We study the performance limits of mono-color cyclic coding applied to Brillouin optical time-domain analysis (BOTDA) sensors that use probe wave dithering. BOTDA analyzers with dithering of the probe use a dual-probe-sideband setup in which an optical frequency modulation of the probe waves along the fiber is introduced. This avoids non-local effects while keeping the Brillouin threshold at its highest level, thus preventing the spontaneous Brillouin scattering from generating noise in the deployed sensing fiber. In these conditions, it is possible to introduce an unprecedented high probe power into the sensing fiber, which leads to an enhancement of the signal-to-noise ratio (SNR) and consequently to a performance improvement of the analyzer. The addition of cyclic coding in these set-ups can further increase the SNR and accordingly enhance the performance. However, this unprecedented probe power levels that can be employed result in the appearance of detrimental effects in the measurement that had not previously been observed in other BOTDA set-ups. In this work, we analyze the distortion in the decoding process and the errors in the measurement that this distortion causes, due to three factors: the power difference of the successive pulses of a code sequence, the appearance of first-order non-local effects and the non-linear amplification of the probe wave that results when using mono-color cyclic coding of the pump pulses. We apply the results of this study to demonstrate the performance enhancement that can be achieved in a long-range dithered dual-probe BOTDA. A 164-km fiber-loop is measured with 1-m spatial resolution, obtaining 3-MHz Brillouin frequency shift measurement precision at the worst contrast location. To the best of our knowledge, this is the longest sensing distance achieved with a BOTDA sensor using mono-color cyclic coding.

We report on two previously unknown non-local effects that have been found to impair Brillouin optical time-domain analysis (BOTDA) sensors that deploy limited extinction ratio (ER) pump pulses. The first one originates in the increased depletion of the pedestal of the pump pulses by the amplified probe wave, which in turn entails a reduced amplification of the probe and a measurement distortion. The second effect is due to the interplay between the transient response of the erbium-doped fiber amplifiers (EDFA) that are normally deployed to amplify the pump and the pedestal of the pump pulses. The EDFA amplification modifies the pedestal that follows the pulses in such a way that it also leads to a distortion of the measured gain spectra after normalization. Both effects are shown to lead to non-local effects in the measurements that have similar characteristics to those induced by pump pulse depletion. In fact, the total depletion factor for calculations of the Brillouin frequency shift (BFS) error in BOTDA sensors is shown to be the addition of the depletion factors linked to the pump pulse as well as the pedestal. A theoretical model is developed to analyze both effects by numerical simulation. Furthermore, the effects are investigated experimentally in long-range BOTDA sensors. The pedestal depletion effect is shown to severely constrain the probe power as well as the minimum ER of the pulses that can be deployed in BOTDA sensors. For instance, it is shown that, in a long-range dual-probe BOTDA, an ER higher that 32-dB, which is above that provided by standard electro-optic modulators (EOM), is necessary to be able to deploy a probe power of −3 dBm, which is the theoretical limit for that type of sensors. Even more severe can be the limitation due to the depletion effect induced by the EDFA transient response. It is found that the impairments brought by this effect are independent of the probe power, hence setting an ultimate limit for the BOTDA sensor performance. Experimentally, a long-range BOTDA deploying a 26-dB ER EOM and a conventional EDFA is shown to exhibit a BFS error higher than 1 MHz even for very small probe power.

In this paper, a number of STEM educational proposals are systematically analyzed from the lens of mathematics education. An extensive innovation project was implemented during the 2019/2020 academic year in a pilot study carried out in Schools and Teacher Training Programs in Navarre (Spain), comprising a bibliographical and source analysis as a previous step to characterize the existing material, and ultimately to design and test STEM projects at different educational levels from the point of view of mathematical education. All activities belong to international publications and widely used and contrasted web repositories, and seize the usual interval of compulsory education, i.e., from the beginning of Primary School (age 6/7) to the end of Secondary School (age 15/16). The findings draw a panorama of STEM activities where mathematics is mostly utilitarian, numbers and units are functionally used to measure quantities of magnitudes, and geometric contents serve the purpose of modeling a technological prototype. As it turns out, some STEM-labelled activities do not fulfill their principles and fundamental purposes. In lower levels, there is a common confusion between STEM activities and science laboratory projects; in higher levels, complex mathematical content could appear. Even though some activities are guided science laboratory projects, it is concluded that most STEM activities have the potential of a-didactical situations, i.e., contexts where students put into practice their personal problem-solving techniques before teachers formalize the mathematical content.

Brillouin optical time-domain analysis (BOTDA) sensors have great potential to provide distributed measurements of temperature and strain over large structures with high spatial resolution and measurement precision. However, their performance ultimately depends on the amount of probe and pump pulse power that can be injected into the sensing fiber, which determines the signal-to-noise ratio of the detected measurement signal. The probe wave power is constrained by the generation of noise induced by spontaneous Brillouin scattering and at lower power by the so-called non-local effects. In this work, we focus on the latter. We review the physical origins of non-local effects and analyze the performance impairments that they bring. In addition, we discuss the different methods that have been proposed to counteract these effects comparing their relative merits and ultimate performance. Particularly, we focus on a technique that we have devised to compensate non-local effects which is based on introducing an optical frequency modulation or dithering to the probe wave. This method is shown to provide a comprehensive solution to most of the impairments associated with non-local effects and also to enable some side benefits, such as amplification of the pump pulses to compensate the attenuation of the fiber.

We investigate the deleterious effect and the error in Brillouin optical time-domain analyzers induced by the combination of a low extinction ratio pulse generation with the transient behavior of erbium-doped fiber amplifiers.

We introduce a simple method to extend the performance of pulse coding techniques in their application to Brillouin optical time-domain analysis sensors (BOTDA). It is based on applying a simple logarithmic processing on the detected probe wave that compensates the deviation from linearity of the sensor response for long code lengths. The technique ensures that the accumulated effect of a sequence of pulses is equal to the linear addition of the effects of the individual components, which is the essential condition to ensure a correct decoding of the probe gain measurement. We experimentally demonstrate the compensation of the Brillouin frequency shift error induced by the accumulated gain nonlinearity. Furthermore, a proof-of-concept 80 km sensing link within a total 200 km fiber loop demonstrated a better than 2 MHz precision with 2 m spatial resolution.