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Abstract
In this paper, a novel refractometer based on Mach-Zehnder Interferometer (MZI) is proposed and experimentally investigated. The MZI is composed of 2 micro bending cores (MBCs), one of which excites the cladding modes and the other couples the modes back. This structure is formed by high-frequency CO2 laser polishing and oxyhydrogen flame heating. With the unique deformation method, the interaction between the fiber core and the external status gets enhanced, moreover, higher modes in the cladding are excited, which leads to a high refractive index (RI) sensitivity. Due to the high temperature of the oxyhydrogen flame, the core of CO2 polished fiber is modulated, furthermore, the cladding shape of MBC tends to be circular. Hence, relatively small modulating regions of 500 μm can form for interference. In the experiment, 2 transmission dips are chosen for RI measuring, which possesses the wavelength of 1530.4 nm and 1600.8 nm, respectively. The RI sensitivities of the 2 transmission dips are -271.7 nm/RIU and -333.8 nm/RIU with the RI range of 1.33-1.42. The temperature characteristic is also experimentally analyzed and the temperature sensitivities of which are 0.121 nm/℃ and 0.171 nm/℃ in the range of 34℃-154℃. By solving the matrix equation, the proposed sensor can be applied for simultaneous measurement of RI and temperature.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Up to now, the development of optical fiber sensors has attracted much attention for its detecting capacity on physics parameters, such as strain, temperature, refractive index and torsion [1–4]. In addition, optical fiber sensors indicate advantages of high integration, electromagnetic immunity and the ability to operate remotely. Among these, optical fiber refractive index (RI) sensors have become hot topics due to their wide application, for instance, the detection of water quality, solution measurement, food quality monitoring and ecological environmental protection [5,6]. Many methods have been presented such as fiber Bragg grating (FBG) [7], long period fiber grating (LPFG) [8,9], Mach-Zehnder interferometer (MZI) [10–12] and Fabry-Perot interferometer (FPI) [13,14]. Although, these sensors possess some drawbacks that need to be solved. For FBG, the relatively low RI sensitivity is inevitable, which cannot meet the demands of high-accuracy measurement. For LPFG, the sensitivity is enhanced, however, the temperature-RI crosstalk becomes the new issue because the LPFG possesses only a single resonant peak. In order to solve it, sensors that are composed of 2 LPFGs have been proposed for simultaneous measurement of temperature and RI [15]. Whereas, the connection of 2 structures ineluctable increases the range of sensing area, which is not applicable for practical measurement. FPI shows high RI sensitivity, but the expensive fabricating devices and complicated methods limit the usage of this kind of sensor. Among these, the RI sensors based on MZI structures reveal excellent capacities of simultaneous measurement, high sensitivity and simple structures.
Traditional MZI is fabricated by splicing a section of special optical fiber between single mode fibers (SMFs), which motivates the coupling between cladding modes and core mode by the mismatch of core diameter. For instance, an MZI formed by an SMF sandwiched between 2 short sections of thin-core fibers was proposed for RI measurement and indicates the sensitivity of 159 nm/RIU [16]. Furthermore, for sensitivity enhancement, some adjustments are applied to the special optical fiber like tapering and side polishing. An MZI was fabricated by tapering several tapers in the multimode fiber part of the SMS fiber structure and the sensitivity reached -261.9 nm/RIU [17]. However, due to the usage of specialty fibers and severe reduction of diameter, these RI sensors possess some problems, for example, relatively high cost and weak mechanical strength. Hence, a new kind of RI sensor composed of SMF needs to be proposed and investigated for cost reduction and considerable mechanical strength.
In this paper, we propose and demonstrate a novel MZI based refractometer, which is constituted by a pair of MBCs. High-frequency CO2 laser polishing and oxyhydrogen flame heating methods are applied for preparing the MBCs and they act as modes exciter and combiner. The relatively high RI sensitivity owe to the special core deformation, which excites the higher-order cladding modes and enhances the interaction between the fiber core and the environment. In the experiment, we chose 2 transmission dips for RI and temperature measuring. By solving the matrix equation, simultaneous measurement of RI and temperature is achieved. The designed RI sensor possesses the advantages of high sensitivity, low cost and excellent mechanical strength, which makes it a considerable candidate for practical usage.
2. Principle and simulation
The schematic diagram MBC-MZI is shown in Fig. 1. Referring to Fig. 1, during the process of CO2 laser polishing, the modulating regions on the upper and lower surfaces are staggered, which leads to the different distances between the surface and the core of SMF. In the process of oxyhydrogen flame heating, a continuous tension is applied on the etched structure, because of uneven modulation on the cladding, the strain distribution of the structure is related to the different distance between the surface and the core. Severe modulation leads to a strong stress condition. Meanwhile, due to the high temperature of the oxyhydrogen flame, the fiber structure tends to be melted. With different stress distribution, the tension will make the optical fiber deforming in the vertical radial direction, so the core will be moved to the surface which is closer. Therefore, an MBC can be obtained. The MBC induces a strong refractive index modulation (RIM), which affects light propagation significantly. Moreover, the movement of the core leads to a distinct interaction with the surrounding, in other words, a portion of lights leak from the core and the cladding modes get excited. The unique shape magnifies the deformation of fiber core, a small modulated region can form the interference. Moreover, this kind of shape staggers the upper and lower surfaces, which attenuates the decrease of fiber diameter. So this design indicates a considerable mechanical strength.
As is shown in Fig. 1, a pair of MBCs are introduced into SMF which work as light beam splitter and combiner, respectively. When the incident light propagates through the first MBC, due to the reduction of cladding diameter and the bent-core, the evanescent field effect is enhanced. A portion of light energy couples to the cladding from the core of SMF and the higher-order mode in the cladding is excited. Therefore, after the light traveling through the first MBC, both core mode and cladding mode are existing in the SMF. Subsequently, the light travels along the SMF until it reaches the second MBC, where the light energy in the cladding couples back into the core. In consequence, an MZI based on inter-mode interference is accomplished. Interference intensity of MBC-MZI can be expressed as:
where and ${I_2}$ are the intensities of the core mode and the coupled cladding mode, $\varphi $ is the phase difference between the 2 modes, which can be expressed as: where the λ represents the wavelength and L is the interference length, when φ equals (2 m + 1) π (m = 0, 1, 2, 3, …), the destructive interference will generate, Δneff is the effective refractive index difference between the core mode and the coupled cladding mode. λ can be expressed as: hence the FSR of MBC-MZI can be expressed as: according to Eq. (4), the FSR decreases when the interference length (L) increases.Moreover, for MBC-MZI, the bent-core enhances the diffraction as well as the interaction between the fiber core and environment, which indicates a larger variation of Δneff. According to Eq. (3), it leads to a blueshift of the transmission dip. When the RI of the environment approaches the effective RI of cladding modes, the effective RI of cladding modes can be considered as a constant. Meanwhile, due to the bending of the core, the interaction between the fiber core and the environment will influence the effective RI of core modes, where Δneff achieves the minimum value. Hence, the closer the surrounding RI is to the effective RI of cladding modes, the greater the RI sensitivity of MBC-MZI is. The sensitivity of MBC-MZI can be expressed as:
When the light travels through the MBC, with the bent-core, the diffraction gets enhanced and the higher modes also get excited, which leads to higher RI sensitivity. Hence, the MBC-MZI is a considerable candidate for RI measurement. In order to prove that the transmitted light can be coupled from the SMF core to the cladding, a simulation by using beam propagation method (BPM) has been conducted for analyzing optical field distribution of the MBC-MZI as shown in Fig. 2, the parameters setting: the diameter core and cladding are 8 μm and 125 μm, respectively. The maximum bent deviation of the core is 2.5 μm, the length of the segments in which the core bent is set as 500 μm. Moreover, the optical field distributions when the light travels through the first MBC and second MBC are also simulated, which can prove that the light intensity of the core is reduced and the cladding modes are excited sufficiently.
3. Fabrication
Figure 3 shows a side view of MBC-MZI, and the preparation process of MBC-MZI can be simply divided into 2 steps, one of which is the asymmetrical reduction of cladding induced by high-frequency CO2 laser, the other is the core modulation caused by oxyhydrogen flame heating. Figure 4 displays an oxyhydrogen flame heating device, and the CO2 polishing device is similar to that introduced in Ref. [18]. During the process of CO2 polishing, a standard SMF (SMF-28) stripped of the coating layer is held between 2 rotating fiber fixtures. Meanwhile, the SMF is also placed beneath the CO2 laser and the spacing is precisely chosen to ensure it lies exactly in the focal plane of the CO2 laser. A broadband light source (BLS) is connected to one end of SMF, which provides continuous incident light. And the other end of SMF is connected to an optical spectrum analyzer (OSA) for real-time monitoring of the transmission spectrum. Otherwise, a charge-coupled device (CCD) is applied to detect the deformation of SMF. The above-mentioned CO2 laser possesses a focal spot of 100 μm and a wavelength of 10.6 μm. In addition, the scanning paths of CO2 laser are controlled by the program in a computer, as well as the laser power and scanning frequency. In the reduction process of cladding, the laser power is set as 4.5 W, which provides accurate polishing depth and high-quality constructions. During the polishing process, the programs which control the scanning path are different for 2 opposite surfaces of SMF. The first program is composed of 2 sections, and the scanning path of one section has 2 periods, each of which is changed from dense to evacuated to dense. After four times scanning, the upper surface of SMF is changed into a w-shape, as is shown in Fig. 2(a). Then rotating 2 fixtures by 180° and changed to another program which is also composed of 2 sections, but each section possesses only 1 period which is the same as the above-mentioned period in program 1. The position of this period is exactly in the middle of the above-mentioned 2 periods. Hence, after the scanning on the lower surface, the SMF is transformed into the shape shown in Fig. 3(a). The length of the deformed region is 500 μm. Moreover, the distance L between the 2 sections is 15 mm.
Fig. 3. Side view of (a) CO2 laser polishing structure, (b) and oxyhydrogen flame heating structure.
Figure 4 shows the oxyhydrogen flame heating device, which is employed to modulate the core of CO2 laser-induced SMF. As is shown in Fig. 4, 2 clamps are used to fix the structure, meanwhile, the clamps are also connected to a stepper motor. In addition, there is a hydrogen outlet placed in the middle of the clamps with a diameter of 1 mm, which is connected to a hydrogen pump. When fixing the structure, we adjust its position to keep one of the deformed sections exactly below the hydrogen outlet. A program in computer controls experimental parameters, for instance, stretching distance and moving speed of stepper motor. During the fabrication process, the SMF is connected to a BLS and an OSA for real-time monitoring. Subsequently, turn on the hydrogen pump which supplies hydrogen gas. When the displayed number is stable at 120, we use a lighter to ignite the hydrogen and then turn on the program, which terminates after 10 s. Then the structure is shifted to another deformed section to produce the same modulation. In our experiment, the moving speed of the stepper motor is set to 0.06 mm/s and the heating temperature is 1800℃. After the heating, the SMF is transformed into the shape shown in Fig. 3(b).
In order to illustrate the deformation of the structure during the oxyhydrogen flame heating, an approximate 3D mechanical analysis is adopted. Material parameters setting: Young's modulus: 72.5 Gpa, Poisson's ratio: 0.17, and material density: 2700 kg/m3. During the simulation, 600 με is applied to the structure. The strain distribution and the core deformation induced by applied tension are displayed in Fig. 5. In the process of oxyhydrogen flame heating, the temperature can reach 1800℃, which exceeds the softening temperature of SiO2, and on this occasion, the glass deforms under its action [19]. Surface tension force plays an important role in the deformation of fiber cross-section. According to [19], with sufficient heating time, the surface tension force can make the fiber cross-section round again. Moreover, the uneven polishing on the upper and lower surfaces leads to different strain distribution, and the maximum strain will be received at the deepest etching depth. Owe to this, the position of the fiber core is also changed, which causes a portion of the light to leak out of the core and form interference. Although the core is slightly bent, the cladding turns into the same as the original shape, in other words, “rounded.” Hence, the proposed RI sensor indicates a considerable mechanical strength, which is quite applicable for practical measurement.
The best contrast ratio is exactly obtained when the dominant cladding mode is close to that of the core mode. The optical field distributions of 3 MBC-MZIs with different L of 15 mm, 20 mm, and 25 mm are simulated in Fig. 6. The simulation indicates that the cladding mode of MBC-MZI with the interference length of 15 mm is effectively excited, for which the best contrast ratio is obtained.
Three MBC-MZIs with different L of 15 mm, 20 mm, and 25 mm are fabricated and the transmission spectrum is shown in Fig. 7. The free spectral range (FSR) of 3 models around 1550 nm is 50.4 nm, 28.6 nm, and 25.4 nm, respectively. The experimental result is consistent with the analysis. Comparing these 3 transmission spectra, the best contrast ratio can be obtained when the interference length L is 15 mm. Hence, the MBC-MZI with L of 15 mm is chosen for RI and temperature measurement. The transmission spectrum is displayed in Fig. 8, which shows both spectra after CO2 laser polishing and after oxyhydrogen flame heating.
The transmission spectrum of MBC-MZI is also simulated as shown in Fig. 9. Compared with the transmission spectrum of the prepared structure, Dip B shows the same wavelength as the simulated dip, but the contrast ratio is 4.8 dB smaller. As for Dip A, the wavelength indicates a blue-shift of 10 nm than the simulated dip, however, they have the same contrast ratio. The difference between the simulated result and actual spectrum can be attributed to deviation in the process of oxyhydrogen flame heating, however, the influence can be negligible.
To investigate the RI detecting potential of the proposed structure, the spectrum variation when surrounding RI changes is simulated, which is shown in Fig. 10. As the surrounding RI increases from 1.33 to 1.42, both the simulated transmission dips indicate a shift to a short wavelength. By polynomial fitting the wavelength of the 2 dips, the quadratic functions are obtained, from which the RI sensitivity of the structures can be calculated. The maximum RI sensitivity of 2 simulated dips reaches -291.16 nm/RIU at 1540.4 nm and -362.16 nm/RIU at 1600.8 nm.
Fig. 10. Simulated results of MBC-MZI when surrounding RI changes (a) Dip A (1540.4 nm), (b) Dip B (1600.8 nm).
4. Results and discussion
The RI characteristic of MBC-MZI is experimentally investigated. Figure 11 shows the detecting device for RI measuring. The structure is placed upon a platform with 2 ends connected to an OSA and a BLS, respectively. The OSA record the spectrum variation with a resolution of 0.2 nm. The glass slide is changed to a metal carrier with a 2 mm deep groove in the middle of it. The groove is designed for placing the structure. After dropping the glycerin solution into v-groove, a cover board made by glass material is applied for enclosure. The metal carrier possesses excellent thermal conductivity, so the glycerin solution can be heated to the designed temperature. The external RI increases from 1.33 to 1.41 with a step of 0.01. Once the external RI is changed, the result is experimentally recorded, then the v-groove is washed by deionized water, which reduces the effect of residual solution and improves the accuracy of measurement.
In the experiment, we chose 2 transmission dips for RI measuring, Fig. 12 illustrates the experiment results of RI measuring, as the external RI increases, Dip A (1530.4 nm) and Dip B (1600.8 nm) tend to blue shift. The reason for the blue shift is due to the MBC, which enhances the interaction between the fiber core and the environment. When the external RI is changed, the effective RI of the core approaches to the external RI, which leads to the decrease of Δneff. According to the Eq. (3), the transmission dip λ shifts to a shorter wavelength. Moreover, the largest wavelength shift is obtained at the largest external RI, which is consistent with the theoretical analysis. By using the polynomial fitting, the RI response functions of 2 dips can be described as y = 3730.15x-1409.09×2-938.27 and y = 5518.31x-2060.61×2-2094.05 with a satisfactory fitting degree (R2 = 0.99). The maximum RI sensitivities can be obtained at RI = 1.42 which are -271.7 nm/RIU and -333.8 nm/RIU, respectively. Compared with simulated results, the experimental RI sensitivity of 2 dips is slightly lower. We attribute it to inevitable residual of deionized water, which dilutes the solution and leads to the decrease of applied RI.
Fig. 12. Spectral response of (a) Dip A, (c) Dip B, the fitting curve between wavelength and RI of (b) Dip A, (d) Dip B.
Except for the measuring of RI characteristics, the temperature sensitivity of MBC-MZI is also investigated. The structure is placed on a heating cabinet, which is electronically controlled and the margin of temperature error is within 1℃. We record the spectrum variation of MBC-MZI when the temperature raises from 34℃ to 154℃ with a step of 20℃, which is shown in Fig. 13. The temperature sensitivities of chosen dips are 0.121 nm/℃ and 0.171 nm/℃, respectively.
Moreover, because of the different RI and temperature sensitivities of Dip A and Dip B, simultaneous measurement of the above-mentioned parameters can be achieved by solving the matrix equation, which can be expressed as:
By Substituting in the experimental results, the matrix equation can be expressed as:
By solving the Eq. (8), the RI and temperature resolution of MBC-MZI can be calculated as ±0.0513℃ and ±4.13 × 10−5 RIU, respectively.
Table 1 shows the comparison between the proposed MBC-MZI and other RI sensors. The evaluation concludes 3 aspects of the used fibers, RI sensitivity, mechanical strength and RI-temperature crosstalk. Conventional RI sensors are fabricated by cascading 2 kinds of fibers or reducing the radius of fibers like tapering, which leads to fragile structures. For the proposed RI sensors, based on the small modulating regions, it indicates higher mechanical strength. Additionally, because only SMF is employed, the cost of reported RI sensors is relatively low. The crosstalk of temperature cannot be ignored, and the RI-temperature crosstalk is investigated. The cross sensitivity of MBC-MZI is relatively lower than that of the reported sensors. Moreover, our sensor can be applied for simultaneous measurement of RI and temperature, so the temperature crosstalk can be eliminated. In consideration of the competitive features such as relatively high RI sensitivity, high mechanical strength and low cost, the MBC-MZI becomes a considerable candidate for RI sensing.
Table 1. Comparison of the Sensing Performance Between MBC-MZI and Other Reported RI Sensors
5. Conclusion
In conclusion, an optical fiber sensor based on MBC-MZI is proposed and experimentally investigated for simultaneous measurement of RI and temperature. This structure is fabricated by relatively slight modulation on SMF, which provides high mechanical strength as well as considerable RI sensitivity. The experimental results indicate that the MBC-MZI possess the maximum RI sensitivities of -271.7 nm/RIU and -333.8 nm/RIU with the RI range of 1.33-1.42, respectively. Moreover, the temperature sensitivities of 0.121 nm/℃ and 0.171 nm/℃ with the range of 34℃ to 154℃ are also obtained. By solving the matrix equation, the resolution of RI and temperature is calculated, which reach ±0.0513℃ and ±4.13 × 10−5 RIU, respectively. Meanwhile, a 3D Beam Propagation Method are applied for simulating the transmission spectrum and the RI sensitivity of MBC-MZI. Due to the above-mentioned advantages, the proposed RI sensor indicates wide application prospects in practical measuring.
Funding
Joint Fund of Astronomy (U1831115, U1931206, U2031130, U2031132); Chinese Academy of Sciences; Natural Science Foundation of Heilongjiang Province (ZD2019H003); National Natural Science Foundation of China; Fundamental Research Funds for Central Universities of the Central South University; Harbin Engineering University.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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