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Abstract
We present a single walled carbon nanotubes (SWCNTs)-coated tilted fiber Bragg grating (TFBG) hot-wire anemometer (HWA) with simple configuration, linear response, and high sensitivity. TFBG is utilized to effectively couple a pumping laser at 1550 nm to the cladding mode that is absorbed by the SWCNTs film immobilized on the fiber surface with good light-heat conversion efficiency. As a result, the TFBG is converted to a “hot wire”, and the wind speed can be deduced from the output power of the laser, which is a function of both the wind-induced temperature change and the spectral profile of the cladding mode. The most significant aspect of the HWA system is that we use the Gaussian shape of the high-order TFBG cladding mode to compensate for the inherent nonlinear relationship between the heat loss and the wind speed that is an undesirable characteristic of existing HWA systems. The validity of this novel operating principle was verified theoretically and experimentally. Via careful control of the parameters, a good linear response of the HWA system was achieved, especially for the low wind speed range where nonlinearity was more conspicuous. It was demonstrated that, with a low input power of only 29.3 mW of the pump laser, an R2 value of 0.9927 was obtained in this fiber-optic HWA system with high sensitivity 7.425 dBm / (m/s) and resolution 0.0027 m/s in a small wind speed range (0-2m/s) considering the intensity resolution of OSA and the noise of the pump laser. Furthermore, the system also exhibits a simple and low-cost design with only one laser source and one low-cost power measurement component.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, fiber optic anemometers have been proven to be a new attractive platform for flow sensing due to their unique advantages, such as high accuracy, long term stability, immunity to electromagnetic interference, compact size and simple fabrication. Different structures or mechanisms have been reported [1–6]. Among them, fiber-optic hot wire anemometer (HWA) is an important type that has gained a great deal of interests. The basic principle is that the wind flow will cool down a heated sensor by taking away the heat on the surface and by measuring the temperature variation of the heated region, the wind speed could be deduced [7–8]. To accurately detect the variation of temperature, fiber Bragg gratings (FBGs) are commonly used in the structure because of its mature development, in-fiber stability and good linear wavelength response to temperature [9–12]. However, an undesirable characteristic of an HWA is the inherent nonlinear relationship between the heat loss, which directly determine the temperature near the FBG region, and the wind speed around the sensing head. Typically, the sensitivity of a HWA reduces as the wind speed increases and vanishes at the wind speed approaches infinity. Efforts to partly overcome this inherent nonlinear response includes abandoning the low speed measurement range where the nonlinear response is more conspicuous and limiting the measurement for only high wind speed where the response is approximately linear [13]. Obviously, such method is not applicable in many applications where a good sensitivity at low wind speed is important. Besides, to effectively heat the sensing area using lasers, either geometry-modified fibers, such as bending, tapering, making bubble in the fiber, mismatch fusing, or special high absorption fiber such as Co2+-doped fiber are needed [14–17]. Obviously, these methods may greatly weaken the strength of the sensor structure or increase the cost. In addition, resulting in relative low efficiency, many of the previously reported fiber-optic HWAs require separate light sources for pumping and sensing, or high cost interrogation system. These characteristics greatly reduce the field applicability of fiber-optic HWA sensing systems.
Aimed at overcoming some of the challenges, in our previous work [18–19], we successfully demonstrated a fiber-optic HWA with high photo-thermal conversion efficiency (up to 93%), high sensitivity, and more compact sensing head structure by an unmodified titled fiber Bragg grating (TFBG) coated with single-walled carbon nanotubes (SWCNTs). Without any modification to the fiber geometry, the TFBG retains the mechanical strength and the SWCNTs serve as an excellent infrared light absorption material with high thermal conductivity [20–21]. Despite of these advantages, several problems still exist and need to be addressed to make the device more practically useful, such as the nonlinear response and the needs for two separated light sources and high cost wavelength-based interrogation components. In this paper, by directly detecting the intensity of a pumping laser and inducing high-order mode Gaussian line-shape compensation of the nonlinear relationship, we achieved a good linear response, high sensitivity and low cost HWA sensing system with SWCNT coated TFBG.
The wind speed and the intensity variation of the output optical power was connected in a better logarithmic relationship through physical mechanism compensation. A good linear response was achieved under some logarithmic detectors or amplifiers in large dynamic interrogation system. Theoretical analysis has been conducted to illustrate the operating principle and experimental demonstration has been provided. It was demonstrated that using a low power of 29.3 mW for the laser, the HWA system obtained a good linear response to wind speed with R2 value of 0.9927 with the sensitivity up to 7.425 dBm / (m/s) and resolution 0.0027 m/s in a particular small wind speed range (0-2m/s) considering the intensity resolution of OSA (0.02 dB) and the noise of the pump laser (∼0.01dBm). The proposed linear-response, simplified anemometer will be valuable in high accuracy wind speed measurements, especially for future long term remote flow sensing or even in-chip applications such as high voltage transmission tower, wind power generation and safe monitoring in mining applications.
2. Experimental system and theory
Figure 1(a) shows the diagram of the proposed fiber-optic HWA system with only one pumping source and one power measurement component. A commercial-off-the-shelf 1550 nm pump laser (intensity noise ∼ 0.01 dBm) was used to heat and interrogate the sensing head simultaneously. The laser’s output intensity can be simply monitored by a power meter. To better explain the principle and mechanism of the demodulation method, here we use an optical spectrum analyzer (OSA) as a temporary alternative with minimum resolution of 0.02 dB. The sensor head structure consisted of a SWCNTs (diameters ∼2 nm and lengths ∼1µm) coated TFBG as shown in Fig. 1(b), which coated by a low cost chemical solution method and has been proved to have high heating efficiency, robust structure, and ability of combing the coupling (making the input power in the core to interact with the materials on the fiber surface) and sensing functions together in our preview work [18–19]. Figure 1(c) shows a 6° TFBG without SWCNTs film transmission spectrum. The gratings of TFBG are tilted with respect to the fiber axis and can couple light from the core to the cladding. Thus, there are a series of cladding modes formant in the spectrum. In this work, the high-order cladding modes near 1550 nm were investigated. Also, the SEM image and micrograph of SWCNTs film coated TFBG were exhibited in Fig. 1(c). The blue curve in Fig. 2 shows the transmission spectrum of the HWA in still air. It shows a peak at the laser wavelength as well as a series of valleys probed by the spontaneous emission of the laser, each corresponding to a cladding mode. When the heated sensor head was placed in the air flow, the heat loss from the flow reduced the temperature of the TFBG, resulting a blue shift of TFBG spectrum (red curve in Fig. 2) that is linearly proportional to the temperature change. As a result, the laser power transmitted through the HWA will be accordingly modulated by the spectral shape of the high-order cladding mode of TFBG.
Fig. 1. Schematic diagram of wind sensor (a) Experimental setup; (b) Fiber-optic anemometer based on SWCNTs coated TFBG; (c) Transmission spectrum of 6° TFBG and SEM image and micrograph of SWCNTs film coated TFBG
The detailed mechanism of linear response between the monitored intensity of the output laser and the wind speed will be discussed and theoretically analyzed first. For a TFBG, the wavelength at which the core mode of the fiber is coupled to the cladding mode ${\lambda _r}$ is expressed as:
where $\Lambda $ is the period of TFBG, and $\theta $ is the tilt angle of the TFBG. $N_{eff}^{core}({\lambda _r})$ and $N_{eff}^r({\lambda _r})$are, respectively, the effective indices of the core mode and the cladding mode at the wavelength where the resonance is observed (${\lambda _r}$). The peak reflectivity ($R$) can be expressed as: where L is the length of the grating and $\kappa $ is the coupling coefficient between the forward propagating fiber core mode and backward propagating cladding mode [22–27]. Considering the transverse components of the electric fields of the fiber modes, the coupling coefficient is evaluated as follows: where $\Delta n(x,y) = \Delta n\cos ((4\pi /\Lambda )(z\cos (\theta ) + y\sin (\theta )))$ is the refractive index perturbation causing by the grating in the cross-section of the fiber and C is a proportionality constant of the normalization of the transverse mode fields. The coupling coefficient depends on the effective refractive index of the cladding modes. When the TFBG coated with the SWCNTs, the external refractive index variates in both the real part and the imaginary part which will obviously affect the effective refractive index of cladding modes. Thus the resonance reflectivity would be changed due to the coating induced influence of coupling coefficient. According to Eq. (2), the spectral shape of a standardized TFBG is almost the same as FBG. The optical spectrum of FBG is closer to Gaussian line shape in physical principle, and the center wavelength obtained by the Gaussian fitting algorithm has become the most widespread peak search algorithm due to a smaller error, higher accuracy and more stability [28]. Meanwhile, a single high-order cladding mode (the certain resonance observed in the transmission spectrum of TFBG) is coupled and superimposed by dozens or even hundreds of guided cladding modes with many different azimuthal orders. Comparing to the FBG spectrum made of a single core mode HE11, the resonances in TFBG transmission spectrum obtained by superposition of multiple mode coupling coefficients should be much closer to Gauss line-shape and can be simulated approximately by a Gaussian function [29].From the theory of hot-wire anemometry [8], the nonlinear relationship between the wind speed v and the heat loss ${H_{loss}}$ is shown as:
where $\Delta T$ is the temperature difference between the optically heated SWCNTs-TFBG and surrounding environment, A and B are empirical calibration constants. According to Eq. (1), the wavelength shift of the cladding mode caused by temperature difference ($\Delta T$) can be obtained by:3. Simulation and experimental results
As discussed above, the output laser intensity will be modulated by the nonlinear Gaussian line-shape of the high order cladding mode as the spectrum of the TFBG shifts according to the wind speed that takes the heat away from the sensor head. It is possible to operate the HWA in an appropriate region of the Gaussian shape to compensate the nonlinear wavelength variation in response to the wind speed, resulting in quasilinear response in terms of transmitted power of the laser vs. the wind speed. This compensation is more useful for measurement of small wind speed (in our experiments less than 2 m/s) at which the nonlinearity of wavelength shift vs. wind speed is more prominent. To obtain the precise relationship between the intensity of the laser output and the wind speed, the transmitted power of a cladding modes of 6° TFBG as a function of wavelength was measured and fit with Gaussian functions in the range of 1551-1551.20 nm (consistent with the wind speed induced wavelength variation), as shown in Fig. 3(a). The function of the fitting curve is given by:
Fig. 3. (a)(b) Fitting of the certain cladding mode, and the curve of wind speed versus wavelength. (c) Linear relationship between the intensity and wind speed after the two fitting curves integrated.
To further verify the results, experiment tests were conducted to record the laser’s intensity with respect to the wind speed with optimized parameters (the input power of the pump laser and thicknesses of the SWCNT film). Here, a 6° and 1.5cm TFBG was written in hydrogen-loaded common Corning SMF-28 fiber via a 248 nm UV excimer laser and phase-mask method (the same TFBG used to fit the curve in Fig. 3(a)). And the grating period was about 555 nm. As shown in Fig. 4(a), as the speed of wind increasing, the reading of the power meter (in unit of dBm) was decreased linearly. The linear fitting shows R2 of 0.9927. Moreover, under a low pump laser power (29.2 mW), the sensitivity of the proposed anemometer is up to -7.425 dBm/(m/s) which is much higher than the recently reported results with a relatively complicated structure (the maximum sensitivity of the anemometer reaches −22.03 µW/(m/s) and the power of pump laser was 150 mW) [30]. To further investigate the accuracy of the HWA, the wind speeds measured by the linear-response fiber optic anemometer were compared with the velocity measured by a standard calibrated electrical anemometer (TESTO405V1), as shown in Fig. 4(b). The accuracy of this sensor for wind speed measurement is evaluated by the maximum absolute error (MAE) and maximum relative error (MRE) between the obtained velocity and the reference value, yielding the MAE of 0.05 m/s and MRE of 4.50% with the full scale accuracy about ±2.5%. Considering intensity resolution of OSA (0.02 dB) and noise of the pump laser (∼0.01 dBm), the calculated resolution of this designed sensor is 0.0027 m/s with sensitivity of 7.425 dBm / (m/s).
Fig. 4. (a) The linear relationship of intensity and wind speed when a 6° TFBG with 1.6 µm SWCNTs coating was measured under the pumping power of 29.2 mW; (b) Comparison between the measured wind speed by the fiber optic sensor and the velocity obtained by an electrical anemometer.
We further evaluated the effects of several system parameters (the input power of the pump laser and thicknesses of the SWCNT film) on the linearity of the response. We first investigate the input power of the pump laser on the same 6° TFBG with 1.6 µm SWCNT coating. As the power of the pump laser was increased from 22.9 mW to 36.3 mW, the anemometer exhibited linear responses to the wind speed with R2 values close to 1, as shown in Fig. 5. Furthermore, it is worth noting that the sensitivity and the value of R-square are the highest when the power was 29.2 mW, which means that we could find a suitable power to balance the sensitivity and the linearity. Besides, the power consumption of the proposed system is also relatively low and it is reasonable to believe that with the laser’s excellent high signal-to-noise-ratio (SNR) quality the anemometer system can work under much lower power consumption condition via sacrificing the sensitivity to an acceptable degree.
SWCNTs are utilized as good thermal conversion films which superior to traditional metal films like silver to raise the fiber temperature locally. The investigation of the linearity of the system was also conducted under different thicknesses of the SWCNT film. Figure 6(a) presents the transmission spectrum of 6° TFBG with different thickness of the films. It is seen that thicker coatings resulted in suppression of core-to-cladding mode coupling, as evidenced by the smaller depths of the valley in the spectrum. This suppression is attributed to the stronger light absorption form thicker films. Figure 6(b) shows the HWA responses for three different coating thickness under the input power of 36.3mW. Although all of them show a good linearity, the sensitivities exhibit large variations. The lowest sensitivity was obtained for the one with 1.0 µm coating. While the thickness increases to 1.3µm and 1.6 µm respectively, the sensitivities were increased significantly to almost the same level. It is believed that as the thickness increased to a point where most of the laser is absorbed, the sensitivity of the anemometer becomes saturated. Besides, the response time of the sensor will also be affected by the thickness and after the optimization, a 5.0 s time response was obtained for the 1.6 µm coating as the wind speed varied from 2.0 to 0 m/s. Furthermore, the response times would be shorten with the decreasing of wind speed.
Fig. 6. (a) The spectrum of TFBG with different thickness of SWCNTs films; (b) Different responds of intensity and wind speed while the thickness was different
4. Conclusions
In conclusion, we proposed a linear response, simplified and low-cost fiber optic HWA system based on a TFBG coated with SWCNT film. The heating and temperature interrogation were realized using a measurement of the transmitted power. By using the Gaussian line-shape of the high-order TFBG cladding mode to compensate the inherent nonlinear relationship between the wind speed and the temperature variation, we achieved a quasilinear response between the transmitted power of the laser and wind speed in small wind speed range where the nonlinear response is more conspicuous. Theoretical analysis has been conducted to illustrate the operating principle and experimental demonstration has been provided. Effects of key system parameters including the thickness of the films and the pumping power of laser on the sensor response were investigated. It was demonstrated that under a suitable power of 29.3 mW, the R-square value of 0.9927 was obtained with a sensitivity as high as 7.425 dBm / (m/s). Another distinguished advantage of our proposed sensing system is the simple sensing head and low cost system components. Only one 1550nm laser, functioning as both the heating and the sensing light source, is needed. Without any power amplifier (commonly erbium-doped fiber amplifier, EDFA), the system noise is greatly reduced and the sensing performance is improved. The intensity-based interrogation is a more practical way to reduce the cost sharply and make the miniaturization of the interrogation part easier compared to wavelength-based interrogation method. Our proposed linear and simple optical fiber HWA system offers a good way for future applications in many special and important fields.
Funding
National Natural Science Foundation of China (61520106013, 61727816); Exchange Fund from Key Laboratory of Optical Fiber Sensing and Communications (ZYGX2019K006); Fundamental Research Funds for the Central Universities (DUT19LAB32).
Acknowledgments
The expert contributions from Dr. Ming Han, Michigan State University, to this article is gratefully acknowledged.
Disclosures
The authors have no relevant financial interests in this article and no potential conflicts of interest to disclose.
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