Design of a single-multimode-single-mode filter demodulator for fiber Bragg grating sensors assisted by mode observation
Jianzhong Zhang,1,* Weimin Sun,1 Libo Yuan,1 and Gang-Ding Peng2 1 2
College of Sciences, Harbin Engineering University, Harbin 150001, China
School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia *Corresponding author:
[email protected] Received 28 April 2009; revised 28 July 2009; accepted 18 September 2009; posted 18 September 2009 (Doc. ID 110724); published 12 October 2009
We propose a simple analysis of a single-multimode-single-mode fiber (SMSMF) filter by observing the excited modes in multimode fiber (MMF). The method is used to design a SMSMF filter demodulator for fiber Bragg grating sensors, and a corresponding demodulation system is created. The static and dynamic measurements based on the system are given to prove the feasibility of the intensity demodulator. © 2009 Optical Society of America OCIS codes: 060.2370, 060.3735.
1. Introduction
Fiber grating sensors [1–7] with demodulator filters [4–7] have been proposed and applied for decades because of their high response speed. Recently, a simple single-multimode-single-mode fiber (SMSMF) structure has received considerable interest and has been used for temperature and strain sensing [8–15]. SMSMF bandpass and edge filters have been demonstrated in [10,11]. A theoretical analysis based on linearly polarized modes is given in [10] for the SMSMF structure composed of multimode fiber (MMF) with a step-index profile. Here we propose a simple analysis for a SMSMF filter by observing the excited modes in MMF based on the fast Fourier transform (FFT) technique. The proposed method can be used to analyze MMF with any index profile. Based on the analysis, we designed a SMSMF filter, and we demonstrate a fiber Bragg grating (FBG) demodulated sensor based on the SMSMF filter. The static and dynamic mea0003-6935/09/305642-05$15.00/0 © 2009 Optical Society of America 5642
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surements of the SMSMF demodulator sensor system are shown by testing the sensor responses to temperature and vibration. 2.
Excited Modes in Multimode Fiber
A SMSMF structure is composed of lead-in and leadout SMF and a section of MMF; see Fig. 1(a). A few modes are excited in MMF when light is coupled from SMF to MMF. The transmission spectrum of the SMSMF filter is decided by the intensities and the propagation constants of the excited modes in MMF. Here we measure the excited modes in MMF based on a Mach–Zehnder interferometer to design a SMSMF filter demodulator for FBG sensors; see Fig. 1(b). A SMSMF structure is introduced in one arm of the interferometer and the other referenced arm is made of standard SMF. The length difference between the two arms is within a few centimeters. Amplified spontaneous emission (ASE) and an optical spectral analyzer (OSA) were used for the measurements. The interference spectrum sðλÞ, monitored by the OSA shown in Fig. 1(b), can be expressed as
sðλÞ ¼
X N i¼1
þ
N X
ηi 2 s0 ðλÞ þ
N X i≠j¼1
ηi ηj s0 ðλÞ cosðΔφij Þ þ s0 sðλÞ
2ηi s0 ðλÞ cosðΔφi-ref Þ =4;
ð1Þ
i¼1
where N is the total number of stimulated modes with different propagation constants in MMF, s0 ðλÞ is the light spectrum of the ASE source, and ηi represents the power coupling coefficients when light is coupled from SMF to the ith excited mode in MMF. Here, the discrimination between excited modes is indicated only by the propagation constants. Figure 2(a) shows an interference spectrum sðλÞ and a fast Fourier transform (FFT) is applied to the spectrum in the kðk ¼ 2π=λÞ domain. The FFT spectrum, as shown in Fig. 2(b), is used to demodulate the interference signal [16]. There are two parts in the FFT spectrum, indicated as S1 and S2 in Fig. 2(b); S1 is introduced by the interference signal between the excited modes in MMF, and S2 is introduced by the interference signal between the referenced SMF and the excited modes of MMF because S1 is still there and S2 disappears if the reference SMF in Fig. 1 is removed. Phase difference Δφij between the ith excited mode and the jth excited mode that introduces interference signal S1 can be expressed as Δφij ¼ ðβi − βj ÞL0 ¼
2π ðn − nj ÞL0 ¼ kOPDi-j ; λ i
ð2Þ
where L0 represents the length of the MMF, βi and βj are the propagation constants of the ith excited mode and the jth excited mode in the MMF, and ni and nj are their effective refractive indices, respectively. Their optical path difference (OPDi-j ), ðni − nj ÞL0 , can be achieved by observing the peaks of S1 when they pass the MMF. However, its accuracy is low because of low frequency noise as shown in Fig. 2(b). The difficulty is resolved by introducing the reference arm. Phase difference Δφi−ref between the ith excited mode in MMF and the reference light that introduces interference signal S2 is
Fig. 2. (Color online) (a) Interference spectrum sðλÞ, (b) FFT spectrum of interference spectrum of S1 and S2 in k space, (c) enlarged FFT spectrum at the S2 position.
2π ðn L − nref Lref Þ ¼ kOPDi-ref ; ð3Þ λ i 0 where Lref represents the length of the reference arm and nref is the effective refractive index of the reference SMF. The OPDi-j , ðni − nj ÞL0 , can be achieved from the peak positions of S2 because Δφij ¼ Δφi-ref − Δφj-ref . The enlarged S2 is shown in Fig. 2(c), and the number of peaks in Fig. 2(c) represents the number of excited modes with different propagation constants in MMF. Here, the outer core and cladding radius of MMF (PDF-S-105 made by FiberHome Technologies, Wuhan, China) are 52:5=62:5 μm and their refractive indices are 1:4574=1:4420; the length of the connected MMF is ∼1:05 m long to discriminate the OPD from the excited modes in MMF. The x-axis values of the FFT peak correspond to ni L0 − nref Lref and the intensities of the FFT peaks correlate linearly with the ηi coupling coefficients, which can be proved by applying the Fourier transform to interference spectrum s in Eq. (1) in k space. The Fourier transform spectrum Γðf Þ can be expressed as Δφi-ref ¼
Γðf Þ ¼ IfsðkÞg X N ¼ η2i þ 1 Gðf Þ=4 i¼1
OPDij OPDij 1 þG f þ ηi ηj G f − þ 2π 2π 2 i≠j¼1 N X OPDi−ref þ ηi G f − 2π i¼1 OPDi−ref Þ =4 þG f þ 2π X N
¼ DCðf Þ þ S1ðf Þ þ S2ðf Þ; Fig. 1. (Color online) (a) SMSMF structure and (b) the measurement setup of the excited mode in SMSMF.
ð4Þ
where I represents the operator of the Fourier transformation. Here we define the first term in Eq. (4) as 20 October 2009 / Vol. 48, No. 30 / APPLIED OPTICS
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DCðf Þ ¼
X N
η2i
þ 1 Gðf Þ=4;
ð5Þ
i¼1
the second term is defined as S1ðf Þ ¼
N X i≠j¼1
ηi ηj
cause the ASE spectrum can be well fitted by a few spectra with a Gaussian profile. The values of OPDi-ref and the relative coupling coefficients are critical parameters that can be used to analyze the SMSMF filter and are listed in Table 1.
OPDij OPDij 1 G f− þG f þ ; 8 2π 2π
3. Simulation Analysis of the Single-Multi-Single-Mode Fiber Filter
ð6Þ
The transmission spectrum of the SMSMF filter can be expressed as
the third term is defined as N X 1 OPDi-ref ηi G f − S2ðf Þ ¼ 2π 4 i¼1 OPDi-ref þG f þ ; 2π
s1 ðλÞ ¼
N X i¼1
ð7Þ
where Gðf Þ is the Fourier transform R of light source spectrum s0 ðkÞ given as Gðf Þ ¼ s0 ðkÞ expð−i2πf kÞ dk. For simple analysis we assume that the light source spectrum 4ðk − k0 Þ2 : s0 ðkÞ ¼ exp − Δk2
Here k0 and Δk are the central wavenumber and the spectral width of the light source in k space, respectively. So Gðf Þ can be expressed as 4ðk − k0 Þ2 expð−i2πf kÞdk exp − Δk2 pffiffiffi 2 pffiffiffi π Δk π Δk ¼ expð−i2πf k0 Þ: exp −π f 2 2 Z
Gðf Þ ¼
According to Eqs. (4) and (8) , the peak absolute values of Γðf Þ are pffiffiffi π Δk þδ 8
ð9Þ
when 2πf ¼ OPDi-ref . Here, δ is a negligible value when the difference between OPDi-ref and OPDij is as much as several hundred micrometers; see Fig. 2(b). So the x-axis values, 2πf , of peaks M1–M6 in Fig. 2(c) correspond to the values of OPDi-ref . The y-axis values of peaks M1–M6 correlate linearly with coupling coefficients ηi, which provide the relative coupling coefficients. A similar conclusion can be readily gained for the actual ASE light source beTable 1.
N X
ηi ηj s0 ðλÞ cosðΔφij Þ:
ð10Þ
i≠j¼1
We obtain the parameters in Eq. (10) from the above measurement of the excited modes. Δφij can be decided by the OPD in Table 1. Coupling coefficients ηi cannot be given directly, but the relative coupling coefficients are listed in Table 1, which do not change the profile of the transmission spectrum of SMSMF. It is a good approximation that modes M1–M6, that correspond to the six main FFT peaks in Fig. 2(c), are used to simulate the transmission spectrum of the SMSMF structure, which has been proved experimentally. The transmission spectra of two SMSMF of 4.2 and 5:8 cm lengths are measured and shown in Figs. 3(a) and 3(b) . The simulated spectra of 4.26 and 5:83 cm are given in Figs. 3(c) and 3(d) , respectively. The profiles of the simulated spectra closely resemble the profiles of the experimental spectra even though there are some deviations. The spectral deviations are caused by the deviations of OPDi-ref and ηi . The accuracies of OPDi-ref are limited by the frequency accuracy and the sidelobe effects of the FFT. The relative deviation of OPDi-ref can be gauged [17] by
ð8Þ
Γðf Þ ¼ ηi
ηi 2 s0 ðλÞ þ
dðOPDi-ref Þ dðΔλÞ ≈ 0:03%; ≈ OPDi-ref Δλ where Δλð∼30 nmÞ and dðΔλÞð∼0:01 nmÞ are the spectral span of light source ASE and the wavelength accuracy of OSA, respectively. The deviation of OPDi-ref introduced by the sidelobe effects can be gauged by Eq. (4) and it is negligible because the interval between the FFT peaks is as large as several hundred micrometers [18]. For the case shown in Fig. 2(c), the relative deviation of 0.03% in OPDi-ref would introduce the relative deviation of ∼1% in Δφij because Δφij ¼ kðOPDi-ref − OPDi-ref Þ. The relative values of coupling coefficient ηi and its accuracy are decided mainly by the sidelobe effects, which is the value of δ in Eq. (9). According to Eq. (4), the theoretical sidelobe effect can be gauged and is
Simulation Parameters of SMSMF Transmission Spectra from Fig. 2(c)
Excited Mode in MMF
M1
M2
M3
M4
M5
M6
OPDðμmÞ ∼ ni L0 − nref Lref Relative coupling coefficient ∝ ηi
11656 0.1548
12801 0.2944
13383 0.3528
14016 0.8046
14494 1
14927 0.416
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Fig. 3. (Color online) (a) Experimental transmission spectra of SMSMF in MMF of (a) 4.2 and (b) 5.8 cm lengths. Simulated transmission spectra of SMSMF in MMF of (c) 4.26 and (d) 5.83 cm lengths.
negligible. However, the obvious sidelobe effects can be observed in Fig. 2(c), which could be caused by other factors, such as material dispersion and the effects of mode coupling and mixing in MMF [19]. According to Fig. 2(c), it is safe to say that the sidelobe values are lower than 0.002 at positions M3–M6 and much lower at positions M1 and M2 because the sidelobes decay exponentially. For two main modes, M4 and M5, with high coupling coefficients, their relative deviations should be less than 5%. The proposed simulation scheme is suitable to predict the main profile of SMSMF transmission spectra as demonstrated in Fig. 3 and to design SMSMF filters.
and demodulated by a photodetector (PD) system combined with a SMSMF structure by means of a 2 × 2 coupler. Here, the isolator is used to stop the FBG reflection from reverting to the ASE source, and the matching liquid is used to reduce unnecessary reflection of fiber endfaces. The light reflected by a FBG would pass the packaged SMSMF structure and the power of the reflected light would be modulated. According to Eq. (9) and Table 1, the simulated transmission spectrum of the SMSMF structure of 5:83 cm MMF length is shown in Fig. 3(d), and it is accurate to demodulate the FBG whose Bragg wavelength is between 1535 and 1540 nm. The up-edge of the experimental SMSMF transmission spectrum of ∼5:8 cm in MMF, shown in Fig. 5(a), can be used to transfer the wavelength shift to the changes in detected light power. Then the intensity demodulation of FBG sensors can be achieved. A FBG of 1535:5 nm in Bragg wavelength is used as the sensor head. We changed the FBG wavelength step by step by increasing the oven temperature in which the FBG is heated. The reflective spectra of FBG, recorded by an OSA at different temperatures, are shown as Fig. 5(b), which demonstrates that the FBG wavelength shifts are transmitted to the light power changes by the SMSMF structure. The demodulation scheme can be readily applied to a dynamic measurement when the PD is used instead of the OSA as shown in Fig. 4. To demonstrate the capability of the dynamic measurement, we apply the sensor system to monitor the vibration by attaching the FBG sensor head onto a tuning fork. A data collection card is used to collect the data from the PD after analog-to-digital conversion. The measurement data are shown in Fig. 5(c) when the tuning fork is vibrated by an electrical control system. Here the sample frequency of the PD system is 25 kHz. A strong characteristic vibration frequency
4. Single-Multimode-Single-Mode Fiber Filter Demodulation and Measurement
The demodulation scheme is shown in Fig. 4. A FBG sensor is interrogated by a broadband source ASE
Fig. 4. (Color online) Demodulation scheme of a FBG sensor based on SMSMF.
Fig. 5. (Color online) (a) Transmission spectrum of SMSMF demodulator in MMF of 5.8 cm length, (b) SMSMF filter conversion between the Bragg wavelength shift and the reflection intensity of a FBG, (c) vibration measurement of the SMSMF demodulator FBG sensor, (d) FFT spectrum of (c). 20 October 2009 / Vol. 48, No. 30 / APPLIED OPTICS
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of the tuning, ∼184:6 Hz, can be found in Fig. 5(d); the FFT spectrum can be found in Fig. 5(c). Note that the measurement error could be introduced by the power vibration of the ASE source. However, it can be readily reduced by introducing another reference PD to monitor the power of the ASE source as in [6,7]. We also note that the SMSMF transmission spectra shift with strain and temperature and the responses of the temperature, ∼13:0 pm=°C, and the strain, ∼2:1 pm=με, as tested in our labortory could introduce extra measurement errors or even invalidate the demodulation scheme. However, strain is easy to separate from MMF and the temperature response of MMF transmission spectra can be drastically reduced by use of a different packaging method as in [14]. 5. Conclusions
In summary, we analyzed the single-multimodesingle-mode filter demodulator for fiber Bragg grating sensors assisted by observation of excited modes in multimode fiber. A FBG sensor based on a demodulator has been demonstrated, and its application of temperature and vibration measurements show that it can be used for static and dynamic sensing. We expect that the demodulator, since it is inexpensive and has high frequency response, will have broad applications in civil engineering. This research was supported in part by the science fund of Heilongjiang Province, LC08C02, and Harbin Techniques Fund, 2007RFLXG007. References 1. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997). 2. B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9, 57 (2003). 3. Y. J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997). 4. A. D. Kersey, T. A. Berkoff, and W. W. Morey, “Multiplexed fiber Bragg grating strain-sensor system with a fiber Fabry–Perot wavelength filter,” Opt. Lett. 18, 1370–1372 (1993).
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