1. Introduction

Optical fiber distributed sensing has been investigated over the past years as a way to replace sensors based on fiber Bragg gratings (FBG) that can only perform sensing on discrete, pre-determined points along the fiber [1–3]. Many techniques based on different types of elastic and inelastic scattering mechanisms have also been developed over the years. Raman scattering-based sensing in the time domain typically allows spatial resolutions of around 1 m over a sensing length of several kilometers, as well as a resolution of a few degrees Celsius [2,4]. Brillouin scattering techniques, such as Brillouin optical time domain reflectometry or analysis (BOTDR/A), were able to push this distributed sensing distance limit to over 100 km, with a spatial resolution of a few meters and a similar temperature resolution [5,6]. Encoding techniques have allowed to further reduce the resolution to only 2 cm over a 2.2 km sensing range [7]. Finally, techniques using Rayleigh scatter can achieve much greater resolution, while sacrificing the sensing dynamic range. Phase optical time-domain reflectometry (φ-OTDR) can obtain resolutions of the order of the milli-Kelvins over a few kilometers of fiber, along with a spatial resolution of under 1 m [8]. Optical frequency domain reflectometry (OFDR) can achieve the highest spatial resolution of all techniques (centimeters or even millimeters scale) while maintaining good temperature resolution (under 1°C), at the expense of the scanning range, typically limited to the hundreds of meters [9,10], or a few kilometers at best [11].

As such, OFDR has been under investigation for various applications requiring a very high spatial resolution, such as shape sensing [12–14], structural health monitoring [15] and flow rate measurements [16]. OFDR has also been used with many different types of fibers for specific applications, such as polymer optical fibers for their better mechanical properties [17] or photonic crystal fibers for their lower radiation-induced attenuation [18]. Many methods have been developed to increase the OFDR accuracy, e.g. optimization of the interpolation method used to recover the strain or temperature information [19], or ways to increase the backscattered signal, using ultrafast laser exposition [20], chirped FBGs written into the sensing fiber [13] or simply by UV exposition of the optical fiber [21]. These methods result in enhanced signal to noise ratio, hence increasing the resolution of measurements in cases where a very high strain or temperature sensitivity is needed or where significant loss in the optical system needs to be compensated for. However, since the spatial resolution is related to the bandwidth of the returned signal, any improvement on the signal strength must be performed on a large bandwidth to avoid resolution loss.

In this paper, we present a novel, noise-driven random Bragg grating, with the unusual property of possessing a large bandwidth which is independent of its length, contrary to uniform FBGs, whose bandwidth is inversely proportional to its length. This new type of structure presents a backscatter cross-section orders of magnitude higher than SMF-28 optical fiber, making it ideal for sensing applications. The technique to achieve those properties consists of adding noise during writing of the FBG, so as to fabricate a Random Optical Grating by Ultraviolet or ultrafast laser Exposure (ROGUE), a grating with a spectrum similar to a very broadband, very short FBG, but that can actually span an indefinite length. This can be modeled as a series of very small, randomly out-of-phase FBGs. As such, this results in a weakly reflective grating with a reflectivity that is much higher than typical Rayleigh backscatter, while at the same time maintaining a large bandwidth, unlike a typical long weak FBG [22]. An in-depth analysis of how these ROGUE gratings enhance the accuracy and precision of strain and temperature sensing, while still maintaining a good spatial resolution, is also presented.

Although the subject of random, out-of-phase FBGs has been studied in the past for applications such as localization [23,24] and random lasing [25,26], this was done using strong gratings, and thus cannot be used efficiently for sensing over long distances. The subject of this paper being related to the use of the ROGUE as a sensor, localization will not be discussed here, but is the subject of an upcoming future article.

2. Methods

2.1 ROGUE fabrication

The ROGUEs were written in the fiber using a Talbot interferometer configuration with a phase-mask. The fiber core is exposed to a 213 nm wavelength laser, using the 5th harmonic of a 1064 nm Q-switched laser (Xiton Photonics), as shown in Fig. 1. The spot size was ~100 µm, with a 30 kHz repetition rate and 7 ns pulse duration. The fiber coating was removed prior to ROGUE inscription. When writing a long FBG, the fiber is moved continuously at a constant speed under the phase mask using a nanometer-precision air-bearing stage (Aerotech). An electrical sawtooth wave is applied to a piezoelectric element driving the phase mask to move the fringe pattern synchronously with the moving fiber, hence preserving and controlling the FBG phase, as detailed in reference [27]. However, the objective is not to write an in-phase grating, as this would lead to a very narrow reflection bandwidth. Therefore, no sawtooth wave is sent to the piezo. In theory, the grating should self-erase as the fiber is moved under the fixed UV fringe pattern and no gain in backscatter signal would be obtained except for pure UV enhancement of the Rayleigh scatter, described in reference [21]. However, the UV exposure is not completely uniform because of noise in the system, hence the erasure of the grating is not perfect. As a result, a random interference pattern will appear in the fiber, leading to enhanced reflectivity over a certain bandwidth at the Bragg wavelength determined by the UV fringe patterns.

 

Fig. 1 Talbot interferometer used for the fabrication of the ROGUE. The phase mask above generates different diffraction orders. The first two orders ( + 1 and −1) are reflected by mirrors onto the fiber, where an interference fringe pattern is created. The UV exposure increases the refractive index periodically, creating an FBG. By changing the angle of the mirrors, the interference fringe pattern (and thus the FBG wavelength) can be modified. The random electrical wave applied to the piezoelectric element induces imperfect overlap of the interference pattern, creating a ROGUE.

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In order to increase the reflectivity of the grating, all that is needed is to increase the noise. To do so, we simply replaced the sawtooth wave by a random electrical signal. This way, the ROGUE is no longer dependent on the small environmental noise in the system, but rather on the noise output of the function generator. The amplitude and frequency of this noise are much greater than the environmental noise, and as such it increases the backscattered signal by orders of magnitude, since it creates a larger number of micro-gratings (µFBGs). The phase-mask movement amplitude and the noise bandwidth were optimized to reach the highest ROGUE reflection amplitude for the same UV exposure to values of ~10 periods (5V) and 20 Hz respectively. The latter is mostly limited by the response time of the piezoelectric element. The applied noise amplitude and bandwidth were found to influence the amount of backscatter, but had no effect on the bandwidth of the backscattered spectrum, which is dependent on the average µFBG length and can be modified by changing the spot size.

2.2 Noise level and accuracy measurements

In order to characterize the increase in accuracy and precision provided by the use of ROGUEs with the enhanced scatter, two sets of experiments were performed. In the first experiment, the precision is evaluated by a measurement of the root mean square (RMS) noise level of strain from a uniform and stable fiber under test (FUT). The fiber was placed inside an insulated box, to remove environmental fluctuations and vibrations. A reference measurement is first taken, and 15 sample measurements are then performed sequentially, to average out idler points. The strain is calculated at every point along the fiber’s length using the algorithm described by Froggatt et al. [9], and using an interpolation inspired from the one described by Cui et al. [19] to improve strain resolution beyond what can be achieved with our OFDR commercial optical backscatter reflectometer (described below). The RMS error between measurement and expected value (zero strain) was calculated across all data points in the selected 300 mm of the fiber, and averaged over the 15 measurements. In order to avoid problems related to the dynamic range of the OFDR unit, two different fibers were used, one in which a ROGUE was inscribed, and another that was left untreated. Both fibers were stripped of their coatings, to ensure repeatability of the measurement.

The second set of experiments was performed to evaluate the accuracy of the strain measurement. A reference measurement was first taken before any strain is applied. Then the 1.15 m fiber is stretched over 20 µm by increments of 1 µm using a nanometer-precision Aerotech stage, leading to strains ranging from 0 to 17.4 µε. A measurement is performed after every 1 µm increment, when the fiber is static, and the strain is calculated using the same algorithm as for the noise level. The accuracy error is the difference between measured strain and the expected value of strain for a given stretch. The total calculated error is the RMS accuracy error of each sensing point of the FUT (80 mm in length) at each stretch point. Again, two different fibers were used to avoid the dynamic range issue described earlier.

All OFDR measurements were performed using a commercial optical backscatter reflectometer (OBR4600) from Luna. Only the raw data from the OBR was used and the rest of the data processing was performed independently using our own software. All the scanning bandwidths available on the OBR software were tested, and the central wavelength of the scan was the same for all measurements, i.e. the central wavelength of the ROGUEs (1555 nm). Except when explicitly specified, a gauge length of 10 mm was used for data processing, and the sensor spacing (distance between every sensing point) was set at 1 mm. Tests were performed on SMF-28 fiber from Corning, and a SM1500(4.2/125) fiber from Fibercore, a highly Ge doped fiber. Due to its high Germanium concentration, the SM1500 is more photosensitive than the regular SMF-28. It also exhibits 4.1 dB more backscattered signal prior to any UV exposure. Both fibers were loaded with molecular deuterium in order to increase photosensitivity, although this technique would still be effective without deuterium, provided the fiber is photosensitive enough (just like regular FBG inscription). The measurements were performed in the weeks following the ROGUE’s inscription, to ensure deuterium out-diffusion.

2.3 Interpolation technique

The OFDR method is detailed by Froggatt et al. [9] for temperature and strain sensing. In order to improve the accuracy of the results given by the OBR4600, an interpolation method similar to the one described by Cui et al. [19] was implemented, as a way to overcome the Fourier uncertainty principle inherent to the calculation. Basically, by adding a number N of padding zeroes at one end of the spatial domain data of both reference and sample signals before performing the Fourier transform and cross-correlation of the two data sets, the spectral resolution is artificially enhanced, allowing more points in the cross-correlation peak. Those points come from a sinc interpolation that is performed by the Fourier transform of the data set with the added zeroes. Indeed, since the Fourier transform of a rectangle is a sinc function, performing the Fourier transform on this new data set results in a sinc interpolation on the original data set. Although this peak does not get narrower (the Fourier limitation remains), the extra points inside the peak allow us to measure more accurately small displacements of the peak.

However, the downside of this method is that it increases the calculation time. The number N of padding zeroes must thus be sufficient to achieve the desired resolution, ideally down to the experimental noise limit, without using an unnecessary high number of zeroes to limit calculation time. For an OFDR measurement using a 5 nm bandwidth, the processing time goes from 83 ms using 10³ zeroes to 633 ms with 10⁶ zeroes. While not a limiting factor in the current application, choosing the correct number of zeroes can become critical when applied to real-time measurements.

Figure 2 shows the result of this interpolation on the quality of the cross-correlation peak. Before the interpolation on Fig. 2(a), the cross-correlation peak is defined by a single point at 0 GHz. At this point, even performing a fit on the neighboring points would result in a bad approximation of the real spectral shift, because of the wide separation in between each point. However, after adding 2,000 padding zeroes, the peak is much better defined, and thus the spectral resolution increases significantly, as shown on Fig. 2(b).

 

Fig. 2 Cross-correlation result (a) before and (b) after the sinc interpolation. The fiber used is a standard SMF-28 fiber inscribed with a ROGUE, interrogated over a 42.90 nm bandwidth with a 10 mm gauge length. The original data set of (a) has 521 points, while the interpolation of (b) is performed by adding 2,000 padding zeroes to the data.

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In addition to the technique presented by Cui et al. [19], an additional quadratic fit was implemented on the processed data, in order to find the maximum of the cross-correlation peak more accurately to values in between interpolation points. The quadratic fit was performed over the maximum cross-correlation value and its two nearest neighbors. Since a quadratic fit over three data points can be resolved analytically, it adds very little to the calculation time and increases the spectral resolution without additional padding zeroes.

3. FABRICATION AND MODELING OF THE ROGUE

Figure 3(a) compares the expected spectra of a meter-long fiber Bragg grating to the one of a ROGUE. Being composed of multiple µFBGs, the ROGUE FWHM will remain constant regardless of the grating’s length, whereas a typical FBG bandwidth will decrease with length (typically 2 pm for a 1 m grating [28]). Using our technique, ROGUEs of strength ranging from under 5 up to 50 dB of backscattered intensity were written. Figure 3(b) and (c) shows the results of such a ROGUE in both temporal and spectral domains, written in standard SMF-28 fiber and measured with OFDR. While the exposed region in Fig. 3(b) shows more noise than the SMF-28 region, this does not influence sensing accuracy, as it is based on the change in backscatter signature of the fiber. It therefore does not matter if this signature is mostly flat or noisy.

 

Fig. 3 (a) Schematic illustration showing the difference between a regular in-phase FBG, exhibiting a very narrow bandwidth (typical full-width at half-maximum (FWHM) taken from [28]), and a ROGUE, composed of multiple out-of-phase µFBGs of different lengths, resulting in a much wider bandwidth. Experimental measurements for a 1-meter-long ROGUE written in SMF-28 fiber are presented (b) in the temporal domain, showing over 30 dB in backscattered amplitude enhancement, and (c) in the spectral domain, where an 8 nm FWHM (41 nm full width) can be observed. Rayleigh scattering baseline can be observed out-of-band of the grating, at around −60 dB. The ROGUE was written using 37 mW of 213 nm UV laser power, at a writing speed of 0.2 mm/s. Measurements were made with the largest bandwidth of 88.24 nm available on the OBR4600.

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The loss induced by the writing of the ROGUE was evaluated by measuring the backscattered intensity of an unexposed SMF-28 fiber portion placed after the exposed region across an 88 nm bandwidth scan (the largest available on our OBR). By comparing the backscattered intensity before and after writing the ROGUE, the loss can be estimated. Averaging over an 800 mm-long section of fiber, after the writing of the 1 meter-long ROGUE shown in Fig. 3b and c, the induced loss was estimated at 0.15 dB/m.

The effect of speed and power on the backscatter signal gain is shown in Fig. 4. It can be shown that decreasing the writing speed leads at first to a slow, steady increase in gain, until writing speeds of under 0.3 mm/s, when the gain starts increasing rapidly. It can be also observed that, for SMF-28, the use of additional power has more impact at fast-writing speeds than for the SM1500. This can be explained by the saturation of the refractive index change of the fiber. Since this SM1500 is significantly more photosensitive, it requires a lower UV exposure in order to achieve the same results. For the lowest writing speed, an average refractive index increase of 4.8x10⁻³ was measured for the SM1500 fiber with an interferometric microscopy system, while the refractive index modification of the SMF-28 was always under 10⁻⁴, below the resolution of our system. This larger refractive index modification resulted in additional losses, and we estimate losses for this type of fiber with this writing speed to be around 1 dB/m. When taking into account the intrinsically higher 4.1 dB backscatter in SM1500, using this writing speed on the SM1500 results in a sensor showing more than 50 dB higher backscatter than regular SMF-28.

 

Fig. 4 Gain of the backscattering signal of the ROGUE as a function of writing speed vs untreated fiber. The ROGUE was written using a noise amplitude of 5 V (~10 periods) and a frequency bandwidth of 20 Hz. A SMF-28 fiber from Corning (orange) and a SM1500 fiber from Fibercore (green) were tested, using 22 mW (solid line) and 37 mW (dashed line) of laser power. 0 dB corresponds to the signal level of untreated fiber both for SMF-28 and SM1500). Measurements made on the OBR4600 using a 21.16 nm scanning bandwidth, the bandwidth most suitable for sensing, as will be shown in the next sections. The gain was measured in the temporal domain (see Fig. 3b).

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The ROGUE was simulated using a probabilistic model describing the position and length of uniform µFBGs, each defined with a random phase. A stochastic process using two distributions was used, the distribution X describing the distance between the end of a µFBG and the beginning of the next one, and the distribution Y describing the length of each µFBG.

The beginning of the first µFBG is x₁, generated from the distribution

 

Fig. 5 FWHM bandwidth of the ROGUE, as a function of length. The experimental data is limited to 400 mm, with models using the parameters k₁ = 500 m⁻¹ and k₂ = 1.4e4 m⁻¹. The µFBG were considered as uniform gratings, with a central wavelength of 1555 nm. The phase and amplitude of each µFBG is random. The bandwidth asymptotically approaches 7 nm for a ROGUE length > 100 mm for an average µFBG length of 72.5 µm.

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4. Advantages for OFDR distributed sensing

4.1 Results of the interpolation

Figure 6 presents the signal of a ROGUE acquired directly from the OBR, as the fiber is being strained (solid blue curve) using a 42.90 nm bandwidth and compared with the expected spectral shift (solid black curve). As can be seen in Fig. 6(a), the spectral shift given by the OBR internal calculation (solid blue curve) is at first much smaller than the applied value, until it suddenly jumps to a much higher value, only to again start increasing much slower than the real value. As such, the results given by the OBR have a very poor sensing resolution (greater than 8 µε). However, by using the interpolation method described previously on the raw measurement data, we can increase the accuracy of the results. These results were obtained with a varying number of padding zeroes added after the gauge length window. As can be seen, for N ≤ 1,000, the resolution obtained by performing the sinc interpolation is actually worse than the one given by the OBR’s calculation. However, if the number of padding zeroes is increased further, the interpolation increases the spectral shift resolution. We demonstrate here that in order to achieve the best possible resolution using solely a sinc interpolation, a number of padding zeroes above 10⁵ must be used, since the spectral shift still varies noticeably while increasing the number of zeroes at this point. It should be noted that we have no information on the exact nature of the OBR’s algorithm, as this is propriety information of Luna.

 

Fig. 6 Calculated spectral shift as a function of the elongation, where the method is compared between the OBR’s internal algorithm and the one described earlier, using a number N of padding zeroes. Solid black curve is the applied strain value. (a) is taken right after the cross-correlation, and (b) is taken after applying an additional quadratic fit. Measurements were made using the OBR4600 from Luna with a 42.90 nm bandwidth, the largest available bandwidth on the OBR for sensing.

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In Fig. 6(b), the additional quadratic fit was added to the data treatment. It can be seen that this implementation decreases the number of padding zeroes needed to achieve the best available resolution by a significant amount. Indeed, using a number of padding zeroes as small as 1,000 yields a spectral shift comparable to the theoretical value, and increasing the number of padding zeroes above 10⁴ results in no noticeable increase in resolution, as can be seen on Fig. 6(b), where the curves of both N = 10⁴ and N = 10⁵ are actually superposed on top of each other. This is because the resolution is no longer limited by the algorithm, but rather by the intrinsic experimental sources of error, such as laser repeatability, environmental fluctuations, etc. As such, the required number of padding zeroes decreases by an order of magnitude when the sinc interpolation is combined with a quadratic fit. However, it should be noted that the calculation time using 10⁴ padding zeroes is 2.6 times longer than when using no padding zeroes (23 times longer with 10⁵).

4.2 ROGUE noise level and accuracy in OFDR sensing

The noise level experiment described earlier was performed on both regular unexposed SMF-28 fiber and ROGUE. The results are presented in Fig. 7. It can be observed that, for the unexposed fiber, the RMS error decreases when the bandwidth is increased. This is to be expected, since an increase in bandwidth leads to more data points in the same gauge length, due to the smaller step size, hence a higher quality cross-correlation.

 

Fig. 7 RMS noise level in a uniform and stable environment of 300 mm of both unexposed SMF-28 fiber and ROGUE written in SMF-28. The fibers are placed in an insulated box, averaged over 15 measurements. A 30 dB enhanced ROGUE was used for these measurements.

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However, surprisingly, the opposite happens in the case of the ROGUE. This is most likely due to the fact that, contrary to the unexposed fiber, most of the signal comes from a narrower spectrum. As such, using a smaller scanning bandwidth increases the signal to noise ratio (SNR), because only the portion of the spectrum where the ROGUE is inscribed is probed during the laser scan, while the data with low SNR is ignored. Although there is less data, the available data is of higher quality, hence the lower noise level. However, scanning across too narrow a bandwidth limits the maximum strain or temperature that can be sensed, limits the spatial resolution and will decrease accuracy, as described in the following section.

Afterwards, the accuracy experiment was performed on those fibers, and is shown in Fig. 8. The behavior for the ROGUE is very similar to the unexposed fiber, but the error is almost an order of magnitude lower for all scanning bandwidths. In the case of the ROGUE, we see that the minimal error is for a 21.16 nm bandwidth (0.34 µε, 4.5 times smaller than the SMF-28). The explanation for this is the same as for the noise level; since most of the signal comes from a narrower bandwidth region, a larger bandwidth does not necessarily yield a more accurate measurement. The higher performance of the noise characterization versus the accuracy characterization is due to the fact that, for the latter, the fibers were not in an environment as controlled as for the former, leading to more environmental noise.

 

Fig. 8 RMS strain error while stretching the fiber as a function of scanning bandwidth, for both unexposed fiber and ROGUE. The spectral shift is calculated for the 20 µm stretching, across 80 mm of sensing fiber along the 1.15 m fiber length. It can be observed that, using a ROGUE, a scanning bandwidth of only 5.24 nm is sufficient to achieve better accuracy to the one obtained with unexposed SMF-28. A 30 dB enhanced ROGUE was used for these measurements.

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4.3 Spatial resolution in noise level

The data treatment for the noise level experiment was repeated while varying the gauge length. A smaller gauge length leads to a higher spatial resolution, but at the cost of the strain resolution. The influence of gauge length on RMS noise level is presented in Fig. 9.

 

Fig. 9 RMS noise level as a function of gauge length, for both unexposed fiber and ROGUE, when placed in an insulated box, averaged over 15 measurements, for bandwidths of 5.24 and 42.90 nm. The gauge length is varied from 0.5 mm to 200 mm. As can be seen, a ROGUE scanned with a 5.24 nm bandwidth requires a gauge length of only 2 mm to beat the noise level of SMF-28 with a 42.90 nm bandwidth and a 10 mm gauge length. A 30 dB enhanced ROGUE was used for these measurements.

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From this figure, it can be easily seen that, for very short gauge length, the spectral and spatial resolution seem to be Fourier-transform-limited, and an increase in gauge length (spatial resolution) leads to a decrease in RMS noise level (spectral resolution). However, for very large gauge lengths, a plateau is met, and the added value of a larger gauge length is minimal. Furthermore, it is obvious that, regardless of the gauge length, the noise level is always much smaller with the ROGUE than with the unexposed SMF-28 fiber. Finally, a ROGUE can provide a greater spatial resolution, while also using a smaller scanning bandwidth, at no cost to measurement resolution.

4.4 ROGUE gain and loss compensation

Finally, the influence of the strength of the ROGUE was evaluated. ROGUEs of various strengths were written and an accuracy error measurement was performed. Only the 21.16 nm scanning bandwidth (the one that showed the smallest error) was used for this study. Figure 10 shows how the error is influenced by the ROGUE gain. For stronger gratings, the mean error decreases, until 25 dB gain when a plateau is reached. We suspect the accuracy to be limited by environmental fluctuations and vibrations, as the accuracy experiment could not be performed inside the insulated box as for the noise level measurements.

 

Fig. 10 Strain RMS error calculated over a 20 µm stretching and 80 mm of sensing fiber along the 1.15 m fiber length. (a) Spectral shift accuracy as a function of ROGUE gain (linear scale in y). The ROGUEs were written using 21 mW of UV power, by varying the writing speed from 0.05 mm/s to 10 mm/s. The 0 dB gain value represents an unexposed SMF-28 fiber.

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In order to characterize the ROGUE’s ability to compensate for signal loss, the same experiment with the three strongest ROGUEs was performed with induced optical loss from a variable optical attenuator placed before the ROGUE. Figure 11 presents these results as a function of induced loss in measurement signal. It can be observed that, as induced loss is increased before the ROGUE, the error increases progressively until a threshold is reached, when the accuracy of the measurement decreases rapidly. When the loss is so high that the noise level is comparable to the ROGUE’s maximum reflectivity, all information is lost in noise, and the algorithm can no longer recover the spectral shift accurately.

 

Fig. 11 Spectral shift accuracy for three ROGUEs of different gains, as a function of optical loss induced before the ROGUE by an optical attenuator (logarithmic scale in y).

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5. Discussion

Several techniques have been investigated in the literature to enhance the signal in a similar fashion as the ROGUE. For example, many authors describe sensing techniques using arrays of either identical [32] or random gratings [33]. However, these are not continuously distributed sensing techniques, and can only perform sensing where the gratings are inscribed in the fiber. These are satisfactory for applications where spatial resolution is not a concern, or when using other techniques such as optical time domain reflectometry (OTDR), but they have not been shown to achieve the 2 mm spatial resolution presented in this article. Other authors, such as Gifford et al. [34], used small-bandwidth FBGs separated by gaps, and reported similar accuracy with a 10 mK noise level using 12 mm gauge length and 5 nm scanning bandwidth. However, these gaps add blind-spots in the time-domain, thus limiting the spatial resolution. As the ROGUE retains a large bandwidth regardless of the grating’s length, it does not have this limitation, allowing it such high spatial resolution.

Other techniques offering continuous scattering enhancement have been explored in the literature. We have previously shown a 20 dB increase in signal by UV exposure on the whole spectrum (demonstrated in C-band), but although simple, this technique requires a highly photosensitive fiber and relatively high UV exposure [21] compared to ROGUEs. Indeed, we tried implementing this technique to compare with the ROGUE inscription, but almost no improvement in backscatter was observed using this power and speed. Xu et al. [35] reported enhancement by the inscription of a random grating using ultrafast laser point by point inscription. However, this resulted in very high losses (~100 dB/m), making them impractical for more than very short range applications. Yan et al. [20], using a similar technique, demonstrated an increase of over 40 dB in backscatter, but observed the formation of nano-gratings in the core of the fiber, leading to transmission loss of 15 to 41 dB/m. More recently, Beisenova et al. [36] presented a technique to enhance the scatter by using nanoparticles doped inside the fiber, enhancing the backscatter by 36.5 dB, while suffering from losses of 25.5 dB/m. The common problem with those techniques is that, while significantly enhancing the scatter, this scatter is omni-directional. As such, only the very small proportion of light captured by the fiber’s numerical aperture is backscattered to the detector, explaining the very high transmission losses. In comparison, our ROGUEs achieve transmission losses of only 0.15 dB/m, due to the directionality of the scatter enhancement.

Some techniques do show directional backscatter enhancement. Westbrook et al. [13,37] presented an enhancement scheme based on the writing of superposed chirped FBGs, resulting in a 20 dB backscatter enhancement, with very low optical losses (0.4 dB/km). However, the superposition of those gratings limits the achievable spatial resolution to the spacing between each exposure (in their case, ~5 mm). The spatial resolution of our technique, being noise-driven and continuous, is only limited by the spot size (in our case, ~100 µm). Using a smaller spot size (such as the 14 µm demonstrated by Scoll et al. [38]) would potentially decrease even further that theoretical limit, and would increase the ROGUE bandwidth. Additionally, we demonstrate much higher backscatter enhancement. Indeed, to the best of our knowledge, this is the first time that a sensor showing more than 50 dB more backscatter than SMF-28 is reported. This increased signal can also be used to multiplex several ROGUEs, allowing sensing on all of them simultaneously, compensating for any additional losses from multiplexing. More importantly, this enhancement is achieved without major increase in transmission loss, while simultaneously achieving an unprecedented 68 nε (8 mK) noise level (with a 5.24 nm bandwidth and 10 mm gauge length).

Since a ROGUE is noise-generated, the alignment of the inscription system is non-critical and insensitive to vibrations, making the ROGUE a simple and affordable solution to amplify the backscattered signal critical to OFDR measurements. Relatively fast writing speeds of 1 or even 10 mm/s show sufficient increase in backscatter to noticeably enhance the accuracy of such sensors without requiring an enormous amount of UV power. The experimental setup described in this paper uses a Talbot interferometer configuration but could as easily use direct inscription of the ROGUE with the fiber directly behind the phase mask, or ultrafast laser exposure. Arguably, environmental fluctuations or equipment vibrations could even potentially increase the strength of the ROGUE by adding other sources of noise. Although the coating was removed prior to ROGUE inscription, making the sensors more brittle, different techniques could be implemented to ensure sensor robustness, such as recoating the fiber after the exposure, using a UV-transparent coating to remove the need to strip the coating, or even writing the ROGUE in the fiber drawing process, before it is coated.

In an ideal lab-controlled case where loss and parasitic reflections are minimized, a ROGUE is only useful for a gain of ~25 dB compared to bare SMF-28, as shown previously in Fig. 10. Indeed, the strain RMS error reaches a plateau, and therefore remains the same for all stronger ROGUEs. However, in many sensing applications, these ideal conditions may not be available, as loss added from connectors or optical components can suppress the detector’s dynamic range. A ROGUE increases the gain optically without losing any of the detector’s dynamic range and without any sacrifice in scanning time. This increased signal can also be used to multiplex several ROGUEs, allowing sensing on all of them simultaneously.

The time it takes to make a measurement can be critical to many sensing applications, more so than sensitivity. Increasing the optical signal through a ROGUE can improve sensitivity, but it can also potentially reduce the measurement time for a constant sensitivity. For instance, as shown in Fig. 4, for the same accuracy observed as standard SMF-28, the scanning bandwidth can be reduced by a factor of 8 for a ROGUE (from 42.9 nm to 5.24 nm). For our OBR, this reduces the 4.5 s scan time for SMF-28 down to 1.2 s (using the Fast Scanning option). Also, having more signal gain can allow the detector to operate at higher bandwidth, hence allowing faster wavelength sweep speed until the maximum scan speed is reached (determined by the time-of-flight of light in the fiber). It should be noted that this enhancement is limited to the bandwidth of the ROGUE. The laser power and writing speed are not sufficient to generate uniform Rayleigh enhancement, and as such scanning outside the ROGUE does very little to enhance backscatter.

6. Conclusion

In conclusion, we have shown here that, simply by adding phase noise during FBG inscription we can write a ROGUE that generates an increase in backscatter of several orders of magnitude and whose large FWHM bandwidth (>7 nm) is independent of written length (for length >100 mm). This enhancement results in a SNR above 50 dB. This gain can be used to reduce noise in distributed sensing. For instance, we have shown that for a 10 mm gauge length, the noise level can be reduced by over an order of magnitude in noise and by 4.5 times in accuracy compared to standard SMF-28. We have also shown that such a high enhancement can be used to compensate system losses of up to 50 dB (25 dB one-way), which can significantly increase the robustness of such sensing equipment to losses and parasitic reflections. Finally, such gains could be used to significantly reduce the sensing time, as we have shown that to obtain similar performance to SMF-28, a ROGUE requires 8 times less bandwidth for the wavelength scan. Also, with increased gain, the tolerance to noise is higher, hence the detector bandwidth can be increased, allowing faster scan speeds. A ROGUE structure requires little exposure and is easy to write in-fiber, as it is noise-generated, making any environmental fluctuation irrelevant, if not advantageous. Therefore, it could potentially be easily implemented directly on a drawing tower.