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Interferometric interrogation of π -phase shifted fiber Bragg grating sensors
Optics Communications 410 (2018) 88–93
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Interferometric interrogation of 𝜋-phase shifted fiber Bragg grating sensors Deepa Srivastava a,b , Umesh Tiwari b , Bhargab Das b, * a b
National Institute of Technical Teachers Training & Research (NITTTR), Chandigarh-160019, India Advanced Materials and Sensors Division, CSIR-Central Scientific Instruments Organization, Chandigarh-160030, India
a r t i c l e
i n f o
Keywords: Optical fiber sensors Fiber Bragg gratings 𝜋-phase-shifted fiber Bragg gratings Interferometric interrogation Wavelength conversion devices
a b s t r a c t Interferometric interrogation technique realized for conventional fiber Bragg grating (FBG) sensors is historically known to offer the highest sensitivity measurements, however, it has not been yet explored for 𝜋-phase-shifted FBG (𝜋FBG) sensors. This, we believe, is due to the complex nature of the reflection/transmission spectrum of a 𝜋FBG, which cannot be directly used for interferometric interrogation purpose. Therefore, we propose here an innovative as well as simple concept towards this direction, wherein, the transmission spectrum of a 𝜋FBG sensor is optically filtered using a specially designed fiber grating. The resulting filtered spectrum retains the entire characteristics of a 𝜋FBG sensor and hence the filtered spectrum can be interrogated with interferometric principles. Furthermore, due to the extremely narrow transmission notch of a 𝜋FBG sensor, a fiber interferometer can be realized with significantly longer path difference. This leads to substantially enhanced detection limit as compared to sensors based on a regular FBG of similar length. Theoretical analysis demonstrates that high √ resolution weak dynamic strain measurement down to 4 𝑝𝜀∕ 𝐻𝑧 is easily achievable. Preliminary experimental results are also presented as proof-of-concept of the proposed interrogation principle. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Optical fiber based sensors have become an indispensable tool for high sensitivity measurement of both static and dynamic strain with detection limits ranging from 10−12 to 10−6 𝜀 Hz−1∕2 , where 𝜀 is the fractional length change. Such low-level strain measurement of relative displacement and deformations is of utmost importance in many research fields encompassing underwater acoustic array detectors, structural health monitoring of civil and aerospace edifices, ultrasonic hydrophones for medical sensing, seismic sensors for geophysical surveys etc. [1–3]. Bragg grating based fiber optic sensors are playing a significant role towards the realization of these ultrasensitive static and dynamic strain detectors. Fiber Bragg gratings (FBGs) offer the possibility to measure all probable physical parameters which can be observed as a derivative of temperature and strain. The widespread popularity of FBG sensors are due to its well-known attributes of electromagnetic immunity, long distance sensing, wavelength selectivity, environmental endurance, reduced size, and multiplexing capability. FBGs encode the physical parameter to be measured into the wavelength shift of their reflection peak known as Bragg wavelength. Sophisticate instruments are required for accurate measurement of wavelength shift especially for small amplitude dynamic perturbation
sensing. The measurement or detection of this Bragg wavelength shift has been the subject of considerable research and several techniques have been developed. The measurement resolution or the detection limit of an FBG sensor system is mostly governed by two factors: the sensitivity characteristics of the sensor head and the wavelength shift measurement resolution of the FBG peak. The sensitivity characteristics of the FBG sensor head can be improved by introducing different types of packaging techniques. Whereas, to improve the spectral measurement resolution (i.e. minimum detectable change), the FBG peak needs to be narrowed because the wavelength shift measurement resolution is highly dependent on the spectral linewidth of the grating sensor. Narrower linewidth of the Bragg reflected light leads to higher spectral resolution thereby substantially improving the minimum detectable change of the measurand. Unfortunately, the spectral linewidth of a reasonable length FBG is relatively wide with typical bandwidth (FWHM) of >100 pm. This limits the spectral measurement resolution and thereby making it difficult to measure small amplitude dynamic strain measurement down to pico-strain (𝑝𝜀) level. A special type of FBG whose reflection spectrum features a notch caused by a 𝜋-phase discontinuity in the center of the grating (called 𝜋−phase-shifted FBG or 𝜋FBG) have attracted a great deal of attention for their enhanced detection limit leading to the measurement of weak
* Corresponding author.
E-mail address: [email protected] (B. Das). https://doi.org/10.1016/j.optcom.2017.09.093 Received 15 June 2017; Received in revised form 8 September 2017; Accepted 26 September 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.
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Optics Communications 410 (2018) 88–93
strain perturbations [4–12]. The superior detection limit is due to the extremely narrow spectral notch (FWHM ∼ 10 pm) of the 𝜋FBG reflection/transmission spectrum that allows high resolution measurement of spectral separation. Furthermore, the 𝜋−phase-shift region at the center of the grating decreases the effective length of the sensor making it extremely suitable for high frequency ultrasonic detection [5–7,10,12]. The considerably narrow spectral notch (or transmission peak) of a 𝜋FBG sensor demands for special approaches for the measurement of their Bragg wavelength shift. This is because the conventional angular interrogation scheme which use a dispersive optical element and a 1D or 2D detector array does not provide enough wavelength shift measurement resolution for this type of sensors. At present, there are two mainstream methods to demodulate the 𝜋FBG Bragg wavelength shift. The basic principle of the first type of interrogation system is based on edge filter detection scheme wherein an extremely narrow linewidth (∼ 0.1 pm) tunable laser source (TLS) is adjusted in the linear region of the reflection/transmission notch. Compared to the spectrum of the 𝜋FBG, the linewidth of the TLS is so narrow that it can be treated as a single wavelength. Strain signal encoded in shift of the 𝜋FBG spectra is demodulated by observing the reflected/transmitted optical power modulation with the help of a high-speed photodetector [5,6,9,10]. Another reported concept, albeit conceptually similar, is the use of two cascaded and identical 𝜋FBGs, where one 𝜋FBG is used a sensor and the other as a filter [7]. Experimental demonstrations have reported the measurement of dynamic strain down to only nano-strain (𝑛𝜀) levels using edge filter based interrogation technique [9]. In the second method, the 𝜋FBG sensor is interrogated by a frequency/phase modulated light from a TLS using Pound–Drever–Hall (PDH) method [2,4,11,12]. The technique is employed to extract the PDH error signal, which reflects the frequency detuning between the laser frequency and the 𝜋-phase-shifted Bragg grating resonance. Ultrahigh resolution measurements corresponding to dynamic strain detection with 𝜋FBG sensor down to 5 𝑝𝜀 Hz−1∕2 has been already demonstrated using PDH [4,12]. Both these above mentioned interrogation methods require a tunable laser source in order to precisely monitor the 𝜋FBG wavelength shift which results in the disadvantage of high cost. Moreover, in order to suppress the low-frequency drift of the TLS frequency and environmental noise during scanning, a tight wavelength tracking method is also needed to lock the TLS frequency to the 𝜋FBG resonance center or to the midpoint of the linear region in the 𝜋FBG spectra. Although, PDH technique can be used to measure wavelength shifts corresponding to pico-strain (𝑝𝜀) perturbations, the practical realization is very complicated & expensive and further does not offer multiplexing capability. In this paper, we propose the concept of interferometric interrogation technique for high resolution measurement of spectral shift of 𝜋FBG sensors. The interferometric interrogation scheme is relatively simpler as compared to PDH architecture and simultaneously it has the ability to measure pico-level (𝑝𝜀) strain perturbations. Interferometric interrogation of regular FBG sensors is already a widely accepted technique for high resolution Bragg wavelength-shift detection [1,13– 18]. In this case, an unbalanced fiber interferometer (e.g. Michelson or Mach–Zehnder type) is used as the wavelength-shift discriminator wherein the fiber interferometer converts the Bragg wavelength-shift of FBG sensor into a corresponding phase shift which is finally recorded as intensity variations. This fiber interferometric wavelength interrogation method has additional advantages of wide-bandwidth, high-resolution, tunable-sensitivity etc. and is more suitable for dynamic measurement of strain modulation as required in the fields of vibration and acoustics. It is noteworthy to realize that dynamic strain measurement down to nano-strain (𝑛𝜀) level is possible to achieve using regular FBG sensors measured with interferometric interrogation technique [17,18]. However, the broader spectral bandwidth (>100 pm) of typical FBG sensors make it difficult to breach this limit.
Fig. 1. Reflection spectrum of an FBG and transmission spectrum of a 𝜋FBG sensor. Both the gratings are of similar length (𝐿 = 25 mm), refractive index modulation (𝛥𝑛 = 1×10−4 ) and apodization (raised cosine profile). FWHM (FBG) ∼ 120 pm and FWHM (𝜋FBG) ∼ 11 pm.
2. Methodology Fig. 1 shows the transmission spectrum of a simulated 𝜋FBG of length 25 mm, which is characterized by a very narrow linewidth transmission notch at the center. The 𝜋FBG is modeled by the transfer matrix method, in which the grating is divided into a number of subsections, each associated with a 2 × 2 matrix and a phase shift matrix that accounts for the 𝜋 phase shift region of the grating [19]. The index modulation depth (𝛥𝑛) is assumed to be 1 × 10−4 with effective refractive index (𝑛𝑒𝑓 𝑓 ) of 1.45. Further, a raised cosine type apodization profile for the index modulation is also considered. The position of the narrow spectral transmission peak formed in a 𝜋FBG is located at the Bragg wavelength (𝜆𝐵 ) of the grating and is governed by the grating equation, 𝜆𝐵 = 2𝑛𝑒𝑓 𝑓 𝛬
(1)
Where, 𝑛𝑒𝑓 𝑓 is the effective refractive index of the optical mode propagating along the fiber and 𝛬 is the grating period. Dynamic strain perturbation acting on the optical fiber sensor modulates the grating period and hence can be measured by monitoring the spectral shift of the narrow transmission peak of a 𝜋FBG sensor. The bandwidth of this transmission notch measured as FWHM (full width at half maximum) is ∼11 pm. For comparison, in the same figure, we also show the reflection spectrum of a regular FBG of similar length (𝐿 = 25 mm). The other parameters are also similar to the 𝜋FBG. The spectral bandwidth i.e. FWHM of this reflection spectrum is ∼ 120 pm. It is worthwhile to note that, the FWHM of the transmission notch appearing in a 𝜋FBG is almost an order of magnitude smaller than the FWHM of the reflection spectrum of a regular FBG of similar length. Our objective here is to use this narrow transmission notch of a 𝜋FBG sensor for interferometric interrogation purpose. Nevertheless, the implementation of interferometric interrogation scheme for 𝜋FBG sensors is not as straight forward as for a regular FBG. Whereas the reflection spectrum of FBG sensors are used for interferometric interrogation purpose, the same cannot be utilized for 𝜋FBG sensors. The reflection spectrum of 𝜋FBGs lack any well-distinguished peak that can be used as source input to an interferometer. Thus, for a 𝜋FBG sensor, it is necessary to exploit the transmission spectrum. For this purpose, the narrow spectral peak appearing in the central position of the total transmission spectrum of a 𝜋FBG needs to be first isolated. This is proposed to be performed by optical filtering the 𝜋FBG sensor output with the help of a suitably designed FBG filter. The schematic diagram presented in Fig. 2 demonstrates this concept, wherein, the transmitted light signal from the 𝜋FBG sensor is fed to an FBG filter with the help of a circulator. The design parameters of the FBG 89
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Fig. 4. Reflection spectra of the designed FBG filter. It has a flat top reflection profile designed to avoid intensity variation. The transmission spectra of the 𝜋FBG sensor for five different Bragg wavelengths with a spacing of 10 pm are also shown.
3. Results and discussion A numerical model is implemented to theoretically simulate the interrogation process. Using transfer matrix method [19], we have simulated the transmission and reflection spectrums of 𝜋FBG sensor and the FBG filter, respectively. The 𝜋FBG sensor is assumed to be of length 25 mm and the 𝜋 phase-shift region is located exactly at the center. A raised cosine apodization profile of the refractive index modulation is assumed with the index modulation depth (𝛥𝑛) being 1 × 10−4 and 𝑛𝑒𝑓 𝑓 = 1.45. The transmission spectrum of this 𝜋FBG sensor is shown in Fig. 1. For our interferometric interrogation purpose, we are interested only in the central part of this spectrum containing the narrow spectral peak. Fig. 3 shows this narrow transmission notch which has an FWHM of ∼ 11 pm, significantly lower than the FWHM of a conventional FBG sensor. In order to isolate this narrow transmission notch, an appropriate FBG based filter is designed. The FBG filter has a length of 60 mm together with a raised cosine apodization profile and a peak index modulation of 0.8 × 10−4 . The reflection spectra of this FBG filter is shown in Fig. 4, wherein, the transmission spectra of the 𝜋FBG sensor for five different Bragg wavelengths with a spacing of 10 pm are also shown. This depicts the shifting of transmission notch around the central position of 1550 nm. The designed FBG filter is placed at one end of a circulator as shown in Fig. 2 and the reflected signal is fed to the fiber interferometer for subsequent measurement and analysis. It is important to note that the designed FBG filter has a flat-top profile which is very necessary to avoid any possible intensity variation when the transmission notch shifts under the influence of external perturbation. Fig. 5 shows the spectrum of the 𝜋FBG sensor output after reflection from the designed FBG filter, which acts as a source for the Mach– Zehnder fiber interferometer for interrogation purpose. The reflection spectra are shown for wavelength shift of ±10 pm on either side of the central position of 1550 nm. As the overall objective is the measurement of very small amplitude dynamic strain perturbation, a wavelength shift of 10 pm of the transmission notch around the central position is sufficient enough. Additionally, we have calculated the integrated light intensity as the 𝜋FBG sensor transmission notch shifts around the central position. The results are shown in Fig. 6, which indicates that within the region of interest i.e. a wavelength shift of ±10 pm, the 𝜋FBG sensor transmission notch does not undergo any intensity modulation. This is very important in the case of interferometric interrogation technique as the wavelength-shift modulation is finally recorded as intensity modulation at the output of fiber interferometer. The significant reduction in the bandwidth (𝛥𝜆: FWHM) of the 𝜋FBG sensor light can now be exploited to maintain a longer optical path
Fig. 2. Schematic of interferometric interrogation technique for 𝜋FBG sensor. Transmission spectrum of the 𝜋FBG sensor is directed to an FBG filter. Parameters of the FBG filter are chosen such that it reflects only the narrow spectral peak which is then guided to a fiber Mach–Zehnder interferometer. ASE: Broadband light source; OPD: Optical Path Difference; DAQ: Data Acquisition Card.
Fig. 3. Narrow transmission notch of the 𝜋FBG sensor. The calculated FWHM (𝛥𝜆) of this transmission notch is ∼ 11 pm, which is almost an order of magnitude smaller than a regular FBG sensor reflection spectrum.
filter i.e. bandwidth, center wavelength, refractive index modulation etc. are chosen in such a way that the reflected light retains only the central narrow spectral peak. This removes the undesired spectral content of 𝜋FBG sensor transmission spectrum. The resulting filtered spectrum retains the entire characteristics of a 𝜋FBG sensor and hence the filtered spectrum can now be interrogated with interferometric principles. This reflected light signal acts as the source input to a fiber Mach–Zehnder interferometer (F-MZI) for high resolution wavelength shift measurement [1,16,17]. It is to be noted that other kinds of fiber interferometers can also be utilized for this purpose. The detailed description of wavelength shift measurement using fiber interferometers can be found elsewhere [1,16] and hence is not elaborated herein. 90
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Where, 𝛥𝜀 is the dynamic strain modulation and 𝛾 is the strain-towavelength shift responsivity of the 𝜋FBG grating sensor. As 𝜋FBG sensors are fabricated in the same type of optical fiber (i.e. silica) as used for normal FBGs, their strain-to-wavelength shift responsivity is also similar. According to the empirical model proposed by Kersey et al. [18], the strain responsivity is 𝛾 = 1.2 pm∕με at 1550 nm. Taking this into account, together with optimum OPD of 80 mm and a wavelength of 1550 nm, would yield a sensitivity 𝛥𝜙∕𝛥𝜀√of 0.25 rad∕με. As typical dynamic phase shift detection of ∼ 10−6 rad∕ Hz is currently possible with interferometric √ techniques [20,21], therefore a dynamic strain resolution of ∼ 4 𝑝𝜀∕ Hz is easily achievable with a 𝜋FBG sensor interrogated with interferometric principle. Thus, the detection limit for dynamic strain sensing can be significantly improved with the proposed methodology. Further, it is interesting to realize that the wavelength shift of 𝜋FBG sensor transmission notch corresponding to 4 𝑝𝜀 is ∼ 4.8 × 10−6 pm. This shows the wavelength-shift measurement resolution capability of the demonstrated technique. Preliminary experimental studies are also carried out to demonstrate the feasibility of the proposed interferometric interrogation principle of 𝜋FBG sensors. The schematic of the experimental setup is as outlined in Fig. 2. A commercially acquired 𝜋-phase-shifted FBG sensor of length 25 mm is used for the experimental studies. Fig. 7(a) shows the transmission spectrum of the 𝜋FBG sensor as recorded in an optical spectrum analyzer (OSA). The FWHM of the narrow transmission notch is ∼ 26 pm. For dynamic strain modulation measurement, the 𝜋FBG sensor is glued onto a stainless steel cantilever plate with dimensions (175 mm × 100 mm × 0.5 mm) and is placed under a speaker with the help of a clamp stand. Sound signal from the speaker excite dynamic vibrations in the cantilever beam thereby inducing dynamic strain modulation in the 𝜋FBG sensor. A generic desktop application is used to control the speaker for generation of sound signals. In order to isolate the narrow transmission notch of phase-shifted FBG sensor, we have fabricated a 10 cm long fiber Bragg grating. The reflection spectrum of this FBG filter is shown in Fig. 7(b). It can be observed that the reflection spectrum of the fabricated FBG has almost a flat top profile. This can be further ascertained by noting the reflected power over a region of ±10 pm around the central position. The vertical lines shown in Fig. 7(b) depict a region of 20 pm and the reflected power within this region varies by only 0.25 dB, which is very minimal. The 𝜋FBG sensor transmission notch (after filtering using the FBG) is then fed to an F-MZI. Fig. 8 shows the interference pattern of the designed and fabricated F-MZI when light from a broadband source (1525–1565 nm) is sent through the fiber interferometer and the output is observed in an OSA. The OPD between the two arms of the interferometer is ∼ 3.6 cm, which is in agreement with the optimum OPD estimated using Eq. (2) for the bandwidth (FWHM ∼ 26 pm) of the transmission notch. The above described experimental configuration is then used for dynamic signal sensing applications. Acoustic sinusoidal signal of 580 Hz is generated with the help of the speaker. The amplitude of this acoustic signal is adjusted in such a way that it is barely audible from a distance of approximately 1 meter. The response of the 𝜋FBG sensor to this acoustical signal is recorded at the output of the F-MZI with the help of a photodetector. Finally, a data acquisition device is used to record the analog signal in terms of digital signal for further processing. Fig. 9(a) shows the recorded time series signal for the acoustic signal of 580 Hz. A sinusoidal curve fitting onto the experimental time signal data is also performed. The red sinusoidal curve shows the fitted data which has a period of 1.72 ms corresponding to a frequency of 580 Hz. The power spectrum of the time signal is calculated in LabVIEW platform and is shown in Fig. 9(b). A very high peak at 580 Hz can be observed and the peak-to-baseline height at 580 Hz is approximately ∼ 37.5 dB. This shows that the applied dynamic signal is successfully sensed with high fidelity. These experimental results demonstrate the feasibility of the proposed interferometric interrogation principle for 𝜋-phase shifted fiber Bragg grating sensors.
Fig. 5. Spectrum of the 𝜋FBG sensor output after reflection from the designed FBG filter. A wavelength shift of ±10 pm on either side of the central position of 1550 nm is depicted.
Fig. 6. Integrated light intensity as the transmission notch of 𝜋FBG sensor shifts around the central position i.e. the unperturbed state. A flat-top profile of the FBG filter within the spectral shift region is necessary for this.
difference (OPD) between the two arms of the fiber Mach–Zehnder interferometer (F-MZI). As the phase shift responsivity of a fiber interferometer is directly related to the OPD, an increased OPD leads to better wavelength-shift detection sensitivity. The optimum OPD for maximum sensitivity can be determined with the following relation, which was suggested by Weis et al. [14]: 𝑂𝑃 𝐷 × 𝛥𝑘 = 2.355
(2)
Where, 𝛥𝑘 is the spectral bandwidth of the optical signal fed to the fiber interferometer expressed in wave-number unit. By substituting, 𝛥𝜆 = 11 pm (corresponding to the transmission notch of the 𝜋FBG sensor after reflection from the FBG filter) and 𝜆 = 1550 nm, this optimum OPD is determined to be ∼ 80 mm. This is significantly higher as compared to a regular FBG sensor of bandwidth ∼ 120 pm, which allows an optimum OPD of only 7.5 mm. For dynamic strain induced modulation in the 𝜋FBG sensor spectral notch wavelength represented by 𝛥𝜆 sin 𝜔𝑡, the phase-shift modulation [𝛥𝜙 (𝑡)] of the fiber interferometer can be represented as: 𝛥𝜙 (𝑡) = −
2𝜋𝑂𝑃 𝐷 2𝜋𝑂𝑃 𝐷 𝛥𝜆 sin 𝜔𝑡 = − 𝛾𝛥𝜀 sin 𝜔𝑡 𝜆2 𝜆2
(3) 91
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Fig. 9. F-MZI based interferometric interrogation results. (a) Response of the 𝜋FBG sensor for acoustical signal of 580 Hz recorded at the fiber interferometer output. The red sinusoidal curve is the fitted data corresponding to a signal of frequency 580 Hz. (b) Power spectrum of the time signal. The peak-to-baseline height at 580 Hz is approximately ∼ 37.5 dB. Fig. 7. Transmission (a) and reflection spectrum (b) of the 𝜋FBG sensor and the FBG filter, respectively, used in our experimental studies. (a) Length of the 𝜋FBG sensor is 25 mm and FWHM of the transmission notch is ∼ 26 pm. (b) Length of the fabricated FBG is 10 cm. The region within the vertical lines show a region of 20 pm around the central position and the reflected power within this region varies by only 0.25 dB.
4. Conclusions In conclusion, we have proposed an innovative concept of interrogating 𝜋FBG sensors using interferometric principle. External perturbation induced modulation of the narrow transmission notch is monitored by using an unbalanced fiber interferometer as a wavelength discriminator. This new technique has lesser complexity as compared to PDH method, without compromising the strain measurement resolution. Leveraging the smaller bandwidth of the narrow transmission notch, which allows for a significantly longer OPD, it is theoretically established that dy√ namic strain resolution down to 4 𝑝𝜀∕ Hz is easily achievable. Further enhancement is possible by increasing the OPD as the coherence length { 2 ( )} 𝜆 ∕ 𝑛𝑒𝑓 𝑓 𝛥𝜆 for spectral bandwidth of 11 pm is ∼ 150 mm and the calculated optimum OPD is still far away from this value. An as alternative approach, the FBG filter can also be replaced with a low chirp rate FBG of suitable bandwidth and flat-top reflection profile. Preliminary experimental results are presented as a proof-of-concept of the proposed interrogation architecture for 𝜋FBG. The proposed interferometric interrogation technique for 𝜋-phase-shifted Bragg grating sensor has potential applications in the field of ultra-high resolution dynamic strain measurement systems such as hydrophones for SONAR & medical sensing, acoustic emission studies etc. References
Fig. 8. Interference pattern of the designed F-MZI as recorded in an OSA. The OPD is calculated to be 3.6 cm.
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Interferometric interrogation of 𝜋-phase shifted fiber Bragg grating sensors Deepa Srivastava a,b , Umesh Tiwari b , Bhargab Das b, * a b
National Institute of Technical Teachers Training & Research (NITTTR), Chandigarh-160019, India Advanced Materials and Sensors Division, CSIR-Central Scientific Instruments Organization, Chandigarh-160030, India
a r t i c l e
i n f o
Keywords: Optical fiber sensors Fiber Bragg gratings 𝜋-phase-shifted fiber Bragg gratings Interferometric interrogation Wavelength conversion devices
a b s t r a c t Interferometric interrogation technique realized for conventional fiber Bragg grating (FBG) sensors is historically known to offer the highest sensitivity measurements, however, it has not been yet explored for 𝜋-phase-shifted FBG (𝜋FBG) sensors. This, we believe, is due to the complex nature of the reflection/transmission spectrum of a 𝜋FBG, which cannot be directly used for interferometric interrogation purpose. Therefore, we propose here an innovative as well as simple concept towards this direction, wherein, the transmission spectrum of a 𝜋FBG sensor is optically filtered using a specially designed fiber grating. The resulting filtered spectrum retains the entire characteristics of a 𝜋FBG sensor and hence the filtered spectrum can be interrogated with interferometric principles. Furthermore, due to the extremely narrow transmission notch of a 𝜋FBG sensor, a fiber interferometer can be realized with significantly longer path difference. This leads to substantially enhanced detection limit as compared to sensors based on a regular FBG of similar length. Theoretical analysis demonstrates that high √ resolution weak dynamic strain measurement down to 4 𝑝𝜀∕ 𝐻𝑧 is easily achievable. Preliminary experimental results are also presented as proof-of-concept of the proposed interrogation principle. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Optical fiber based sensors have become an indispensable tool for high sensitivity measurement of both static and dynamic strain with detection limits ranging from 10−12 to 10−6 𝜀 Hz−1∕2 , where 𝜀 is the fractional length change. Such low-level strain measurement of relative displacement and deformations is of utmost importance in many research fields encompassing underwater acoustic array detectors, structural health monitoring of civil and aerospace edifices, ultrasonic hydrophones for medical sensing, seismic sensors for geophysical surveys etc. [1–3]. Bragg grating based fiber optic sensors are playing a significant role towards the realization of these ultrasensitive static and dynamic strain detectors. Fiber Bragg gratings (FBGs) offer the possibility to measure all probable physical parameters which can be observed as a derivative of temperature and strain. The widespread popularity of FBG sensors are due to its well-known attributes of electromagnetic immunity, long distance sensing, wavelength selectivity, environmental endurance, reduced size, and multiplexing capability. FBGs encode the physical parameter to be measured into the wavelength shift of their reflection peak known as Bragg wavelength. Sophisticate instruments are required for accurate measurement of wavelength shift especially for small amplitude dynamic perturbation
sensing. The measurement or detection of this Bragg wavelength shift has been the subject of considerable research and several techniques have been developed. The measurement resolution or the detection limit of an FBG sensor system is mostly governed by two factors: the sensitivity characteristics of the sensor head and the wavelength shift measurement resolution of the FBG peak. The sensitivity characteristics of the FBG sensor head can be improved by introducing different types of packaging techniques. Whereas, to improve the spectral measurement resolution (i.e. minimum detectable change), the FBG peak needs to be narrowed because the wavelength shift measurement resolution is highly dependent on the spectral linewidth of the grating sensor. Narrower linewidth of the Bragg reflected light leads to higher spectral resolution thereby substantially improving the minimum detectable change of the measurand. Unfortunately, the spectral linewidth of a reasonable length FBG is relatively wide with typical bandwidth (FWHM) of >100 pm. This limits the spectral measurement resolution and thereby making it difficult to measure small amplitude dynamic strain measurement down to pico-strain (𝑝𝜀) level. A special type of FBG whose reflection spectrum features a notch caused by a 𝜋-phase discontinuity in the center of the grating (called 𝜋−phase-shifted FBG or 𝜋FBG) have attracted a great deal of attention for their enhanced detection limit leading to the measurement of weak
* Corresponding author.
E-mail address: [email protected] (B. Das). https://doi.org/10.1016/j.optcom.2017.09.093 Received 15 June 2017; Received in revised form 8 September 2017; Accepted 26 September 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.
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strain perturbations [4–12]. The superior detection limit is due to the extremely narrow spectral notch (FWHM ∼ 10 pm) of the 𝜋FBG reflection/transmission spectrum that allows high resolution measurement of spectral separation. Furthermore, the 𝜋−phase-shift region at the center of the grating decreases the effective length of the sensor making it extremely suitable for high frequency ultrasonic detection [5–7,10,12]. The considerably narrow spectral notch (or transmission peak) of a 𝜋FBG sensor demands for special approaches for the measurement of their Bragg wavelength shift. This is because the conventional angular interrogation scheme which use a dispersive optical element and a 1D or 2D detector array does not provide enough wavelength shift measurement resolution for this type of sensors. At present, there are two mainstream methods to demodulate the 𝜋FBG Bragg wavelength shift. The basic principle of the first type of interrogation system is based on edge filter detection scheme wherein an extremely narrow linewidth (∼ 0.1 pm) tunable laser source (TLS) is adjusted in the linear region of the reflection/transmission notch. Compared to the spectrum of the 𝜋FBG, the linewidth of the TLS is so narrow that it can be treated as a single wavelength. Strain signal encoded in shift of the 𝜋FBG spectra is demodulated by observing the reflected/transmitted optical power modulation with the help of a high-speed photodetector [5,6,9,10]. Another reported concept, albeit conceptually similar, is the use of two cascaded and identical 𝜋FBGs, where one 𝜋FBG is used a sensor and the other as a filter [7]. Experimental demonstrations have reported the measurement of dynamic strain down to only nano-strain (𝑛𝜀) levels using edge filter based interrogation technique [9]. In the second method, the 𝜋FBG sensor is interrogated by a frequency/phase modulated light from a TLS using Pound–Drever–Hall (PDH) method [2,4,11,12]. The technique is employed to extract the PDH error signal, which reflects the frequency detuning between the laser frequency and the 𝜋-phase-shifted Bragg grating resonance. Ultrahigh resolution measurements corresponding to dynamic strain detection with 𝜋FBG sensor down to 5 𝑝𝜀 Hz−1∕2 has been already demonstrated using PDH [4,12]. Both these above mentioned interrogation methods require a tunable laser source in order to precisely monitor the 𝜋FBG wavelength shift which results in the disadvantage of high cost. Moreover, in order to suppress the low-frequency drift of the TLS frequency and environmental noise during scanning, a tight wavelength tracking method is also needed to lock the TLS frequency to the 𝜋FBG resonance center or to the midpoint of the linear region in the 𝜋FBG spectra. Although, PDH technique can be used to measure wavelength shifts corresponding to pico-strain (𝑝𝜀) perturbations, the practical realization is very complicated & expensive and further does not offer multiplexing capability. In this paper, we propose the concept of interferometric interrogation technique for high resolution measurement of spectral shift of 𝜋FBG sensors. The interferometric interrogation scheme is relatively simpler as compared to PDH architecture and simultaneously it has the ability to measure pico-level (𝑝𝜀) strain perturbations. Interferometric interrogation of regular FBG sensors is already a widely accepted technique for high resolution Bragg wavelength-shift detection [1,13– 18]. In this case, an unbalanced fiber interferometer (e.g. Michelson or Mach–Zehnder type) is used as the wavelength-shift discriminator wherein the fiber interferometer converts the Bragg wavelength-shift of FBG sensor into a corresponding phase shift which is finally recorded as intensity variations. This fiber interferometric wavelength interrogation method has additional advantages of wide-bandwidth, high-resolution, tunable-sensitivity etc. and is more suitable for dynamic measurement of strain modulation as required in the fields of vibration and acoustics. It is noteworthy to realize that dynamic strain measurement down to nano-strain (𝑛𝜀) level is possible to achieve using regular FBG sensors measured with interferometric interrogation technique [17,18]. However, the broader spectral bandwidth (>100 pm) of typical FBG sensors make it difficult to breach this limit.
Fig. 1. Reflection spectrum of an FBG and transmission spectrum of a 𝜋FBG sensor. Both the gratings are of similar length (𝐿 = 25 mm), refractive index modulation (𝛥𝑛 = 1×10−4 ) and apodization (raised cosine profile). FWHM (FBG) ∼ 120 pm and FWHM (𝜋FBG) ∼ 11 pm.
2. Methodology Fig. 1 shows the transmission spectrum of a simulated 𝜋FBG of length 25 mm, which is characterized by a very narrow linewidth transmission notch at the center. The 𝜋FBG is modeled by the transfer matrix method, in which the grating is divided into a number of subsections, each associated with a 2 × 2 matrix and a phase shift matrix that accounts for the 𝜋 phase shift region of the grating [19]. The index modulation depth (𝛥𝑛) is assumed to be 1 × 10−4 with effective refractive index (𝑛𝑒𝑓 𝑓 ) of 1.45. Further, a raised cosine type apodization profile for the index modulation is also considered. The position of the narrow spectral transmission peak formed in a 𝜋FBG is located at the Bragg wavelength (𝜆𝐵 ) of the grating and is governed by the grating equation, 𝜆𝐵 = 2𝑛𝑒𝑓 𝑓 𝛬
(1)
Where, 𝑛𝑒𝑓 𝑓 is the effective refractive index of the optical mode propagating along the fiber and 𝛬 is the grating period. Dynamic strain perturbation acting on the optical fiber sensor modulates the grating period and hence can be measured by monitoring the spectral shift of the narrow transmission peak of a 𝜋FBG sensor. The bandwidth of this transmission notch measured as FWHM (full width at half maximum) is ∼11 pm. For comparison, in the same figure, we also show the reflection spectrum of a regular FBG of similar length (𝐿 = 25 mm). The other parameters are also similar to the 𝜋FBG. The spectral bandwidth i.e. FWHM of this reflection spectrum is ∼ 120 pm. It is worthwhile to note that, the FWHM of the transmission notch appearing in a 𝜋FBG is almost an order of magnitude smaller than the FWHM of the reflection spectrum of a regular FBG of similar length. Our objective here is to use this narrow transmission notch of a 𝜋FBG sensor for interferometric interrogation purpose. Nevertheless, the implementation of interferometric interrogation scheme for 𝜋FBG sensors is not as straight forward as for a regular FBG. Whereas the reflection spectrum of FBG sensors are used for interferometric interrogation purpose, the same cannot be utilized for 𝜋FBG sensors. The reflection spectrum of 𝜋FBGs lack any well-distinguished peak that can be used as source input to an interferometer. Thus, for a 𝜋FBG sensor, it is necessary to exploit the transmission spectrum. For this purpose, the narrow spectral peak appearing in the central position of the total transmission spectrum of a 𝜋FBG needs to be first isolated. This is proposed to be performed by optical filtering the 𝜋FBG sensor output with the help of a suitably designed FBG filter. The schematic diagram presented in Fig. 2 demonstrates this concept, wherein, the transmitted light signal from the 𝜋FBG sensor is fed to an FBG filter with the help of a circulator. The design parameters of the FBG 89
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Fig. 4. Reflection spectra of the designed FBG filter. It has a flat top reflection profile designed to avoid intensity variation. The transmission spectra of the 𝜋FBG sensor for five different Bragg wavelengths with a spacing of 10 pm are also shown.
3. Results and discussion A numerical model is implemented to theoretically simulate the interrogation process. Using transfer matrix method [19], we have simulated the transmission and reflection spectrums of 𝜋FBG sensor and the FBG filter, respectively. The 𝜋FBG sensor is assumed to be of length 25 mm and the 𝜋 phase-shift region is located exactly at the center. A raised cosine apodization profile of the refractive index modulation is assumed with the index modulation depth (𝛥𝑛) being 1 × 10−4 and 𝑛𝑒𝑓 𝑓 = 1.45. The transmission spectrum of this 𝜋FBG sensor is shown in Fig. 1. For our interferometric interrogation purpose, we are interested only in the central part of this spectrum containing the narrow spectral peak. Fig. 3 shows this narrow transmission notch which has an FWHM of ∼ 11 pm, significantly lower than the FWHM of a conventional FBG sensor. In order to isolate this narrow transmission notch, an appropriate FBG based filter is designed. The FBG filter has a length of 60 mm together with a raised cosine apodization profile and a peak index modulation of 0.8 × 10−4 . The reflection spectra of this FBG filter is shown in Fig. 4, wherein, the transmission spectra of the 𝜋FBG sensor for five different Bragg wavelengths with a spacing of 10 pm are also shown. This depicts the shifting of transmission notch around the central position of 1550 nm. The designed FBG filter is placed at one end of a circulator as shown in Fig. 2 and the reflected signal is fed to the fiber interferometer for subsequent measurement and analysis. It is important to note that the designed FBG filter has a flat-top profile which is very necessary to avoid any possible intensity variation when the transmission notch shifts under the influence of external perturbation. Fig. 5 shows the spectrum of the 𝜋FBG sensor output after reflection from the designed FBG filter, which acts as a source for the Mach– Zehnder fiber interferometer for interrogation purpose. The reflection spectra are shown for wavelength shift of ±10 pm on either side of the central position of 1550 nm. As the overall objective is the measurement of very small amplitude dynamic strain perturbation, a wavelength shift of 10 pm of the transmission notch around the central position is sufficient enough. Additionally, we have calculated the integrated light intensity as the 𝜋FBG sensor transmission notch shifts around the central position. The results are shown in Fig. 6, which indicates that within the region of interest i.e. a wavelength shift of ±10 pm, the 𝜋FBG sensor transmission notch does not undergo any intensity modulation. This is very important in the case of interferometric interrogation technique as the wavelength-shift modulation is finally recorded as intensity modulation at the output of fiber interferometer. The significant reduction in the bandwidth (𝛥𝜆: FWHM) of the 𝜋FBG sensor light can now be exploited to maintain a longer optical path
Fig. 2. Schematic of interferometric interrogation technique for 𝜋FBG sensor. Transmission spectrum of the 𝜋FBG sensor is directed to an FBG filter. Parameters of the FBG filter are chosen such that it reflects only the narrow spectral peak which is then guided to a fiber Mach–Zehnder interferometer. ASE: Broadband light source; OPD: Optical Path Difference; DAQ: Data Acquisition Card.
Fig. 3. Narrow transmission notch of the 𝜋FBG sensor. The calculated FWHM (𝛥𝜆) of this transmission notch is ∼ 11 pm, which is almost an order of magnitude smaller than a regular FBG sensor reflection spectrum.
filter i.e. bandwidth, center wavelength, refractive index modulation etc. are chosen in such a way that the reflected light retains only the central narrow spectral peak. This removes the undesired spectral content of 𝜋FBG sensor transmission spectrum. The resulting filtered spectrum retains the entire characteristics of a 𝜋FBG sensor and hence the filtered spectrum can now be interrogated with interferometric principles. This reflected light signal acts as the source input to a fiber Mach–Zehnder interferometer (F-MZI) for high resolution wavelength shift measurement [1,16,17]. It is to be noted that other kinds of fiber interferometers can also be utilized for this purpose. The detailed description of wavelength shift measurement using fiber interferometers can be found elsewhere [1,16] and hence is not elaborated herein. 90
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Where, 𝛥𝜀 is the dynamic strain modulation and 𝛾 is the strain-towavelength shift responsivity of the 𝜋FBG grating sensor. As 𝜋FBG sensors are fabricated in the same type of optical fiber (i.e. silica) as used for normal FBGs, their strain-to-wavelength shift responsivity is also similar. According to the empirical model proposed by Kersey et al. [18], the strain responsivity is 𝛾 = 1.2 pm∕με at 1550 nm. Taking this into account, together with optimum OPD of 80 mm and a wavelength of 1550 nm, would yield a sensitivity 𝛥𝜙∕𝛥𝜀√of 0.25 rad∕με. As typical dynamic phase shift detection of ∼ 10−6 rad∕ Hz is currently possible with interferometric √ techniques [20,21], therefore a dynamic strain resolution of ∼ 4 𝑝𝜀∕ Hz is easily achievable with a 𝜋FBG sensor interrogated with interferometric principle. Thus, the detection limit for dynamic strain sensing can be significantly improved with the proposed methodology. Further, it is interesting to realize that the wavelength shift of 𝜋FBG sensor transmission notch corresponding to 4 𝑝𝜀 is ∼ 4.8 × 10−6 pm. This shows the wavelength-shift measurement resolution capability of the demonstrated technique. Preliminary experimental studies are also carried out to demonstrate the feasibility of the proposed interferometric interrogation principle of 𝜋FBG sensors. The schematic of the experimental setup is as outlined in Fig. 2. A commercially acquired 𝜋-phase-shifted FBG sensor of length 25 mm is used for the experimental studies. Fig. 7(a) shows the transmission spectrum of the 𝜋FBG sensor as recorded in an optical spectrum analyzer (OSA). The FWHM of the narrow transmission notch is ∼ 26 pm. For dynamic strain modulation measurement, the 𝜋FBG sensor is glued onto a stainless steel cantilever plate with dimensions (175 mm × 100 mm × 0.5 mm) and is placed under a speaker with the help of a clamp stand. Sound signal from the speaker excite dynamic vibrations in the cantilever beam thereby inducing dynamic strain modulation in the 𝜋FBG sensor. A generic desktop application is used to control the speaker for generation of sound signals. In order to isolate the narrow transmission notch of phase-shifted FBG sensor, we have fabricated a 10 cm long fiber Bragg grating. The reflection spectrum of this FBG filter is shown in Fig. 7(b). It can be observed that the reflection spectrum of the fabricated FBG has almost a flat top profile. This can be further ascertained by noting the reflected power over a region of ±10 pm around the central position. The vertical lines shown in Fig. 7(b) depict a region of 20 pm and the reflected power within this region varies by only 0.25 dB, which is very minimal. The 𝜋FBG sensor transmission notch (after filtering using the FBG) is then fed to an F-MZI. Fig. 8 shows the interference pattern of the designed and fabricated F-MZI when light from a broadband source (1525–1565 nm) is sent through the fiber interferometer and the output is observed in an OSA. The OPD between the two arms of the interferometer is ∼ 3.6 cm, which is in agreement with the optimum OPD estimated using Eq. (2) for the bandwidth (FWHM ∼ 26 pm) of the transmission notch. The above described experimental configuration is then used for dynamic signal sensing applications. Acoustic sinusoidal signal of 580 Hz is generated with the help of the speaker. The amplitude of this acoustic signal is adjusted in such a way that it is barely audible from a distance of approximately 1 meter. The response of the 𝜋FBG sensor to this acoustical signal is recorded at the output of the F-MZI with the help of a photodetector. Finally, a data acquisition device is used to record the analog signal in terms of digital signal for further processing. Fig. 9(a) shows the recorded time series signal for the acoustic signal of 580 Hz. A sinusoidal curve fitting onto the experimental time signal data is also performed. The red sinusoidal curve shows the fitted data which has a period of 1.72 ms corresponding to a frequency of 580 Hz. The power spectrum of the time signal is calculated in LabVIEW platform and is shown in Fig. 9(b). A very high peak at 580 Hz can be observed and the peak-to-baseline height at 580 Hz is approximately ∼ 37.5 dB. This shows that the applied dynamic signal is successfully sensed with high fidelity. These experimental results demonstrate the feasibility of the proposed interferometric interrogation principle for 𝜋-phase shifted fiber Bragg grating sensors.
Fig. 5. Spectrum of the 𝜋FBG sensor output after reflection from the designed FBG filter. A wavelength shift of ±10 pm on either side of the central position of 1550 nm is depicted.
Fig. 6. Integrated light intensity as the transmission notch of 𝜋FBG sensor shifts around the central position i.e. the unperturbed state. A flat-top profile of the FBG filter within the spectral shift region is necessary for this.
difference (OPD) between the two arms of the fiber Mach–Zehnder interferometer (F-MZI). As the phase shift responsivity of a fiber interferometer is directly related to the OPD, an increased OPD leads to better wavelength-shift detection sensitivity. The optimum OPD for maximum sensitivity can be determined with the following relation, which was suggested by Weis et al. [14]: 𝑂𝑃 𝐷 × 𝛥𝑘 = 2.355
(2)
Where, 𝛥𝑘 is the spectral bandwidth of the optical signal fed to the fiber interferometer expressed in wave-number unit. By substituting, 𝛥𝜆 = 11 pm (corresponding to the transmission notch of the 𝜋FBG sensor after reflection from the FBG filter) and 𝜆 = 1550 nm, this optimum OPD is determined to be ∼ 80 mm. This is significantly higher as compared to a regular FBG sensor of bandwidth ∼ 120 pm, which allows an optimum OPD of only 7.5 mm. For dynamic strain induced modulation in the 𝜋FBG sensor spectral notch wavelength represented by 𝛥𝜆 sin 𝜔𝑡, the phase-shift modulation [𝛥𝜙 (𝑡)] of the fiber interferometer can be represented as: 𝛥𝜙 (𝑡) = −
2𝜋𝑂𝑃 𝐷 2𝜋𝑂𝑃 𝐷 𝛥𝜆 sin 𝜔𝑡 = − 𝛾𝛥𝜀 sin 𝜔𝑡 𝜆2 𝜆2
(3) 91
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Fig. 9. F-MZI based interferometric interrogation results. (a) Response of the 𝜋FBG sensor for acoustical signal of 580 Hz recorded at the fiber interferometer output. The red sinusoidal curve is the fitted data corresponding to a signal of frequency 580 Hz. (b) Power spectrum of the time signal. The peak-to-baseline height at 580 Hz is approximately ∼ 37.5 dB. Fig. 7. Transmission (a) and reflection spectrum (b) of the 𝜋FBG sensor and the FBG filter, respectively, used in our experimental studies. (a) Length of the 𝜋FBG sensor is 25 mm and FWHM of the transmission notch is ∼ 26 pm. (b) Length of the fabricated FBG is 10 cm. The region within the vertical lines show a region of 20 pm around the central position and the reflected power within this region varies by only 0.25 dB.
4. Conclusions In conclusion, we have proposed an innovative concept of interrogating 𝜋FBG sensors using interferometric principle. External perturbation induced modulation of the narrow transmission notch is monitored by using an unbalanced fiber interferometer as a wavelength discriminator. This new technique has lesser complexity as compared to PDH method, without compromising the strain measurement resolution. Leveraging the smaller bandwidth of the narrow transmission notch, which allows for a significantly longer OPD, it is theoretically established that dy√ namic strain resolution down to 4 𝑝𝜀∕ Hz is easily achievable. Further enhancement is possible by increasing the OPD as the coherence length { 2 ( )} 𝜆 ∕ 𝑛𝑒𝑓 𝑓 𝛥𝜆 for spectral bandwidth of 11 pm is ∼ 150 mm and the calculated optimum OPD is still far away from this value. An as alternative approach, the FBG filter can also be replaced with a low chirp rate FBG of suitable bandwidth and flat-top reflection profile. Preliminary experimental results are presented as a proof-of-concept of the proposed interrogation architecture for 𝜋FBG. The proposed interferometric interrogation technique for 𝜋-phase-shifted Bragg grating sensor has potential applications in the field of ultra-high resolution dynamic strain measurement systems such as hydrophones for SONAR & medical sensing, acoustic emission studies etc. References
Fig. 8. Interference pattern of the designed F-MZI as recorded in an OSA. The OPD is calculated to be 3.6 cm.
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