Application of spectrum differential integration method in an in-line fiber Mach-Zehnder refractive index sensor

doi:10.1364/OE.18.008135

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Application of spectrum differential integration method in an in-line fiber Mach-Zehnder refractive index sensor

Yi Li, Edouard Harris, Liang Chen, and Xiaoyi Bao »View Author Affiliations

Optics Express, Vol. 18, Issue 8, pp. 8135-8143 (2010)
http://dx.doi.org/10.1364/OE.18.008135

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▸ Article Outline
– Abstract
1. Introduction
2. Basic principle of SDI
3. Application of the SDI method in an in-line fiber MZI RI sensor
4. Device dependence
5. Conclusion
– References and links

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Abstract

A novel spectrum differential integration (SDI) method has been proposed and verified in an in-line fiber Mach-Zehnder (MZ) refractive index (RI) sensor using salt solutions. In SDI method, the difference between two interference spectra is determined by pointwise subtraction at each wavelength, followed by integration of the absolute differences along the scan range. Compared with the widely used peak wavelength shift method, the SDI method is more reliable over a wide wavelength range (on the order of 400 nm) and results in higher sensitivity as well as reduced device-dependence. The SDI method can also be utilized with other kinds of modal interferometric sensors.

1. Introduction

Recently, different optical fiber in-line MZ and Michelson interferometers have been proposed and have attracted attention because of their low cost, ease of fabrication and intrinsic in-line characteristics. They have been successfully demonstrated as RI, temperature, curvature angle, pH and strain sensors [1

R. Jha, J. Villatoro, G. Badenes, and V. Pruneri, “Refractometry based on a photonic crystal fiber interferometer,” Opt. Lett. 34(5), 617–619 (2009). [CrossRef] [PubMed]

–13

M. Jiang, A. P. Zhang, Y. C. Wang, H. Y. Tam, and S. He, “Fabrication of a compact reflective long-period grating sensor with a cladding-mode-selective fiber end-face mirror,” Opt. Express 17(20), 17976–17982 (2009). [CrossRef] [PubMed]

]. These in-line optical sensors are based on core-cladding mode interference. In order to couple light from the core mode to the cladding modes and couple these modes back to the core mode, structural disturbances such as abrupt tapers [2

Z. Tian, S. S. Yam, and H. P. Loock, “Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber,” Opt. Lett. 33(10), 1105–1107 (2008). [CrossRef] [PubMed]

Z. Tian, S. S.-H. Yam, and H.-P. Loock, “Single-mode fiber refractive index sensor based on core-offset attenuators,” IEEE Photon. Technol. Lett. 20(16), 1387–1389 (2008). [CrossRef]

,10

J. Ju, L. Ma, W. Jin, and Y. Hu, “Photonic bandgap fiber tapers and in-fiber interferometric sensors,” Opt. Lett. 34(12), 1861–1863 (2009). [CrossRef] [PubMed]

], long period gratings (LPG) [7

O. Frazão, R. Falate, J. L. Fabris, J. L. Santos, L. A. Ferreira, and F. M. Araújo, “Optical inclinometer based on a single long-period fiber grating combined with a fused taper,” Opt. Lett. 31(20), 2960–2962 (2006). [CrossRef] [PubMed]

,13

], connector-offset attenuators [3

J. Villatoro and D. M. Hernández, “Low-cost optical fiber refractive index sensor based on core diameter mismatch,” J. Lightwave Technol. 24(3), 1409–1413 (2006). [CrossRef]

L. V. Nguyen, D. Hwang, S. Moon, D. S. Moon, and Y. Chung, “High temperature fiber sensor with high sensitivity based on core diameter mismatch,” Opt. Express 16(15), 11369–11375 (2008). [CrossRef] [PubMed]

,11

H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). [CrossRef] [PubMed]

], and splicing interfaces between two types of fibers [1

R. Jha, J. Villatoro, G. Badenes, and V. Pruneri, “Refractometry based on a photonic crystal fiber interferometer,” Opt. Lett. 34(5), 617–619 (2009). [CrossRef] [PubMed]

B. Gu, M. J. Yin, A. P. Zhang, J. W. Qian, and S. He, “Low-cost high-performance fiber-optic pH sensor based on thin-core fiber modal interferometer,” Opt. Express 17(25), 22296–22302 (2009). [CrossRef]

S. H. Aref, R. Amezcua-Correa, J. P. Carvalho1, O. Frazão, P. Caldas, J. L. Santos, F. M. Araújo, H. Latifi, F. Farahi, L. A. Ferreira, and J. C. Knight, “Modal interferometer based on hollow-core photonic crystal fiber for strain,” Opt. Express 17(21), 18669–18675 (2009). [CrossRef]

,12

J. Villatoro, V. P. Minkovich, V. Pruneri, and G. Badenes, “Simple all-microstructured-optical-fiber interferometer built via fusion splicing,” Opt. Express 15(4), 1491–1496 (2007). [CrossRef] [PubMed]

] have been introduced. Two different kinds of structural disturbances, such LPGs and abrupt tapers [7

], can be used simultaneously in one interferometer. When light propagates through these disturbances, some portion of the incident optical power is coupled into one or several cladding modes and the rest remains in the core mode. In MZ configurations, a second disturbance is required to couple the light from the excited cladding modes back into the core, following the sensing region. For Michelson configurations, a cleaved fiber end or gold-coated fiber end [2

Z. Tian, S. S. Yam, and H. P. Loock, “Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber,” Opt. Lett. 33(10), 1105–1107 (2008). [CrossRef] [PubMed]

] is used to reflect the light back through the initial disturbance. Thus, the light coupled to the cladding modes behaves as the interferometer’s sensing arm and the light that remains in the core acts as the reference arm. The relative phase change between the interferometer’s two arms occurs because the cladding modes respond differently from the core mode to environmental factors, such as temperature, applied strain, and the RI of the surrounding medium. This relative phase change is ascertained from measurable differences in the observed transmission spectra, such as shifts in the positions of attenuation peaks. In many previous studies [1

R. Jha, J. Villatoro, G. Badenes, and V. Pruneri, “Refractometry based on a photonic crystal fiber interferometer,” Opt. Lett. 34(5), 617–619 (2009). [CrossRef] [PubMed]

–6

–10

J. Ju, L. Ma, W. Jin, and Y. Hu, “Photonic bandgap fiber tapers and in-fiber interferometric sensors,” Opt. Lett. 34(12), 1861–1863 (2009). [CrossRef] [PubMed]

,12

,13

], the peak wavelength shift method was widely utilized to analyze relative phase changes. However, this approach limits sensors’ sensitivities in some applications. For MZ interferometers, multiple interferences are often observed between one core mode and many cladding modes [2

Z. Tian, S. S. Yam, and H. P. Loock, “Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber,” Opt. Lett. 33(10), 1105–1107 (2008). [CrossRef] [PubMed]

–6

–10

J. Ju, L. Ma, W. Jin, and Y. Hu, “Photonic bandgap fiber tapers and in-fiber interferometric sensors,” Opt. Lett. 34(12), 1861–1863 (2009). [CrossRef] [PubMed]

,12

,14

Z. Tian and S. S. Yam, “In-Line single-mode optical fiber interferometric refractive index sensors,” J. Lightwave Technol. 27(13), 2296–2306 (2009). [CrossRef]

]. The resultant transmission spectrum is then not a simple cosine curve as in common two-beam MZ interferometers, but a superposition of many cosine curves representing different mode interferences. Due to the different propagation constants of these cladding modes, their transmission spectra have different oscillation periods, hereafter referred to as free spectra ranges (FSR). Therefore, different attenuation peaks in the spectrum may exhibit different peak profiles. And they may also shift at different rates relative to one another due to the superposition of different modes. When the peak shape is not precisely known, the peak wavelength cannot be reliably determined by peak fitting. Thus, measurements of peak wavelength shifts could be problematic when two spectra differ from each other by a very small amount. To overcome this limitation, a novel spectrum differential integration (SDI) method has been proposed in this study. The SDI method is generally an intensity measurement method. Essentially, the absolute intensity differences between two spectra, each of which corresponds to a different external RI or other disturbances, are integrated over a wide wavelength range (50-400nm). A fiber in-line taper MZ RI sensor was built to verify the new method. The experimental results indicate that the SDI method generally leads to increased sensitivity and reduced device-dependence, as compared to the wavelength shift method. Also, the implementation of SDI method was found to be related to OSA (optical spectrum analyzer) resolution bandwidth (RBW) and wavelength scan range.

2. Basic principle of SDI

The basic principle of SDI will now be discussed. It is well known that the wavelength response of a MZI follows a cosine curve. Suppose a relative phase change Δφ between the two arms leads to a spectral shift, as shown in Fig. 1(a) . The initial spectrum and the phase-shifted spectrum were subtracted from one another, and the absolute intensity difference was then integrated along the spectrum. The resulting integrations were normalized and are plotted against the relative phase changes in Fig. 1(b). The resulting plot is well-approximated by a sine function. In an actual in-line fiber taper MZI, the relative power ratios between the various cladding modes are often unknown. Additionally, different modes generally respond differently to the same environmental change [5

T. Wei, X. Lan, and H. Xiao, “Fiber inline core–cladding-mode Mach–Zehnder interferometer fabricated by two-point CO₂ laser irradiations,” IEEE Photon. Technol. Lett. 21(10), 669–671 (2009). [CrossRef]

,14

Z. Tian and S. S. Yam, “In-Line single-mode optical fiber interferometric refractive index sensors,” J. Lightwave Technol. 27(13), 2296–2306 (2009). [CrossRef]

]. Therefore, the actual response curve of the sum of spectral differentials may not be an exact sine curve.

Fig. 1 Schematic of the basic principle of SDI.

Next, we discuss the RI sensitivity of the MZI in the context of the SDI method. The mode polarization and mode field changes due to environmental RI are neglected for simplicity. The transmission intensity at a certain wavelength is expressed in Eq. (1), where L,

n_{e f f}^{c o r e}

, and

n_{e f f}^{c l a d d i n g, j}

are the cavity length, the effective mode index of the core mode, and the effective mode index of the j^th cladding mode, respectively. The I_core , I_cladding ,

n_{e f f}^{c o r e}

, and

n_{e f f}^{c l a d d i n g, j}

are all in general wavelength dependent.

I = I_{C o r e} + \sum_{j} I_{C l a d d i n g}^{j} + \sum_{j} 2 \cdot \sqrt{I_{C o r e} \cdot I_{C l a d d i n g}^{j}} \cdot Cos {\frac{2 π}{λ} \cdot [n_{e f f}^{c o r e} - n_{e f f}^{c l a d d i n g, j} (R I)] \cdot L}

(1)

Since the fiber core does not contact the surrounding medium, its mode index is considered to be approximately independent of environmental RI [2

Z. Tian, S. S. Yam, and H. P. Loock, “Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber,” Opt. Lett. 33(10), 1105–1107 (2008). [CrossRef] [PubMed]

Z. Tian, S. S.-H. Yam, and H.-P. Loock, “Single-mode fiber refractive index sensor based on core-offset attenuators,” IEEE Photon. Technol. Lett. 20(16), 1387–1389 (2008). [CrossRef]

]. Then, by taking the derivative of Eq. (1) with respect to RI, we obtain Eq. (2), the intensity sensitivity (

\frac{d I}{d R I}

) of the sensor at a given wavelength.

\frac{d I}{d R I} = \sum_{j} \sqrt{I_{C o r e} \cdot I_{C l a d d i n g}^{j}} \cdot Sin {\frac{2 π}{λ} \cdot [n_{e f f}^{c o r e} - n_{e f f}^{c l a d d i n g, j} (R I)] \cdot L} \cdot \frac{4 π}{λ} \cdot L \cdot \frac{d n_{e f f}^{c l a d d i n g, j} (R I)}{d R I}

(2)

It is noted that the mode index sensitivity,

\frac{d n_{e f f}^{c l a d d i n g, j} (R I)}{d R I}

is quite different for each cladding mode. A simulation reported in Ref.14 showed that the abrupt taper can excite up to 9 cladding modes from LP₀₂ to LP₀₁₀. Our calculations show that higher order cladding modes generally exhibit lower mode indices and higher sensitivities. This is because high order cladding modes have larger mode field areas, and so are more easily affected by the surrounding RI. Besides the mode index term, the intensity sensitivity is also proportional to the cavity length L and the product

\sqrt{I_{C o r e} \cdot I_{C l a d d i n g}^{j}}

. If we consider the superposition of these cladding modes as one effective mode, this product is maximized, and therefore the spectrum has its highest average contrast, when

I_{C o r e} = I_{C l a d d i n g}^{j}

. The total absolute differential power is given in Eq. (3), where N is the finite number of data points collected in actual measurements,

Δ λ

is the wavelength step spacing between neighboring data points and RBW is the OSA’s resolution bandwidth.

I n t e g r a t i o n = \sum_{λ_{0}}^{λ_{0} + N \cdot Δ λ} | I_{examined} (λ) - I_{base} (λ) | \cdot \frac{Δ λ}{R B W}, (I_{examined} (λ) - I_{base} (λ) = \frac{d I}{d R I} \cdot δ R I)

(3)

To acquire enough spectral information, at least two data points are needed for a width of one RBW. This new method collects the spectral differences along the wavelength range of a light source, as opposed to the peak shift method, which instead considers only a single peak within a small wavelength range.

3. Application of the SDI method in an in-line fiber MZI RI sensor

In the following, we built an in-line taper MZ RI sensor to verify the SDI method. Based on Ref.2, abrupt fiber tapers were fabricated by using a fusion splicer (Ericsson FA995). The cavity length L was about 20 cm. The transmission spectrum was recorded by an OSA (Agilent 86142b). For the RI test, 10 batches of NaCl solution were prepared with mass concentrations from 2% to 20%. A 1% concentration change corresponds to a RI change of 0.0018 at room temperature [15

D. R. Lide, “Concentrative Properties of Aqueous Solutions,” in CRC Handbook of Chemistry and Physics, 88^th Edition (Internet Version 2008 ) (CRC Press/Taylorand Francis, Boca Raton, FL., 2007), pp. 2640–2640.

]. Figure 2(a) shows the transmission spectra at different concentrations. Now let us analyze the spectrum using the conventional wavelength shift method. From Fig. 2(a), we found that the peak wavelength shift is different for each peak. This peak shift discrepancy leads to a large device dependence, which will be discussed later. Three typical peaks, labeled as a, b and c, were selected for the following discussion. It is noticed that peak c exhibits the largest wavelength shift, but peak b exhibits no wavelength shift. The final measured peak shift is an integrative result of all the peak shifts of each excited cladding mode. However, these cladding modes have different mode index sensitivities and therefore different responses to RI changes at specific wavelengths. The wavelength shifts of peaks a and c were plotted in Fig. 2(b), where the data points corresponding to the lowest local intensities were chosen to represent the positions of peaks in the wavelength domain. In peak a, the peak wavelength shows an approximately linear response to the RI increase. But for peak b, the peak wavelength has no shift. From Fig. 2(a), we found that the profile of peak c changed slightly as RI changes. It is likely that, as external RI was increased, peak c became dominated by different cladding modes. So three very different slopes appear in Fig. 2(b). Peak c is clearly not appropriate for RI measurement, despite its large wavelength shift, as its wavelength shift varies nonlinearly with external RI. Peak a, on the other hand, does exhibit a linear relation between peak shift and RI change. Therefore, in using the wavelength shift method, it is important to select the correct peak, one with a linear relation, for accurate RI measurements to be taken. In the SDI method, however, there is no such problem due to the wide wavelength range over which the spectral difference is integrated. The results, using the SDI method, are presented in Fig. 2(c), where pure water (0% NaCl) was selected as the base spectrum for every subtraction. When the solution is below 10%, the integration curve is quite linear. As the solution’s RI was increased further, the sensitivity began to decline. The curve as a whole was seen to follow a sine-like function. This is because the average phase change is close to π compared to the initial phase in the base spectrum. We repeated the experiment several times and obtained almost the same SDI values for each concentration with a deviation of within 1%.

Fig. 2 (a) Transmission spectra (0.1 nm resolution, 4000 points) of in-line fiber taper MZI under different salt solutions from 0% to 20%. (b) Peak wavelength shifts of peak a and c read from spectra. (c) Integrations of the absolute spectrum differentials.

To further compare the SDI and wavelength shift methods, we used another 5 batches of NaCl solutions having much smaller RI increments. For each solution, the concentration was changed by only 0.1%, equivalent to a change of 0.00018 RIU at room temperature. In taking these measurements, the OSA was configured for maximum RBW (0.06 nm), over 100 nm scan range. The spectra and SDI results are shown in Fig. 3 . When the solution concentration was changed from 0% to 2.0%, the peak shift was obvious. But when concentration varied from 2.0% to 2.5%, it was much more difficult to distinguish the peak shift. As discussed above, we cannot fit these peaks because the peak shape is unknown. However, the SDI results clearly discriminate the small RI variations as shown in Fig. 3(b). Within a small RI range, the SDI curve was considered to be linear. The sensitivity obtained with the SDI method was 2.268 × 10⁴ dBm/RIU. From this experiment, SDI was proved to be more reliable than the conventional wavelength shift method.

Fig. 3 (a) Transmission spectra with smaller RI incremental. (b) SDI results with the scan range of 100 nm and the RBW of 0.06 nm.

As shown in Eq. (3), a wider wavelength range results in a higher sensitivity when the SDI method is used. We kept both the RBW (0.1 nm) and the wavelength step

Δ λ

constant, but varied the wavelength range from 10 to 100 nm to measure the refractive index changes of salt solutions. Pure water was again taken as the base spectrum. The experimental results in Fig. 4(a) indicate that the sensitivities are proportional to the wavelength range of integration. This is because a wider wavelength range represents a larger differential area and provides more spectral information that can be used to assess RI changes. By keeping the number of data points and the spectral step

Δ λ

constant, the OSA resolution’s influence on sensitivity could be examined. The resolution bandwidth was varied from 0.06 nm to 1 nm during these measurements. It was found that a higher resolution led to increased sensitivities, as expected, since small spectral changes (phase shifts) could be detected with a narrower bandwidth. It should also be noted that low sensor sensitivity can be compensated by increasing the scan range if OSA resolution (RBW) is limited. By comparison, in the peak wavelength shift method, the sensitivity is strictly limited by the OSA’s resolution. We also evaluated how peak contrasts (defined as the highest intensity divided by the lowest intensity of one peak) influenced the sensitivities of different devices with different shapes of fiber tapers. Four sensors were built having the same cavity length (with a deviation of several mm), but under different fabrication conditions, which led to different average peak contrasts (between 0.9 dB and 7.5 dB) over the range of 1500 nm to 1600 nm. The results indicate that MZI having larger average peak contrasts tend to display higher sensitivity to external refractive index change. As shown in Eq. (2), a larger contrast yields a larger value of

\sqrt{I_{C o r e} \cdot I_{C l a d d i n g}^{j}}

and thus higher intensity sensitivity. Although a larger peak contrast is also helpful in discriminating peak shifts in the wavelength shift method, it does not directly contribute to the sensitivity if this method is used.

Fig. 4 (a) A larger scan range leads to improved sensitivities. (b) Smaller OSA resolution bandwidth with higher sensitivities. (c) Higher average peak contrast with higher sensitivities.

4. Device dependence

It has been observed in the above experiments that peak shift as a function of RI change could be different for each peak. These peak shift discrepancies also introduce a large device-dependence. In the following experiment, we fabricated three similar devices and compare their performances. Under the same fabrication conditions, three sensors were built with the same cavity lengths. Their taper profiles are shown in Fig. 5 .

Fig. 5 Shape profiles of tapers for the three devices.

We tested these devices with a scan range of 400 nm (1300 nm to 1700 nm) and a resolution of 0.1 nm. For discussion, parts of the devices’ transmission spectra are shown in Fig. 6(a-c) . Six peaks in the spectra are labeled for comparison. Their wavelength shifts are plotted against concentrations in Fig. 6(e-f) and their corresponding sensitivities are summarized in Table 1 . It was found that the sensitivities of the six peaks were not consistent among the devices. For example, peak 5 in device 1 and 2 exhibit almost no wavelength shift but the same peak is seen to shift markedly in device 3. Additionally, peak 1 does not respond linearly to refractive index change in device 2. Although these devices were built using similar tapers and have the same cavity length (20 cm, with a deviation of several mm), they present significantly different sensitivities using wavelength shift method, regardless of the peak chosen. However, when the SDI method is used, the sensitivities of devices 1, 2 and 3 are found to be 1.478 × 10⁵ dBm/RIU, 1.421 × 10⁵ dBm/RIU and 1.458 × 10⁵ dBm/RIU, respectively, differing by only 4%. Apparently, much reduced device-dependence was obtained with the SDI method.

Fig. 6 Part of the transmission spectra of three devices (a-c) and their corresponding peak wavelength shifts (d-f).

Table 1 Sensitivities of the six peaks in transmission spectra by linear fitting the wavelength shifts at different concentrations.

Peak number	Device 1 (nm/RIU)	Device 2 (nm/RIU)	Device 3 (nm/RIU)
1	12.07	39.54	18.96
2	20.25	17.94	33.96
3	30.50	8.52	14.17
4	14.29	14.77	7.85
5	1.99	1.69	12.16
6	11.76	16.73	7.37

Because of fluctuations in temperature, humidity and discharge current during the fabrication of abrupt tapers, it is extremely difficult to produce two tapers of identical shape, even if they are manufactured only a few minutes apart. Although these tapers probably excite similar cladding modes, the initial phases of these modes could be random. These different initial phases will generate different transmission spectra, with peaks having completely different profiles and contrasts. More importantly, similar-looking peaks might be comprised of different cladding modes, which would directly affect the peak shifts. But the SDI method can naturally eliminate the influence of different initial phases in devices after the subtraction when a relatively large scan range is used. In general, the SDI method includes the mode shifts within a certain range rather than focusing on a specific peak. This compensates for a portion of the intrinsic difference between devices, especially when a large scan range is used. In Fig. 7 below, the normalized sensitivities are plotted against scan ranges, where the normalized sensitivity is defined as the sensitivity per nm. The scan ranges were examined for three devices with normalized sensitivities. The analysis indicated that the discrepancy in observed sensitivities resulted from the spectral difference at relatively small ranges. But when the scan range is significantly enlarged, the difference is greatly reduced. This can be understood as an averaging effect. Therefore, a larger scan range not only increases sensitivity, but also decreases device-dependence. Based on these results, a scan range of 300-400 nm should be large enough to essentially eliminate device-dependence for tapers fabricated under similar conditions. This makes our devices useful as practical RI sensors.

Fig. 7 Normalized device sensitivities under different scan ranges.

5. Conclusion

A novel SDI method to interrogate phase-induced spectrum change has been reported in this study. It offers higher reliability as a RI sensor than the widely used wavelength shift method, since more spectral information is utilized in computing the final measurements. However, it also suffers from a decrease in sensitivity when the averaged relative phase change approaches π. This problem can be avoided by choosing a different base spectrum for subtraction. Future efforts will be focused on the optimization of the fiber taper profile to achieve a linear response curve over a larger concentration range and to improve mode index sensitivity. The device-dependence of the SDI method has also been compared to that of the wavelength shift method. The experimental results have showed that the SDI method has a better tolerance to small differences between devices. In general, SDI is well-suited to applications in which high reliability is required. Finally, it must be pointed out that the SDI method can be utilized in other kinds of interferometric sensors. This method can be easily automated for faster data analysis and leads to greatly improved sensor reliability.

References and links

1.	R. Jha, J. Villatoro, G. Badenes, and V. Pruneri, “Refractometry based on a photonic crystal fiber interferometer,” Opt. Lett. 34(5), 617–619 (2009). [CrossRef] [PubMed]
2.	Z. Tian, S. S. Yam, and H. P. Loock, “Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber,” Opt. Lett. 33(10), 1105–1107 (2008). [CrossRef] [PubMed]
3.	J. Villatoro and D. M. Hernández, “Low-cost optical fiber refractive index sensor based on core diameter mismatch,” J. Lightwave Technol. 24(3), 1409–1413 (2006). [CrossRef]
4.	Z. Tian, S. S.-H. Yam, and H.-P. Loock, “Single-mode fiber refractive index sensor based on core-offset attenuators,” IEEE Photon. Technol. Lett. 20(16), 1387–1389 (2008). [CrossRef]
5.	T. Wei, X. Lan, and H. Xiao, “Fiber inline core–cladding-mode Mach–Zehnder interferometer fabricated by two-point CO₂ laser irradiations,” IEEE Photon. Technol. Lett. 21(10), 669–671 (2009). [CrossRef]
6.	L. V. Nguyen, D. Hwang, S. Moon, D. S. Moon, and Y. Chung, “High temperature fiber sensor with high sensitivity based on core diameter mismatch,” Opt. Express 16(15), 11369–11375 (2008). [CrossRef] [PubMed]
7.	O. Frazão, R. Falate, J. L. Fabris, J. L. Santos, L. A. Ferreira, and F. M. Araújo, “Optical inclinometer based on a single long-period fiber grating combined with a fused taper,” Opt. Lett. 31(20), 2960–2962 (2006). [CrossRef] [PubMed]
8.	B. Gu, M. J. Yin, A. P. Zhang, J. W. Qian, and S. He, “Low-cost high-performance fiber-optic pH sensor based on thin-core fiber modal interferometer,” Opt. Express 17(25), 22296–22302 (2009). [CrossRef]
9.	S. H. Aref, R. Amezcua-Correa, J. P. Carvalho1, O. Frazão, P. Caldas, J. L. Santos, F. M. Araújo, H. Latifi, F. Farahi, L. A. Ferreira, and J. C. Knight, “Modal interferometer based on hollow-core photonic crystal fiber for strain,” Opt. Express 17(21), 18669–18675 (2009). [CrossRef]
10.	J. Ju, L. Ma, W. Jin, and Y. Hu, “Photonic bandgap fiber tapers and in-fiber interferometric sensors,” Opt. Lett. 34(12), 1861–1863 (2009). [CrossRef] [PubMed]
11.	H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). [CrossRef] [PubMed]
12.	J. Villatoro, V. P. Minkovich, V. Pruneri, and G. Badenes, “Simple all-microstructured-optical-fiber interferometer built via fusion splicing,” Opt. Express 15(4), 1491–1496 (2007). [CrossRef] [PubMed]
13.	M. Jiang, A. P. Zhang, Y. C. Wang, H. Y. Tam, and S. He, “Fabrication of a compact reflective long-period grating sensor with a cladding-mode-selective fiber end-face mirror,” Opt. Express 17(20), 17976–17982 (2009). [CrossRef] [PubMed]
14.	Z. Tian and S. S. Yam, “In-Line single-mode optical fiber interferometric refractive index sensors,” J. Lightwave Technol. 27(13), 2296–2306 (2009). [CrossRef]
15.	D. R. Lide, “Concentrative Properties of Aqueous Solutions,” in CRC Handbook of Chemistry and Physics, 88^th Edition (Internet Version 2008 ) (CRC Press/Taylorand Francis, Boca Raton, FL., 2007), pp. 2640–2640.

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Sensors

History
Original Manuscript: February 11, 2010
Revised Manuscript: March 22, 2010
Manuscript Accepted: March 23, 2010
Published: April 1, 2010

Citation
Yi Li, Edouard Harris, Liang Chen, and Xiaoyi Bao, "Application of spectrum differential integration method in an in-line fiber Mach-Zehnder refractive index sensor," Opt. Express 18, 8135-8143 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-8135

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References

R. Jha, J. Villatoro, G. Badenes, and V. Pruneri, “Refractometry based on a photonic crystal fiber interferometer,” Opt. Lett. 34(5), 617–619 (2009). [CrossRef] [PubMed]
Z. Tian, S. S. Yam, and H. P. Loock, “Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber,” Opt. Lett. 33(10), 1105–1107 (2008). [CrossRef] [PubMed]
J. Villatoro and D. M. Hernández, “Low-cost optical fiber refractive index sensor based on core diameter mismatch,” J. Lightwave Technol. 24(3), 1409–1413 (2006). [CrossRef]
Z. Tian, S. S.-H. Yam, and H.-P. Loock, “Single-mode fiber refractive index sensor based on core-offset attenuators,” IEEE Photon. Technol. Lett. 20(16), 1387–1389 (2008). [CrossRef]
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