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In this study, a novel fiber-optic sensor consisting of a tapered bend-insensitive fiber based Mach-Zehnder interferometer is presented to realize damped and continuous vibration measurement. The double cladding structure and the central coating region of the in-fiber interferometer ensure an enhanced mechanical strength, reduced external disturbance, and a more uniform spectrum. A damped vibration frequency range of 29-60 Hz as well as continuous vibration disturbances ranging from 1 Hz up to 500 kHz are successfully demonstrated.
©2013 Optical Society of America
1. Introduction
Detection and monitoring of vibration, acceleration, and mechanical shock are crucial for nondestructive inspection of civil infrastructures such as buildings, bridges, highway pavements, and dams, structural health monitoring of automobiles, ships, aircraft, and spacecraft, as well as environmental surveillance of seismic activity and volcanic eruptions. A piezoelectric accelerometer is the most conventional vibration sensor for structural monitoring which utilizes the piezoelectric effect to measure dynamic changes in mechanical variables. However a lack of an effective electrical isolation scheme makes it unsuitable in a total electromagnetic sensitive environment. A fiber optic sensor will be a good alternative over its electric counterpart with several unique advantages, such as immunity to electromagnetic interference, compact size, light weight, and distributed measurement over a long distance [1]. A variety of fiber optic sensing techniques have been extensively studied and among them, in-fiber Mach-Zehnder interferometer (MZI) sensors have recently been applied to measure temperature, strain, pressure, and refractive index with salient merits of high sensitivity, a high degree of integration, simplicity, and compact in-line measurement [2–16]. For these static measurements, the fiber sensors rely on the demodulation of external disturbance induced interference peak wavelength shift, which needs a relatively long time to obtain a steady spectrum. Thus the spectral shift detection algorithm with a slow response time is not suitable for sensing a rapidly and dynamically changing environment, such as shock impulses and mechanical vibrations. In addition, previously reported in-fiber MZIs are required to remove protective jackets between two light steering elements in order to prevent the excited cladding modes from suffering high attenuation loss. Consequently the fiber mechanical strength is reduced and the uncoated fiber cladding layer is directly exposed to the surrounding environment which leads the fiber interferometer to be vulnerable to undesirable disturbance.
In recent years, various types of bend-insensitive fibers (BIF) have been developed to allow for better light confinement at a smaller bending radius with ultralow bending loss in Fiber-to-the-Home applications [17–23]. High-order cladding modes can be excited by an optical connection with an imperfect mode match between two fibers and to be guided by a structure of a depressed-index area [24, 25]. If the high-order modes are not fully attenuated as they propagate along the fiber, they may couple back to the core at a following optical connection to induce a multipath-interference phenomenon. Suppression of excited high-order cladding modes and minimization of modal interference with the fundamental mode could be implemented using mode strippers realized by filling a section of air holes with epoxy [26]. In this paper, a novel tapered bend-insensitive fiber based in-line Mach-Zehnder interferometer (BIF-MZI) is fabricated by a fusion splicing technique for damped and continuous vibration sensing applications. An intensity-based demodulation scheme is developed to monitor the dynamic vibration induced power fluctuation at a specific wavelength selected from the transmission spectrum of the BIF-MZI.
2. Operation principle
The bend-insensitive single-mode fiber (ClearCurve, Corning) used in this study comprises an innermost layer of a germanium-doped silica core surrounded by a narrow layer of randomly distributed air holes in the pure silica cladding [21]. A schematic of the bend-insensitive fiber cross-section in Fig. 1 shows that the depressed index ring of nanoscale gas filled voids divides the fiber cladding region into two areas of an inner cladding region and an outer cladding region. A schematic illustration of the BIF-MZI is shown in Fig. 1. The BIF-MZI consists of two abrupt tapers which function as light steering elements to pilot split-merge propagation of the fundamental core mode and high-order cladding modes along the middle fiber section between the two fiber tapers. The double cladding structure of the bend-insensitive fiber enables a selective excitation of multiple cladding modes by the first taper. According to mode field patterns, the cladding modes of the bend-insensitive fiber can be categorized into two groups: inner-cladding modes that travel within the inner cladding region due to the total internal reflection and outer-cladding modes that tunnel into the outer cladding region through the depressed index ring. When the polymer coating is removed from the middle fiber section, both the inner-cladding modes and the outer-cladding modes excited by the first taper will be coupled back to the core mode by the second taper to form a fiber Mach-Zehnder interferometer. The phase difference ΔΦ between the fundamental core mode of LP01 and multiple high-order cladding modes of LPij can be expressed as
where ∆nijeff is the effective refractive index difference between the fundamental core mode and an individual high-order cladding mode, l is the interference length, and λ is the operation wavelength. When the phase difference satisfies ΔΦij = 2mπ, the mth order transmission peak wavelength is located atwhere m is an integer. The intensity in the interference pattern can then be written aswhere Icore,01 and Iclad,ij are the intensities of the fundamental core mode and an individual high-order cladding mode, respectively. Provided that the polymer coating between the two abrupt tapers is retained in the process of fabricating a BIF-MZI, optical energy in the outer-cladding modes would be sharply attenuated due to high refraction loss at the unsmoothed cladding-coating interface and a significant absorption band in the telecommunication window of the high index polymer coating, while energy in the inner-cladding modes could still travel down the inner cladding region with little attenuation and reach the second taper. Thus a novel in-fiber Mach-Zehnder interferometer will be developed based on a tapered bend-insensitive fiber while still preserving its original protective jacket.
Fig. 1 Left: A schematic illustration of the bend-insensitive fiber based Mach-Zehnder interferometer. Right: A schematic cross-section of the bend-insensitive fiber.
As a mechanical strain ε is applied on the BIF-MZI, the changing phase difference between the core mode and each cladding mode will lead to a shift in the corresponding spectrum where an interference peak wavelength λm shifts to a new wavelength of λm' by
where δl is the variation of the fiber length due to the axial strain, δneff is the photo-elastic effect induced change in the effective refractive index difference, and peff is the effective strain-optic coefficient. When a tapered bend-insensitive fiber is mounted on a cantilever, the fiber length will increase or decrease when the cantilever undergoes a convex or concave deflection as shown in Fig. 2(a) . The change in the interference length δl of the BIF-MZI can be expressed as δl ≈2dD/l, where D is the cantilever deflection and d is the separation of the neutral axis between the optical fiber and the steel cantilever. Thus damped vibrations of the cantilever will cause a dynamic strain variation on the BIF and a fluctuation in power spectrum of the BIF-MZI. In case a piezoelectric cylinder is used to provide a continuous dynamic strain on the tapered bend-insensitive fiber by wrapping the fiber on it as shown in Fig. 2(b), the transmission spectrum of the BIF-MZI will periodically red-shift or blue-shift when the fiber interferometer length experiences an elongation or compression due to the piezoelectric effect of the lead zirconate titanate (PZT) ceramic material. Figure 2(c) shows a schematic illustration of fiber interferometer vibration sensing based on an intensity modulation scheme. According to a typical sinusoidal variation of the output intensity of a two-mode interferometer as a function of wavelength, a linear intensity response can be acquired for low-amplitude vibrations observed at a quadrature bias wavelength.Fig. 2 A schematic illustration of fiber interferometer vibration sensing based on an intensity modulation scheme.
3. Experimental details
In the vibration sensing systems, the in-fiber Mach-Zehnder interferometer was fabricated on the bend-insensitive fiber that was connected to two standard single-mode fibers (SMF28, Corning) on both sides to form a SMF-BIF-SMF structure. If a mechanical splicing method is adopted such as using optical fiber connectors, a splice loss modulation will result in weak modal interference due to a refractive index profile difference induced mode-field mismatch between the SMF and the BIF. Therefore the SMF-BIF-SMF structure was implemented based on a fusion splicing technique using a fusion splicer (S182PM, Fitel). A customized clad alignment fusion splicing program with appropriate fusion current and fusion time was employed to line up the fibers, minimize the splice loss and avoid the modal interference. The electrical arc discharge zone was adjusted to introduce an offset of 10 μm deviated from the junction point to the SMF side, which could accommodate the presence of the nanostructural features and guarantee the intactness of the air-hole structure of the BIF during the fusion splicing process. Figure 3(a) shows an optical microscope image of the fusion joint area between the SMF and the BIF where they are in good alignment. Intermodal interference was not detected in the output spectrum of the SMF-BIF-SMF structure by launching light from a combined C + L band erbium-doped fiber amplifier (EDFA) to an optical spectrum analyzer (86142A, Agilent). Another fusion splicer (FA995, Ericsson) with a built-in taper manufacturing program was utilized to fabricate fiber tapers on the bend-insensitive fiber. Selecting a taper specification of a large waist diameter should ensure that fiber mode coupling efficiency is small and thus the attenuation of the interferometer is minimized and fewer high-order modes are excited [27]. An optical microscope image of an abrupt taper with a taper length of 900 μm and a waist diameter of 80 μm is shown in Fig. 3(b). Two individual in-fiber MZIs, BIF-MZI-a and BIF-MZI-b, were constructed along the bend-insensitive fibers by creating double abrupt tapers of the above specifications separated by distances of 5 cm and 15 cm, respectively.
Fig. 3 (a) An optical microscope image of the fusion joint area between the BIF (left) and the SMF (right). (b) An optical microscope image of one abrupt taper fabricated on the BIF.
Figure 4(a) shows the attenuation spectrum of the BIF-MZI-a which was obtained from the difference between the emission spectrum of the EDFA and the transmission spectrum of the BIF-MZI. Although the central coating region was preserved, the tapered bend-insensitive fiber still performed well as an in-fiber interferometer which is evident from the prominent interference fringes due to a superposition of several inner-cladding modes interferences. A fast Fourier transform (FFT) of the wavelength spectrum in Fig. 4(a) provides a spatial frequency spectrum as shown in Fig. 4(b). The spatial frequency ξ can be expressed as ξ ≈ ΔneffL/λ02, where λ0 is the center peak wavelength around which a first-order Taylor series is expanded [2]. In Fig. 4(b), a power spectrum in the spatial frequency domain exhibits two dominant intensity peaks corresponding to two inner-cladding modes with their corresponding simulated optical field patterns shown in the inset of Fig. 4(b). It is noticed that the light energy of the inner-cladding modes are completely confined in the inner cladding region. Figure 4(d) shows a spatial frequency spectrum of the BIF-MZI-b with two dominant intensity peaks obtained by fast Fourier transform of the corresponding attenuation spectrum in Fig. 4(c). The simulated optical field patterns of the inner-cladding modes are shown in the inset of Fig. 4(d). Since the BIF-MZI allows only very few inner-cladding modes to pass through the central fiber coating region, the superimposed interference spectrum of this few-mode interferometer still monotonically shifts with a changing strain and thus the power fluctuation at the operation wavelength exhibits an approximate linear response relation to dynamic vibrations. Compared to the conventional in-fiber MZIs based on a standard single-mode fiber with a single cladding layer, the BIF-MZI has very few order numbers of interference due to its double cladding structure and central coating region, and accordingly a more uniform spectrum which is suitable for dynamic vibration sensing applications.
Fig. 4 (a, b) and (c, d) show attenuation spectra and corresponding spatial frequency spectra of the BIF-MZI-a and BIF-MZI-b, respectively. Insets of (b, d) show the simulated optical field patterns of the inner-cladding modes of BIF-MZI-a and BIF-MZI-b.
Figure 5 shows a schematic experimental setup of vibration measurement using the BIF-MZI. Light from a 1550 nm planar waveguide based external cavity laser with the 3 kHz spectral linewidth (PLANEX, Rio) was launched into the BIF-MZI and then guided through an attenuator and an AC photodetector (PDB450C-AC, ThorLabs) to a high-speed oscilloscope (WaveRunner 64Xi-A, LeCroy). Experiments were carried out in a temperature controlled room with the temperature maintained at 25.0 ± 0.5 °C. The temperature change can be neglected since it is a rather slow process relative to the dynamic vibration measurement with a fast response. At a specific operation wavelength, 1550 nm for example, the changing power due to vibrations becomes a strong function of time. By monitoring the power variation in a time domain, the vibration frequency could be detected in real time.
Fig. 5 A schematic experimental setup of vibration measurement. LD, laser diode; ATT, attenuator; PD, Photodetector.
4. Experimental results and discussion
4.1 Detection of damped vibration
Figure 6 shows a schematic measurement setup to detect damped vibration frequency using the 5 cm BIF-MZI-a. A stainless steel cantilever of rectangular cross-section (width w = 0.5 cm, thickness h = 0.1 cm) and a total length of 40 cm was used to generate a damped vibration. The tapered bend-insensitive fiber was slightly pre-stretched and attached to the free end of the steel cantilever using epoxy glue. The set point of the pre-strained value was about 103 με, which was selected to avoid fiber breakage or movement during a convex or concave deflection process. Another end of the cantilever was fastened on a fixed base by a metal clamp and the cantilever length could be controlled by adjusting the position of the metal clamp on the cantilever. When the free end of the cantilever was deflected by a specific displacement from its initial stabilized position and instantly released, the cantilever would experience a damped vibration about its equilibrium position soon afterwards. A standard ruler was used to measure the initial deflection of the cantilever.
Figures 7(a) and 7(c) show the time-domain spectra of the BIF-MZI-a with a 10 cm cantilever length under damped vibrations that the free end of the cantilever were initially flipped down to a distance of 5 mm and 3 mm, respectively. Figure 7(a) shows that the initial output voltage recorded by the oscilloscope is 0.12 V for the damped vibration of the 5 mm deflection. As the vibration continued, the damping effect caused a continuous attenuation of the output voltage with a specific damping time defined as a timescale for an output voltage dropping to 90% of its initial value. The vibration finally vanished and a noise floor was obtained with a stable output voltage of 0.01 V. The damping time was measured to be 5.0 seconds by performing an envelope analysis on the time-domain signal shown by the red curves in Fig. 7(a). For the damped vibration of the 3 mm deflection, a relatively small initial peak voltage of 0.06 V and a damping time of 4.0 seconds were obtained in Fig. 7(c). In addition, two insets of Figs. 7(a) and 7(c) extracted from enlarged regions of the vibration time trace signal exhibit regular sinusoidal waveforms which indicate a stable periodicity of the power oscillations. Figures 7(b) and 7(d) show the same fundamental frequency of 62.0 Hz by fast Fourier transform of the time-domain spectra in Figs. 7(a) and 7(c). When the initial deflection of the cantilever was varied from 1 mm to 7 mm, the fundamental frequencies were in the range from 61.8 ± 0.5 Hz to 62.4 ± 0.5 Hz as shown in Fig. 7(e). It is indicated that the fundamental frequencies of the damped vibrations is independent of the initial deflection of the cantilever.
Fig. 7 Time-domain spectra and frequency-domain spectra of the BIF-MZI-a with a cantilever length of 10 cm under damped vibrations of (a, b) 5 mm and (c, d) 3 mm deflections, respectively. (e) Fundamental frequencies as a function of initial deflections of the cantilever.
Various fundamental frequencies of the damped vibrations can be obtained by changing the cantilever length. The fundamental frequency should be proportional to the reciprocal of the square of the cantilever length, which follows
where c is the coefficient of the first vibration mode, E is the Young’s modulus of the stainless steel, I is the moment of inertial, ρ is the density of the material, A is the cross section area, and L is the cantilever length. The damped vibrations of different cantilever lengths under the same initial deflection were detected using the BIF-MZI-a to demonstrate this relationship. Figure 8(a) shows the time-domain spectrum of the BIF-MZI-a with a cantilever length of 15 cm under a damped vibration of a 3 mm deflection and Fig. 8(b) shows the corresponding frequency-domain spectrum where the fundamental frequency was located at 29.2 Hz. The normalized power spectra of the BIF-MZI-a with six different cantilever lengths ranging from 10 to 15 cm are shown in Fig. 8(c). Figure 8(d) shows a linear relationship between f and 1/L2, where the fundamental frequencies corresponding to these cantilever lengths are 62.0 Hz, 52.8 Hz, 44.1 Hz, 38.5 Hz, 33.0 Hz, and 29.2 Hz, respectively.Fig. 8 (a) Time-domain spectrum of the BIF-MZI-a with a cantilever length of 15 cm under a damped vibration of 3 mm deflection and (b) the corresponding frequency-domain spectrum. (c) Normalized power spectra of the BIF-MZI-a with different cantilever lengths. (d) Fundamental frequencies as a function of cantilever lengths.
4.2 Detection of continuous vibration
Figure 9 shows a schematic setup to measure a continuous vibration frequency using the 15 cm BIF-MZI-b. A piezoelectric cylinder (Americanpiezo) with an external diameter of 38 mm was utilized as a continuous vibration source driven by a function generator. The piezoelectric cylinder has a frequency response range up to a maximum of 500 kHz. The central coating region of the tapered bend-insensitive fiber was wound around the piezoelectric cylinder and tightly bonded on the exterior surface using epoxy glue. The double abrupt taper regions were attached on two fixed bases and slightly stretched to keep the fiber straight. A periodic sinusoidal driven signal with a peak-to-peak voltage of 10 volts caused a continuous vibration of the piezoelectric cylinder that was transmitted to the fiber and generated about 1 micro-strain equivalent dynamic stretch.
Firstly the BIF-MZI-b underwent low frequency vibrations of the piezoelectric cylinder. Figures 10(a) -10(d) show the frequency-domain spectra of the BIF-MZI-b when the piezoelectric cylinder was driven by sinusoidal signals of 1.0 Hz, 3.0 Hz, 5.0 Hz, and 10.0 Hz, respectively, and the corresponding time-domain spectra are shown in the insets. In the frequency-domain spectra, dominant peaks are located at 1.0 Hz, 3.0 Hz, 5.0 Hz, and 9.5 Hz, respectively, which are close to their corresponding driven frequencies. In Fig. 10(d), three other peaks at frequencies of 19.0 Hz, 29.0 Hz, and 38.5 Hz are obviously distinguished beyond the fundamental frequency of 9.5 Hz which agrees well with the high-order harmonics resonance phenomenon.
Fig. 10 (a, b, c, and d) show the frequency-domain spectra of the BIF-MZI-b when the piezoelectric cylinder was driven by sinusoidal signals of 1 Hz, 3 Hz, 5 Hz, and 10 Hz, respectively. The insets show the corresponding time-domain spectra.
The vibration frequency of the piezoelectric cylinder was then tuned from 100 Hz to 15 kHz. Figures 11(b) and 11(e) show two enlarged regions of the vibration time trace signal extracted from Figs. 11(a) and 11(d) which present good sinusoidal waveforms with a constant power oscillation periodicity. Figure 11(c) plots the frequency-domain spectrum from Fourier transform of the corresponding 0.8 seconds time-domain data with a peak at 98.9 Hz when the piezoelectric cylinder was driven by a 100 Hz sinusoidal signal. Figure 11(f) shows a FFT spectrum with a peak at 15.0 kHz as the piezoelectric cylinder was driven by 15 kHz sinusoidal wave. Figures 11(c) and 11(f) show high signal-to-noise-ratios (SNR) of 45 dB and 50 dB, respectively. When the driven frequencies of the piezoelectric cylinder were set to 500 Hz, 1 kHz, 5 kHz, and 10 kHz, the corresponding FFT spectra had obvious peaks with SNRs of 50 dB at 497.9 Hz, 998.9 Hz, 4.99 kHz, and 9.98 kHz, respectively.
Fig. 11 (a, b) and (d, e) show the time-domain spectra as well as (c) and (f) the corresponding frequency-domain spectra of the BIF-MZI-b when the piezoelectric cylinder was driven by sinusoidal signals of 100 Hz and 15 kHz, respectively.
High frequency continuous vibrations of the BIF-MZI-b were investigated by tuning the vibration frequency of the piezoelectric cylinder up to 500 kHz. Figure 12 shows obvious peaks in the FFT spectra with high SNRs from 40 dB to 50 dB at 99.96 kHz, 199.91 kHz, 299.89 kHz, 399.88 kHz, and 499.78 kHz, respectively, as the driven frequencies of the piezoelectric cylinder were increased from 100 kHz to 500 kHz in 100 kHz steps.
Fig. 12 The frequency-domain spectra of the BIF-MZI-b when the piezoelectric cylinder was driven by high frequency sinusoidal signals from 100 kHz to 500 kHz.
4. Conclusion
In conclusion, a tapered bend-insensitive fiber interferometer sensor has been proposed and experimentally demonstrated. A high sensitive and fast response intensity based demodulation scheme has been adopted by monitoring power fluctuation of the BIF-MZI at the operation wavelength to detect damped and continuous vibrations. The possibility of manufacturing an in-fiber Mach-Zehnder interferometer without removing its central protective jacket provides many great advantages in vibration sensing applications, such as maintaining high mechanical strength, isolating the optical fiber from external physical damage, and allowing easy fiber attachment to a substrate. Furthermore, attenuated outer-cladding modes due to optical coating absorption leaves a few inner-cladding modes propagating along the bend-insensitive fiber and a more uniform spectral response is available for dynamic vibration sensing. The in-fiber interferometer sensor has an extremely wide frequency response from 1 Hz up to 500 kHz. The experimental results imply that the proposed BIF-MZI could be effectively employed in applications on intrusion detection and structure health monitoring.
Acknowledgment
The research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants and Canada Research Chairs (CRC) Program. Ping Lu would like to acknowledge the Province of Ontario Ministry of Research and Innovation and the University of Ottawa for the financial support of the Vision 2020 Postdoctoral Fellowship.
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