## Abstract

We report a high-spatial-resolution and long-range distributed temperature sensor through optimizing differential pulse-width pair Brillouin optical time-domain analysis (DPP-BOTDA). In DPP-BOTDA, the differential signal suffers from a signal-to-noise ratio (SNR) reduction with respect to the original signals, and for a fixed pulse-width difference the SNR reduction increases with the pulse width. Through reducing the pulse width to a transient regime (near to or less than the phonon lifetime) to decrease the SNR reduction after the differential process, the optimized $8/8.2\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{ns}$ pulse pair is applied to realize a 2 cm spatial resolution, where a pulse generator with a 150 ps fall-time is used to ensure the effective resolution of DPP-BOTDA. In the experiment, a 2 cm spatial-resolution hot-spot detection with a 2 °C temperature accuracy is demonstrated over a 2 km sensing fiber.

© 2012 Optical Society of America

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### Equations (6)

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(1)
$$-\frac{\partial {E}_{p}}{\partial z}+\frac{n}{c}\frac{\partial {E}_{p}}{\partial t}=i{g}_{2}{E}_{s}Q,$$
(2)
$$\frac{\partial {E}_{s}}{\partial z}+\frac{n}{c}\frac{\partial {E}_{s}}{\partial t}=i{g}_{2}{E}_{p}{Q}^{*},$$
(3)
$$\frac{\partial Q}{\partial t}+\mathrm{\Gamma}Q=i\frac{{g}_{1}}{\eta}{E}_{p}{E}_{s}^{*}.$$
(4)
$$Q=i\frac{{g}_{1}}{\eta}{\int}_{0}^{t}{E}_{p}{E}_{s}^{*}\text{\hspace{0.17em}}\mathrm{exp}[-\mathrm{\Gamma}(t-\tau )]\mathrm{d}\tau .$$
(5)
$$-\frac{\partial {E}_{p}}{\partial z}+\frac{n}{c}\frac{\partial {E}_{p}}{\partial t}=-\frac{{g}_{0}\mathrm{\Gamma}}{2}{\int}_{0}^{t}{E}_{p}{E}_{s}^{*}\text{\hspace{0.17em}}\mathrm{exp}[-\mathrm{\Gamma}(t-\tau )]\mathrm{d}\tau ,\phantom{\rule{0ex}{0ex}}\frac{\partial {E}_{s}}{\partial z}+\frac{n}{c}\frac{\partial {E}_{s}}{\partial t}=\frac{{g}_{0}\mathrm{\Gamma}}{2}{\int}_{0}^{t}{E}_{p}^{*}{E}_{s}\text{\hspace{0.17em}}\mathrm{exp}[-{\mathrm{\Gamma}}^{*}(t-\tau )]\mathrm{d}\tau ,$$
(6)
$${R}_{\mathrm{SNR}}=-10\text{\hspace{0.17em}}\mathrm{log}\frac{{I}_{\tau 2}-{I}_{\tau 1}}{{I}_{\tau 1}},$$