and this is only feasible if the Bragg condition given by the following equation is met: [79]

$${\lambda }_B=2·\Lambda ·n_{\mathit{eff}}$$E1

where n_eff is the effective refractive index of the fiber core, λ_B is the Bragg wavelength, and Λ is the grating period that establishes the separation between two consecutive grating planes. Along the grating length, the refractive index changes regularly as follows:

$$n_{\mathit{eff}}\left(z\right)=n_0+f\left(z\right)·{\mathit{\Delta n}}_{\mathit{ac}}\left(z\right)·\mathit{cos}\left(\frac{2\pi ·z}{\Lambda }+\theta \left(z\right)\right)+n_2·E^2\left(z\right)$$E2

where n₀ is the refractive index before grating inscription, Δn_ac is the refractive index modulation amplitude, z is the position, f(z) is the apodization function, θ(z) = (2π/Λ)Cz² is the chirp function, C is the chirp parameter, E(z) is the electric field, and n₂ is the nonlinear Kerr coefficient [78].

In this work, the main apodization profiles we have investigated are given below:

• Gaussian [78]:

$$f\left(z\right)=exp\left(-4·ln\left(2\right)·{\left(\frac{2·\mathrm{z}-\mathrm{L}}{L}\right)}^2\right)$$E3

• Tan hyperbola [80]:

$$f\left(z\right)=0.5\left[1+\mathit{tanh}\left(\beta \left(1-2{\left(\frac{2z}{L}\right)}^{\alpha }\right)\right)\right]$$E4

• Uniform [80]:

$$f\left(z\right)=1$$E5

• Nuttall:

$$f\left(z\right)={\mathrm{a}}_0-{\mathrm{a}}_1·cos\left(2·\mathrm{\pi }·\frac{z}{L}\right)+{\mathrm{a}}_{2}cos\left(4·\mathrm{\pi }·\frac{z}{L}\right)-{\mathrm{a}}_3·cos\left(6·\mathrm{\pi }·\frac{z}{L}\right)$$E6

where a₀ = 0.3635819, a₁ = 0.4891775, a₂ = 0.1365995, and a₃ = 0.0106411 are Nuttall coefficients, L is the grating length, and z is the coordinate of light propagation along the length of FBG [78].

In this practical experiment, where all OptiGrating simulations were carried out, the typical parameters of single-mode optical fiber with a core diameter of 8.2 μm and a cladding diameter of 125 μm were set. The central wavelength of each grating for FBG is set to 1550 nm.

In this experiment, different grating parameters were obtained from various FBG-reflected signal spectrums. In this experiment, we investigated FBG apodization performance to obtain an optimized reflection spectrum with high reflectivity (greater than 90%) and effective side-lobe suppression based on reflectivity level, full width at half maximum (FWHM) (less than 0.2 nm), and side-lobe suppression (SLS) (at least 20 dB) across various values of grating length, modulated refractive index (MRI), segment numbers, and different apodization profiles. In general, reflectivity (%), bandwidth (nm), and SLS (dB) are the three primary factors that need to be regulated while developing the FBGs. The research findings suggest highly efficient FBG grating apodizations that can be physically implemented for optical sensor networks and long-range (more than 40 km) structural health monitoring applications. Because reflectivity depends on both grating strength and length, the grating length may be adjusted to increase signal reflectivity. The following formula can be used to determine the signal’s reflectivity [76]:

$$\text{Reflectivity}\left[\%\right]={10}^{\frac{P_{\mathit{max}}\left[\mathit{dB}\right]}{10}}$$E7

where P_max is the maximal signal power of the reflected signal spectrum.

SLS depends on the value of the side-lobe layer and the peak power value.

In this work, we have analyzed the signal spectrum at different grating lengths from 1 to 20 mm. While varying the grating length, different grating modulation indices were also set to get the optimal values of reflectivity, bandwidth, and side-lobe suppression of the spectral data. The modulation indices, which were set to determine the optimal values of the FBG sensors’ key parameters are Δn = 1.5 × 10⁻⁵, Δn = 2.5 × 10⁻⁵, Δn = 5 × 10⁻⁵, Δn = 15 × 10⁻⁵ and Δn = 25 × 10⁻⁵. The refractive index modulation is consistently raised and uniformly decreased over the length of the FBG, which is an essential point to be emphasized based on the apodization approach. However, an increase in the overall grating length could be necessary to obtain a certain peak (reflectivity) of the reflected signal in this design.

3.1 Bandwidth versus grating length of FBG with apodizations

While testing the Gaussian apodization, FBG bandwidth decreases by increasing the grating length. For modulation indices 1.5 × 10⁻⁵, 2.5 × 10⁻⁵, and 5 × 10⁻⁵, the bandwidth is the same, and the initial bandwidth - 1.072 nm, which is higher than the required threshold bandwidth, see Figure 3. However, increasing the grating length helped to reduce the bandwidth. It was less than 0.2 nm when the grating length was 7 mm, and it gradually decreased to 0.048 nm at 20 mm. For 15 × 10⁻⁵, the bandwidth with the grating length of 1 mm was 1.072 nm, but then, with the increment of grating length, it started to decrease. It reached 0.176 nm at 7 mm grating length and 0.128 nm at 20 mm. For 25 × 10⁻⁵, the bandwidth at 1 mm grating length was 1.088 nm, which was too high. After increasing the grating length, it fell less than 0.2 nm at 15 mm grating length (0.128 nm) and remained constant till 20 mm grating length.

Figure 3.

Bandwidth versus grating length for Gaussian apodization profile simulation in Bragg grating profile.

For hyperbolic tangent apodization (Figure 4), the bandwidth for modulation indices 1.5 × 10⁻⁵ and 2.5 × 10⁻⁵ were almost the same. The bandwidth with the grating length of 1 mm was 0.72 nm, reaching 0.144 nm at a 5 mm grating length. From 5–20 mm grating length, the bandwidth was between 0.144 and 0.032 nm, which is below 0.2 nm. For 5 × 10⁻⁵, the bandwidth was 0.144 nm at 5 mm grating length, dropping to 0.048 nm at 20 mm grating length. For 15 × 10⁻⁵, the bandwidth was comparatively higher than 1.5, 2.5, and 5 modulation indices. Its lowest bandwidth at the grating length of 20 mm was 0.128 nm, which also fell within the required range. For 25 × 10^–5, the bandwidth was high till the grating length was 20 mm. At 15 mm, the bandwidth increased to (0.256 nm) and remained almost constant till 20 mm grating length.

Figure 4.

Bandwidth versus grating length for hyperbolic tangent apodization profile simulation in Bragg grating profile.

For Nuttall apodization (Figure 5), the bandwidth was too high initially for all the modulation indices (around 1.55 nm). For 2.5 × 10⁻⁵, the bandwidth dropped to half when the grating length was increased. It reached <0.2 nm at 9 mm grating length and continued reducing till 20 mm grating length (0.08 nm at 20 mm grating length). For 5 × 10⁻⁵, the bandwidth reached the required threshold at 9 mm grating length, with a value of 0.176 nm. The bandwidth was very small at 20 mm grating length, around 0.08 nm. For 15 × 10⁻⁵, the bandwidth we achieved was 0.14 nm at 9 mm grating length, and it remained constant till 20 mm grating length. There was a slight rise at 13 mm (0.16 nm), then again, it dropped to 0.14 nm. For 25 × 10⁻⁵, the bandwidth never dropped down less than 0.2 nm. It reached 0.2 nm at 17 mm grating length and remained constant till 20 mm grating length.

Figure 5.

Bandwidth versus grating length for Nuttall apodization profile simulation in Bragg grating profile.

3.2 Reflectivity versus grating length of FBG with apodizations

The coherence between reflectivity, grating length, and grating modulation index of FBG gratings is evident in Figures 6–8. From the Gaussian apodization graph, with the gradual increment of grating length, reflectivity in % increases.

Figure 6.

Reflectivity versus grating length for Gaussian apodization profile simulation in Bragg grating profile.

Figure 7.

Reflectivity versus grating length for hyperbolic tangent apodization profile simulation in Bragg grating profile.

Figure 8.

Reflectivity versus grating length for Nuttall apodization profile simulation in Bragg grating profile.

For the modulation index Δn = 1.5 × 10⁻⁵, the reflectivity is too low (the highest value is 5.64%). For grating length 1–5 mm, it remains close to 0%, which means Gaussian apodization requires higher modulation indices to achieve the defined threshold reflectivity. For 2.5 × 10⁻⁵, it shows slightly better results compared to 1.5 × 10⁻⁵. Still, it does not reflect the spectrum any closer to 90%. With a 20 mm grating length, its highest reflectivity is 14.66%. If we observe the reflectivity for 5 × 10⁻⁵, it is noticeable that it shows better results compared to other modulation indices. The lowest reflectivity for a grating length of 1 mm is 0.16%; however, when the grating length is gradually increased, it rises to 44.6%, which is still not suitable for such FBG sensors. If we observe the reflectivity in % for modulation indices of 15 × 10⁻⁵ and 25 × 10⁻⁵, they show improved results. For both modulation indices, the initial reflectivity was approximately 1%. However, the rise in grating length led them to achieve higher reflectivity (>90%). For 15 × 10⁻⁵, the reflectivity reached 90% when the grating length was 17 mm, while for 25 × 10⁻⁵, it reached 90% when the grating length was 11 mm and it continued to rise.

For hyperbolic tangent apodization (Figure 7), modulation indices of 1.5 × 10⁻⁵, 2.5 × 10⁻⁵, and 5 × 10⁻⁵ could not achieve the required reflectivity even after increasing the grating length (at 20 mm, the highest reflectivity was 18.07, 40.83 and 82.35%, respectively). Though the reflectivity increased gradually with the rise of grating length, it could not reach a reflectivity greater than 90%. For 15 × 10⁻⁵ and 25 × 10⁻⁵, the recommended reflectivity was obtained with the increase in grating length. For 15 × 10⁻⁵, it gained reflectivity of 93.49% at 9 mm grating length, and it increased to 99.95% at 20 mm grating length. For 25 × 10⁻⁵, the required reflectivity was gained at a 5 mm grating length (91.29%), and it reached 100% at 15 mm.

For Nuttall apodization (Figure 8), a modulation index of 1.5 × 10⁻⁵ did not provide any significant result as it was too small to produce any values. Therefore, a modulation index of 2.5 × 10⁻⁵ was used as a simulation starting point. With the grating length of 1 mm, the reflectivity achieved was 0.02%. However, after increasing the grating length to 20 mm, it showed only 7.27%. For 5 × 10⁻⁵, when the grating length was increased, the reflectivity also gradually increased, and at 20 mm, it reached 25.29%, which is also unacceptable. For 15 × 10⁻⁵, the reflectivity with the grating length of 1 mm is 0.69%, but after setting up the grating length to 3 mm, it rose to 5%. It was increasing with the increment of grating length, and at 20 mm, it reached 86.51%. The reflectivity reached the aimed value after setting the modulation index to 25 × 10⁻⁵. Although the initial value was 1.89%, the rise of grating length helped to achieve 93.88% (at 15 mm), it rose to 98.43% (at 20 mm).

3.3 Side-lobe suppression versus grating length of FBG apodizations

By increasing grating length, the side-lobe suppression of Gaussian apodization decreases. The achieved SLS was almost the same for modulation indices 1.5 × 10⁻⁵, 2.5 × 10⁻⁵, and 5 × 10⁻⁵. The SLS was approximately 37 dB when the grating length was 1 mm, and after increasing the grating length, the SLS started dropping slightly. The highest drop (∼3 dB) can be observed at 5 mm grating length (dropping from 37 to 34 dB). After that, it decreased relatively slowly and reached almost 32.5 dB (for 5 × 10⁻⁵ index) at the grating length of 20 mm.

For 15 × 10⁻⁵, the SLS with 1 mm grating length was 36.98 dB, and after increasing the grating length, it continued dropping and reached 26.28 dB at 20 mm. For modulation index 25 × 10⁻⁵, the initial SLS was 36.86 dB, and by increasing the grating length, the SLS fell to 21.93 dB at 20 mm, see Figure 9.

Figure 9.

Side-lobe suppression versus grating length for Gaussian apodization profile simulation in Bragg grating profile.

For hyperbolic tangent apodization (Figure 10), no modulation could reach the threshold value for SLS (at least 20 dB).

Figure 10.

Side-lobe suppression versus grating length for hyperbolic tangent apodization profile simulation in Bragg grating profile.

For 1.5 × 10⁻⁵ and 2.5 × 10⁻⁵, the initial SLS value was almost 13.6 dB. After increasing the grating length, the SLS value did not decrease drastically. At 20 mm grating length, the SLS was 13.39 dB for a modulation index of 1.5 × 10⁻⁵ and 12.68 dB for 2.5 × 10⁻⁵. For 5 × 10⁻⁵, 15 × 10^–5, and 25 × 10⁻⁵, the starting value with a 1 mm grating length was around 13 dB. However, after increasing the grating length, it changed dramatically. With 20 mm grating length, the SLS was 9.7 dB for Δn = 5 × 10⁻⁵, 3.9 dB for Δn = 15 × 10^–5, and 2.42 dB for Δn = 25 × 10⁻⁵, which is not suitable for FBG sensors and remote monitoring in such SHM solutions.

Figure 11 shows SLS vs. grating length for Nuttall apodization. The SLS is very high for all the modulation indices, around 59 to 60 dB. For 2.5 × 10⁻⁵ and 5 × 10⁻⁵, the SLS fluctuated a lot within the range of 59 to 61 dB while increasing the grating lengths. For 15 × 10⁻⁵, the SLS was gradually decreasing, and it reached 52.54 dB at 20 mm grating length.

Figure 11.

Side-lobe suppression versus grating length for Nuttall apodization profile simulation in Bragg grating profile.

For 25 × 10⁻⁵, SLS also decreased smoothly till 11 mm grating length, but at 13 mm grating length, it rose from 53 to 57 dB, and then again it continued to decrease and reached 54.45 dB at 20 mm. Such a pattern of sudden SLS increase (while increasing the grating length) and then again a decrease of the SLS while further increasing the grating length can be noticed due to the periodical function of SLS. Thus, when using even higher modulation indices than shown here, even more noticeable shifts in SLS values can be observed. Similar tendencies in a scientific journal article [76] and conference paper [81], where a modulation index of 2 × 10⁻⁴ [76] and 4 × 10⁻⁴ [81] is used and well seen when the SLS vs. grating length function is periodical.

3.4 Comparison analysis of apodization profiles

A modulation index of 15 × 10⁻⁵ was used for the comparison to more thoroughly examine and evaluate the FBG characteristics such as reflectivity (Figure 12), bandwidth (Figure 13), and SLS (Figure 14), and their relationship to the apodization profiles. In the comparison, the raised sinus apodization was additionally included, which showed the highest results in the previous study [76]. Choosing 15 × 10⁻⁵ modulation depends on how all the parameters produce the required result for different apodizations.

Figure 12.

Comparison of FBG apodization profiles regarding reflectivity and grating length.

Figure 13.

Comparison for FBG apodization profiles regarding bandwidth and grating length.

Figure 14.

Comparison for FBG apodization profiles regarding side-lobe suppression and grating length.

While analyzing the signal spectral reflectivity, it can be seen from Figure 12 that by increasing the grating length, the reflectivity for all of the apodization profiles also increases. The most rapid changes are noticed for hyperbolic tangent apodization within the 1–7 mm grating length interval. Hyperbolic tangent apodization shows the highest reflectivity results (99.95% at 20 mm) in the grating length range from 0 to 20 mm. Rapid changes are also observed for the sensors with grating lengths increasing from 1–11 mm in Gaussian and raised-sine apodizations. Meanwhile, the reflectivity increases almost linearly by increasing uniform (no apodization) and Nuttall apodization FBG grating length. So, choosing a higher number of grating lengths is important to get optimal reflectivity.

Figure 13 shows that by increasing the grating length, the reflected signal spectrum bandwidth decreases for all apodization profiles.

The most rapid changes are noticed for grating length 1–5 mm for hyperbolic tangent, 1–7 mm for Nuttall, raised sine, and Gaussian apodizations. Larger grating lengths (at least 7 mm) for FGBs should be selected for operating with a smaller bandwidth to preserve the optical frequency spectrum band. When grating lengths are selected between 1 and 7 mm, Gaussian provides the narrowest bandwidth, followed by hyperbolic tangent and Nuttall. As for the gratings between 9 and 20 mm in length, the narrowest bandwidth can be reached by applying the Gaussian and then hyperbolic tangent apodizations. The longer grating lengths for FGBs should be used to offer FBG with a smaller bandwidth (FWHM <0.2 nm) and high reflectivity (at least 90%).

Yet longer FBG gratings do not necessarily imply greater values for the SLS parameter (Figure 14). Therefore, it is essential to evaluate the most suitable FBG settings for each kind of grating. For hyperbolic tangent, the SLS is relatively low, around 13.48 dB. When the grating length increases, the SLS starts to decrease and at 20 mm, it reaches 3.91 dB. For Gaussian, the SLS falls abruptly for 1–5 mm grating length. After that, it decreases less, and at 20 mm grating length, the SLS is 26.28 dB. For Nuttall, the SLS is highest with a 1 mm grating length (60.69 dB). After that, it continuously decreases, and at 20 mm grating length, it reaches 52.54 dB.

4. Conclusions

In this study, we evaluated and analyzed the optical sensor and FBG, particularly integration solution possibilities in SHM applications. A clear and continuous increase in topicality trend could be observed. Additional analysis and segregation of the most topical FBG optical sensor types and SHM applications were conducted. This was done by segregating them based on the main measured parameters (such as pressure, temperature, vibration, displacement, and strain), as well as based on the modulation principle (intensity, phase, polarization, wavelength), and placement (point, quasi-distributed, distributed).

We also showed the simulation of multiple SHM potential grating apodization profiles (Gaussian, hyperbolic tangent, Nuttall). From the calculated data and set key performance indicators (reflectivity >90%, FWHM <0.2 nm, and SLS at least 20 dB), a comparison was made regarding various modulation indices, grating lengths, and apodization types. All of the three apodizations profiles with longer (9+ mm) grating lengths could reach a set 0.2 nm bandwidth. However, a slight advantage could be noticed when applying hyperbolic tangent and Gaussian apodizations. Reflectivity-wise, hyperbolic tangent apodization also shows a steeper rise while increasing the grating lengths, yet raised-sine and Gaussian apodizations can still reach the set 90% reflectivity rate. From the perspective of SLS, the increase of the grating length does not offer any such advantages, and all of the apodizations show a relatively stable trend. Yet, in this aspect, the hyperbolic tangent is the least effective. At the same time, Nuttall shows the highest dB ratio. Additionally, Gaussian and raised-sine also have an acceptable level of SLS.

While Nuttal apodization could be applied in configurations where efficient SLS management is of the most importance, bandwidth-wise and reflectivity-wise, it showed the least effective performance. In turn, the hyperbolic tangent was the least effective SLS-wise, yet it performed well regarding bandwidth and reflectivity. Gaussian and raised-sine apodization profiles, while possibly not being the most efficient in any of the measured parameters compared to other apodizations, still showed the possibility of reaching certain required thresholds. Therefore, these could also be evaluated for SHM and FBG optical sensor setups that require more stable and less risk-prone operations.

Acknowledgments

The chapter covering the literature review partly includes the content available in the doctoral thesis in the Latvian language by the same author: Janis Braunfelds. Characterization of development of the multifunctional fiber optical sensing system and its application in monitoring solutions. 2023. Riga Technical University. Available from: https://doi.org/10.7250/9789934229220.

Funding

This research was funded by the National Research Program within project No. VPP-EM-FOTONIKA2022/1–0001.

Data availability

The data used to support the findings of this study are available from the first author upon request.