1. Introduction

Refractive index (RI) sensing is of great importance to physical, chemical and biological applications. Optical fiber RI sensors have attracted much attention due to their inherent advantages, such as high sensitivity, compact size, electromagnetic immunity and short response time. In addition, the easy realization of remote monitoring is very attractive. So far, numerous optical fiber RI sensors have been reported based on different principles, including fiber Bragg gratings (FBGs) [1, 2], long period fiber gratings (LPGs) [3, 4], surface plasmon resonance (SPR) [5, 6] and interferometers [7–9]. Particularly, Mach-Zehnder interferometer (MZI)-based RI sensors have become a research hotspot because of simple fabrication and high sensitivity. An all-fiber RI sensor based on offset-spliced single mode fibers (SMFs) was realized with its RI sensitivity of 27 nm/RIU [10]. To improve the sensitivity, a gentle taper was introduced between two offset splicing points of the MZI to enhance the RI response [11], and the sensitivity of 78.7 nm/RIU was obtained. Although all aforementioned RI sensors have low cost and simple fabrication, their sensitivities are not high, which limits their potential applications. Therefore, numerous processing methods were used to improve the performance of fiber MZI sensors, such as special tapering [12, 13] and fusion splicing [14], and femtosecond (fs) laser micromachining [15, 16]. By these methods, the RI sensitivity can reach hundreds even thousands nm/RIU. However, special tapering or fusion splicing may degrade the mechanical strength of sensors, which hampers their practical applications. Fs laser micromachining can significantly enhance the sensitivity and make the sensor more compact, but the fabrication cost is increased greatly. To avoid above disadvantages, many special fibers were used to fabricate MZIs for RI sensing, such as photonics crystal fibers [17], thin-core fibers [18], thinned fibers [19] and multimode microfibers [20]. Especially, photonics crystal fiber-based RI sensors have obvious advantages due to their natural microfluidic channels. However, the order of valleys cannot be identified. This type of sensor encounters a problem in remote monitoring applications, in which the monitored valley is difficultly re-locked after it is missing because of the continuous change of the monitored parameter. The other valley may replace the original monitored valley in the missing time, which will lead to an incorrect measurement. This disadvantage limits the potential application of these optical fiber sensors in remote monitoring. If the interference spectrum may help the demodulating system ascertain the order of interference valleys, the issue can be addressed.

In this work, we theoretically designed and experimentally demonstrated a new in-fiber MZI based on single eccentric hole-assisted dual-core fiber (SEHADCF) for RI measurement. The interferometer is fabricated by splicing a section of SEHADCF to two SMFs with an appropriate offset. The interferometer has a piecewise interference spectrum, and the discontinuous region can be employed as a mark to identify the order of interference valleys. Glycerinum solution with different refractive indices was injected into the air-hole of the SEHADCF to test the RI response of the proposed in-fiber SEHADCF-based MZI. The order of interference valleys of the in-fiber SEHADCF-based MZI can be distinguished, which have a great significance for remote monitoring applications.

2. Operation principle of the sensor

The schematic diagram of the proposed SEHADCF-based MZI is shown in Fig. 1, and the top inset is the microscope image of the cross-section of the SEHADCF. The SEHADCF is composed of a center core, a large eccentric air-hole, a side core suspended on the wall of the air-hole closest to the center core, and a common cladding. The diameters of the center core, suspended core, air-hole and cladding are 8.5, 12.1, 44.8 and 125 μm, respectively. The separation between two core centers is 17.3 μm. The RI distribution of the SEHADCF was measured using a RI profiler (S14, Photon Kinetics, Inc.). The RIs of two cores are 1.45702 at 632.8 nm, and the RI difference between the core and cladding is 0.00425. The proposed SEHADCF-based MZI is composed of a section of the SEHADCF and two SMFs, which is spliced into the SMF-SEHADCF-SMF structure. There are appropriate lateral-offsets between ends of SMFs and the SEHADCF to ensure that cores of SMFs can simultaneously cover a part of two cores of the SEHADCF, as shown in Fig. 1. The lateral-offset splicing points are employed as splitting and combining couplers. When light beam passes the left SMF into the offset splicing point І, the modes in two cores of the SEHADCF can be excited because of the overlapping mode distributions of the SMF and the SEHADCF. Therefore, the light is split into two beams and transmits in the center core and the suspended core of the SEHADCF, respectively. The two beams are combined and coupled into the right SMF at the offset splicing point ІІ to form a MZI. Because the two cores of the SEHADCF are different, a phase difference Δφ will be produced after the two beams propagate through the SEHADCF. Δφ = 2πΔn_effL/λ, where L is the length of the SEHADCF, and λ is the light wavelength. $\Delta n_{\text{eff}}=n_{\text{eff}}^{\text{cc}}-n_{\text{eff}}^{\text{sc}}$ is the effective RI difference between the modes in the center and suspended cores. The combined light intensity of the MZI can be written as

 

Fig. 1 The schematic diagram of the SEHADCF-based MZI. Insets: The top and bottom insets are the cross-section of the SEHADCF sample and the micrograph of an etched microhole, respectively.

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Injecting liquid into the air-hole, $n_{\text{eff}}^{\text{sc}}$ will increase observably owing to the direct contact between suspended core and solution, while the $n_{\text{eff}}^{\text{cc}}$ will be hardly affected. Therefore, the suspended and center cores are employed as sensing and reference arms, respectively. The change of RI of liquid results in the change of phase difference between the suspended and center cores, so the destructive interference valley will shift.

Compared with the core of SMF, due to the large size of the suspended core and the large RI difference between suspended core and air, the suspended core can support many modes. The guided modes of the SEHADCF are numerically calculated by using the finite element method (FEM). The dispersion curves of the supported modes and the electric field distributions at different wavelengths are shown in Fig. 2. The effective RIs of these modes decrease with the increasing wavelength. Specially, effective RIs of LP₀₁ modes in the center and suspended cores are equal at ~1700 nm, hence the strong resonant coupling occurs due to the small distance between the cores, which has been confirmed by our previous research [21]. Thus, the operating wavelength of the proposed MZI sensor must be far away from this resonant wavelength. The light from the left SMF can excite simultaneously modes of center and suspended cores of the SEHADCF at the lateral-offset splicing point. The excitation coefficient used to describe the excitation efficiency is given as follow [22]

 

Fig. 2 The dispersion curves for different modes and typical field distributions in the SEHADCF. (a) The effective RI of modes in the SEHADCF at different wavelengths. (b) - (i) Field distributions of different modes in the SEHADCF. (b) and (c) LP₀₁ and LP₁₁ modes of the center core at 980 nm. (d) and (e) LP₀₁ and LP₁₁ modes of the suspended core at 980 nm. (f) LP₂₁ mode at 940 nm. (g) and (h) LP₀₁ mode of the center and suspended cores at 1310 nm. (i) LP₁₁ mode of the suspended core at 1310 nm.

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Fig. 3 The relationship between excitation coefficients of modes of the SEHADCF and the lateral-offset of the spicing point for different wavelengths. (a) 980 nm. (b) 1310 nm.

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According to the calculated results, the suspended core modes can be excited strongly with the increasing lateral-offset, while the center core modes are weakly excited. In addition, when the lateral-offset exceeds 3 μm at 980 nm, the LP₁₁ mode is excited mainly in center core due to the larger excitation coefficient than that of LP₀₁ mode. When the lateral-offset reaches ~8 μm, the LP₁₁ modes in the center core and suspended core can be excited almost equally. At 1310 nm, the tendency of excitation coefficients of modes is similar to the situation at 980 nm. It is noteworthy that excitation coefficients of every mode are higher than those with same lateral-offset at 980 nm. It can be attributed to the larger effective mode field area at 1310 nm. Moreover, in the suspended core, the LP₁₁ mode is easier excited than LP₀₁ mode. When the lateral-offset reaches 6 μm, the LP₁₁ mode in suspended core and LP₀₁ mode in the center core can be excited almost equally. To obtain a large fringe visibility of the interference spectrum, the lateral-offset is selected in the range of 6 ~8 μm.

3. Fabrication of the sensor

The proposed SEHADCF-based MZI was fabricated by using a commercial fusion splicer. Initially, a section of SEHADCF is spliced to a SMF with a slight lateral-offset, about ~7 μm, to guarantee the light from the left SMF can be coupled into the center and suspended cores, simultaneously. Then aligning the other end of SEHADCF and the right SMF, and the transmission spectrum from right SMF is detected using an OSA. The lateral-offset between the SEHADCF and right SMF is adjusted, and the two fibers are spliced when the fringe visibility of the interference spectrum reaches a maximum. The slight lateral-offset ensures that the sensor has a good mechanical strength. The micrograph of the splicing point between the SMF and the SEHADCF is shown in the bottom-left inset of Fig. 4(a). The air hole has no obvious deformation. Figure 4 shows the transmission spectrum of the fabricated SEHADCF-based MZI with the SEHADCF length of 41 mm. The insertion loss of the MZI is ~15 dB. Three piecewise discrete envelopes in the interference spectrum can be observed in wavelength range from 600 to 2400 nm and are sequentially named as the first (in the red dashed line frame), the second (in the green dashed line frame) and the third (in the purple dashed line frame) interference regions, respectively, as shown in Fig. 4. In the first interference region, the interference with the FSR of ~20.6 nm arises from LP₁₁ modes in the center and suspended cores. According to Eq. (3), the measured effective RI difference between LP₁₁ modes in two cores is 0.00109, which coincides well with the numerical calculation result 0.00095 (at 962 nm). The interference spectrum in the first interference region is not very smooth. The unsmooth interference spectrum is attributed to the multimode interference, since the two cores of SEHADCF can support multiple modes in the range of 920 ~1140 nm. Nonetheless, the interference valley is formed dominantly by LP₁₁ modes in the two cores. Due to the cut-off of the LP₁₁ mode in center core above ~1160 nm (as shown in Fig. 2(a)) and the center core operates as a single mode core at the long wavelength above 1160 nm, a discontinuous region is introduced. In the second interference region, LP₀₁ mode in the center core and LP₁₁ mode in suspended core generate an interference with the FSR of ~26.1 nm. The experimentally measured and numerically calculated effective RI differences between these two modes are 0.00164 and 0.00189 (at 1321 nm), respectively, which are also coincident well with each other. In addition, there is an obvious damping of the amplitude in the interference spectrum, because the LP₁₁ mode in the suspended core leaks into the cladding more and more when approaching to the cut-off wavelength (~1420 nm). After ~1420 nm, the LP₁₁ mode in the suspended core is cutoff, so the interference disappears. In the third interference region, the interference with FSR of 29.1 nm is formed by LP₀₁ mode of the center core and high order cladding mode. The experimentally measured and numerically calculated effective RI differences between these two modes are 0.00335 and 0.00385 (at 1996.5 nm), respectively, which agree well with each other. From the right side of the discontinuous region, the order of interference valleys is numbered as 1, 2, 3, … in turn. Comparing to other structure interferometric sensors, the obvious advantage of the proposed sensor is that the order of interference valley is identifiable by the discontinuous region,which is beneficial to improve the reliability of optical fiber sensors in remote monitoring applications.

 

Fig. 4 Transmission spectra of SEHADCF-based MZI. (a) The transmission spectrum of SEHADCF-based MZI in the wavelength range from 600 to 1600 nm. 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 bottom-left inset is the micrograph of the splicing point between the SMF and the SEHADCF. (b) The transmission spectrum of SEHADCF-based MZI with the wavelength range from 1200 to 2400 nm. The light source is an ultra-continuous spectrum fiber laser (SuperK Compact, NKT Photonics Inc.), and the OSA is AQ6375B (YOKOGAWA Inc.).

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To form a microfluidic channel, two microholes on the side wall of the air-hole are etched near the offset splicing points by using a high-frequency CO₂ laser, as shown in Fig. 1. To ensure the air-hole facing to the laser beam, a lens is employed to observe the orientation of the SEHADCF. The etched microhole is shown in the bottom inset of Fig. 1. The suspended core is undamaged and the air hole does not deform obviously. A syringe needle is employed to cover a microhole to inject fluid into the air-hole.

4. Experimental results and discussion

A SEHADCF-based MZI RI sensor with the SEHADCF length of 36.2 mm was employed in the experiment. The typical spectrum of the sensor without glycerinum solution injected into the air-hole is shown in Fig. 5(a) (the blue line). Two different envelopes in the interferencespectrum can be observed in wavelength ranges of 920 ~1140 nm and 1270 ~1510 nm. To test the RI sensing performance, glycerinum solutions with RI range from 1.335 to 1.395 were used. And a micro-flow syringe pump was employed to inject glycerinum solution into the sensor. The transmission spectra of the sensor with injected glycerinum solutions are shown in Fig. 5(a). To avoid the effect from the discontinuous region, the 5th interference valley is chosen to test the RI response. Details of the spectra are illustrated in Fig. 5(b). The interference valley shifts linearly towards longer wavelength with the increasing RI. Due to the increasing RI of the solution in the air-hole, LP₁₁ mode in the suspended core cuts off at shorter wavelength and the cladding mode can be excited. Hence, the interference in the range of 1320 ~1580 nm is formed by LP₀₁ mode in the center core and high-order cladding mode. The excited high-order cladding mode, shown in the inset of Fig. 5(a), is sensitive to the change of RI of air-hole due to the strong field distribution in the suspended core. The change of Δn_eff between the core mode and high-order cladding mode is positive with the increasing RI of the solution in the air-hole, which is similar to long-period fiber grating RI sensing [12, 23]. Therefore, according to the Eq. (2), the interference valley will shift towards longer wavelength. The relationship between glycerinum solution RI and the interference valley wavelength is shown in Fig. 5(d). The interference valley wavelength shifts linearly in the RI range from 1.335 to 1.395, and the measured RI sensitivity is 294.5 nm/RIU. At the longer wavelength the sensor is more sensitive to the RI change, so the sensitivity of the 13th valley is tested, and the results are shown in Fig. 5(c) and 5(e). The RI sensitivity is 353.9 nm/RIU, which is higher than those of some special fiber-based MZIs [14, 18]. For different wavelengths, the splitting ratio of LP₀₁ mode in the center core and the cladding mode of the SEHADCF slightly fluctuates at the offset splicing point. For the 5th interference valley, the intensity of LP₀₁ mode in the center core is slightly weaker than that of the high-order cladding mode, but it is reversed for the 13th interference valley. Because the intensity of the high-order cladding mode decreases with increasing RI of the solution, therefore the opposite intensity changes of 5th and 13th valleys are observed. Besides the high sensitivity, remarkably the discontinuous region of the interference spectrum can be employed as a mark to distinguish the order of valleys. The monitored valley can be again found and locked depending on the discontinuous region after the monitoring is interrupted. As a result, the remote monitoring can become more reliability by use of this sensor. Therefore, the proposed SEHADCF-based MZI RI sensor has a great potential for remote monitoring.

 

Fig. 5 The RI response of the sensor. (a) The transmission spectra of the sensor injected solutions with different RIs. (b) and (c) are partial zoomed views of the transmission spectra in the wavelength range from 1415 to 1455 nm and from 1495 to 1530 nm, respectively. (d) and (e) are the relationships between wavelengths of the 5th and the 13th interference valley and RI, respectively. Inset: the field distribution of the excited high-order cladding mode by simulating calculation.

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5. Conclusion

An in-fiber SEHADCF-based MZI was proposed and experimentally demonstrated. The interferometer has an interference spectrum with piecewise discrete envelopes formed by different modes of the SEHADCF due to the different core characteristics. A discontinuous region formed by the cut-off of LP₁₁ in the center core near the 1160 nm can be used to distinguish the order of the interference valley of the transmission spectrum. It is of great significance for optical fiber MZI remote applications, in which the monitored interference valley can be again found and locked after the monitoring is interrupted. The RI response of the interferometer was investigated, the experimentally measured RI sensitivities of the 5th and 13th interference valleys are 294.5 and 353.9 nm/RIU, respectively, which are higher than those of some other MZI-based RI sensors. In addition, by covering a functional film on the surface of the suspended core, the online detection of bio-medical parameters can be realized. Due to the high RI sensitivity, good mechanical strength, and the ability of distinguishing the order of the interference valley, the proposed fiber RI sensor has a great potential in remote monitoring, biological and chemical applications.