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Distributed temperature and train measurements can be realized by using stimulated Brillouin scattering. This effect can be described as a three-wave interaction of pump laser wave, a Stokes wave and an acoustic wave of characteristic Brillouin frequency. This frequency depends on temperature and strain. This effect is used for distributed measurements and realized in Brillouin optical time-domain analysis. In the method, the continuous wave light of narrow linewidth pump laser is coupled into one end of the sensor fiber and a sinusoidal modulated intensity of a probe laser is coupled to the other end. If the frequency difference between both lasers equals to characteristic Brillouin frequency, the pump light will interact with the modulated probe light in the fiber. By analyzing the transmitted pump intensity at different frequency differences between probe and pump lasers, the temperature and strain distribution along the fiber can be determined. In this numerical simulation several fiber lengths with different but spatial constant gain coefficients were placed one after another. For each fiber part the fundamental oscillation of the transmitted pump intensity is calculated by the derived analytical expression with respect to individual Brillouin gain coefficients. The DC components of the input pump and stokes powers of each region are determined by numerical iteration. Only the DC component of the pump power produces Brillouin interaction. Considering the phase shift of the transmitted alternating components of the pump powers of each different located fiber regions, the baseband modulation transfer function is calculated. By means of inverse Fourier transformation pulse response is calculated. Pulse response is a 2D function of length of fiber and frequency difference between probe and pump lasers. It gains maximum when frequency difference is correspondent to characteristic Brillouin frequency of certain temperature and strain. So, pulse response represent distribution of temperature and strain along optic fiber.
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