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We report an open-cavity optical fiber Fabry-Pérot interferometer (FPI) capable of measuring refractive index with very low temperature cross-sensitivity. The FPI was constructed by splicing a thin piece of C-shaped fiber between two standard single-mode fibers. The refractive index (RI) response of the FPI was characterized using water-ethanol mixtures with RI in the range of 1.33 to 1.36. The RI sensitivity was measured to be 1368 nm/RIU at the wavelength of 1600 nm with good linearity. Thanks to its all-glass structure, the FPI exhibits very low temperature cross-sensitivity of 3.04 × 10−7 RIU/°C. The effects of cavity length on the performance of the sensor were also studied. A shorter cavity gives rise to broader measurement range while offering larger detection limit, and vice versa. What’s more, the effect of material dispersion of analyte on the sensitivity of open-cavity FPIs was identified for the first time. The sensor is compact in size and easy to fabricate. It is potentially useful for label-free optical sensing of chemical and biological samples.
© 2014 Optical Society of America
1. Introduction
Fiber-optic Fabry–Pérot interferometers (FPIs) have received considerable interest for sensing applications in recent years due to their many outstanding advantages, such as compact size, high sensitivity, and ease of fabrication [1]. So far, many methods have been developed for fabricating optical fiber FPIs, such as those based on splicing/bonding different types of fibers or tubes [2–14], chemical etching [15–17], and laser micromachining [18–25]. According to the architecture of the cavity, FPIs can be classified into two kinds, i.e., sealed cavity FPIs and open cavity FPIs. Most sealed-cavity FPIs are limited to sense physical parameters, such as pressure [2, 3, 18], strain [5, 6, 15], and temperature [3, 6, 15]. A few sealed-cavity FPIs were used to measure refractive index of liquid through the modulation of Fresnel reflectivity at the fiber end facet [7, 8, 20]. However, such method based on optical intensity detection is not particularly sensitive, and the signal is adversely affected by power fluctuation within the system. In contrast, open cavity FPIs allow gaseous and liquid samples to fill in the cavity. Hence, the optical path difference (OPD) of the FPI is directly related to the refractive index of the medium filling in the cavity, opening a new door for label-free optical sensing.
An open-cavity FPI can be simply achieved by aligning two well-cleaved single-mode fibers on a glass substrate [9] or within a microfluidic chip [10]. However, the use of the substrate/chip makes the sensor bulky and not suitable for in situ measurement. And the non-permanent alignment of the fibers is unstable for long-term use. Xiao et al. demonstrated an open-cavity FPI utilizing a bonding technique [11], in which multi-material were used to construct the sensor head, causing large cross sensitivity to temperature due to the large thermal-expansion coefficient of the glue used within the structure. Recently, Coelho et al. reported a hybrid FPI for simultaneous measurement of the partial pressure of O2 and CO2 [12]. This hybrid FPI exhibits a superimposed interference spectrum which increases the complexity for demodulation of the sensor. More recently, Tian et al. reported a microfluidic FPI with the help of a two-hole microstructred fiber [13]. The splicing joint of the lead-in normal fiber and the microstructured fiber was chemically etched in order to provide access to the FPI cavity through the air hole channels of the microstructured fiber. Duan et al. demonstrated an open-cavity FPI by introducing a large lateral offset of 67.5 µm during splicing and used it as a gas refractometer [14]. The large lateral offset degrades the mechanical strength of splicing point and make the sensor fragile. Open-cavity FPIs were also reported [16, 17] by selectively etching specially designed P2O5-doped fibers. Another popular approach to create open cavity FPIs is based on femto-second (fs) laser micromachining, which was first demonstrated by Rao et al. [19]. Later, the morphology, extinct ratio, and functionality of FPIs fabricated using the same technique were improved by Ran et al. [21, 22], Wei et al. [23], Liao et al. [24], and Tian et al. [25], respectively. Sharing the concept of laser micromachining, open-cavity FPIs were also produced by focused ion beam (FIB) milling [26, 27]. However, these micromachining systems require high-quality laser/FIB source and bulky optics, as well as high-resolution monitoring setups, rendering the device expensive to produce.
In this paper, we propose and demonstrate a new fiber-in-line open-cavity FPI constructed by splicing a thin piece of C-shaped fiber between two standard single-mode fibers. The whole fabrication process only involves a standard fusion splicer and a microscope, making the device cost-effective to produce. The C-shaped fiber functions as an open FP cavity, allowing liquid sample to fill in the gap between the two single-mode fibers. The refractive index (RI) response of the FPI was characterized using water-ethanol mixtures with RI in the range of 1.33 to 1.36. Experimental results reveal that it has a linear response with respect to the change in refractive index, with a very high sensitivity of 1368 nm/RIU at the wavelength of 1600 nm. The temperature sensitivity of the FPI was measured to be 0.42 pm/°C, indicating a very low temperature cross-sensitivity of 3.04 × 10−7 RIU/°C. In addition, the effect of cavity length on the performance of the sensor was studied. We find that a shorter cavity gives rise to broader measurement range and larger detection limit, and vice versa. What’s more, the effect of material dispersion of analyte on the RI sensitivity of open-cavity FPIs was identified for the first time. We find that the sensor exhibits different RI sensitivities at 1550 nm when it is calibrated by different kinds of analyte. This is because the nominal RI refers to its value at 589.3 nm and different kinds of analyte have different dispersion properties. With advantages of high sensitivity, linear response, compact size, and temperature-insensitive response, the proposed sensor is an excellent candidate for label-free optical sensing of chemical and biological samples.
2. Fabrication
The C-shaped fiber was fabricated in-house using an optical fiber drawing tower (NEXTROM OFC20) [28]. Firstly a fused silica tube with inner diameter of 4 mm and outer diameter of 12 mm was machined to create a lateral slot along the axial direction, resulting in a C-shaped preform. Then the preform was drawn into fiber with outer diameter of 145 μm, inner diameter of 48 μm, and an opening of ~40 µm. During the fiber drawing process, the oven of the tower was set to a relatively low temperature of 1890 °C to maintain the cross-sectional shape of the fiber. Figure 1(a) shows the scanning electronic microscope (SEM) photo of the cross section of the fabricated C-shaped fiber.
Fig. 1 Fabrication process of the C-FPI. (a) Scanning electronic microscope (SEM) photo of the cross section of the C-shaped fiber. (b) Side-view of fusion splicing the C-shaped fiber and the SMF. (c) Side-view of the SMF with a thin piece of C-shaped fiber fused spliced to it. (d) Side-view of the fabricated open-cavity C-FPI.
To fabricate the proposed FPI, a piece of C-shaped fiber was first spliced to a standard single-mode fiber (SMF) as shown in Fig. 1(b). We used a normal fiber cutter (FITEL S325) to cut the C-shaped fiber. During loading the C-shaped fiber on the fiber cutter, we carefully adjusted the orientation of the fiber to make sure the opening side is vertically upward. This was done with the help of a microscope. Because the C-shaped fiber has a non-circular cross section, manual alignment was adopted for splicing. After that, the C-shaped fiber was cut to less than 40 μm, as shown in Fig. 1(c), with the help of a microscope with 100 times amplification. Then the resultant structure was spliced to another SMF using the same manual splicing program with its other end angled cleaved to avoid unwanted reflection. Figure 1(d) shows the fabricated C-shaped fiber open-cavity FPI, labeled as C-FPI in Fig. 2.
Fig. 2 Schematic of the experimental setup for characterization of the liquid refractive index response of the C-FPI.
3. Experimental setup and principle of operation
Figure 2 illustrates the experimental setup for characterization of the refractive index response of the C-FPI. A broadband super-luminescent diode (SLED) with output wavelength range from 1420 nm to 1620 nm was used to illuminate the C-FPI through a 3-dB directional coupler. The C-FPI was connected to one arm at the other side of the coupler, and was immersed into a chamber filled with ethanol-water mixture. The other arm at the same side of the coupler was made an angled end facet to remove unwanted reflection. The reflected signal from the C-FPI was measured by an optical spectrum analyzer with a resolution of 0.02 nm (OSA, AQ6370). An optical circulator was not used here because it cannot cover such a wideband wavelength range. The use of 3-dB coupler introduces a loss of ~6 dB to the reflected signal as compared with the case of using an optical circulator. However, this is acceptable since the sensing information is encoded in the wavelength shift and not intensity based.
According to the theory of Fresnel reflection, the two mirrors formed at the interface of the C-shaped fiber and the SMF have very low reflectivity (R ≈3.5% and 0.2% for the cavity filled with air and water, respectively). Consequently, multiple reflections between the mirrors can be neglected, and the FPI can be treated as a two-beam interferometer [1]. Its interference spectrum can be expressed as follow:
where I(λ) is the optical intensity of the interference spectrum as a function of wavelength; I1 and I2 are the reflections from the two mirrors of the C-FPI; φo is the initial phase difference of the two beams; L is the cavity length; nm is the refractive index of the medium filling in the cavity; λ is the free space wavelength.For two adjacent dips in the interference spectrum of the C-FPI with wavelengths of λ1 and λ2, the accumulated phase difference from λ1 to λ2 is 2π. The wavelength spacing λ1−λ2 is also known as free spectral range (FSR). Using the aforementioned information, the FSR can be derived as
When the C-FPI is used for liquid refractive index measurement, the change in nm causes the shift of the interference spectrum and thus the variation of the dip wavelength. The dip wavelength is a function of nm. For a spectral dip tracked for measurement, its phase keeps to be a constant value of (2k + 1)π, where k is an integer. Thus we have
Differentiating both sides of Eq. (3) with respect to nm, considering L as a constant for refractive index sensing, we obtain
Then the refractive index sensitivity of the C-FPI is deduced to be
This equation indicates that the wavelength shift of the interference spectrum has a linear relationship with the refractive index of the medium filling in the cavity. The linear response feature of the FPI refractometer is an important advantage over the refractometers based on evanescent wave detection, which usually has a nonlinear response to refractive index change. Furthermore, Eq. (5) indicates that longer operation wavelength provides higher sensitivity. Longer wavelength broadband source could be employed to improve the sensitivity of the sensor. SLED with emission up to 1700 nm are commercially available. In this work, we used an SLED with emission up to 1620 nm.
4. Results and discussion
4.1 Spectra of C-FPIs with different cavity lengths
Following the procedure described in Section 2, several C-FPIs were fabricated. Figure 3 shows the reflection spectra of four C-FPIs with increasing cavity lengths, which were measured in air. The output intensity of the light source is not flat over the whole wavelength range; the spectra shown in figures are the measured reflected spectra minus the light source spectrum. In Figs. 1(b)–1(c), the view window of the splicer has an amplification of only 100 times. From the pictures it is difficult to measure the cavity length accurately. Therefore, the cavity lengths of the C-FPIs are estimated according to Eq. (2), and the values of them are found to be 9.4 μm, 13.8 μm, 20.3 μm, and 33.5 μm, respectively. The extinction ratio of the spectra ranges from 14 dB to 18 dB, which is comparable with that of the existing open-cavity FPIs.
Fig. 3 Interference spectra measured in air of the C-FPIs with increasing cavity lengths. (a) L = 9.4 μm. (b) L = 13.8 μm. (c) L = 20.3 μm. (d) L = 33.5 μm.
4.2 Refractive index response
The response to the change of liquid refractive index of two C-FPIs with cavity lengths of 13.8 μm and 20.3 μm were characterized employing the setup illustrated in Fig. 2. The liquid sample used in the experiment is ethanol-water mixture. The refractive index of the liquid was adjusted by stepwise adding small amount of ethanol (purity better than 99.5%, ACS grade) to deionized (DI) water. The values of the refractive index of the mixtures were measured by a handheld Abbe refractometer (Reichert AR200) working at the wavelength of 589.3 nm with measurement accuracy of 10−4 RIU.
The measurement results for two C-FPIs with cavity lengths of 13.8 μm and 20.3 μm are presented in Fig. 4. The spectral shifts with respect to increasing liquid refractive index are shown in Figs. 4(a) and 4(b); the dip wavelengths as functions of liquid refractive index are shown in Figs. 4(c) and 4(d). As can be seen from Figs. 4(a) and 4(b), the spectra linearly red shift with the increase of liquid refractive index, which is consistent with Eq. (5). We also observed that the peak power of the spectra degrades during the increasing of the liquid refractive index due to the reduction of the Fresnel reflectivity of the mirrors, which is given by [(n1-n2)/(n1 + n2)]2 for normal incidence. When water replaces air in the cavity, the value of n2 changes from 1 to 1.33, thus resulting in lower reflection at the glass/medium interface. In Figs. 4(c) and 4(d), the response curves of all the spectral dips have good linearity with R2 better than 0.99. For the operation wavelength around 1550 nm, a sensitivity of ~1300 nm/RIU was achieved for both C-FPIs and 1368 nm/RIU when operating around 1600 nm. It is important to note that higher sensitivity could be attained with this sensor by using a broadband light source emission at longer wavelength.
Fig. 4 Experimental results of refractive index response of two C-FPIs. (a) & (b) Spectral shifts with respect to increasing liquid refractive index for L = 13.8 μm and L = 20.3 μm, respectively. (c) & (d) Dip wavelengths as functions of liquid refractive index for L = 13.8 μm and L = 20.3 μm, respectively.
4.3 Effects of cavity length on the sensing performance
Detection sensitivity is an obviously important parameter for any sensor. In practical applications, other parameters such as measurement range and detection limit are also very important. For an interferometric sensor, the measurement range is usually defined as the FSR of the interference spectrum divided by its sensitivity. In general, the measurement range is limited by the FSR. A larger FSR provides a broader measurement range. As can be seen from Fig. 4(b), when the refractive index increased from 1.3330 to 1.3634, the dip wavelength shifted by 40.4 nm, approaching the FSR (43.9 nm). The detection limit of a sensor is related to its sensitivity, the resolution of the OSA (0.02 nm in our experiment), the full width at half maximum (FWHM) of the dip or peak, and the signal to noise ratio (SNR, ~50 dB in our experiment) of the spectrum. The detection limits of the two C-FPIs presented in Section 4.2 were calculated according to the formula reported in [29], and the results are given in Table 1. The C-FPI with shorter cavity length provides larger measurement range but also larger value of detection limit due to its broader wavelength dip. Consequently, there is a tradeoff between the measurement range and the detection limit for such kind of refractometer. One should choose proper cavity length according to the demands of the application.
Table 1. Performance comparison of two C-FPIs with different cavity lengths.
4.4 Intrinsic temperature response
One C-FPI was place in an oven to evaluate its temperature sensitivity. The oven was first heated and maintained at a temperature of 600 °C for half an hour, and then cooled naturally down to room temperature. The dip wavelength was recorded during the cooling process in a step of 100 °C. The measured result is plotted in Fig. 5. Through linear fitting, a very low sensitivity of 0.42 pm/°C was achieved, indicating a temperature cross-sensitivity of 3.04 × 10−7 RIU/°C. For a temperature variation of 100 °C, it only induces an error of 3.04 × 10−5 RIU for refractive index measurement. Therefore, temperature compensation is not required for most applications.
4.5 Effect of analyte dispersion on RI sensitivity
The RI sensitivity of all the open-cavity FPIs are governed by Eq. (5) in spite of how they are produced; therefore, in principle, they should give the same RI sensitivity for a certain RI value and operation wavelength. However, distinct RI sensitivities ranging from 994 nm/RIU to 1731 nm/RIU were reported in the literature (see Table 2). The reason leading to different RI sensitivities is the different material dispersion properties of the analytes they used to calibriate the sensor, which was neglected in previous studies. Due to material dispersion, the RI of an analyte is a function of wavelength. Generally, the nominal RI refers to its value at 589.3 nm. But the sensing signal used here and in the literature are at the wavelength band of 1550 nm. The slope achieved by linear fitting of the curves in Figs. 4(c) and 4(d) is actually the value of Δλ/Δn589nm, whereas Eq. (5) refers to Δλ/Δn1550nm. Their relationship is associated with a dispersion term and can be written as follow:
where Γ = Δn1550nm/Δn589nm is a term due to material dispersion. For different analytes used to calibrate the RI sensitivity of the open-cavity FPIs, they have different values of Γ, leading to different measured RI sensitivities. In other words, given the same amount of RI change at 589 nm (usually determined by an Abbe refractometer operating at 589 nm), the counterpart at 1550 nm is not the same for different materials. This means that if the sensor is calibrated using a certain analyte, the calibration will be invalid for other kinds of analyte due to their different RI sensitivities. One solution to overcome this problem is to operate at 589.3 nm wavelength band, i.e., to use a 589.3 nm broadband source and coupler. Otherwise it may suffer from an error that may be as large as 70% in practical applications.Table 2. RI sensitivities of open-cavity FPIs calibrated using different kinds of analyte
For better understanding how the dispersion of analyte affects the RI sensitivity, further experiment using deionized water to calibriate the RI response was carried out. As we have shown in section 4.4, the C-FPI has very low intrinsic temperature sensitivity; therefore, this allows us to tune the RI of water by temperature controlling without affecting the C-FPI. The same C-FPI studied in section 4.2 with cavity length of 13.8 um was immerged in a chamber filled with deionized (DI) water. The DI water was first heated to ~90 °C, and then it cooled down naturally to room temperature. Figure 6(a) shows the spectral shift during the cooling process. The RI of DI water at both 589.3 nm and 1520 nm as a function of temperature were accurately reproduced using the formula reported in [30]. Figure 6(b) and 6(c) shows plot the dip wavelength as a function of water RI at 589.3 nm and 1520 nm, respectively. Through linear fitting, the achieved slopes for the two curves are 1016.7 nm/RIU and 1146.3 nm/RIU. According to Eq. (5), the RI sensitivity is calculated to be 1520 nm / 1.312 RIU = 1141.8 nm/RIU, which agrees well with the experimental value of 1146.3 nm/RIU. This verifies that the RI sensitivity of C-FPIs can be directly estimated using Eq. (5) even without experimental calibration if the RI to be measured refers to its value at the operating wavelength rather than its nominal value at 589.3 nm. The absolute value of RI at 1550 nm can be roughly estimated according the FSR of the spectrum. It can be a useful tool for relative measurement of the RI change at 1550 nm, since most existing refractometers can only measure the RI at 589.3 nm.
Fig. 6 (a) Spectral shift of a C-FPI immerged in DI water at different temperatures. (b) Dip wavelength as a function of RI of DI water at 589.3 nm. (c) Dip wavelength as a function of RI of DI water at 1520 nm.
5. Conclusion
In conclusion, we have demonstrated a new approach to construct in-line open-cavity FPIs for measuring liquid refractive index with very low temperature cross-sensitivity. The fabrication process of the device is very simple and only involves splicing a thin piece of C-shaped fiber to standard SMFs. The sensitivity and the fringe visibility of this new open-cavity FPI are comparable with existing sensors of the same type. The effect of the cavity length on the performance of the sensor was studied experimentally. The effect of material dispersion of analyte on the RI sensitivity was identified. The advantages of compact size, ease and low-cost for fabrication, high sensitivity, linear response, and very low temperature cross-sensitivity of the proposed sensor render it a promising candidate for label-free optical sensing of chemical and biological samples.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under grants 11304122 and 61225023, in part by the Guangdong Natural Science Foundation under grant S2013040015234 and S2013030013302, in part by the Fundamental Research Funds for the Central Universities under grant 1613334, in part by the Planned Science and Technology Project of Guangzhou under grant 2012J5100028, and in part by The Hong Kong Polytechnic University under grant 4-ZZBE.
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