1. Introduction

Optical frequency-domain reflectometry (OFDR) is one of the most popular approaches for high-resolution fault allocation [1], optical fiber component characterization [1–4], and distributed temperature and strain sensing [5]. Coherent optical frequency domain reflectometry (C-OFDR) utilizes a tunable laser and an interferometer to superpose a swept-laser signal with a time-delayed version of the same signal leading to a beat [1]. Spectral analysis of the beat signal allows for the location of reflection points along a laser path at high spatial-resolution and high dynamic-range [1, 2, 6]. The utilization of an interferometer makes C-OFDR highly dependent of the laser coherence properties limiting the range of reflection detection [1].

Several approaches have been used for range extension in C-OFDR. Utilization of a highly-coherent swept-laser implemented using a narrow linewidth fiber laser and a piezoelectric tuner has allowed for the location of Fresnel reflection from the end of a 95 km long fiber at an unspecified spatial-resolution [7]. Phase-noise-compensation has allowed for the location of reflection points as far as 80 km at a spatial-resolution of 20 cm [8]. Band-width division has been combined with phase-noise-compensation to locate reflections as far as 40 km at an improved spatial-resolution of 5 cm [9]. Most recent, phase-noise measurement for a swept-laser reflected from points beyond the laser coherence length has allowed the location of Fresnel reflections as far as 170 km at a spatial resolution of 200 m [10].

Incoherent optical frequency domain reflectometry (I-OFDR) has been investigated as an alternative for C-OFDR because it intrinsically allows for long-range reflection measurements [11–13]. In I-OFDR, the beat between a frequency-swept sinusoidal optical signal and a time-delayed version of the same signal determines the location of reflection points along the signal path. Existing implementations of I-OFDR utilize opto-electronic components and electronic signal processors for beat acquisition. Unfortunately, the bandwidth cap of electronic and opto-electronic devices limits the maximum sweep frequency-span and the minimum achievable spatial-resolution. The bandwidth cap can be eliminated by development of an all-optical approach for beat acquisition. The Kerr phase-interrogator presented in [14] can be utilized for all-optical beat acquisition which will potentially allow for long-range I-OFDR at micron-level spatial-resolution.

In this paper, we present a novel approach for I-OFDR based on Kerr phase-interrogator. The I-OFDR setup based on a Kerr phase-interrogator and frequency-swept sinusoidal optical signal is presented first. Theoretical analysis shows that the output of the Kerr phase-interrogator corresponds to the beat of the powers of orthogonally-polarized frequency-swept sinusoidal optical signals. Utilization of the novel I-OFDR approach for the location of reflection points on a fiber is experimentally demonstrated.

2. Experimental setup

Figure 1(a) shows the Kerr phase-interrogator configured for optical frequency domain reflectometry. A continuous-wave (CW) laser (Agilent 81980A), illustrated in Fig. 1(b), is amplitude-modulated using an electro-optic modulator (EO-Space) and a sinusoidal electrical signal generator (HP 83752A) with a time-varying frequency f_m (t) = 0.5 (f₀ + ρt). The output of the modulator is a sinusoidal optical signal with a frequency f_s (t) = f₀ + ρt, and the optical spectrum of this sinusoidal signal is composed of two distinct peaks with time-varying separation Δν = f_s (t) where ν is the optical frequency, as illustrated in Fig. 1(c). The power of the sinusoidal signal is split using a fiber-coupled polarization beam splitter with polarization maintaining fiber ports into a sensor path and a reference path corresponding to the parallel and perpendicular components, respectively. A circulator connects the a fiber under test (FUT) that is terminated with a reflector to the sensor path. The signals from the reference and the sensor paths are recombined using fiber-coupled polarization beam combiner with polarization maintaining fiber ports. Figure 1(d) illustrates the spectrum and the time-trace of the combined signal at the output of the fiber polarization combiner.

 

Fig. 1 Schematic of (a) the I-OFDR setup based on a Kerr phase-interrogator, and illustrations of the spectrum and the power trace of (b) the CW laser signal, (c) the sinusoidal laser signal, (d) the combined reference and reflected sinusoidal signals, (e) the phase-modulated sinusoidal signal, and (f) the filtered side-band. RF: radio-frequency; CW: continuous-wave; EOM: electro-optic modulator; FUT: fiber under test; FPS: fiber polarization splitter; FPC: fiber polarization combiner; EDFA: Erbium-doped fiber amplifier; PD: photo-diode.

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The parallel and perpendicular components at the output of the polarization beam combiner are given by $A_{\perp }=\sqrt{P_p/2}\text{cos}(\pi f_{\mathit{ref}}t+{\varphi }_{\perp })$, $A_{\Vert }=\sqrt{P_p/2}\text{cos}(\pi f_{\mathit{sen}}t+{\varphi }_{\Vert })$, where ϕ_⊥ = πf_reft_⊥, ϕ_‖ = πf_sent_‖, f_ref = f₀ + ρ (t − t_⊥), and f_sen = f₀ + ρ (t − t_‖) with t_⊥ and t_‖ being the delay-times required for the sinusoidal signal to travel the reference and the sensor paths, respectively. The combined signal at the output of the fiber polarization combiner is amplified using an Erbium-doped fiber amplifier (Amonics AEDFA-33-B-FA) and then launched into a 4 km long fiber with low chromatic dispersion D = 3 ps/nm-km, which serves as a nonlinear Kerr medium. The amplitudes of the perpendicular and the parallel field components at the output of the Kerr medium become

The Kerr-induced sinusoidal phase modulation of A_⊥ and A_‖ leads to the formation of distinct sidebands P_i with i = 1, 2, 3,..., as illustrated in Fig. 1(e). The ratio of P₁ (t) to P₀ (t) is obtained analytically by applying the Jacobi–Anger expansion to Eqs. (1)–(2) [14–16] leading to

3. Experimental results

A CW laser with a wavelength λ₀ = 1550.202 nm is amplitude-modulated using a Mach-Zehnder modulator and a sinusoidal electrical signal generator to obtain a sinusoidal optical signal with a frequency varying linearly from $f_s^{\mathit{min}}=18.5$ GHz to $f_s^{\mathit{max}}=19.5$ GHz over a duration of 50 ms leading to ρ = 20 GHz/s. The FUT has a length of 2.2 km and is terminated with an ultra-polished connector (UPC) to induce Fresnel back reflection. Figure 2(a) presents the measured value of P₁ (t) at the oscilloscope, and Fig. 2(b) presents a magnified section of P₁ (t) showing a sinusoidal variation with time in agreement with Eq. (5). The spectrum of P₁ (t) is calculated using |ℱ {P₁ (t)}|², where ℱ is the Fourier transform operator, and then the frequency f is replaced by the distance d = fc/2ρn_g, where c is the speed of light and n_g = 1.46 is the group refractive index of the FUT, to obtain the relative reflectivity as a function of distance, as shown in Fig. 2(c). The signal P₁ (t) is zero-padded to increase the frequency resolution of the Fourier transform allowing for the determination of the spatial-resolution Δd_3dB = 9.3 cm, as shown in Fig. 2(d).

 

Fig. 2 (a) Measured P₁ (t), (b) magnified section of P₁ (t), (c) relative reflectivity as a function of distance in the fiber under test, and (d) magnified section of the reflection at d_peak = 2272.49278 m.

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Similar to existing implementations of I-OFDR, the novel approach allows for the detection of multiple reflection points. Figure 3(a) presents the measured reflectivity as a function of distance for a combination of two fibers connected using non-matching fiber connectors, a UPC connector and an angle-polished connector (APC), to induce strong back-reflection at the interface between the two fibers. Reflection peaks are observed at d = 2.2725 km and d = 6.6480 km corresponding to the locations of end-facets of the first and the second fibers. Furthermore, the novel approach can detect reflection points on hundreds of kilometers of fiber. Figure 3(c) presents the measured reflection at the end of 151 km long fiber obtained with ρ = 4 GHz/s. An erbium doped fiber amplifier is used for amplification of the signal reflected from the end of the 151 km long fiber to compensate for the attenuation induced by traveling along the fiber.

 

Fig. 3 (a) Relative reflectivity for two concatenated fibers, (b) magnified image of the peak at d_peak = 6.6480 km, (c) relative reflectivity for a 151 km long fiber, and (d) reflection peaks at the end of the 151 km fiber (solid curve) and at the end of a 37.4 cm fiber cord connected to the 151 km fiber (dashed curve).

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4. Spatial-resolution

The frequency corresponding to a reflection point located at distance d is given by f = 2ρdn_g/c leading to a spatial resolution Δd = Δfc/2ρn_g. The spectrum of the measured time-trace P₁ (t) is a squared sinc function for which the 3 dB frequency resolution is calculated from the measured time-trace interval t_span using Δf_3dB = 0.88/t_span leading to Δd_3dB = 0.88c/2ρn_gt_span. Using ρ = 20 GHz/s, n_g = 1.46, and t_span = 50 ms leads to Δd_3dB = 9.04 cm in close agreement of the measured values at Δd_3dB = 9.3 cm at d = 2.2725 km and Δd_3dB = 9.4 cm at d = 6.6480 km, as shown in Fig. 2(d) and Fig. 3(b), respectively. To further investigate the spatial-resolution, Fig. 3(d) presents the reflection peak at the end of the 151 km fiber and the peak that results after connecting a 37.4 cm fiber cord at the 151 km fiber end. The 3 dB spatial-resolution for the peak at d = 151.2952 km is Δd_3dB = 11.2 cm showing that the spatial-resolution is maintained over long distances. Furthermore, the reflection peaks in Fig. 3(d) are clearly distinguishable and are separated by 38.5 cm in close agreement with the length of the fiber cord.

The sweep frequency-span in the presented experiments is $f_{\mathit{span}}=f_s^{\mathit{max}}-f_s^{\mathit{min}}=\rho t_{\mathit{span}}=1.0$ GHz. Utilization of wide-bandwidth electro-optic modulators and sinusoidal electrical signal generators can increase f_span up-to ∼ 100.0 GHz allowing for Δd_3dB ∼ 0.9 mm. Furthermore, the presented approach for I-OFDR utilizes all-optical signal processing which eliminates the electronic bandwidth limitation in existing I-OFDR implementations. A frequency-swept sinusoidal optical signal with f_span > 1.0 THz can be generated by superposition of a continuous-wave laser and a swept-laser allowing for micron-level spatial-resolution Δd_3dB < 90 μm.

5. Dynamic-range

The measured signal is given by $P_1^{\mathit{meas}}(t)=\left[P_1^{\mathit{ideal}}(t)+\nu (t)\right]\times \text{rect}(t)$ where $P_1^{\mathit{ideal}}(t)$ is the ideal signal, ν(t) is the noise, and rect(t) is a square pulse with a duration t_span. The signal-to-noise ratio (SNR) of $P_1^{\mathit{meas}}(t)$ can be increased by using a highly-nonlinear chalcogenide fiber as a Kerr medium to induce nonlinear Kerr effects at lower signal powers eliminating the need for optical amplifiers that generate noise through amplified spontaneous emission. The SNR can also be increased by using low-noise photo-diodes to reduce dark-current noise and shot-noise such that $P_1^{\mathit{ideal}}(t)\gg \nu (t)$. Finally, the SNR penalty induced by the finite measurement duration t_span is obtained from the normalized spectrum of rect (t) given by sin² (πft_span) / (πft_span)². Increasing the sweep frequency-span N times increases t_span by a factor N, and consequently, reduces the SNR penalty of rect(t) by a factor N².

Similar to C-OFDR, the power of the reflected signal must be weak in the presence of multiple reflectors to prevent the generation of artificial peaks that arise from mixing of the frequencies corresponding to actual reflection peaks. Unfortunately, the dynamic-range is reduced when the signal from the sensor path is weaker than the signal from the reference path. Enhancement of the dynamic-range is essential for the detection of Rayleigh back-scattering in the FUT allowing for distributed sensing of strain and temperature [5, 17]. Future work will focus on enhancement of the dynamic-range for the implementation of distributed temperature and strain sensors.

6. Conclusion

We present a novel approach for incoherent optical frequency domain reflectometry based on a Kerr phase-interrogator. Reflections measurement as far as 151 km at a spatial-resolution of 11.2 cm has been experimentally demonstrated. The novel approach for I-OFDR utilizes all-optical signal processing to obtain the beat between two frequency-swept sinusoidal optical signals. This approach will enable processing a wide sweep frequency-span for long range detection of reflection points at micron level spatial-resolution.