All-optical enhancement of minimum detectable perturbation in intensity-based fiber sensors

Benoit Vanus; Chams Baker; Liang Chen; Xiaoyi Bao

doi:10.1364/OE.441217

1. Introduction

Over the last few decades, intensity-based optical fiber sensors have been extensively used in the oil and gas industry, for medical diagnostics, and for buildings structural health monitoring [1–8]. One main objective when developing fiber sensors is to detect weak perturbations of environmental variables such as temperature or strain. This is particularly important when detecting ultrasound signals, commonly used for locating and characterizing damages in structures and for medical imaging, since the detected signal amplitude decreases when the frequency increases due to larger attenuation at high ultrasound frequencies [9,10]. Gravitational wave detection using intensity-based sensors also requires measuring extremely small environmental perturbations [11,12].

The detection limit of an intensity-based fiber sensor can first be improved by appropriately choosing and designing the sensor for a targeted application. Interferometric sensors, such as a Mach-Zehnder interferometer (MZI), are commonly utilized intensity-based sensors due to their good low-frequency response and performance across a wide frequency band [13]. The sensitivity of an intensity-based interferometric sensor can be increased by adjusting the length of the interferometer arms [14], coating or etching the sensing fiber [15,16], and operating the sensor at a quadrature point [17]. Second, using an appropriate detection algorithm also allows for improving the fiber-based sensor performance [18], particularly when the sensor is intensity-noise limited [19]. Finally, stabilization of the light source also plays a key role in enhancing the detection limit of a fiber-based sensor. Because most intensity-based sensors are also sensitive to the input signal polarization, a polarization control scheme was proposed to stabilize a laser signal and therefore improve the detection limit [20]. However, the use of control loops on the laser frequency or polarization comes at the expense of the laser intensity and phase noises which limit the minimum detectable environmental perturbation (MDEP).

We have previously demonstrated a proof of concept for all-optical magnification of small environmental perturbations [21]. In an intensity-based sensor, magnification increases the environmental perturbation induced power variation $\Delta P$ with respect to the initial power $P_{0}$ that is measured in the absence of environmental perturbations, leading to an increase in $\Delta P/P_{0}$. Magnification must be distinguished from amplification which increases both $\Delta P$ and $P_{0}$ such that $\Delta P/P_{0}$ remains the same. Magnification is especially practical when $\Delta P\ll P_{0}$ because it increases $\Delta P$ while keeping $P_{0}$ below the saturation level of a photodetector, which enables the measurement of the increased $\Delta P$. All-optical magnification can be used for enhancing the MDEP of an intensity-based sensor when the signal noise is mainly contributed by the photodetector. However, to achieve an MDEP enhancement in a general case, the laser intensity at the input of the sensor must be stabilized. Without the stabilization step, the intensity noise of the laser will be magnified and will thus limit the MDEP. Therefore, both the stabilization and magnification steps must be combined to enhance the MDEP in a practical sensing application.

In this paper, we propose and demonstrate the use of self-phase modulation (SPM) to all-optically improve the minimum detectable perturbation of an intensity-based fiber sensor using a novel stabilization-magnification (SM) sensing scheme. First, we derive a theoretical prediction of the minimum detectable strain provided by our proposed scheme and compare it with the minimum detectable strain of a conventional sensing scheme. Then, we present an experimental setup for measuring a damped vibration of a cantilever using our SM scheme and a conventional sensing scheme, and compare the results from both sensing schemes to demonstrate an enhancement of 3.93 in minimum strain detection by our SM scheme. Finally, we discuss the prospect and limitations of our novel sensing scheme.

2. Minimum detectable strain improvement by SM sensing

Figure 1 shows a conceptual schematic of an SM sensing scheme where the output power of the laser is expressed as $P_{\textrm {L}} = P + \delta P$, with $P$ being the mean output power, and $\delta P$ being the variation of power around $P$. The light intensity is first stabilized and the power after stabilization is expressed as $P_{\textrm {S}} = P + \eta \delta P$, with $\eta$ being the power fluctuation reduction factor. The intensity-stabilized light is then sent to an intensity-based interferometric sensor whose transfer function is sinusoidal, as shown in Fig. 2. The transfer function of an interferometric intensity-based sensor is given by

(1)$$P_{\textrm{out}} = P_{\textrm{in}}\alpha\cos^2\left(\frac{\phi_d}{2}\right)$$

where $P_{\textrm {out}}$ is the sensor output power, $P_{\textrm {in}}$ is the power entering the sensor, $\alpha$ is the attenuation factor, and $\phi _d$ is the phase difference between the optical paths of the interferometer. Using the linear approximation for small phase-shift variations when operating at a quadrature point, illustrated by the dashed green line in Fig. 2, the output power becomes

(2)$$P_{\textrm{out}} = \frac{1}{2}P_{\textrm{in}}\alpha\left[1+\sin\left(\Delta\phi_{d}\right) \right] \approx \frac{1}{2}P_{\textrm{in}}\alpha \left(1 + \Delta\phi_{d}\right)$$

for $\vert \Delta \phi _{d}\vert <0.1$, where $\phi _d=\Delta \phi _{d} \pm (\pi /2)+2l\pi$, with $l$ being an integer. An expression of the output power of the sensor with a stabilized input power is obtained from Eq. (2) by replacing $P_{\textrm {in}}$ with $P_{\textrm {S}}$ leading to

(3)$$P_\textrm{out,S}= \Omega(1 + \eta F)(1+\Delta\phi_{d}),$$

where $F=\delta P /P$ and $\Omega = 0.5\alpha P$.

Fig. 1. Conceptual schematic of a stabilization-magnification sensing scheme

Download Full Size | PDF

Fig. 2. Transfer function of an interferometric intensity-based sensor, with $P_{\textrm {out}}$ the output power of the sensor, $P_{\textrm {in}}$ the input power, and $\phi _d$ the phase-shift induced by strain $\epsilon$, temperature $T$ or voltage $V$ changes applied on the sensor.

Download Full Size | PDF

The sensor output power is magnified by imposing a sinusoidal intensity modulation and extracting a sideband generated after the light experiences SPM in a nonlinear Kerr medium [21]. The general expression for the power evolution of an SPM-generated sideband of order $m$ is given by

(4)$$P^{(m)}\left(\phi_{\textrm{SPM}}\right) = \frac{1}{4} P_p \Bigg[J_m^2\left(\frac{\phi_{\textrm{SPM}}}{2}\right) + J_{m+1}^2\left(\frac{\phi_{\textrm{SPM}}}{2}\right) \Bigg],$$

where the accumulated nonlinear phase-shift is $\phi _{\textrm {SPM}} = P_p\gamma L$, with $P_p$ being the signal peak power, $\gamma$ being the waveguide nonlinear parameter, and $L$ being the length of the nonlinear Kerr medium [22]. In the magnification regime, the amount of nonlinear phase-shift experienced by the light remains small and allows for approximating the Bessel functions in Eq. (4) with $J_m\left (\phi _{\textrm {SPM}}/2\right ) \sim \left (\phi _{\textrm {SPM}}/4\right )^m /(m!)$. This asymptotic approximation is valid for $0<\phi _{\textrm {SPM}} \ll 2\sqrt {m+1}$, which comprises the magnification regime.

The output power of the SM sensing scheme using the $m^{\textrm {th}}$-order sideband applied to an interferometric intensity-based sensor is

(5)$$P^{(m)}_{\textrm{out,SM}}= \xi_m\Omega^{2m+1}\left(1 + \eta F\right)^{2m+1} \left(1+\Delta\phi_{d}\right)^{2m+1},$$

with $\xi _m =\left (0.25\right )^{2m+1} \left (m!\right )^{-2} \left (\gamma L\right )^{2m}$. When the sensor is subjected to an external strain $\Delta \epsilon$, the phase difference between the optical paths becomes $\phi _{d}\big \vert _{\Delta \epsilon } = \phi _{d,0} + \Delta \phi _{d,\Delta \epsilon } + 2l\pi$, where $\phi _{d,0}$ is the initial phase difference between the interferometer optical paths and is equal to $\pm (\pi /2)$ at the quadrature points, and $\Delta \phi _{d,\Delta \epsilon }$ is the phase difference variation induced by the applied strain. The induced phase variation is directly related to the applied strain by $\Delta \phi _{d,\Delta \epsilon } = \phi _{d,0} \theta _\epsilon \Delta \epsilon$, where $\theta _\epsilon =\left (\partial n_d/\partial \epsilon \right )n_d^{-1} +\left (\partial L_s/\partial \epsilon \right )L_s^{-1}$, with $L_s$ being the length of the sensor, and $n_d$ being the refractive index difference between the sensor optical paths. Similar relationships between the induced phase difference and the applied external strain can be found for the majority of interferometric intensity-based fiber sensors [23–25], and this proportionality is well established in the field. The output power at the $m^{\textrm {th}}$-order sideband of the SM scheme is

(6)$$P^{(m)}_{\textrm{out,SM}}\big\vert_{\Delta\epsilon} = \xi_m\Omega^{2m+1}\left(1 + \eta F\right)^{2m+1} \Big(1+ \left(2m+1\right)0.5\pi\theta_\epsilon\Delta\epsilon\Big),$$

and the generated output power variation induced by $\Delta \epsilon$ is

(7)$$\Delta P^{(m)}_{\textrm{out,SM}}\big\vert_{\Delta\epsilon} = \xi_m \Omega^{2m+1}\left(1 + \eta F\right)^{2m+1} \left(2m+1\right)0.5\pi\theta_\epsilon \Delta\epsilon.$$

After the magnification stage, the optical signal is converted into an electrical signal by a photodetector, and then acquired using an oscilloscope. The voltage measured at the oscilloscope is $V_{\textrm {out}} = G_DP+ N_D+ N_O$, where $G_D$ is the detector conversion factor, $P$ is the optical power, $N_D$ and $N_O$ are the noises of the detector and the oscilloscope, respectively. Using the approximation $(1 + \eta F)^{2m+1}\approx 1+ (2m+1)\eta F$ when $\eta F\ll 1$ in Eq. (6), and defining $A_0 = 0.5\pi \theta _\epsilon$, the measured voltage at the oscilloscope in the SM sensing system when strain is applied on the sensor is

(8)$$ \begin{aligned} V_\textrm{out,SM}\big\vert_{\Delta P} &= G_D \xi_m\Omega^{2m+1} \bigg(1 + \left(2m+1\right)\eta F+\left(2m+1\right) A_0 \Delta\epsilon \\ & +\left(2m+1\right)^2\eta FA_0\Delta\epsilon \bigg)+ N_D+ N_O. \end{aligned}$$

Similarly, the measured voltage in a conventional sensing scheme using a similar sensor under identical strain conditions is

(9)$$V_\textrm{out,C}\big\vert_{\Delta P} = G_D \Omega \left(1 + F+A_0\Delta\epsilon+FA_0\Delta\epsilon \right)+ N_D+ N_O.$$

The minimum detectable strain of the SM sensing scheme, $\Delta \epsilon _{\textrm {min,SM}}$, is obtained by equating the signal and the noise contributions in Eq. (8) leading to

(10)$$\Delta\epsilon_{\textrm{min,SM}} = \frac{1}{0.5\pi\theta_\epsilon\Big(1- \left(2m+1\right)\eta F\Big)} \left(\eta F+\frac{N_{\textrm{SM,r}}}{2m+1}\right),$$

where $V_{\textrm {0,SM}} = G_D \xi _m\Omega ^{2m+1}$ is the initial voltage in the absence of strain, and $N_{\textrm {SM,r}}=(N_D+ N_O)/V_{\textrm {0,SM}}$ is the relative detection noise. Similarly, the minimum detectable strain of a conventional sensing system is

(11)$$\Delta\epsilon_{\textrm{min,C}} = \frac{1}{0.5\pi\theta_\epsilon \left(1 - F\right) } \left(F+N_{\textrm{C,r}}\right).$$

where $V_{\textrm {0,C}} = G_D\Omega$, and $N_{\textrm {C,r}}=(N_D+ N_O)/V_{\textrm {0,C}}$. A comparison between minimum detectable strain values of conventional and SM sensing schemes can be performed when their respective initial voltage values are equal, $V_{\textrm {0,C}} = V_{\textrm {0,SM}}$. The minimum detectable strain improvement provided by the SM sensing scheme in comparison to the conventional scheme is

(12)$$\Gamma_{\epsilon} = \frac{\Delta\epsilon_{\textrm{min,C}}}{\Delta\epsilon_{\textrm{min,SM}}} = \frac{1- (2m+1)\eta F}{1 - F}\left(\frac{F+N_{\textrm{C,r}}}{\eta F+\frac{N_{\textrm{SM,r}}}{2m+1}}\right).$$

Based on the first factor of Eq. (12), $m$ and $\eta$ must satisfy the condition $(2m+1)\eta \leq 1$ to avoid magnifying the initial laser amplitude noise. Based on the second factor of Eq. (12), reducing $\eta$ improves the minimum detectable strain by reducing the impact of the laser intensity noise, and increasing the extracted sideband order $m$ improves the minimum detectable strain by reducing the impact of the detection noise.

3. Experimental setup

Figure 3 presents a schematic of the experimental setup used for demonstrating the enhancement in minimum strain detection provided by the SM sensing scheme compared to a conventional sensing scheme when using an interferometric intensity-based fiber sensor. The setup contains a reference branch representing the conventional sensing scheme and an SM sensing branch, shown with a dashed purple line and a solid black line, respectively. For reliable comparison, identical polarimetric sensors (PSs) are utilized in both schemes, and each PS contains a 20-cm long polarization-maintaining (PM) fiber acting as a fiber under test (FUT). The PS behaves similar to an intensity-based interferometric sensor with each principal polarization axis of the PM FUT acting as an arm of the interferometer. Both PM FUTs are glued on a thin metallic cantilever, depicted by the grey rectangle in Fig. 3. One end of the cantilever is fixed to the optical table, while the other end is free, and thus applying a force on the free-end deforms the cantilever and induces identical strain on both sensors, which allows for reliable comparison.

Fig. 3. Schematic of the experimental setup. BPF: Band-Pass Filter, EDFA: Erbium-Doped Fiber Amplifier, EOM: Electro-Optical Modulator, HG-EDFA: High-gain EDFA, HP-EDFA: High-power EDFA, KM: Kerr Medium, OSC: Oscilloscope, PBS: Polarization Beam Splitter, PC: Polarization Controller, PD: Photodiode, PS: Polarimetric Sensor.

Download Full Size | PDF

The configuration of a conventional polarimetric sensor is shown in Fig. 4(a). A laser light is launched into a polarization controller (PC) which aligns the light polarization with the perpendicular axis of a fiber-coupled polarization beam splitter (PBS, from Thorlabs). The PBS, which is connected with polarization-maintaining (PM) fibers, decomposes the light into two orthogonally polarized components, respectively referred to as perpendicular $\perp$ and parallel ${\mathbin{\!/\mkern-5mu/\!}}$ polarizations. Polarized light exiting the PBS by the common port passes to a second PC that aligns the laser light at 45° from the the principal axes of the PM sensing fiber that acts as an FUT. The 45° incident angle allows the power of the polarized light at the input of the FUT to split evenly between the FUT principal polarization axes. The light at the output of the FUT propagates to a second fiber-coupled PBS through a PC that ensures the light from each principal polarization axis of the FUT reaches the PBS at a 45° angle. As a result, half the power propagating from each principal polarization axis of the FUT is projected onto the parallel axis of the PBS, which causes light interference. The power of the interference signal is then converted to an electrical signal using a photodetector (PD) and the electrical signal is measured by an oscilloscope (OSC).

Fig. 4. Schematic of (a) a conventional polarimetric sensor, (b) the polarimetric sensor used in our experimental setup presented in Fig. 3. The $\perp$ and ${\mathbin{\!/\mkern-5mu/\!}}$ signs refer to the perpendicular and parallel axes of the polarization beam splitter, respectively. FUT: Fiber Under Test, OSC: Oscilloscope, PBS: Polarization Beam Splitter, PC,45°: Polarization Controller aligned at 45°, PD: Photodetector.

Download Full Size | PDF

Figure 4(b) presents a schematic of the polarimetric sensor configuration used in this experiment. The configuration in Fig. 4(b) differs from the classical polarimetric sensor in Fig. 4(a) by the Fresnel reflection and by the 45°-splice utilized instead of a PC, but both configurations are effectively equivalent. The Fresnel reflection from the end of the FUT makes it possible to use a single PBS instead of the two required in the conventional configuration. Moreover, the laser light passes twice through the FUT making the effective sensing length twice as long as that in a conventional configuration. Finally, the 45-degree splices are created by a commercial fiber-splicer and do not change over time, which makes them preferable to the PCs in the conventional configuration. The transmission spectrum of this polarimetric sensor, presented by the blue line in Fig. 5, is obtained by sending amplified spontaneous emission (ASE) noise from an erbium-doped fiber amplifier (EDFA) to the input and calculating the ratio between the output and the input spectra. The central wavelength of the laser is tuned to match the quadrature point of the polarimetric sensor, as shown by the red line in Fig. 5.

Fig. 5. Measured transmission spectrum of the polarimetric sensor that is utilized in this experiment. Also presented is the measured laser spectrum, shown in red, which is aligned with the quadrature point of the polarimetric sensor. PSD: Power Spectral Density

Download Full Size | PDF

In the SM sensing branch of the setup presented in Fig. 3, a tuneable laser (HP 81980A) generates a coherent continuous light at 1550.196 nm, which is tuned such that the wavelength of the first-order SPM-generated sideband is aligned with the quadrature point of the polarimetric sensor. The light first passes through an electro-optic modulator (EOM, OC-192) driven by a radio frequency source (HP 83752A) applying an 8.825 GHz sinusoidal intensity modulation. The light is then pulse-modulated by a second EOM (OC-192) driven by a function generator (Tektronix AFG 3252) to create a 10 ns wide pulse with a 1 kHz repetition rate. The pulsed light is then amplified by an EDFA (Amonics AEDFA-PA-25-B-FA) before being filtered by a dual-grating filter with central wavelengths tuned to the sinusoidally-modulated laser wavelengths ($\lambda _{1}= {1550.110}\,\textrm{nm}$ and $\lambda _{2}= {1550.268}\,\textrm{nm}$). The power of the pulse is then boosted by a high-power EDFA (Amonics AEDFA-33) and filtered again by an inverted version of the same dual-grating filter before entering a 2-km long dispersion-shifted fiber acting as a Kerr medium. Sidebands are generated at the output of the Kerr medium as the sinusoidally-modulated pulse experiences SPM [22], and the first-order sideband is extracted using a band-pass filter (BPF, Teraxion TFC-C-Band). To stabilize the pulse peak power intensity, the amount of amplification is adjusted to achieve $\phi _{\textrm {SPM}}/ {1}\,\textrm{rad}= {6.4}\,\textrm{dB}$ [26]. The intensity-stabilized pulse is then amplified by an EDFA (Amonics AEDFA-PA-25-B-FA) and the light polarization is aligned with the input of the polarimetric sensor using a PC. The output of the polarimetric sensor enters an EOM that is sinusoidally-driven with an 8.825 GHz modulation frequency (OC-192 with HP 8673D driver). The sensor output is then amplified by a high-gain EDFA (Amonics APEDFA-C-10-B-FA) and filtered by a BPF (Newport OSP-9100). A second step of amplification and filtration is applied using a high-power EDFA (Amonics AEDFA-C-30B-B-FA) and a dual-grating filter ($\lambda _{1}= {1550.332}\,\textrm{nm}$ and $\lambda _{2}= {1550.470}\,\textrm{nm}$) before the signal reaches a second Kerr medium, composed of 6-km long dispersion-shifted fiber. Optical sidebands are generated by SPM and the second-order sideband is extracted using a BPF (Teraxion TFC-C-Band). The peak power of the pulse at the input of the second Kerr medium is adjusted to align with the signal magnification regime [21].

The reference branch of the setup is composed of a tuneable laser (Agilent 81940A) emitting light at 1555.689 nm. The light is pulse-shaped using an EOM (JDSU 10020461) driven by the second output of the same function generator that is utilized to create the pulse in the SM branch to ensure both SM and reference pulses are synchronized and aligned for comparison. The generated pulse is amplified by an EDFA (Amonics AEDFA-PA-25-B-FA) and sent through a polarimetric sensor that is effectively identical to the one in the SM branch.

The reference and SM signals are combined when reaching the 50-50 fiber coupler but do not interfere due to a time delay imposed on the reference signal by the function generator. The signals are finally detected using a low-noise photodetector (New Focus 1811- IR DC 125MHz) and the generated electrical signal is captured using an oscilloscope (LeCroy 64Xi-A). Detection of the signals from both branches using the same photodiode and oscilloscope makes the detection noises identical and allows for reliable comparison of both schemes.

4. Results and discussion

To compare the minimum detectable strain of the SM and conventional sensing schemes, a damped vibration is induced on the sensors by applying and suddenly releasing a force on the free-end of the cantilever. The vibrational deformation of the cantilever induces an equal strain on the FUTs of both sensors and the resulting signal amplitude changes are measured at the oscilloscope. The solid blue and red traces in Fig. 6 respectively show the measured initial output signals from the SM and reference schemes in the absence of vibrations. The peaks of these initial signals, representing $V_{\textrm {0,SM}}$ and $V_{\textrm {0,C}}$, are made equal so that the detected vibration amplitudes can be reliably compared. The dashed blue and red traces in Fig. 6 respectively show the vibration-induced amplitude changes of the SM and reference signals when subjected to the same vibration. The vibration profile is obtained by tracking the evolution of the peak amplitude of the SM and reference signals over time.

Fig. 6. Continuous oscilloscope trace recording the SM and reference sensors outputs, respectively in blue and red, and their respective amplitude changes under a given applied vibration.

Download Full Size | PDF

Figure 7 presents the measured damped vibration from the SM and the conventional schemes relative to $V_{\textrm {0,SM}}$ and $V_{\textrm {0,C}}$, respectively. As the vibration dampens, the conventional signal becomes buried in the noise while the SM signal can still be detected, therefore showing an increased minimum detectable strain. The signal-to-noise ratios are $\mathrm {SNR}_{\textrm {C}}=\Delta V_{\textrm {out,C}}/N_{\textrm {C}}=\alpha _{\textrm {C}}\Delta \epsilon /N_{\textrm {C}}$ for the conventional scheme and $\mathrm {SNR}_{\textrm {SM}}=\Delta V_{\textrm {out,SM}}/N_{\textrm {SM}}=\alpha _{\textrm {SM}}\Delta \epsilon /N_{\textrm {SM}}$ for the SM scheme, where $\alpha _{\textrm {C}}$ and $\alpha _{\textrm {SM}}$ are the strain-to-voltage conversion factors for the conventional and the SM schemes, and $N_{\textrm {C}}$ and $N_{\textrm {SM}}$ are the noise levels of the conventional and SM schemes, respectively. The value of $\Delta \epsilon _{\textrm {min,C}}=N_{\textrm {C}}/\alpha _{\textrm {C}}$ is obtained by setting $\mathrm {SNR}_{\textrm {C}}=1$, and the value of $\Delta \epsilon _{\textrm {min,SM}}=N_{\textrm {SM}}/\alpha _{\textrm {SM}}$ is obtained by setting $\mathrm {SNR}_{\textrm {SM}}=1$, which leads to an enhancement in the minimum detectable strain $\Gamma _{\epsilon }=\Delta \epsilon _{\textrm {min,C}}/{\Delta \epsilon _{\textrm {min,SM}}}=\left (\alpha _{\textrm {SM}}/\alpha _{\textrm {C}}\right )\left (N_{\textrm {C}}/N_{\textrm {SM}}\right )$. Using $\Delta V_{\textrm {out,C}}=\alpha _{\textrm {C}}\Delta \epsilon$ and $\Delta V_{\textrm {out,SM}}=\alpha _{\textrm {SM}}\Delta \epsilon$, leads to $\alpha _{\textrm {SM}}/\alpha _{\textrm {C}}=\Delta V_{\textrm {out,SM}}/\Delta V_{\textrm {out,C}}$ at a non-zero value of $\Delta \epsilon$, and by reference to Fig. 7, the measured ratio is $\alpha _{\textrm {SM}}/\alpha _{\textrm {C}}=4.65$. The measured peak-to-peak noise amplitudes in the SM and reference branches are 0.13 V, 0.11 V, respectively, leading to $N_{\textrm {C}}/N_{\textrm {SM}}=0.85$. Therefore, the measured enhancement in the minimum detectable strain is $\Gamma _{\epsilon }=\left (\alpha _{\textrm {SM}}/\alpha _{\textrm {C}}\right )\left (N_{\textrm {C}}/N_{\textrm {SM}}\right )=4.65\times .85=3.93$, which is comparable to the value of 4.40 predicted by Eq. (12) using $F= {0.3}\,{\%}$, $N_{\textrm {C,r}} = {7.9}\,{\%}$, and $N_{\textrm {SM,r}} = {9.3}\,{\%}$. The discrepancy can be attributed to the difference between the FUT lengths, the time jitter of the electronic equipment, and the imperfect alignment of the lasers and dual-grating filters with the quadrature points of the sensors.

Fig. 7. Relative amplitude variation of the peak power from each sensor output under identical damped vibration.

Download Full Size | PDF

The FUT length of the polarimetric sensors is selected to be relatively short, 20 cm, for reduced sensitivity and increased difficulty of detecting weaker signals, to better highlight the effectiveness of the proposed SM scheme. The FUTs in the SM and the conventional schemes are made from the same fiber and their lengths are equal within 2 millimeters, and hence, the intrinsic sensitivity of these sensors is effectively identical. We do not measure the absolute value of the strain because our focus is on measuring the enhancement of the minimum detectable strain by our SM scheme in comparison to a conventional scheme, which is possible because the two sensors are effectively identical, subjected to the same external vibration, and an identical average peak power reaches the photodetector connected to the oscilloscope.

The bandwidth limit of our SM scheme depends on the nonlinear Kerr effect which has a response time on the order of femtoseconds. The frequency of the sinusoidal intensity modulation may limit the maximum detectable vibration frequency, but this parameter can be tuned according the desired application by using appropriate modulators and dual-grating filters. The detection of ultra-high vibration frequencies also requires using CW light instead of pulsed light. Currently, our proposed sensing scheme utilizes pulses because available Kerr media can not generate enough SPM when CW light is utilized due to the rise of stimulated Brillouin scattering (SBS). Indeed, SBS decreases the amount of induced nonlinear phase shift as most of the signal power passing through the nonlinear Kerr medium is transferred to the SBS Stoke’s frequency. We are currently working to develop an approach that allows for the suppression of SBS to enable the implementation of the proposed SM scheme using a CW laser instead of laser pulses.

The minimum detectable strain can be further enhanced by cascading multiple stabilization steps prior to the sensor and multiple magnifications steps at the detection end. The minimum detectable strain enhancement of an SM sensing scheme composed of $N$ stabilization steps and $M$ magnification steps is given by

(13)$$\Gamma_{\epsilon}^{ N,M} = \frac{1- \mu H F}{1 - F}\left(\frac{F+N_{\textrm{C,r}}}{H F+\frac{N_{\textrm{SM,r}}}{\mu}}\right),$$

where $\mu = \prod _{i=1}^M (2m_i+1)$ with $m_i$ being the extracted sideband order at the $i^{\textrm {th}}$ magnification step, and $H = \prod _{j=1}^N \eta _j$ with $\eta _j$ being the power fluctuation reduction at the $j^{\textrm {th}}$ stabilization step. The denominator of the second factor in Eq. (13) rapidly tends to 0 as $N$ and $M$ increase, and the minimum detectable strain enhancement tends to infinity providing a theoretically unlimited performance enhancement. In practice however, environmental noises and amplification noises between the magnification stages must also be considered because these noises will get magnified and increase the detection noise floor limiting the minimum detectable strain enhancement. Systems equipped with multiple stabilization and magnification stages, and the impact of environmental noises between the stages will be investigated in future works.

5. Conclusion

We present a novel all-optical approach based on self-phase modulation for enhancing the minimum detectable strain of an intensity-based fiber sensor. A detection limit enhancement is achieved by first stabilizing the intensity of the light before reaching the sensor, and then magnifying the sensor induced power fluctuations to overcome detection noises. Experimental results show an enhancement of the minimum detectable vibration amplitude when using a stabilization-magnification sensing scheme over a conventional sensing scheme. This stabilization-magnification sensing approach will allow for detection of environmental parameters previously too weak to be detected using intensity-based sensors, and thus allow for the potential discovery of new physical behaviours.

Funding

Natural Sciences and Engineering Research Council of Canada (7RGPIN-2020-06302); Canada Research Chairs (950-231352).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. C. T. M. Doyle, A. R. Martin, M. Q. Wu, T. Liu, S. A. Hayes, D. Brooks, R. A. Badcock, and G. F. Fernando, “Intensity-based optical fiber sensors for condition monitoring of engineering materials,” in Fiber Optic Sensors V, vol. 2895 (International Society for Optics and Photonics, 1996), pp. 288–299.

2. B. H. Lee, Y. H. Kim, K. S. Park, J. B. Eom, M. J. Kim, B. S. Rho, and H. Y. Choi, “Interferometric Fiber Optic Sensors,” Sensors 12(3), 2467–2486 (2012). [CrossRef]

3. F. Liu, X. He, L. Yu, Y. Pan, B. Xie, D. Yi, L. Gu, and M. Zhang, “The Applications of Interferometric Fiber-Optic Sensors in Oilfield,” in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), (IEEE, Toyama, 2018), pp. 1664–1671.

4. W. H. Png, H. S. Lin, C. H. Pua, and F. A. Rahman, “Pipeline Monitoring and Vibrational Sensing Using Loop Integrated Mach Zehnder Interferometer Optical Fiber Sensor,” in 2018 IEEE 7th International Conference on Photonics (ICP), (2018), pp. 1–3. ISSN: 2330–5665.

5. J. W. Arkwright, N. G. Blenman, I. D. Underhill, S. A. Maunder, M. M. Szczesniak, P. G. Dinning, and I. J. Cook, “In-vivo demonstration of a high resolution optical fiber manometry catheter for diagnosis of gastrointestinal motility disorders,” Opt. Express 17(6), 4500–4508 (2009). [CrossRef]

6. S. Poeggel, D. Tosi, D. Duraibabu, G. Leen, D. McGrath, and E. Lewis, “Optical Fibre Pressure Sensors in Medical Applications,” Sensors 15(7), 17115–17148 (2015). [CrossRef]

7. K. Bremer, M. Wollweber, F. Weigand, M. Rahlves, M. Kuhne, R. Helbig, and B. Roth, “Fibre Optic Sensors for the Structural Health Monitoring of Building Structures,” Procedia Technol. 26, 524–529 (2016). [CrossRef]

8. D.-H. Kim, B.-Y. Koo, C.-G. Kim, and C.-S. Hong, “Damage detection of composite structures using a stabilized extrinsic Fabry–Perot interferometric sensor system,” Smart Mater. Struct. 13(3), 593–598 (2004). [CrossRef]

9. B. Culshaw, G. Thursby, D. Betz, and B. Sorazu, “The Detection of Ultrasound Using Fiber-Optic Sensors,” IEEE Sensors J. 8(7), 1360–1367 (2008). [CrossRef]

10. Y. Xu, L. Zhang, S. Gao, P. Lu, S. Mihailov, and X. Bao, “Highly sensitive fiber random-grating-based random laser sensor for ultrasound detection,” Opt. Lett. 42(7), 1353 (2017). [CrossRef]

11. D. Reitze, “Chasing gravitational waves,” Nat. Photonics 2(10), 582–585 (2008). [CrossRef]

12. G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the Ultimate Limit of Fiber-Optic Strain Sensing,” Science 330(6007), 1081–1084 (2010). [CrossRef]

13. W. Png, H. S. Lin, C. H. Pua, J. Lim, S. K. Lim, Y. Lee, and F. Abd-Rahman, “Feasibility use of in-line Mach–Zehnder interferometer optical fibre sensor in lightweight foamed concrete structural beam on curvature sensing and crack monitoring,” Struct. Heal. Monit. 17(5), 1277–1288 (2018). [CrossRef]

14. Y. Xie, M. Zhang, and D. Dai, “Design Rule of Mach-Zehnder Interferometer Sensors for Ultra-High Sensitivity,” Sensors 20(9), 2640 (2020). [CrossRef]

15. M. Batumalay, S. W. Harun, N. Irawati, H. Ahmad, and H. Arof, “A Study of Relative Humidity Fiber-Optic Sensors,” IEEE Sens. J. 15(3), 1945–1950 (2015). [CrossRef]

16. X. Chong, K. Kim, P. R. Ohodnicki, E. Li, C. Chang, and A. X. Wang, “Ultrashort Near-Infrared Fiber-Optic Sensors for Carbon Dioxide Detection,” IEEE Sens. J. 15(9), 5327–5332 (2015). [CrossRef]

17. C. Flueraru, H. Kumazaki, S. Sherif, S. Chang, and Y. Mao, “Quadrature Mach–Zehnder interferometer with application in optical coherence tomography,” J. Opt. A: Pure Appl. Opt. p. 5 (2007).

18. H. Moradi, F. Hosseinibalam, and S. Hassanzadeh, “Improving the signal-to-noise ratio in a fiber-optic Fabry–Pérot acoustic sensor,” Laser Phys. Lett. 16(6), 065106 (2019). [CrossRef]

19. R. C. Rabelo, R. T. d. Carvalho, and J. Blake, “SNR enhancement of intensity noise-limited FOGs,” J. Lightwave Technol. 18(12), 2146–2150 (2000). [CrossRef]

20. A. Kersey, M. Marrone, A. Dandridge, and A. Tveten, “Optimization and stabilization of visibility in interferometric fiber-optic sensors using input-polarization control,” J. Lightwave Technol. 6(10), 1599–1609 (1988). [CrossRef]

21. B. Vanus, C. Baker, L. Chen, and X. Bao, “All-optical intensity fluctuation magnification using Kerr effect,” Opt. Express 28(3), 3789 (2020). [CrossRef]

22. C. Baker, B. Vanus, M. Wuilpart, L. Chen, and X. Bao, “Enhancement of optical pulse extinction-ratio using the nonlinear Kerr effect for phase-OTDR,” Opt. Express 24(17), 19424 (2016). [CrossRef]

23. Y. Wang, H. Yuan, X. Liu, Q. Bai, H. Zhang, Y. Gao, and B. Jin, “A Comprehensive Study of Optical Fiber Acoustic Sensing,” IEEE Access 7, 17 (2019). [CrossRef]

24. T. R. Woliński, “Polarimetric optical fibers and sensors,” in Progress in Optics, vol. 40 E. Wolf, ed. (Elsevier, 2000), pp. 1–75.

25. S. Gao, C. Baker, L. Chen, and X. Bao, “High-Sensitivity Temperature and Strain Measurement in Dual-Core Hybrid Tapers,” IEEE Photonics Technol. Lett. 30(12), 1155–1158 (2018). [CrossRef]

26. B. Vanus, C. Baker, L. Chen, and X. Bao, “All-optical pulse peak power stabilization and its impact in phase-OTDR vibration detection,” OSA Continuum 4(5), 1430–1436 (2021). [CrossRef]

All-optical enhancement of minimum detectable perturbation in intensity-based fiber sensors

Abstract

1. Introduction

2. Minimum detectable strain improvement by SM sensing

3. Experimental setup

4. Results and discussion

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (7)

Equations (13)

Optics Express