EFFECT OF GeO 2 DOPANTS IN FBG SENSOR PERFORMANCE FOR TEMPERATURE AND STRAIN †

,


INTRODUCTION
Due to their sensitivity, dependability, low intrusiveness, galvanic insulation, and potential for quasi-distributed remote measurements, optical fiber sensors based on fiber Bragg grating (FBG) technology are used in a variety of fields, including civil engineering and aviation [1].In addition, monitoring strain [2], vibration [3] and temperature [4].
FBGs are extensively utilized in optical sensing and can compete with traditional electrical strain gauges to determine various parameters, such as temperatures, strain, refractive index, pressure, gas, etc.Furthermore, FBG sensors have been widely recognized for their features such as erosion resistance, resistance to electro-magnetic (EMI) and radio frequency interference, and ability to operate in harsh environments where traditional sensors cannot [12].
Since more than few decades, FBG sensors have meets a lot of attention in the field of structural health monitoring [13] [14].Earlier application of these types of sensors is load screening and characterizing absolute strain and temperature variations, either individually [15] or at the same time [16].Changes in average strain and temperature would primarily cause a change in the location of the resonance wavelength of the FBG output due to their linear wavelength shift response [17].The whole reflection spectra of the sensor output signal are, however, affected by the strain (or even temperature) field.
The shape and wavelength shift of the reflection spectra were measured and studied by simulation in this study to investigate the impacts of strain and temperature changes dispersed along the length of FBG sensors.Under these two circumstances, shifts were examined using various FBG architectures.
More benefits than that mentioned above are recorded to FBG based sensors, such as small size, light weight, high resolution, multiplexing capability, and immunity to electromagnetic fields.They have been used in biological diagnosing and structural health monitoring [18].Due to its uniquely intelligent physical properties, such as its innately huge multiplexing capacities, remote sensing, resistance to electromagnetic fields, and safety, the uniform FBG sensor has been extensively used in sensing applications [12].The UFBG sensor are also used in dynamical spectral filters invented inside fibers [19].

THEORETICAL CONCEPTS
The FBG transmits all wavelengths of light while reflecting some due to the periodic (or aperiodic) disruption in the refractive index of its core, known as gratings.The Bragg wavelength, at which there is the most reflection, can be determined by applying the following equation [15]: where n eff is the effective refractive index of the grating and Λ is the grating period.
Strain has two distinct impacts on a Bragg grating.First, the grating's Bragg wavelength will shift as a result of the alteration in the physical distance between succeeding index modulations.Second, a change in refractive index brought on by the strain-optic effect will result in a shift in the Bragg wavelength.For a specific change in strain, the change in a Bragg grating's center wavelength is given by [20]: where  is the effective length.
An optical fiber's strain effect is depicted in equation ( 2).This is consistent with a shift in grating spacing and the strainoptic-induced shift in refractive index.[20].Under the condition of a uniform strain along the optical fiber axis and no temperature changes, the wavelength shift is related to the strain via the elastic-optical coefficient  [20]: Equation ( 3) points out that the resulted shift in Bragg peak wavelength is linearly proportional to the applied strain.In the sensing theory of FBG, the strain value should be expressed as; where  is the strain along the lengthwise direction of the fiber and  is an effective strain optic constant, which is defined as [1]: Such that  and  are strain-optic tensor two components, and  is the ratio of Poisson.For a typical Germano-Silicate optical fiber, p 11 = 0:113, p 12 = 0:252, = 0:16, and n eff = 1.45, giving [21]  = 0:213.

SIMULATION PART Selection for refractive index concentration by COMSOL Software
By applying the last values in eq. ( 5), we got the value of  (effective strain optic constant).The calculated value of  was then used in eq. ( 3) for the specific wavelengths 1550, 1600, and 1650 nm for each strain value (0.005, 0.006, 0.007, 0.008, 0.009).Finally, we got the values of shift in wavelength for each value of strain, and for each wavelength, as shown in tables 1, 2, and 3. Via COMSOL simulation, numerical Finite Element Method (FEM) has been used for the modal analysis of an optical fiber.This fiber is designed to investigate the effect of doping concentration of both core and clad silica glass to the application as a sensor.The variation of the effective refractive index has a significant impact on the sensitivity of such fiber sensors.The influence of doping silica optical fiber with Ge in a different concentration.Also doping concentration effect on effective refractive index and optical intensity has been.The refractive index has been calculated for the doped silica fiber with Ge samples by Sellmeier formula: For dopants GeO 2 , n is the optical index at light wavelength  and  is a constant such that  ,  ,  and A 1 , A 2 , A 3 are called Sellmeier coefficients to be determined by the fitting process.This means measuring the refractive index of the medium at least for six different wavelengths.In this study, identical last coefficients are calculated, to approximate the dispersion curve.

Measurement of temperature by FBGs
Measurement of temperature, a crucial parameter in various sectors of industry, can be done with the help of FBGs.As reported by Ref. [22], both low and high temperatures can be measured using FBGs with equal accuracy.However, practically measurement of high temperature with FBGs poses some additional challenges compared to others.In this section, we shall discuss the FBG-based temperature sensors subjected to no variation in other physical parameters of the FBG.

Analytical formulation for temperature measurement
The Bragg wavelength () of an FBG can be expressed as [23] [17]: Hence, a small change in operating temperature T will result a change in the peak wavelength which can be represented as [17]: So, the change in the temperature can be retrieved directly from  [24]: Therefore, it is possible to control the mechanical and thermal expansion coefficients by changing the cross-section characteristics.It is important that the packaging allows for a limited range of temperature variation.At high temperatures approaching the melting point of the packaging material, the packaging starts to distort whereby the Young's modulus begins to change and thus the thermal expansion coefficient will no longer exist.The work has been done on achieving the highest sensor sensitivity [25].

Simulation set-up design for FBG operation by Optisystem software
As given in Figure (1), a VCSEL laser source with 1550 nm operation wavelength is selected to submit the optical signal.This source is followed with a directional coupler with equivalent splitting ratio.One of these two new paths is considered as a reference path, while the remaining path represents the tested path.Both reference and tested paths include a distinct FBG, i.e., the refence one contains a standard Uniform FBG sensor, the remaining path contains a laboratory Nonuniform FBG sensor.Two types of observation tools are connected, which are, Optical spectrum analyzers (OSA) and optical time domain, virtual oscilloscopes (OTV) both for track the development for passed signals during the experiment conditions variations.

RESULTS AND DISCUSSION
The two types of suggested FBGs have identical constant Bragg wavelengths before the application of the external environmental effect.Original effective length in the software is changed by values 10, 20, 30 all in mm units.The selected effective refractive index for both FBGs is n eff =1.45, with length of 2mm.

Measurements for UFBG Effect of strain on sensing wavelength shift
Three Bragg wavelengths ( .) for investigated FBG sensors were tested, these wavelengths are: 1550, 1600 and 1650 nm.Calculations for the deflected wavelength shift is carried out manually and individually for each wavelength by using of eq. ( 5).Where the measured shifts are resulted from the virtually applied strain.The latter effect selected values are: (0.005, 0.006, 0.007, 0.008, 0.009, 0.01) µm, as shown in tables 1.According to calculated results for sensitivity given in table (4), the selection is located at the maximum value, which is 5.7 pm/ 0 c which corresponds to 1550 nm.A strain-wavelength A strain-wavelength relation, with an effective wavelength of 1.45, is plotted in Figure (2), and the resultant shape is followed by a linear fitting.Accordingly, from Figure (2), part A, 1550 nm, the maximum measured sensitivity value is (5.7) corresponding to wavelength (1550) with a sensitivity of 5.7 pm/ 0 c, while in the same figure, part B, 1600nm, the maximum measured sensitivity value is (2.6) corresponding to wavelength (1600) with a sensitivity of 2.6 pm/ 0 c, finally in part C, 1650nm, the maximum measured sensitivity value is (1.77) corresponding to wavelength (1650) with a sensitivity of 1.77 pm/ 0 c.

Effect of temperature on sensing wavelength shift
In current study, the stabilization of type I gratings complies with telecommunication requirements, thus the selected temperature range is 20-60 o C, this is based on range given in Ref. [26].In the following Figure (2), deflected measured Bragg wavelength shift is plotted against sensitivity for seven temperature values, all ranging from 20 to 60 o C. The FBGs parameters are as follows: effective refractive index of 1.45, length 2mm, wavelength of 1550nm.The temperature and wavelength are changing as given in Figure 3

Measurements of NUFBG Effect of temperature on sensing wavelength shift
In this section, insertion of a signal of 1550 nm wavelength into the input of NUFBG has been carried out where the FBG has specific active lengths; 10, 20, and 30mm and a constant effective refractive index of 1.45 with variable applied temperature.Results observed from the deflection side give different responses, as shown in Figure (5) and its entire subfigures A, B, C and D based on equation (6).As shown in part (A), the FBG active length was 10mm from T=20.1264 o C to T=59.9646844 o C, but the wavelength ranged from 1.54989965 nm to 1.54996984 nm, as shown in part (A).The FBG active length was 20 mm from T = 20.1264525o C to T = 59.9646844 o C in part (B), but the wavelength ranged from 1.54992244 nm to 1.54984271 nm in part C. Finally, in part D, after doping, the effective refractive index is constant at 1.46 with variable applied temperature gives different responses as deflected wavelengths from T=19.8416496 o C to T=5 8735 o C. The wavelengths are 1.54996967 nm to 1.54984357 nm.

EEJP. 3 (2023)
Wasmaa A. Jabbar, et al.These results indicate the existence of three types of behavior functions followed by the NUFBG under the influence of applied temperature.In the dopant case, these two functions are Boltzmann and sine in additional logarithm.Under the influence of variable applied temperature, we expect to meet a different response than that measured by UFBG.Previous results shown in Figure (3), indicates the response with only a sine function.

Effect of temperature on sensing power
In the case of measuring power instead of wavelength, the results for NUFBG response indicate variant Gauss functions depending on active sensor wavelength, shown in Figure (6).In comparison to last section results, in which the response obeys varied functions.For the same previous setup, transmitted spectrum power is measured for each applied temperature.Observed values for temperature and wavelength is shown inside part (A) from that figure, for the original length of 10 mm.While in part (B) and (C), another observed value is diagnosed.With comparisons by Ref. [27], the current combination is 1.5 times larger sensitivity than it.Uniform and nonuniform FBG Sensor design of (L=10mm) active length with Bragg wave length 1550 nm tested under temperatures (20-60 o C) with step 10 degree.Where the values plotted in figure (7) are drawn from radio frequency spectra for all tested values which is given in figure (8).In which the frequency shift is easy to observe versus the changed parameter in comparisons with multi regions FBG that experimentally investigated by Ref. [6].CONCLUSIONS Constructing FBG combination improves the sensing properties for the FBG sensor.Uniform and non-uniform FBGs plays the role of precise filter to the temperature and strain fluctuations.The sensitivity becomes high with introducing impurities of GeO 2 dopants.Results for shifted wavelength -applied temperature for a NUFBG shows variations from Poltizman to Log.Functions, while the same measurements for power-temperature relations for lengths shows behaviors fluctuated within one function which is a Gauss function.

Figure 1 .
Figure 1.Simulation set-up for the investigated design.

Figure 3 .
Figure 3. Results for temperature -shifted wavelengths with changed sensor temp.(A) L=10mm, (B) L=20mm, (C) L=30mm (D) after dopping For the same previous set-up, the transmitted power spectrum is observed separately for each FBG applied temperature.Results are given in the following Figure (4), with which transmitted power behavior fluctuates from sine function to Gauss.The temperature and wavelength are changed as the following form: in part (A) for the original length 10mm from 20.0353156 to 60.1583504 o C, but the transmitted power (TR) was changed from TR=8.96362864 to 9.02625248 o C. In part (B), for the original length of 20mm, T is changed from 20.0353156 to T=60.0672135 o C, but the transmitted power is changed from TR=8.49448061 to 8.5161336 o C. Finally, in part (C), T is changed from 20.4226475 to 60.0672135 o C, while the transmitted power is changed from TR = 7.4483448 to 7.45740164 o C.

Figure 7 .
Figure 7. Measured values of wavelengths and intensity for uniform FBG before and after doping

Table 1 .
(2)oretical computed wavelengths shift for tested UFBGs sensors  Results for the first run measurements are given in the following table(2)and resulted relations are shown in the next Figure(2).

Table 2 .
Calculated sensitivity for indicated UFBGs sensors  .
Figure 2. Resulted for strain -wavelength relations to the tested UFBGs sensor.
(A), for an original length of 10 mm.Temp.values range from 20.3331 to 60.067 o C, while wavelengths range from 1.549976 nm to 1.54995272 nm.While in the same figure, part (B), for the original length of 20mm, T values range from 20.0353 to 60.0672135 o C, but wavelength range from 1.54997726 to 1.54997686 nm.In part (C) from the same figure, for an original length of 30mm, the temperature ranges from 19.9327865, to 59.9646844 o C, but the wavelength is now ranging from 1.54991417 to 1.54995338 nm.In part (D), after doping, T values range from 20.0353156 to 59.8735475 o C, but wavelengths range from 1.54984538 to 1.54984468 nm.