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Abstract
A nonlinear temperature sensor was proposed drawing on dispersive wave (DW) and soliton in an in-house made silica microstructured optical fiber (MOF). Glycerin with high thermo-optical coefficient was filled into the MOF air holes as the thermal medium. Using a 1050 nm femtosecond laser as the pump source, DW and soliton were experimentally and theoretically explored for temperature sensing by detecting their central wavelength shift of 3-dB bandwidth. The results showed that the higher the average pump power, the higher the temperature sensitivity of DW and soliton. When the DW blue-shifted relative to the soliton, the temperature sensitivity of DW was higher than that of soliton, and the experimental maximum values were 0.928 nm/℃ (DW) and -0.923 nm/℃ (soliton). Our work explored the nonlinear phenomenon for optical fiber-based sensing technology and verified that both DW and soliton can be used to realize temperature sensors of high sensitivity and good mechanical strength. The sensing characteristic difference of DW and soliton revealed in this work might provide a new way for solving the cross-sensitivity of dual-parameter sensing in biological engineering, disease detection and environmental monitoring without introducing extra structural complexity.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Because temperature detection is essentially important in the fields of clinical diagnosis, food quality control and biological engineering, temperature sensing of high sensitivity, high mechanical strength and high stability has long been a key research goal [1–5]. In recent decades, optical fiber-based temperature sensors have increasingly become an investigation hotpot due to their extraordinary advantages of corrosion resistance, compact size, lightweight, immunity to electromagnetic interference, high sensitivity and fast response [6–8]. Up to now, various sensor types have been developed, such as fiber Bragg grating-based temperature sensors, surface plasmon resonance-based temperature sensors and interferometer-based sensors. However, these optical fiber-based temperature sensors usually have shortcomings such as difficult operation, easy damage, poor mechanical strength, etc., which greatly limits their application [9–12].
More recently, optical fiber sensors developed drawing on nonlinearity including four-wave mixing, modulation instability and self-phase modulation have attracted researchers’ attention because of their high superiority in the sensing field [13–16]. The generation of solitons and dispersive wave (DW) are also nonlinear phenomena commonly observed in optical fibers. Fiber-based solitons are formed in the anomalous dispersion regime by the interplay of group velocity dispersion (GVD) and self-phase modulation. Due to the nonlinear effect of stimulated Raman scattering, the frequencies of solitons can be continuously shifted to the longer wavelength region, which is well-known as soliton self-frequency shift (SSFS). When the solitons are perturbed by the third- or higher-order dispersions, the energy can be transferred to DWs located in the normal dispersion wavelength regime. The DW wavelength is governed by the optical trapping effect with respect to the optical soliton [17–18].
So far, DW and soliton have been widely investigated in optical fibers. Particularly, microstructured optical fiber (MOF), compared with traditional optical fibers, offers an ideal environment for the generation of soliton and the trapping of DW due to its variety of air holes arrangement, flexible design and easy fabrication [19–21]. Moreover, the air holes of MOFs can be filled with functional materials, the refractive index (RI) of which can change with the external physical field. For instance, temperature-sensitive materials such as organic polymer, liquid crystal and organic liquids can be adopted as the filling to help realize the temperature sensing purpose [22–25]. Commonly used temperature-sensitive organic liquids include: alcohol, glycerin, toluene, carbon disulfide, etc. Generally speaking, alcohol has a low boiling point (∼78 ℃) and is easy to volatilize, while toluene and carbon disulfide have toxicity and relative low boiling point (∼110.6 ℃ and ∼46.5 ℃). In comparison, glycerin has high thermo-optical coefficient (∼ -1.1888 × 10−4 /℃), high boiling point (∼ 290 ℃) and high safety, which has great superiority in temperature detection.
As far as we know, despite the fact that DW and soliton in MOFs have been widely applied to the development of all-optical switches, ultra-fast lasers, biological imaging and 3-photon microscopy, their usage for temperature sensing has been rarely reported [26–29]. To the best of our knowledge, the temperature sensing characteristics of the soliton-trapped DW and the sensing differences between DW and soliton have not been explored. Therefore, to develop high-performance temperature sensors, a detailed investigation and comparison, especially a thorough experimental verification concerning the DW-based and soliton-based temperature sensing technology is in urgent demand.
In this work, we conducted an in-depth study on the temperature sensing characteristics of DW and soliton. With the increase of the average pump power, the temperature sensitivities drawing on DW and soliton were both enhanced. When the DW blue-shifted relative to the soliton, the DW-based temperature sensitivity was found to be higher than the soliton-based one. Our work presented a novel idea concerning the nonlinerality-based sensing technology, and it offers a new perspective for exploring temperature sensors of simple structure, high stability, good mechanical strength and low cost.
2. Basic theory
Concerning the pulse propagation in optical fibers, both fiber dispersion and nonlinearity need to be taken into consideration. Derived from the well-known Maxwell equation, optical pulse propagation is described using the nonlinear Schrodinger equation (GNLSE) as follows [30]:
In the anomalous dispersion regime of soliton generation, the frequency chirp can be eliminated by balancing the GVD effect and the nonlinear effect. The energy of soliton can be transferred to DW located in the normal dispersion wavelength regime, which can either blue shift or red shift with respect to the central wavelength of soliton [31]. The DW frequency governed by the nonlinear PM condition can be shown by the following equation [32]:
When the third-order dispersion is mainly concerned, the frequency shift of DW relative to the soliton can be expressed as follows:
Using the perturbation methodology, the frequency shift difference between two generated soliton pulses at constant temperature can be written as:
The frequency shift difference of two DWs trapped by two solitons at constant temperature can be expressed as:
If DW occurs blue shift with respect to the soliton, namely, β3>0, then ΔωDW> Δωs; if red shift, namely, β3<0, then ΔωDW< Δωs.
Due to the thermo-optic effect and thermal expansion effect, a temperature change would induce a difference in RI, and the GVD and γ of the optical fiber would change, which will in turn lead to changes in the second and third terms on the right side of GNLSE [33]. Consequently, the DW and soliton output spectrum (ΔωDW and Δωs) will occur a wavelength shift. Conversely, by observing the spectral shift of the output spectrum, temperature sensing can be realized, and the resultant sensing sensitivity can be respectively expressed as [34]:
In our work, glycerin was used as the sensitive intermediate. Because its thermo-optic coefficient is two orders of magnitude higher than that of silica glass, within a limited temperature variation range, the RI change of the silica glass was ignored. Additionally, both the thermal expansion of silica glass and glycerin were ignored for they play little influence on the DW and the soliton. For glycerin, its RI variation with temperature can be expressed by the following formula [35]:
where n0 (1.4631) is the glycerin RI at the temperature of T0(25 ℃), and α is the thermal-optical coefficient (∼ -1.1888 × 10−4 /℃) of glycerin.For the proposed temperature sensor based on the glycerin-filled MOF, we can see from the above equations that if DW blue shifts with respect to the soliton, the DW-based temperature sensitivity would be slightly higher than the soliton-based value. On the contrary, if DW red shifts, its temperature sensitivity would be slightly lower than the soliton-based value. Previously we have carried out a detailed investigation on SSFS-based temperature sensing. Here, in order to further explore temperature sensors of high-performance, this work focuses on the temperature sensing in the case of DW generation with a blue shift relative to the soliton.
3. Experiments and results
3.1 Sensor design and experimental setup
The MOF used in the experiments comprised one layer of three air holes around a central core, and a scanning electron microscope image of its cross section was described in the inset of Fig. 1(a). The core diameter was measured to be ∼3.72 µm and the air hole diameter ∼30.63 µm. The inset of Fig. 1(b) showed the fundamental mode, and the calculated effective RI, effective mode area, nonlinear coefficient and chromatic dispersion of the fundamental mode from 800 nm to 1800 nm were respectively shown in Fig. 1(a)∼(d). Glycerin was infiltrated into those three air holes through the vacuum-pressure process. Both ends of the glycerin-filled MOF was cut flat using a fiber cutter.
Fig. 1. (a). Calculated effective reflective index of the MOF. The inset showed the scanning electron microscope image of the cross section of the MOF; (b). Calculated effective mode area of the MOF. The inset showed the fundamental mode of the MOF; (c). Calculated nonlinear coefficient curve of the fundamental mode; (d). Calculated chromatic dispersion curve of the fundamental mode.
In the experiment, an OPO with a duration of ∼200 fs and a repetition rate of ∼80 MHz was adopted as the light source, and the wavelength was operated at 1050 nm. The light pulse passed through a neutral density (ND) filter and an aspheric lens with a focal length of ∼6.24 mm, and then was coupled into the core of a 15-cm glycerin-filled MOF aligned by five-dimensional adjusting frames. The output signal was butt-coupled into a large-mode-area (LMA) optical fiber connected to an optical spectrum analyzer (OSA) with a measurement range of 350∼1200 nm (Yokogawa, AQ6373B) or 1200∼2400 nm (Yokogawa, AQ6375B). The temperature was adjusted by a heating coil. A schematic diagram of the experimental system was shown in Fig. 2. It is worth noting that the choice of 15 cm was the best result considering the nonlinear phenomenon and the loss. Before investigating the temperature sensing performance of the DW and soliton, the output spectrum was investigated with the variation of the average pump power (120, 220, 320 and 420 mW) at room temperature (25 ℃), as shown in Fig. 3. Considering the coupling efficiency (10%), the peak powers launched into the glycerin-filled MOF were 750, 1375, 2000 and 2625 W. It was clear that DW occurred an obvious blue shift, the 3-dB bandwidth central wavelength of which was 815.1151 nm, 806.1061 nm, 795.5956 nm and 786.5866 nm, respectively; the soliton exhibited an obvious red shift, the 3-dB bandwidth central wavelength of which were 1080.8809 nm, 1105.9059 nm, 1113.4134 nm and 1136.9369 nm. These simultaneous wavelengths shift of DW and soliton indicated that the former was trapped by the latter. Furthermore, the stability and reproducibility of the DW and the soliton spectrum were tested with time changing from 10 min to 50 min at 1050 nm, 220 mW, as shown in Fig. 4. It can be seen that the output spectra hardly showed any change throughout the whole-time span, indicating that the DW-based and soliton-based temperature sensing under investigation would have good stability and high reproducibility.
3.2 Experiment results
Drawing on the experimental setup and based on the above analysis, the temperature sensing characteristics were respectively investigated by detecting the 3-dB bandwidth central wavelength shift of DW and soliton as the temperature varied from 55 ℃ to 75 ℃ with an interval of 5 ℃. The pump wavelength was 1050 nm and the average pump power was adjusted to be 120, 220, 320 and 420 mW. The output spectra were respectively displayed by Fig. 5. We can see that DW moved to the long wavelength direction while soliton shifted to the short wavelength direction, and both exhibited a good temperature sensing linearity as shown in Fig. 6.
Fig. 3. Output spectra with the variation of average pump power (120 mW, 220 mW, 320 mW and 420 mW).
Fig. 5. (a). Output spectra with different temperatures at 1050 nm, 120 mW, (b). at 1050 nm, 220 mW, (c). at 1050 nm, 320 mW, (d). at 1050 nm, 420 mW.
Fig. 6. (a). Fitting curve of the 3-dB bandwidth central wavelength of DWs and soliton with different temperatures at 1050 nm, 120 mW, (b). at 1050 nm, 220 mW, (c). at 1050 nm, 320 mW, (d). at 1050 nm, 420 mW.
The center wavelength of the 3-dB bandwidth of DW and soliton and the corresponding temperature sensitivity were listed in detail in Table 1. We can see that the wavelength difference between the DW and the soliton decreases, and the experimentally obtained DW-based temperature sensitivity is slightly greater than the soliton-based value. On the other hand, using the aforementioned equations in Part 2, the wavelength shift difference between the soliton and DW at 420 mW was calculated. As the temperature changed from 55 °C to 75 °C, the calculated values were respectively 329.01, 316.81, 304.94, 293.41 and 282.21 nm, which gradually decreased with the temperature rise. The center wavelength shift of the 3-dB bandwidth of DW was 27.788 nm and that of soliton was -20.022 nm, thus the theoretically calculated temperature sensitivity of the DW would be higher than that of the soliton, as stated in the conclusion in Prat 2, which was consistent with the experimental results.
Table 1. The temperature sensitivity and 3-dB bandwidth center wavelength of DW and soliton at 1050nm with different average pump power (120 mW, 220 mW, 320 mW and 420 mW).
Figure 7 presented the DW-based and soliton-based temperature sensitivity as a function of the average pump power. It was to be noted that both sensitivities increased with the rise of the average pump power. This may be induced by the following reasons: (1) the higher the average pump power, the higher the power of the optical soliton, and thus the narrower the corresponding pulse width and the wider the output spectrum. Consequently, more spectral components would overlap with the Raman gain spectrum, and the energy would be more effectively transferred to the soliton at the long wavelength direction, resulting in a more obvious SSFS effect. Therefore, a higher soliton-based temperature sensitivity could be obtained. Meanwhile, trapped by the soliton under the nonlinear PM condition, DW would also produce a higher temperature sensitivity. (2) In the actual experiment, a higher average pump power would induce a greater thermal energy of the glycerin-filled MOF, which would in turn result in a larger value change in GVD and γ, leading to a more obvious spectral movement and a higher temperature sensitivity.
Fig. 7. Temperature sensitivity of DW-based sensor and soliton-based sensor as a function of average pump power
To further evaluate the sensor’s robustness with the temperature variation, a temperature jump experiment was carried out at 420 mW. During each testing circle, the output spectra were recorded after 10 minutes of temperature change. After the post-processing, all the wavelengths of DW and soliton were shown in Fig. 8. The standard deviation was about 0.0443 nm for DW and 0.0235 nm for soliton, indicating that both the DW-based and soliton-based temperature sensing had good robustness in changeable temperature conditions. Based on the accuracy of OSA (0.02 nm), the maximum resolution of these two nonlinear phenomena was 0.0215 nm/℃.
Considering the practical application, we reconducted the experiment using a wider temperature sensing range (30 ℃ ∼ 80 ℃) and different detection step sizes (2 ℃, 6 ℃ and 8 ℃) at 1050 nm, 420 mW. Under the same experimental condition, the output spectra and temperature sensing sensitivity were shown in Fig. 9(a) and (b), respectively. The corresponding temperature sensitivity was 0.928 nm/℃ for DW and -0.923 nm/℃ for soliton, which correspond well with our previous experimental results. This experiment ensured the reliability of our sensing accuracy.
4. Numerical modeling and discussion
To verify the experimental observation, a numerical simulation was performed using GNLSE based on the same MOF parameters and the same temperature variation range. The pump condition was set to be 1050 nm with the average pump power of 220, 320 and 420 mW. Other parameters used for the simulation were listed in Table 2. Figure 10(a) showed the calculated GVD curves at different temperatures and (b) showed the calculated GVD and γ value as a function of temperature. We can see that when temperature increased gradually from 55 ℃ to 75 ℃, the values of absolute GVD and γ became larger.
Fig. 9. (a). Output spectra with different temperatures at 1050 nm, 420 mW, (b). Fitting curve of the 3-dB bandwidth central wavelength of DWs and soliton with different temperatures at 1050 nm, 420 mW.
Fig. 10. (a). Calculated GVD curves of the glycerin-filled MOF with different temperatures. (b). Calculated GVD and γ of the glycerin-filled MOF at 1050 nm as a function of different temperatures.
Table 2. Parameters used for simulation
The simulated output spectra with the temperature change at different average pump power were respectively shown in Fig. 11. When temperature changed from 55 ℃ to 75 ℃, DW shifted to the long wavelength direction while soliton shifted to the short wavelength direction, which corresponded well with the experimental observation. Table 3 listed the simulated center wavelength of the 3-dB bandwidth of DW and soliton and the corresponding temperature sensitivity. We can see that the wavelength difference between the DW and the soliton decreased, and the sensitivity enhanced with the increase of the average pump power. The DW-based temperature sensitivity was slightly greater than the soliton-based value, which was consistent with the experimental observation.
Fig. 11. (a). Simulation output spectra with different temperatures at 1050 nm, 220 mW, (c). at 1050 nm, 320 mW, (e). at 1050 nm, 420 mW; (b). Fitting curve of the 3-dB bandwidth central wavelength of DW and soliton with temperature change at 1050 nm, 220 mW, (d). at 1050 nm, 320 mW, (f). at 1050 nm, 420 mW.
Table 3. The simulation temperature sensitivity and 3-dB bandwidth center wavelength of DW and soliton at 1050nm with different average pump power (220 mW, 320 mW and 420 mW).
Figure 12 was an explicit comparison of the temperature sensitivities obtained through the experimental investigation and through the numerical simulation, which exhibited a good matching. However, slight disparities still existed, the difference can be attributed to the following aspects: (1) the experimental device was not perfectly stable, which inevitably introduced external factors into the sensing performance; (2) glycerin was not evenly filled in the MOF; (3) the MOF parameters were not well controlled in the fiber drawing process; (4) a targeted compensation was not added into the sensing system to offset the deviation.
Fig. 12. Comparison of temperature sensitivity between experiment and simulation of DW and soliton as a function of average pump power.
Furthermore, to highlight the sensing advantage of the proposed glycerin-filled MOF, the temperature sensing characteristics of a 15-cm MOF of the same fiber parameters but without the glycerin filling was theoretically simulated under the pump condition of 1050 nm, 420 mW. Due to the good linearity of the DW-based and soliton-based temperature sensing mechanism, a temperature variation range of 55∼ 75 ℃ with a step of 10 ℃ was chosen for simplicity. The output spectra were shown in Fig. 13. Because of the positive thermo-optical coefficient of silica glass, DW moved to the short wavelength direction, and the soliton moved to the long wavelength direction. After calculation, the DW-based temperature sensitivity was -0.186 nm/℃ with R2=0.9999, and the soliton-based value was 0.184 nm/℃ with R2=0.9841. Both values were much lower compared with the results obtained in glycerin-filled MOF (0.917 nm/℃ for DW-based, -0.891 nm/℃ for soliton-based). This proved that the filling of the temperature-sensitive material glycerin enhanced greatly the sensing performance of the proposed MOF.
Fig. 13. (a). Simulation output spectra with different temperatures at 1050 nm, 420 mW in a 15-cm MOF; (b). Fitting curve of the 3-dB bandwidth central wavelength of DW and soliton with temperature change.
Combined with our previous soliton-based temperature sensing research, we can conclude that if DW blue shifts with respect to the soliton, the DW-based temperature sensitivity would be slightly higher than the soliton-based value. The higher the average pump power, the higher the temperature sensitivity of DW and soliton. It is clear that DW and soliton have different sensing characteristics, which implies a good potentiality for solving the cross-sensitivity in dual-parameter sensing without introducing structural complexity or cost increase. Concerning this, we will deepen our research in the future work.
5. Conclusions
In this paper, a systematic investigation and comparison were conducted on the temperature sensing characteristics of the DW and the soliton in an in-house fabricated silica MOF filled with glycerin. A 1050 nm femtosecond laser was used as the pump source, the average pump powers was adjusted from 120 mW to 420 mW, and the temperature was varied from 30 ℃ to 80 ℃. The investigation showed that with the temperature rise, the wavelength difference between the DW and the soliton decreased. Both sensitivities enhanced with the increase of the average pump power. When the DW blue-shifted relative to the soliton, the sensitivity of DW was slightly higher than that of soliton, and the experimental maximum values were 0.928 nm/℃ (DW) and -0.923 nm/℃(soliton). Both DW and soliton could be used to realize temperature sensors of high sensitivity, good mechanical strength and simple structure. The sensing characteristic difference of DW and soliton revealed in this work might provide a new way for solving the cross-sensitivity of dual-parameter sensing in biological engineering, disease detection and environmental monitoring without introducing extra structural complexity or cost increase. At the same time, we also think it is very useful to finely produce special wavelength ultrafast laser with temperature controlling.
Funding
China Postdoctoral Science Foundation (2021M690563); 111 Project (B16009); Natural Science Foundation of Science and Technology Department of Liaoning Province (2020-BS-046); Fundamental Research Funds for the Central Universities (N180408018, N180704006, N2004021, N2104022); Natural Science Foundation of Hebei Province (F2020501040); National Natural Science Foundation of China (61775032); National Key Research and Development Program of China (2017YFA0701200).
Acknowledgement
The authors thank Liao Ning Revitalization Talents Program.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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