1734 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 9, MAY 1, 2014
Refractive Index Sensing Characteristics ofSingle-Mode Fiber-Based Modal Interferometers
Yaxun Zhang, Ai Zhou, Boyang Qin, Hongchang Deng, Zhihai Liu, Jun Yang, and Libo Yuan
Abstract—We present a theoretical and experimental investiga-tion on refractive index (RI) sensing characteristics of single modefiber (SMF) based modal interferometers. Theoretical analysis re-veals that interference between different modes in an SMF has aquite different response to the RI variation of the external medium.The interference between the core and lower order cladding modeshas negative RI sensitivity whereas that between the core andhigher order modes, or between two different order claddingmodes have positive sensitivity. A single-mode-multimode-single-mode (SMS) fiber Michelson interferometer with a large-core step-index multimode fiber (MMF) is employed for experimental verifi-cation. In the SMS-based Michelson interferometer, the MMF actsas a mode coupler to excite cladding modes in the SMF. The RIresponse of the SMS-based structures with two different lengths ofMMF are respectively tested in sodium-chloride water solutions.Experimental results show excellent agreements with the theoreti-cal analysis.
Index Terms—Cladding mode, fiber modal interferometer, fiberoptic sensor, refractive index sensitivity.
I. INTRODUCTION
IN-FIBER modal interferometers based on single mode fiber(SMF) are particularly attractive as refractive index (RI) sen-
sors due to the dependence of the cladding modes on the sur-rounding medium RI change. Various configurations have beenreported to construct modal interferometers for RI measure-ment. Examples include abrupt taper pair [1], [2], core-offsetsplice [3], [4], double cladding fiber [5], fiber Bragg grating(FBG) [6], long period grating (LPG) [7], [8] and core diametermismatch [9]–[13]. If we pay attention to the RI sensitivity ofthese reports, we could find that the RI sensitivities in someinvestigations are negative [1], [3]–[5], [7], [12] whereas inothers are positive [2], [6], [8]–[11]. Here, the negative and pos-itive RI sensitivities means blue- and red-wavelength shift withexternal RI increase, respectively. The more interesting thing
Manuscript received November 9, 2013; revised February 20, 2014; acceptedMarch 10, 2014. Date of publication March 16, 2014; date of current versionApril 3, 2014. This work was supported in part by the National Natural ScienceFoundation of China (Grants No. 11204047, 61275087, 61227013, 61377085,61307104, 41174161, 61377084), in part by the 111 project (B13015), and inpart by the Natural Science Foundation of Heilongjiang Province in China underGrant LC2011C11, to Harbin Engineering University.
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2014.2311579
is that the RI sensitivity may be opposite even for a similarconfiguration [7], [8], [11]–[14]. We believe that such a phe-nomenon is due to that different cladding modes were excitedin the above references and these cladding modes had differentresponse to the external RI. In addition, in most of the refer-ences the interferences among cladding modes were neglectedand only the interference between the core mode and claddingmodes was considered. However, in practical SMF-based modalinterferometer, it is difficult to only excite one cladding mode inthe SMF and the interference between different cladding modesplays a significant role in the RI sensitivity of the modal inter-ferometer. But unfortunately, the effect of the cladding mode onRI sensitivity of the modal interferometer has not been detailedinvestigated to our best knowledge.
IN this paper, we attempt to explain the observed sign rever-sal of the RI sensitivity and give a general description of the RIsensing characteristics of the SMF-based modal interferome-ters by means of a single-mode-multimode-single-mode (SMS)Michelson interferometer. The SMS configuration is totally dif-ferent from the SMS structure in which the multimode fiber(MMF) acts as the sensing fiber and SMFs serves as transmis-sion fibers. In the present study, the sensing fiber is SMF and theMMF plays a role of mode coupler to excite both core mode andcladding modes in the sensing SMF. The reason that we employsuch a configuration is that the MMF-SMF structure can eas-ily excite much more higher order cladding modes than othercladding-mode exciting methods. In addition, the order of theexcited cladding mode could be tailored by changing the lengthof the MMF. In fact the MMF-SMF structure for cladding modeexciting were firstly proposed for temperature sensing [11], [12],and the RI responses of such kind of structures have already beenreported [13]–[16]. However, in Refs. [13]–[16] only the RI re-sponse of some certain cladding modes were presented and theeffect of cladding mode order on the interferometer’s RI sensingproperty was not investigated. Moreover, the sensitivity of thestructure in [13] and [14] is opposite to that in [15] and [16].Therefore, in this study, we mainly focus on the investigation ofthe effect of the cladding mode on the RI sensitivity of the SMF-based modal interferometer. By choosing two different length ofthe MMF, 212 μm and 2.1 mm, different order cladding modeswere excited in the sensing SMF, and both positive and negativeRI sensitivities were obtained.
The paper is organized as follows. In Section II, we give abrief introduction to the SMS Michelson interferometer, andpresent a general analytic expressions for the RI sensitivityof the SMF-based modal interferometers. We respectively de-fine RI sensitivity coefficients that associate with the disper-sion of the mode for cases of core-cladding mode interference
ZHANG et al.: REFRACTIVE INDEX SENSING CHARACTERISTICS OF SINGLE-MODE FIBER-BASED MODAL INTERFEROMETERS 1735
Fig. 1. Schematic diagram of the SMS-based Michelson interferometer.
and cladding-cladding mode interference. By analyzing thewavelength dependence of the effective RI (ERI) for the coreand cladding modes, the RI sensitivity coefficients for severalcladding modes (HE11 − HE1,16) are calculated and the resultsshow that the signs of the coefficients are negative for core-lower order cladding mode interference, whereas positive forcore-higher order cladding mode, or cladding-cladding mode in-terference. In Section III, we present the experimental researchon RI sensitivity of the structure with different MMF length.The experimental results validate the theoretical prediction onthe RI sensitivity. In Section IV, we give a general conclusionfor the RI response of the SMF-based modal interferometers.
II. THEORETICAL ANALYSIS OF RI SENSITIVITY
A. Core-Cladding Mode InterferometerBased on SMS Structure
Generally, the RI sensitivity of a SMF-based modal interfer-ometer is primary determined by the cladding mode due to itssensitiveness to the surrounding medium. Therefore, to compre-hensively investigate the response of the modal interferometersto the external medium, we have to stimulate cladding modesas much as possible in conventional SMF. Although claddingmodes can be easily excited through lots of methods such asabrupt tapers, core-offset splice, small core diameter differenceand fiber gratings, these methods can only stimulate one or sev-eral cladding modes. It is difficult to obtain sufficient lowerorder and higher order cladding modes simultaneously. Stepindex MMF with a large core diameter, thanks to the uniformindex distribution and large core diameter, can excite plentyof cladding modes in SMF at the MMF-SMF splice region.More importantly, varying the length of the MMF can changethe exciting light field of the SMF, which may results differentcladding modes excitement. Therefore, in the present study, wechoose a SMS-based Michelson interferometer as the sensinghead.
The schematic diagram of the SMS-based Michelson inter-ferometer is presented in Fig. 1. A short piece of MMF is fusionspliced in between two SMFs. One SMF acts as the lead-in/outfiber for light transmission, and the other one whose coatingis stripped away serves as the sensing element. The end of thesensing SMF is cleaved carefully and then deposited with agold film as a reflector. In the SMS structure, the MMF playsthe role of mode coupler to couples the fundamental core modeof the lead-in/out SMF into the fundamental core mode andcladding modes of the sensing SMF due to the large mode fieldmismatch. Here, the SMF is a conventional SMF fabricated byYangtze Optical Fiber and Cable Company, and the pure silicacore MMF is a power delivery fiber (Nufern MM-S105/125-22A) with a core/cladding diameter of 105/125 μm and a
Fig. 2. Simulated transvers filed profiles of the MMF with length of (a) 212 μmand (b) 2.1 m.
numerical aperture of 0.22. Such a large core diameter of MMFcould guarantee for the excitement of higher order claddingmodes in the sensing SMF. The lengths of the MMF sectionwas chosen to be about 0.2 mm and 2.1 mm to obtain differentinput light field at the MMF-SMF splice point and then to excitedifferent cladding mode distribution. All the fibers were fusionspliced by a Fujikura arc fusion splicer (FMS-60S) under “AutoSM/NZ/DS/MM” operation model.
The light beam behavior in the MMF section of the SMSfiber structure has been detailed investigated by using beampropagation method [17]–[19]. Previous researches reveal thatthe light in the MMF spreads and converges periodically alongthe MMF. Here, we only give the transvers field profile (theinput field to the sensing SMF) for MMF length of 212 μm and2.1 mm (the actual length of the MMFs used in our experiment)by using the BeamPROP software of the RSoft Design Group,Inc [20]. In the simulation, the refractive indices were set to be1.4446/1.4271 for the core/cladding of the MMF. The simulatedmode profiles at 1550 nm are presented in Fig. 2. From thefigure, we can predict that at the MMF-SMF interface lowerorder cladding modes will be dominantly stimulated by the212 μm MMF and both lower and higher order cladding modescan be excited by the 2 mm MMF.
1736 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 9, MAY 1, 2014
B. RI Sensitivity
Firstly, we consider the interference between the fundamentalcore mode and the mth-order cladding mode. The transmissiondips caused from the destructive interference satisfy the phasecondition [9]
2π[neff
co (λ) − neffcl,m (λ, nex)
]L
λdip,i= (2i − 1) π (1)
where neffco (λ) and neff
cl,m (λ, nex) are the ERI of the fundamen-tal core mode and the mth order cladding mode respectively, Lis the length of the sensing SMF, nex is the RI of the externalmedium, λdip,i is the wavelength of the ith dip and i is an integer.It has to be noted here that both of neff
co (λ) and neffcl,m (λ, nex)
are the function of the wavelength. The wavelength dependenceof the effective indices is caused by material and waveguidedispersion. As will be subsequently shown, the difference be-tween the ERI of the core mode and cladding modes is the keyparameter determining the sign of the sensitivity. Here, materialdispersion can be assumed to have the same effect on neff
co andneff
cl,m due to the nearly same material, and waveguide dispersionis the dominant contributor to the dispersion difference.
From (1) the wavelength of a certain transmission dip λdip,i
can be expressed as
λdip,i =2L
[neff
co (λ) − neffcl,m (λ, nex)
]
2i − 1. (2)
Taking a derivative of λdip,i with respective to the external RInex , we can get the analytic expressions for the RI sensitivity ofthe transmission dip λdip,i
dλdip,i
dnex= χ
∂neffcl,m
∂nex(3)
where
χ = − λdip,i
Δneff ,m
/[1 − λdip,i
Δneff ,m
(∂neff
co
∂λ−
∂neffcl,m
∂λ
)](4)
is defined as sensitivity coefficient of the core-cladding modeinterference. Here, Δneff ,m = neff
co (λ) − neffcl,m (λ, nex) is the
effective index difference between the core mode and the mthorder cladding mode, ∂neff
co/∂λ and ∂neff
cl,m
/∂λ denotes the
wavelength dependences of the ERI of the core mode and themth order cladding mode, respectively. For the right side of (4),λdip,i and Δneff ,m are always positive, therefore the sign of χis determined by the denominator whose sign depends on theterm of
(∂neff
co/∂λ − ∂neff
cl
/∂λ
).
To quantitatively analyze the sensitivity, the ERI of the coremode and some cladding modes were calculated. For the sensingSMF in Fig. 1, it is a three-layer structure considering surround-ing medium. Because the cladding diameter of the SMF is muchgreater than the core diameter, for sake of simplicity, two two-layer models are introduced to calculate guiding mode of thesensing SMF instead of a three-layer structure: one is composedof the core and cladding of the sensing SMF to calculate theHE11 core mode, and the other is consists of the cladding of thesensing SMF and the surrounding medium to calculate HE1m
Fig. 3. Wavelength dependences of the ERI for the core mode and severalcladding modes.
cladding modes. Exact solutions for those two models can befound in Ref. [21].
The ERI of the core mode and several cladding modesin wavelength range of 1 μm to 1.6 μm are plotted inFig. 3. The curves from top to bottom, corresponds tothe HE11 core mode and HE11 ,HE13 ,HE15 ,HE17 ,HE19 ,and HE1,11 cladding modes. Here, the cladding mode’s ra-dial number is named start from the first cladding moderather than from the core mode. In the calculation, the di-ameters and RI of the core and cladding were set to be8.2 μm, 125 μm, 1.449 and 1.444, respectively. From Fig. 2we can see that for lower order cladding modes we have∂neff
cl,m /∂λ > ∂neffco /∂λ (|∂neff
cl,m /∂λ| < |∂neffco /∂λ|), whereas
for higher order ones ∂neffcl,m /∂λ < ∂neff
co /∂λ(|∂neffcl,m /∂λ| >
|∂neffco /∂λ|). Therefore for cladding modes whose∂neff
cl,m /∂λ
is larger than∂neffco /∂λ, the sensitivity coefficient χ is
negative. For higher order cladding modes there ex-ists two cases: λ(∂neff
co /∂λ − ∂neffcl,m /∂λ)/Δneff ,m < 1 and
λ(∂neffco /∂λ − ∂neff
cl,m /∂λ)/Δneff ,m > 1. For the first case χ isstill negative and for the second one χ changes to be positive.
In fact, (4) can also be written as the format of
χ = − λdip,i
Δneff ,m − λdip,i
(∂neff
co/∂λ − ∂neff
cl,m
/∂λ
) . (5)
Looking at the denominator, Δneff ,m − λdip,i(∂neffco /∂λ −
∂neffcl,m /∂λ), it is same as the group index difference
Δng = ngco − ng
cl,m in form, where ngco = neff
co − λdneffco /dλ and
ngcl,m = neff
cl,m − λdneffcl,m /dλ are the group index of the core
mode and the mth order cladding mode. From (5), the sign ofχ only depends on the sign of Δng , which coincides with theanalysis on LPG in [22].
In practice, it is difficult to excite only one cladding mode inthe SMF, and the interference in a SMF-based modal interfer-ometer is generally a multi-mode interference. Therefore, theinterference between two different order cladding modes hasto be considered. For a two-cladding-mode interference, the RIsensitivity of the transmission dip is
dλdip,i
dnex= χcl
(∂neff
cl,m
∂nex−
∂neffcl,j
∂nex
)(6)
ZHANG et al.: REFRACTIVE INDEX SENSING CHARACTERISTICS OF SINGLE-MODE FIBER-BASED MODAL INTERFEROMETERS 1737
TABLE ICALCULATED RI SENSITIVITY COEFFICIENT OF THE FIRST 11 HE1m MODES
where neffcl,j is the ERI of thejth order (j < m) cladding mode,
and χcl defined as the sensitivity coefficient of cladding modeinterference, is expressed as
χcl = − λdip,i
Δneff ,jm − λdip,i
(∂neff
cl,j
/∂λ − ∂neff
cl,m
/∂λ
) . (7)
χ and χcl correspond to the first 16 HE1m cladding modesat wavelength of 1550 nm were calculated and the results arepresented in Table I.
From the calculation results in Table I, for the core-claddingmode interference, the RI sensitivity coefficient is negative whenthe mode order m ≤ 10 and positive when m ≥ 11. For thecladding-cladding mode interference, the sensitivity coefficientis always positive. From (3) and (6), the RI sensitivity of theinterferometer is determined by both the sensitivity coefficientand the nex dependence of the ERI of each mode. Therefore,to confirm the RI sensitivity, the external RI dependence of theERI of several cladding modes were calculated and the resultsare plotted in Fig. 4. From the figure, we can see that the ERIof each cladding mode increases with the external RI, whichmeans that ∂neff
cl
/∂nex > 0. Moreover, the ERI of higher or-
der cladding modes increase faster than that of lower order one,
which indicates that ∂neffcl,m
/∂nex−∂neff
cl,j
/∂nex > 0(m > j).
Therefore, from (3) the RI sensitivity of the core-cladding modeinterference is negative for m ≤ 10 and positive for m ≥ 11, andfrom (6) the RI sensitivity of the cladding-cladding mode inter-ference is always positive. As a result, the final RI sensitivity ofa SMF-based multi-mode interferometer is determined by both
Fig. 4. External RI dependence of the ERI of several cladding modes.
the core-cladding mode interference and the cladding–claddingmode interference. Therefore the sensitivity not only depends onwhich cladding modes are excited but also on the power distribu-tion of the modes. That is to say that different power distributionamong the excited modes may lead to different sensitivity. Forsimplicity, we consider a simplest case that the core mode as wellas two cladding modes (m ≤ 10) are stimulated in the sensingSMF. There are two extreme conditions: Eco ≈ Ecl 1 � Ecl 2 ,and Ecl 1 ≈ Ecl 2 � Eco(Eco , Ecl 1 andEcl 2 are the energy ofthe core mode and the two cladding modes, respectively). For thefirst case, the spectrum shape is determined by the interferencebetween the core and cladding modes, the cladding-claddingmode interference modulate the spectrum slightly, therefore thesensitivity mainly shows up as negative. For the second case,the spectrum shape is determined by the interference betweenthe two cladding modes, and the core-cladding mode interfer-ence modulate the spectrum slightly, which results in positivesensitivity. For other cases, the sensitivity is positive for sometransmission dip whereas negative for others. To intuitively il-lustrate effect of the power distribution on the wavelength shiftwith external RI, the interference among the fundamental coremode and cladding modes HEcl
13 and HEcl17 were simulated. The
calculated results are shown in Fig. 5. Fig. 5(a) is the situation ofEco : Ecl 13 : Ecl 17 = 0.45:0.1:0.45, and Fig. 5(b) correspondsto the case of Eco : Ecl 13 : Ecl 17 = 0.1:0.45:0.45. From Fig. 5we can see that all the wavelengths of the transmission dips ex-perience blue-shift for the first case, and red-shift for the secondcase. Generally, for the case that two cladding modes are ex-cited, the sensitivity is mainly determined by the modes whoseenergy are mostly similar. For the case that more cladding modesare stimulated, the sensitivity is complicated and it is difficultto give a general description to the RI sensitivity.
III. EXPERIMENTAL RESULTS AND DISCUSSION
A. Spectral Characteristics of the SMS-BasedMichelson Interferometer
To obtain different cladding mode distribution in the sensingSMF, two SMS-based Michelson interferometers (SMS1 andSMS2) with MMF length of 212 μm and 2.1 mm were fabri-cated. The length of the sensing SMFs in the SMS structureswere designed to be same (20 mm) to facilitate comparing the
1738 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 9, MAY 1, 2014
Fig. 5. Stimulated interference spectra of the core mode, the cladding modesHEcl
13 and HEcl17 when the external RI is 1.34 and 1.36, (a)Eco ≈ Ecl 1 �
Ecl 2 and (b)Ecl 1 ≈ Ecl 2 � Eco .
spectral characteristics of the SMS structure. A broadband lightwith a wavelength range of 1520 nm to 1610 nm was coupledinto the lead-in\out SMF and the reflected interference beamwas detected by an optical spectrum analyzer (OSA). The inter-ference spectra of the two interferometers are shown in Fig. 6.From the figure, both of the two interference pattern are inho-mogeneous, which indicates that more than one cladding modeswere excited and interfered with the core mode of the sensingSMF. Even so, we can still clearly observe that the interval ofthe interference fringe Δλ decreases with the increase of theMMF length.
To more intuitively display the cladding modes that partici-pates the interference, the spectra in Fig. 6 were Fourier trans-formed to the spatial frequency domain, as shown in Fig. 7. Themulti-peaks in each frequency spectrum verifies the predictionthat several cladding modes were excited and participated theinterference. The amount of cladding modes in SMS2 is morethan that in SMS1. Moreover, the power of higher order claddingmodes in SMS2 is more than that in SMS1. The difference ofthe two spectra is due to the input field variation of the sensingSMF which caused from the length difference of the MMF, asshown in Fig. 2. It has to be noted that although the longer MMFexcite more cladding modes than the shorter one in the presentcase, it is not always true that the longer the MMF, the morecladding modes are stimulated, this because the light spreadsand converges while propagating along the MMF, as illustratedin [17] and [18].
Fig. 6. Transmission spectra of the SMS Michelson interferometer with dif-ferent lengths of the MMF, (a) 212 μm and (b) 2.1 mm.
Fig. 7. Spatial spectrum of the SMS Michelson interferometer with differentlength of MMF.
B. Experimental Demonstration for RI Sensitivityof the SMS-based Michelson Interferometer
To investigate the RI responses of different cladding modes,the fabricated SMS structures SMS1 and SMS2 were tested in aseries of NaCl solutions whose RI ranges from 1.341 to 1.3676.The experimental results are shown in Figs. 8 and 9, respec-tively. For SMS1 with MMF length of 212 μm, as shown inFig. 8(a), dip A2 keeps fixed and dips A1 ,A3 and A4 experi-ence blue-shifts with the increase of the external RI. The sensi-tivities obtained from Fig. 8(b) are SA 1 = −110.5 nm/RIU,SA 3 = −31.3 nm/RIU, and SA 4 = −110.5 nm/RIU, respec-tively. The negative RI sensitivity of the transmission dips showthat the core mode and lower order cladding modes were dom-inantly excited. In addition, the sensitivities of each dip arenot the same. Such an inconsistent sensitivity as well as the
ZHANG et al.: REFRACTIVE INDEX SENSING CHARACTERISTICS OF SINGLE-MODE FIBER-BASED MODAL INTERFEROMETERS 1739
Fig. 8. (a) Transmission spectra of the SMS Michelson interferometer withMMF length of 212 μm in NaCl-water solution and (b) the wavelength shift ofdifferent transmission dips versus refractive index.
Fig. 9. (a) Transmission spectra of the SMS Michelson interferometer withMMF length of 2.1 mm in NaCl-water solution and (b) the wavelength shift ofdifferent transmission dips versus refractive index.
unshifted dip indicates that the interference between claddingmodes participates the modulation of the sensitivity.
For SMS2 with MMF length of 2.1 mm, the shift of thetransmission dips are inconsistent. As shown in Fig. 9, dipsB1 and B2 move to shorter wavelength with sensitivities ofSB1 = −20.7 nm/RIU, and SB2 = −27.5 nm/RIU, dips B3and B7 remains unchanged, and dips B4 ,B5 , and B6 moveto longer wavelength with sensitivities of SB4 =20.4 nm/RIU,SB5 =52.6 nm/RIU, and SB6 =12.5 nm/RIU. The negative andpositive sensitivities of the transmission spectrum show thatboth the lower and higher order cladding modes were domi-nantly excited in SMS2. The overall response of the spectrum isthe consequence of the combined action of these modes. The RIresponses of the transmission spectra of the two interferometersare in keeping with the theoretical analysis.
It has to be noted that we did not give a quantitative descriptionto the RI response of each cladding mode in the experiments.This because that we cannot confirm the exact order and energyof each excited cladding mode either theoretically or experi-mentally due to the unknown exact parameters of the fibers, andthe similar RI difference of two different mode pairs.
IV. CONCLUSION
The refractive index sensing characteristics of SMF-basedmodal interferometer by using SMS structure has been inves-tigated theoretically and experimentally in this paper. The the-oretical analysis reveals that the transmission spectrum form-ing from the interference between the core mode and differentorder cladding modes has a quite different response to the ex-ternal RI. For interference happened between the core modeand HE1m (m ≤ 10) cladding mode, the RI sensitivity is nega-tive, whereas for interference happened between the core modeand HE1m (m ≥ 11) cladding mode or between two claddingmodes, the RI sensitivity is positive. The feature of the RI sensi-tivity is due to different wavelength dependence for ERI of eachcladding mode. Modal interferometers based on SMS Michelsoninterferometer have been constructed for experimental verifica-tion. The SMS interferometer with short length of MMF mainlyhas negative RI sensitivity, whereas the interferometer with longMMF has hybrid sensitivity. The experimental results conformthe prediction of the theoretical analysis.
REFERENCES
[1] Z. Tian, S. S-H. Yam, and H-P. Loock, “Refractive index sensor basedon an abrupt taper Michelson interferometer in a single-mode fiber,” Opt.Lett., vol. 33, no. 10, pp. 1105–1107, May 2008.
[2] J. Yang, L. Jiang, S. Wang, B. Li, M. Wang, H. Xiao, Y. Lu, and H. Tsai,“High sensitivity of taper-based Mach–Zehnder interferometer embeddedin a thinned optical fiber for refractive index sensing,” Appl. Opt., vol. 50,no. 28, pp. 5503–5507, Oct. 2011.
[3] Z. Tian, S. S.-H. Yam, and H-P. Loock, “Single-mode fiber refractiveindex sensor based on core-offset attenuators,” IEEE Photon. Technol.Lett., vol. 20, no. 16, pp. 1387–1389, Aug. 2008.
[4] W. C. Wong, C. C. Chan, Y. F. Zhang, and K. C. Leong, “Miniature single-mode fiber refractive index interferometer sensor based on high ordercladding mode and core-offset,” IEEE Photon. Technol. Lett., vol. 24,no. 5, pp. 359–361, Aug. 2008.
1740 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 9, MAY 1, 2014
[5] F. Pang, H. Liu, H. Guo, Y. Liu, X. Zeng, N. Chen, Z. Chen, and T. Wang,“In-fiber Mach–Zehnder interferometer based on double cladding fibersfor refractive index sensor,” IEEE Sensors J., vol. 11, no. 10, pp. 2395–2400, Oct. 2011.
[6] X. Zhang, W. Peng, Y. Liu, and L. Pan, “Core–cladding mode recou-pling based fiber optic refractive index sensor,” Opt. Commun., vol. 294,pp. 188–191, May 2013.
[7] D. W. Kim, Y. Zhang, K. L. Cooper, and A. Wang, “In-fiber reflectionmode interferometer based on a long-period grating for external refractive-index measurement,” Appl. Opt., vol. 44, no. 26, pp. 5368–5373, Sep.2005.
[8] S. M. Tripathi, W. J. Bock, A. Kumar, and P. Mikulic, “Temperature in-sensitive high-precision refractive-index sensor using two concatenateddual-resonance long-period gratings,” Opt. Lett., vol. 38, no. 10, pp. 1666–1668, May 2013.
[9] T. Xia, A. Zhang, B. Gu, and J. Zhu, “Fiber-optic refractive-index sensorsbased on transmissive and reflective thin-core fiber modal interferome-ters,” Opt. Commun., vol. 283, pp. 2136–2139, May 2010.
[10] Q. Rong, X. Qiao, R. Wang, H. Sun, M. Hu, and Z. Feng, “High-sensitive fiber-optic refractometer based on a core-diameter-mismatchMach–Zehnder interferometer,” IEEE Sensors J., vol. 12, no. 7, pp. 2501–2505, Oct. 2012.
[11] L. V. Nguyen, D. Hwang, S. Moon, D. S. Moon, and Y. Chung, “Hightemperature fiber sensor with high sensitivity based on core diametermismatch,” Opt. Exp., vol. 16, no. 15, pp. 11369–11375, Jul. 2008.
[12] E. Li, “Design and test of multimode interference based optical fibertemperature sensors,” Proc. SPIE, vol. 7157, pp. 71570F-1–71570F-9,2009.
[13] Y. Ma, X. Qiao, T. Guo, R. Wang, J. Zhag, Y. Weng, Q. Rong, M. Hu,and Z. Feng, “Mach–Zehnder interferometer based on a sandwich fiberstructure for refractive index measurement,” IEEE Sensors J, vol. 12,no. 6, pp. 2081–2085, Jun. 2012.
[14] F. Xua, D. Chen, B. Peng, J. Xu, and G. Wu, “All fiber refractometer basedon core mismatch structure,” Laser Phys., vol. 22, no. 10, pp. 1577–1580,Oct. 2012.
[15] Q. Rong, X. Qiao, Y. Du, D. Feng, R. Wang, Y. Ma, H. Sun, M. Hu, andZ. Feng, “In-fiber quasi-Michelson interferometer with a core–cladding-mode fiber end-face mirror,” Appl. Opt., vol. 52, no. 7, pp. 1441–1447,Mar. 2013.
[16] L. Li, L. Xia, Z. Xie, and D. Liu, “All-fiber Mach–Zehnder interferometersfor sensing applications,” Opt. Exp., vol. 20, no. 10, pp. 11109–11120,May 2012.
[17] Q. Wang, G. Farrell, and W. Yan, “Investigation on single-mode–multimode–single-mode fiber structure,” J. Lightw. Technol., vol. 26, no. 5,pp. 512–519, Mar., 2008.
[18] W. S. Mohammed, A. Mehta, and E. G. Johnson, “Wavelength tunablefiber lens based on multimode interference,” J. Lightw. Technol., vol. 22,no. 2, pp. 469–477, Mar. 2004.
[19] S. Silva, O. Frazao, J. Viegas, L. A. Ferreira, F. M. Araujo, F. X. Malcata,and J. L. Santos, “Temperature and strain-independent curvature sensorbased on a singlemode/multimode fiber optic structure,” Meas. Sci. Tech-nol., vol. 22, p. 085201, 2011.
[20] R. Soft. (2013). [Online]. Available. http://optics.synopsys.com/rsoft/[21] A. W. Snyder and J. D. Love, Optical Waveguide Theory. New York,
NY, USA: Chapman & Hall, 1983.[22] X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long-
period fiber gratings,” J. Lightw. Technol., vol. 20, no. 2, pp. 255–266,Mar. 2002.
Yaxun Zhang received the B.S. degree in optical information science andtechnology, from Shenyang Ligong University, Shenyang, China, in 2009, theM. Eng. degree in optical engineering from Harbin Engineering University,China, in 2012, where he is currently working toward the Ph. D. degree withthe Photonics Research Center, College of Science.
His research interests include the fiber micromachining and fiber sensors.
Ai Zhou received the B.S. degree in electronic science and technology, the M.Eng. degree in optical engineering, and the Ph. D. degree in photonics fromHarbin Engineering University, China, in 2003, 2005 and 2009, respectively.
She is currently the Key Lab of In-fiber Integrated Optics, Ministry Educationof China, Harbin Engineering University, China. Her research interests includefiber-optic sensing and fiber Bragg grating.
Boyang Qin received the B.S. degree in physics from Northeast Forestry Uni-versity, China, in 2013. He is currently working toward the M. Eng. degreewith the Photonics Research Center, College of Science, Harbin EngineeringUniversity, China.
His research interests include the optical fiber sensors.
Hongchang Deng received the B.S. degree in electronic science and technologyfrom Harbin Engineering University, China, in 2008. He is currently workingtoward the Ph. D. degree at College of Science, Harbin Engineering University.
His research interests include in-fiber integrated optics and fiber-opticsensing.
Zhihai Liu received the B.S. degree in optoelectronics, the M.Eng. degree inoptical engineering, and the Ph.D. degree in photonics from Harbin EngineeringUniversity, Harbin, China, in 1999, 2002, and 2006, respectively.
He is currently a Professor in the Key Lab of In-fiber Integrated Optics, Min-istry Education of China, Harbin Engineering University. His research interestsinclude fiber optic sensors and fiber optic tweezers.
Jun Yang received the B.S. degree in optoelectronics, the M.Eng. degree inoptical engineering, and the Ph.D. degree in photonics from the Harbin Engi-neering University, Harbin, China, in 1999, 2002, and 2005, respectively.
He is currently a Professor in the Key Lab of In-fiber Integrated Optics, Min-istry Education of China, Harbin Engineering University, China. His researchinterests include fiber optic sensors and optic interferometers.
Libo Yuan received the B.S. degree in physics from Heilongjiang University,Harbin, China, in 1984, the M. Eng. degree in communication and electronicsystem from Harbin Ship building Engineering Institute, Harbin, in1990, andthe Ph.D. degree in photonics from The Hong Kong Polytechnic University,Kowloon, Hong Kong, in 2003.
He is currently a Professor in the Key Lab of In-fiber Integrated Optics,Ministry Education of China, Harbin Engineering University, China. His re-search interests include microstructured fiber-based in-fiber integrated optics,fiber optic devices and components, and fiber optic sensors and its applications.He is the author or coauthor of more than two book, four book chapters, and280 of his research papers. He is the holder of 25 patents.
