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Abstract
In this paper, we present a simple cascaded Fabry-Perot interferometer (FPI) that can be used to measure in real-time the refractive index (RI) and length variation in silica optical fibers caused due to external physical parameters, such as temperature, strain, and radiation. As a proof-of-concept, we experimentally demonstrate real-time monitoring of temperature effects on the RI and length and measure the thermo-optic coefficient (TOC) and thermal expansion coefficient (TEC) by using the cascaded FPI within a temperature range of 21–486°C. The experimental results provide a TEC of 5.53 × 10−7/°C and TOC of 4.28 × 10−6/°C within the specified temperature range. Such a simple cascaded FPI structure will enable the design of optical sensors to correct for measurement errors by understanding the change in RI and length of optical fiber caused by environment parameters.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Real-time monitoring of refractive index (RI) and length variation in an optical fiber induced by environmental parameters, such as temperature, strain, pressure, and radiation has been of great importance in characterizing optical devices since the birth of optical fibers [1–3]. In practice, the sensors based on optical fibers can be calibrated with the knowledge of parametric influence on the RI and length changes. For a widespread application, namely real-time temperature sensing, fiber optic sensors such as fiber Bragg gratings (FBGs) and Fabry-Perot interferometer (FPI), have been applied to measure the change in RI with temperature [3–5]. However, the thermo-optic coefficient (TOC) which is a measure of the RI change as a function of temperature maybe positive or negative, and this depends on two processes which are driven by change in temperature [6]. The density of an optical fiber may decrease with increasing temperature because of thermal expansion. Reduction in density leads to negative RI [7]. However, heating the optical fiber polarizes it significantly and increases RI [6,8]. Although these two individual mechanisms can lead to positive or negative RI, the net effect has shown to be positive for silica optical fibers [9]. The TEC, which provides the variation of length with temperature at constant pressure, is always positive for silica optical fiber and almost one order of magnitude smaller than the TOC. Several methods have proven to be effective for measuring RI and hence the TOC; these include interferometric [10,11] and prismatic methods [12,13]. However, prismatic methods are non-fiber methods, and their direct application for TOC measurement may provide inaccurate results for optical fiber. RI due to temperature and hence the TOC can also be measured by direct techniques such as refracted near-field, multiwavelength interferometry, computerized tomography, differential interference-contrast microscopy, and quantitative phase microscopy [14]. However, some of these measurements require the cut of the fiber (destructive analysis) and may not provide real-time changes of RI due to the post recovery. Recent years FBGs, FPIs, and combination of them have been used to measure the TOC and the TEC in real-time of optical fibers; however, fabrication of FBGs, inclusion of femtosecond(fs) laser, etching, and so on make sensor’s structure complex and increase the cost [3–5]. Moreover, FBG-based techniques may have temperature limitation due to the dependence on temperature for grating stability. So far, the reported values for the TOC of silica-based optical fibers using existing methods are between $3 \times {10^{ - 6}}$/°C and $2.37 \times {10^{ - 5}}$/°C at different temperatures and wavelengths [3–5, 12,15,16]. While there are several techniques for real-time monitoring of TEC and TOC of silica optical fibers currently exist, an optical structure having the following advantages such as ease of fabrication, ability to survive in harsh environment, and cost-effective are yet to be expected.
Very recent in our modeling work, a cascaded FPI to measure the RI and length due to mixed radiation has been reported [17]. In this paper, as a proof-of-concept, we experimentally demonstrate real-time monitoring of temperature effects on the RI and length and measure TEC and TOC using the cascaded FPI. The proposed structure consists of an extrinsic FPI (EFPI) and an intrinsic FPI (IFPI) as a way to accurately measure the TOC and TEC for silica optical fibers within a temperature range of 21–486°C. The EFPI can be used to measure the physical cavity length since it is air filled, and the RI of air is almost invariant with temperature. On the other hand, temperature alters the RI and the length of the IFPI for being a solid cavity made of pure silica. Because the TEC of a silica capillary tube and pure silica fiber is same, it is possible to extract the RI change from IFPI by using length in the EFPI. Due to differences in the cavities, air versus silica, the Fabry-Perot responses would be different. To separate individual signals for each cavity from the mixed signal of cascaded FPI, we apply a fast Fourier transform (FFT) algorithm to convert the wavelength domain signal to the spatial-frequency domain and then use Butterworth filters. Inverse Fourier transform is applied on the filtered signals to reconstruct the individual signal again in wavelength domain. Since the proposed structure is made of silica capillary and optical fiber, simple cleaving and splicing processes are required for the fabrication. Moreover, for being all silica structure, the cascaded FPI structure can be applied in extreme radiation environment to determine the effect of other parametric influences such as pressure and radiation as these effects are directly coupled to the RI and length changes.
2. Fabrication and working principle of cascaded FPI
Our design architecture consists of an EFPI and an IFPI as shown in Fig. 1(a), where ${L_1}$ and ${L_2}$ denote the cavity length for the EFPI and the IFPI, respectively. The interface ${M_1}$ between the lead in SMF-28 fiber and the capillary and the interface, ${M_2}$, between the capillary and the coreless (CL) silica fiber constitute the EFPI (first cavity/air cavity). On the other hand, the interface ${M_2}$ and ${M_3}$ between the CL fiber and air constitute the IFPI (second cavity/silica cavity). One additional cavity is called the hybrid cavity (third cavity/air-silica cavity), and it forms between interfaces ${M_1}$ and ${M_3}$. These interfaces work as mirrors to reflect light. In this cascaded FPI, the incoming light that reflects from interfaces ${M_1}$, ${M_2}$, and ${M_3}$ are ${I_1}$, ${I_2}$, and ${I_3}$, respectively. Then total reflection of light based on the three-beam interference can be expressed by [18] :
Fig. 1. Schematic and fabrication of cascaded FPI: (a) schematic of cascaded FPI, (b) cleaving of required fibers and capillary, (c, d) splicing and cleaving steps, and (e) microscopic image of fabricated cascaded FPI.
Fig. 2. Spectral response of fabricated cascaded FPI: (a) total reflection spectrum, (b) optical frequency domain distribution of the total reflection spectrum, (c) reconstructed cavity length of EFPI, and (d) reconstructed cavity length of IFPI.
3. Thermal effects on cavities
With the basic specifications of the two cavities determined and baseline spectrum measured, we next studied the effect of temperature on both cavities. In order to measure the TEC and TOC, the fabricated cascaded FPI was placed inside a tube furnace with endcaps to ensure no air flow. A k-type thermocouple was also placed very close to the FPI to measure the temperature at the location of the FPI in the furnace to improve measurement accuracy. A schematic of the measurement setup is shown in Fig. 3. The temperature of the furnace was increased from ambient to 486°C with a ramp rate of 5°C/min. The total reflection signal was recorded at different temperatures using the optical sensing instrument (Hyperion si255, Luna). For each measurement, a hold time of 30 minutes was used to stabilize the temperature before recording data. The recorded data were then analyzed to reconstruct the signal for each cavity discussed in Section 2. The air cavity shows a thermal expansion only with temperature because it is made of silica capillary tubes. On the other hand, the silica cavity is an IFPI, and temperature changes both the RI and the length of the cavity. These properties from both cavities can be used to measure TEC and the TOC in real time.
3.1 Thermal expansion coefficient
The TEC of an optical fiber plays a key role in optical fiber sensing technology. Although the TEC (${\sim} 5.5 \times {10^{ - 7}}/^\circ \textrm{C}$) is well defined for fused silica sample, it changes for optical fiber with temperature [3,5]. To monitor the TEC in real-time, the fabricated cascaded FPI was used. Since the EFPI is hollow and the change in air RI with temperature is very small, which calculated by the following expression [19]
where P is the absolute pressure and T is the operating temperature. In this equation, the change in RI of air with temperature is negligible because the second term in the right-hand side remains almost constant by the increased temperature and temperature-induced increased pressure because the air is sealed in a nearly constant-volume cavity. Because the spectrum of an FPI is governed by the optical length of the cavity, and for the air cavity, the effect of RI is so small as to be neglected. The length expansion of the cavity is the parameter expected to be dominant. The inner diameter of the capillary tube is of 39.2 µm, which leaves a 42.9 µm wall thickness, which experiences a length expansion. The response of air cavity at different temperatures were recorded from the experiment described above. Then the cavity length of the air cavity was calculated from the measured spectrum using the following two peak methods [20]: where ${\lambda _1}$ and ${\lambda _2}$ are the wavelengths of adjacent peaks or dips in the reflection spectrum.Because the spectrum of the air cavity contains many peaks, to retrieve the cavity length, the cavity length for each set of adjacent peaks were calculated and then averaging that. We obtained a cavity length of ∼147 µm at room temperature from the measured spectrum using the Eq. (3). The spectra of the air cavity at six temperatures – 21, 100, 197, 291, 388, and 486°C are shown in Fig. 4. Because this is an air cavity, the dip/peak wavelength shifts a small amount with temperature. As temperature expands the cavity length, the interference spectra get closer.
The cavity length at each temperature was calculated from each spectrum using the Eq. (3). Then these cavity lengths at each temperature were plotted against temperature to find the TEC, which is shown in Fig. 5. We performed the experiment twice to confirm the repeatability of the cascaded FPI structure. The solid red circles are the mean experimental data at each temperature, and the solid blue line shows the linear fitting of these data. The error bar in Fig. 5 indicates the standard deviation from the mean values. It is seen that the data follow a linear trend upward to the specified temperature range with a linear fit of ${R^2}$ of 0.9892 and root mean square error (RMSE) of 0.001678. The obtained TEC from these data was found to be $5.53 \times {10^{ - 7}}$/°C, which is in good agreement with literature values. The TEC and the temperature as a function of heating time can be seen in Supplement 1. Once the air-cavity length is known for each temperature, then the length expansion ($\alpha $) can be represented as
where ${L_{a,i}}$ is the initial air-cavity length at room temperature, and ${L_{a,T}}$ is the final air-cavity length at any temperature. Please note that the optical-cavity length and the physical-cavity length are same for the air cavity because air has an RI of 1.3.2 Thermo-optic coefficient (TOC)
The TOC is the change in RI with temperature at constant pressure. To measure the TOC real-time, the same experimental setup of Fig. 3 was used, and the experiment was repeated twice. Because the IFPI is made of coreless pure silica fiber, temperature alters both the RI and the cavity length. Therefore, the spectrum of the silica cavity contains information about both the RI and the length of the cavity. The spectrum of the silica cavity at different temperatures is shown in Fig. 6. It is seen that the spectral position changes continuously with temperature. Since the silica capillary tube and the silica cavity both are made of silica and for being very close proximity of both cavities to each other, it is expected that both the cavities will experience the same length expansion. Please note that length expansion is a relative value and always defined as the change in physical length with respect to the initial physical length. The silica cavity length expansion ($\alpha $) can be deduced by using the Eq. (5),
Because the silica-cavity length, ${L_{Si,i}}$ at room temperature, and $\alpha $ are known, the cavity length ${L_{Si,T}}$ can be calculated from Eq. (6). The optical silica-cavity length (${L_{Si,opt}}$) is also known from the measured spectrum of the silica cavity. However, ${L_{Si,opt}} = {n_{2f}} \times {L_{Si,T}}$ where ${n_{2f}}$ is the final RI of silica cavity with temperature, which can be easily deduced. The variation of RI of silica optical fiber with temperature is shown in Fig. 7. The solid red circles are the mean experimental data, and the solid blue line shows the linear fitting of these data. The error bar in Fig. 7 indicates the standard deviation from the mean values. It is seen that the data follow a linear trend upward to the specified temperature range with a linear fit of ${R^2}$ of 0.9914 and root mean square error (RMSE) of 0.0001134.The obtained TOC from these data were found to be $4.28 \times {10^{ - 6}}$/°C, which is in a good agreement with literature values reported in Refs [3–5,12,15,16]. The TOC and the temperature as a function of heating time can be seen in Supplement 1.
4. Discussions and applications
The change in length and RI of optical fiber has been measured using a simple structure, based on EFPI and IFPI. Because only silica material is used to construct the structure, it is possible to use this structure at high temperatures, unlike FBGs where grating stability depends on the operating temperature. Through this work, we have demonstrated the potential of our simple cascaded FPI structure in accurately determining the RI and length change due to an applied stimulus. In situ measurement of RI and length can find a potential application in the nuclear environment. Incoming radiation (gamma ray, neutron fluence, or both) changes the optical as well as the mechanical properties of optical fibers [21–24]. Radiation-induced attenuation (RIA) significantly affects the signal strength by creating different types of defects [25,26] whereas radiation-induced compaction (RIC) causes signal drift by compacting the material [22,27]. For optical-fiber sensors, it is the RIC over the RIA which causes temperature-measurement errors in the nuclear environment, thanks to radiation-hardened optical fibers [28,29]. If the RIC is known, it is possible to calculate the RI induced by RIC by using well-established Lorentz-Lorenz relation [30,31] and point dipole theory [32]. However, these methods only consider the RIC-induced RI change. It has also been shown that RIA, in addition to RIC, causes signal drift [33]. As a result, RIA-induced RI change must also be known to understand radiation-induced signal drift. While Kramers-Kronig relation can be used to assess the change in RI from RIA [34,35], it requires the full spectrum in a wide frequency range for which dose-dependent data are not available. Besides RIA and RIC, there may be other phenomena, like dopant diffusion, stress relaxation of fiber, temperature, and so on, which alter the RI and the length of the optical fiber [36,37] . Moreover, their individual effects on the RI and the length of the optical fiber may be different from their combined effects. Online measurement may provide the change in RI and length of optical fiber caused by any specific phenomena to which the fiber is subjected, including RIC, RIA, dopant diffusion, and temperatures. Once the individual contribution of RI and length on signal drift are known, it is possible to model an optimized sensor design to correct radiation-induced signal drift while measuring other physical parameters. Because the proposed cascaded FPI can make online measurements of the RI and length changes, it has the potential to be used in high pressure or radiation environments to compensate for signal drift.
5. Summary
An online measurement of both the RI and length of an optical fiber, using a simple cascaded FPI under different temperatures, has been performed. In the cascaded FPI, the first cavity is the air cavity, which has been used to measure the length expansion because the RI of air shows no significant change with temperature. Next, this length-expansion has been applied to the silica cavity (i.e., the second cavity) to measure the RI of this cavity. Frequency-domain optical-signal processing has been adopted to extract signals for each cavity. This simple structure, based on cascaded FPI may find application in the nuclear environment, where radiation-induced change in RI and the length of optical fiber is of utmost importance to reduce the radiation-induced signal drift’s causing measurement error in temperature monitoring when fiber-optic sensors are dedicated as temperature sensors.
Funding
Idaho Operations Office, U.S. Department of Energy (DE-AC07-05ID14517).
Disclosures
The authors declare no conflicts of interest. This work was supported in part through the Department of Energy Advanced Sensors and Instrumentation program. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the corresponding author upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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