Refractive index sensor based on etched eccentric core few-mode fiber dual-mode interferometer

Min Yang; Jing Yang; Chunying Guan; Mingjie Wang; Pengcheng Geng; Yize Shen; Jiaming Zhang; Jinghui Shi; Jun Yang; Libo Yuan

doi:10.1364/OE.27.028104

1. Introduction

The refractive index (RI) is one of the most important parameters to guide light and control light-matter interaction. Sensing refractive index is widely adopted in the fields of physics, photonics, chemistry, biology and environment monitoring. A variety of optical fiber RI sensors have been proposed because of their advantages of high sensitivity and reliability, compact size and anti-electromagnetic interference. Fiber Bragg gratings (FBGs) were widely applied in RI sensors because of their durable measurement capability and narrow bandwidth [1,2]. However, the sensitivities of FBG-based RI sensors are low, which limits their practical applications. RI sensors based on long period fiber gratings (LPFGs) have higher sensitivities than FBG-based sensors [3,4]. Nevertheless, the fabrication procedures of both LPFG- and FBG-based RI sensors are complex and expensive lasers are also required. Numerous RI sensors based on surface plasmon resonance (SPR) [5–7], interferometers [8,9] and evanescent field [10] have been realized. In particular, fiber-based mode interferometers (MIs) have attracted tremendous attention because of their high sensitivity, flexible configuration and simple fabrication. The mode interferometers are similar to Mach-Zehnder interferometers (MZIs), in which interference modes are regarded as the two arms of the MZI. A RI sensor based on three cascaded single-mode fiber (SMF) tapers was realized with the sensitivity of 28.6 nm/RIU [11]. To enhance the sensitivity and the practical application capability of MZI-based RI sensors, several methods have been proposed, including embedding FBG and LPG [12,13], fiber tapering [14,15], femtosecond (fs) laser micromachining [16,17]. Fs laser micromachining can improve the sensor's sensitivity to a great degree, but it is high cost due to the need of expensive laser, similar to the fabrication of FBGs and LPGs. In addition, numerous special fibers were adopted to fabricate RI sensors based on multimode interference such as twin core fiber [18], coreless fiber [19,20]. Nevertheless, the modes transmitted in aforementioned fibers are plenty and complex, which causes the difficulty of theoretical analysis and limits their applications. Few-mode fibers (FMFs) have unique advantages such as simple construction, low nonlinearity, low mode dispersion, and controllable modes. The decreasing number of the transmitting modes in the fiber makes the interference spectrum simple and the tested field more stable, which is beneficial to realize the simplification and practical application of sensors. Therefore, novel FMF-based sensors have received extensive concerns in recent years. Various FMF sensors have been reported to accomplish physical parameter measurements such as bending [21], temperature [22], strain [22,23]. However, the detection of environment RI based on FMF sensors has not been sufficiently explored due to the fact that the thick cladding prevents an efficient interaction between the core modes and the ambient environment.

In this work, we proposed and experimentally demonstrated a compact dual-mode interferometer (DMI) based on an eccentric core few-mode fiber (ECFMF) for RI measurement. The ECFMF-DMI based on the interference between core modes was realized by hydrofluoric acid (HF) chemical etching and simply core-offset splicing. The fabrication process of the DMI is quite simple and the cost is low. In addition, compared with microfibers, the diameter of the etched ECFMF is much larger, so the proposed device is more robust. The DMI based on the core-core mode interference has a higher RI sensitivity of 2565.2 nm/RIU in comparison with those based on the core-cladding mode interference. The temperature responses of two DMIs were also investigated and they show a low sensitivity of temperature.

2. Fabrication of the sensor

The cross-section image of the ECFMF is displayed in Fig. 1(a). The ECFMF was commercially purchased from the 46th Research Institute of China Electronics Technology Group Corporation. The core is not at the center of the fiber and deviates from the center of the cladding by 35.3 µm. Only two modes can transmit in the eccentric core in the wavelength range from 1150 to 1450 nm. The diameters of the eccentric core and cladding are 9.6 and 125 µm, respectively. The RI distribution of the ECFMF was measured using a RI profiler (S14, Photon Kinetics, Inc.). The RI of the eccentric core is 1.463339 at 632.8 nm, and the RI difference between the core and cladding is 0.63%. The ECFMF is soaked in 40% HF acid solution at room temperature to remove the sectional cladding until the diameter of the fiber is reduced to 80 µm, thus the eccentric core is exposed exactly to the outside environment. Figure 1(b) shows the cross-section of the etched ECFMF. The etched fiber still has a good mechanical strength due to the thick diameter. The schematic configuration of the etched ECFMF-DMI based on the core-core mode interference is shown in Fig. 1(c), the inset shows the cross-section view of the position of outward lateral-offset. The DMI is composed of two SMFs and a piece of etched ECFMF. The proposed etched ECFMF-DMI was fabricated by using a commercial fusion splicer with the manual mode. Firstly, one end of etched ECFMF was spliced to a lead-out SMF, where the eccentric core of the ECFMF was directly aligned with the core of the SMF without any offset. Then, at the other splicing point, the core of the lead-in SMF was spliced to the core of the ECFMF with an outward lateral-offset along the radial direction of the ECFMF. As a result, the etched ECFMF-DMI based on the core-core mode interference was realized. If the ECFMF is not etched, the ECFMF-DMI based on the core-core mode interference is insensitive to the RI, so this situation is not discussed here. For comparison, the unetched ECFMF-DMI based on the core-cladding mode interference was fabricated and its schematic configuration is shown in Fig. 1(d). In addition, at two splicing points between the eccentric core of ECFMF and the cores of both lead-in/out SMFs have the same outward lateral-offset in the radial direction.

Fig. 1. The cross-section of (a) the ECFMF and (b) etched ECFMF. Schematic configuration of (c) the eathed ECFMF-DMI based on core-core mode interference and (d) the uneathed ECFMF-DMI based on core-cladding mode interference. Inset shows the cross-section view of the position of outward lateral-offset.

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3. Operation principle of the sensor

For etched ECFMF-DMI, when light beam propagates through the first lateral-offset point, the LP₀₁ and LP₁₁ modes in the eccentric core of the ECFMF can be excited simultaneously in the wavelength range of 1150-1450 nm. The different propagation constants of both modes cause a mode beating along the propagation direction and form a spatial core-core mode interference. The interference spectra in the LP₀₁ mode can be measured by splicing a lead-out SMF to the FMF without any offset. There is no energy of cladding modes coupling back to the lead-out SMF because the eccentric core of the etched ECFMF is directly aligned with the core of the lead-out SMF without any offset. However, for unetched ECFMF-DMI, the core modes and cladding modes can be excited at first lateral-offset, then they are recoupled into the lead-out SMF at the second spliced point to generate the interference and form a DMI based on core-cladding mode interference. The transmission spectrum from the lead-out SMF is measured by an optical spectrum analyzer (OSA). Because the effective RIs of interference modes are different, therefore a phase difference Δφ will be generated. According to the interference theory, Δφ can be expressed as

(1)$$\Delta \varphi =\frac{{2{\pi }\Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )L}}{\lambda }$$

where L is the length of the ECFMF, λ is the input light wavelength, and n_ex is external medium RI, Δn_eff (λ, n_ex) is the effective RI difference between interference modes that is the function of wavelength and external medium RI. When the phase difference meets the condition Δφ=(2m + 1)π, where m is an integer, the destructive interference will be generated, the output light intensity reaches a minimum value. Therefore, the wavelength of the destructive interference valley can be represented as

(2)$${\lambda _m} = \frac{{2\Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )L}}{{2m + 1}}$$

The separation distance between adjacent interference peaks and valleys, described as the free spectra range (FSR), can be expressed as

(3)$$\textrm{FSR}=\frac{{{\lambda ^2}}}{{\Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )L}}$$

The effective RI difference between interference modes changes with the external medium RI, so the interference valleys will shift. The RI sensitivity can be expressed as

(4)$$\frac{{d{\lambda _m}}}{{d{n_{\textrm{ex}}}}} = \frac{{{\lambda _m}({{{\partial \Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )} \mathord{\left/ {\vphantom {{\partial \Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )} {\partial {n_{\textrm{ex}}}}}} \right.} {\partial {n_{\textrm{ex}}}}}} )}}{{\Delta {n_g}}}$$

where the group index difference is defined as

(5)$$\Delta {n_g} = \Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )- {\lambda _m}({{{\partial \Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )} \mathord{\left/ {\vphantom {{\partial \Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )} {\partial \lambda }}} \right.} {\partial \lambda }}} )$$

In the etched ECFMF, the calculated effective RI difference between LP₀₁ and LP₁₁ modes (at 1310 nm) is shown in Fig. 2(a). It is apparent that the effective RI difference decreases nonlinearly as external medium RI increases, and ${{\partial \Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )} \mathord{\left/ {\vphantom {{\partial \Delta {n_{\textrm{eff}}}({\lambda ,{n_{\textrm{ex}}}} )} {\partial {n_{\textrm{ex}}}}}} \right.} {\partial {n_{\textrm{ex}}}}}\,<\,0$ can be derived. Meanwhile, the effective RI differences with the wavelength for different external medium RIs are shown in Fig. 2(b). The effective RI difference increases linearly as the wavelength increases, and $\Delta {n_g}\,<\,0$ can be obtained. According to Eq. (4), the RI sensitivity of the etched ECFMF-DMI is positive, which predicts that the interference valleys will shift to the long wavelength with the increasing external medium RI.

Fig. 2. The changes of the effective RI difference between LP₀₁ and LP₁₁ modes of etched ECFMF (a) with external medium RI at 1310 nm and (b) with wavelength for different external medium RIs.

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When the light from lead-in SMF passes through the first lateral-offset splicing point, the core and cladding modes of the ECFMF will be excited, the excitation coefficient, describe as the excitation efficiency, can be given as [24]:

(6)$$b = \frac{1}{4}\int\!\!\!\int {({{{\bf E}_{\bf m}} \times {\bf H}_{\bf n}^ \ast + {\bf E}_{\bf n}^ \ast \times {{\bf H}_{\bf m}}} )} \cdot {\bf z}\textrm{dxdy}$$

where E_m and H_m are the normalized electric and magnetic fields of a mode in the SMF, respectively. ${\bf E}_{\bf n}^\ast $ and ${\bf H}_{\bf n}^\ast $ are the complex conjugates of the normalized electric and magnetic fields of a mode in the ECFMF, respectively. z is the unit vector along the propagation direction of the light.

With different lateral-offsets between the core of the SMF and the eccentric core of the ECFMF, the calculated excitation coefficients of LP₀₁ and LP₁₁ modes in the eccentric core of etched ECFMF (at 1310 nm) are shown in Fig. 3(a). The excitation coefficient of LP₀₁ mode is always larger than that of LP₁₁ mode and decreases as the lateral-offset displacement increases. When the lateral-offset displacement is ∼ 3.2 µm, the excitation coefficient of the LP₁₁ mode in the eccentric core reaches its maximum. However, the excitation coefficient of LP₀₁ mode is much larger than that of LP₁₁ mode at the lateral-offset of ∼ 3.2 µm, thus the extinction ratio in the interference spectrum is lower. The excitation coefficients of LP₀₁ and LP₁₁ modes are approximately equivalent at the offset displacement of ∼ 5 µm. Therefore, in order to improve the fringe visibility of the interference spectrum and obtain a large extinction ratio, the lateral-offset displacement is fixed at ∼ 5 µm. Moreover, the calculated excitation coefficients of LP₀₁ and LP₁₁ modes in the eccentric core and cladding mode of unetched ECFMF (at 1310 nm) with different lateral-offsets are shown in Fig. 3(b), and the insert shows the electric field distribution of the cladding mode with a large excitation coefficient. The changing trend of the excitation coefficient of LP₀₁ and LP₁₁ modes in unetched ECFMF is similar to that of etched ECFMF. As expected, the cladding mode can be excited strongly with increasing lateral-offset displacement. When the intensities of LP₁₁ mode and the cladding mode are equal, the larger fringe visibility can be obtained. Therefore, the lateral-offset displacement can be kept at ∼ 9 µm in the experiment.

Fig. 3. The excitation coefficients of the modes of etched ECFMF (a) and unetched ECFMF (b) with different lateral-offsets at the spicing point (at 1310 nm). Inset shows the electric field distribution of the cladding mode with a large excitation coefficient.

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4. Experimental results and discussions

Both the etched and unetched ECFMF-DMIs based on core-core and core-cladding mode interferences are investigated. The light source is an ultra-continuous spectrum fiber laser (SC-5, Yangtze Soton Laser Co., Ltd.), and the OSA is AQ6370C (YOKOGAWA Inc.). The proposed sensor is compact and its total length is only 3.2 cm. The transmission spectra of etched and unetched ECFMF-DMIs in the air are shown in the Figs. 4(a) and 4(b), respectively. The inserts show the field distributions of interference modes at 1310 nm and the splicing point between the SMF and the ECFMF of etched ECFMF-DMI. The insertion loss of the DMIs are ∼ 2.5 dB. The interference spectrum of the etched ECFMF-DMI is smoother and has a larger extinction ratio compared to the unetched ECFMF-DMI. The measured FSR of the etched ECFMF-DMI is 20 nm. According to Eq. (3), the effective RI difference between LP₀₁ and LP₁₁ modes in the eccentric core is 0.00277, which coincides well with the numerical calculated value 0.00291 (at 1320 nm). In the unetched ECFMF-DMI, the LP₁₁ mode in the eccentric core and the higher order cladding mode generate an interference with a FSR of 38.2 nm. The measured effective RI difference is 0.00147, in consistent with the calculated value 0.00143 (at 1329 nm). Figure 4(c) shows the effective RIs of different modes, the cutoff wavelength of the LP₂₁ mode is ∼1020 nm, therefore, only LP₀₁ and LP₁₁ modes operate in the eccentric core within 1150–1450 nm. In order to intuitively exhibit the number of interference modes of etched and unetched ECFMF-DMIs, their spatial frequency spectra are shown in Fig. 4(d). The spatial frequency is defined by the reciprocal of the wavelength. The frequency spectra of ECFMF-DMIs have the only main peak, therefore both of etched and unetched ECFMF-based interferometers are dual-mode interference. In addition, the calculated birefringence of the etched ECFMF is only 9 × 10⁻⁶ at 1310 nm, therefore, the polarization dependent phenomenon of the devices can be ignored.

Fig. 4. (a) The transmission spectrum of the etched ECFMF-DMI based on core-core mode interference. The inset is the micrograph of the splicing point between ECFMF and SMF. (b) The transmission spectrum of the unetched ECFMF-DMI based on core-cladding mode interference. The inserts show the field distributions of interference modes. (c) The effective RI with the wavelength for different modes. (d) The spatial frequency spectra of etched and unetched ECFMF-DMIs.

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To measure RI response, glycerinum solutions with different RIs in a large range of 1.335∼1.400 were used and the RIs of glycerinum solutions were determined by an Abbe refractometer. The schematic of the experimental setup is shown in Fig. 5. The sensor was taped on a glass slide and two pigtail fibers of the DMI were fixed on fiber holders in order to keep straight. Then the glycerinum solution were dropped on the glass slide and covered the sensor entirely. After each RI solution measurement, the solution was rinsed by deionized water and wiped away. Compared to unetched ECFMF-DMI, the etched ECFMF-DMI based on core-core mode interference should have a higher RI sensitivity. Since the eccentric core of the etched ECFMF lies on the periphery of the cladding, the enhanced evanescent field can strengthen the interaction between the light and ambient medium. To demonstrate this concept, we measure RI and temperature responses of two kinds of DMIs under the same experimental condition. The transmission spectra of the etched ECFMF-DMI for different RIs are displayed in Fig. 6(a). The details of the spectra are displayed in Fig. 6(b). The interference valley shifts towards longer wavelength with increasing external medium RI, which coincides well with aforementioned theoretical prediction. The calculated and measured wavelength of the interference valley (marked by “A”) with external medium RI is presented in Fig. 6(c), the variation trend of the measured wavelength coincides well with that of the calculated wavelength. Here a nonlinear wavelength response is obtained, which is attributed to the nonlinear change of the effective RI difference between LP₀₁ and LP₁₁ modes. As expected, in the RI range from 1.335 to 1.400, the maximum sensitivity is 2565.2 nm/RIU at the RI of ∼1.4, which is higher than those of twin-core (240.22 nm/RIU) [18] and coreless (148.6 nm/RIU) fiber-based RI sensor [20], FBG-based RI sensor (231.4 nm/RIU) [2], and tapered-based RI sensor (2066 nm/RIU) [14]. Meanwhile, the temperature response is also tested in the range from 20 to 200 °C. Figure 5(d) shows the temperature response of the interference valley (marked by “A”) of the DMI. The valley shows a blue shift as the temperature increases and a sensitivity of 9.6 pm/°C is obtained. The cross sensitivity between the RI and temperature is as low as 3.74×10⁻⁶ RIU/°C so that it can be neglected.

Fig. 5. The schematic of the experimental setup for measuring RI response.

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Fig. 6. (a) The transmission spectra of the etched ECFMF-DMI based core-core mode interference for different RIs. (b) Zoomed view of transmission spectra in the wavelength range from 1300 to 1400 nm. (c) The calculated and measured interference valley (marked by “A”) wavelength shifts with different RI solutions. (d) The interference valley (marked by “A”) wavelength shifts with different temperatures.

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The transmission spectra of unetched ECFMF-DMI based on core-cladding mode interference for different RI solutions are displayed in Fig. 7(a). The wavelength response of the interference valley (marked by “B”) for external RI is shown in Fig. 7(b). In the unetched ECFMF-DMI, the effective RI of the cladding mode changes with external RI, however, the effective RI of the LP₁₁ mode remains unchanged. Therefore, the valley shifts towards shorter wavelength due to the decreasing effective RI difference between LP₁₁ mode and the cladding mode when the external RI increases, which is contrary to the etched ECFMF-DMI, and a sensitivity of 8.5 nm/RIU is obtained in Fig. 7(b). As expected, the sensitivity of etched ECFMF-DMI is hundreds times than that of the unetched ECFMF-DMI. The shift of interference valley (marked by “B”) wavelength with the increasing temperature is shown in Fig. 7(c). The valley also exhibits a blue shift with the increasing temperature and the sensor has a sensitivity of 33.1 pm/°C. The cross sensitivity between the RI and temperature is as low as 0.0039 RIU/°C. The temperature sensitivities of the etched and unetched ECFMF-DMIs mainly arise from the thermo-optic coefficients of interference modes. The thermo-optic coefficients of the core and cladding materials are different. Therefore, the temperature sensitivity of the unetched ECFMF-DMIs based on the interference between the core and cladding modes with different thermo-optic coefficients is larger than that of the etched ECFMF-DMI based the interference between core modes with approximate thermo-optic coefficients. According to experimental results, the etched ECFMF-DMI is much more desirable for RI measurement due to its high RI sensitivity, reliability and quite lower cross sensitivity. In addition, the unteched ECFMF-DMI has great potentials in direction bending measurement because the ECFMF core deviates from the center of the cladding.

Fig. 7. (a) The transmission spectra of unetched ECFMF-DMI based on core-cladding mode interference for different RIs. (b) The interference valley (marked by “B”) wavelength shifts with different RI solutions. (c) The interference valley (marked by “B”) wavelength shifts with different temperatures.

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5. Conclusion

In conclusion, a RI sensor based on ECFMF-DMI has been proposed and demonstrated. The etched ECFMF-DMI has a high stability because interference modes consist of LP₀₁ and LP₁₁ modes in the same eccentric core. The RI and temperature response are investigated. The proposed etched ECFMF-DMI has a maximum RI sensitivity of 2562.5 nm/RIU at the external RI of ∼1.4, and a low temperature sensitivity of 9.6 pm/°C. However, the unetched ECFMF-DMI based on core-cladding mode interference has a quite low RI sensitivity of 8.5 nm/RIU and a slightly higher temperature sensitivity of 33.1 pm/°C. Compared with the ECFMF-DMI based on core-cladding interference, the etched ECFMF-DMI based on core-core mode interference has hundreds times higher RI sensitivity. In addition, it can reduce temperature cross sensitivity more effectively. Therefore, the etched ECFMF-DMI based on core-core modes interference possesses advantages such as compact structure, high sensitivity and practicability and has great potentials in chemical, biological, physical, and environment monitoring fields.

Funding

National Natural Science Foundation of China (61675054, 61875044, 91750107); Natural Science Foundation of Heilongjiang Province (ZD2018015); Harbin Engineering University (B13015); Fundamental Research Funds for the Central Universities (3072019CF2501).

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Refractive index sensor based on etched eccentric core few-mode fiber dual-mode interferometer

Abstract

1. Introduction

2. Fabrication of the sensor

3. Operation principle of the sensor

4. Experimental results and discussions

5. Conclusion

Funding

References

Cited By

Figures (7)

Equations (6)

Optics Express