A simple method to identify the spatial location complication due to the transient phonon relaxation on the Brillouin loss spectrum

For the pump-probe stimulated Brillouin scattering with probe pulse of a few nanoseconds duration and with a finite DC level, the acoustic wave relaxation time varies with the pump power and DC level. For the pump power of 1- 6mW, the acoustic wave relaxation changes between 9 to 90 ns for polarization maintained fiber (PMF) at temperature of -45°C for 2 ns pulse width. When pulse to DC ratio of the probe varies from 10 to 20dB, the acoustic relaxation time changes between 24 to 45ns for single mode fiber (SMF) at 25°C. This induced a power increment spectral feature in detected AC pump signal in the Brillouin loss spectrum of two temperature or strain sections, where both spectral components appeared at the positions much longer than natural phonon relaxation time (~10ns) equivalent length. This can cause problem for the distributed sensor in determining the strain/temperature boundary, and central Brillouin peak fitting due to the multiple peak convolution, and it affects temperature and strain accuracy. We propose the 2nd order partial derivative of Stokes signal with respect to frequency and position giving a maximum or minimum at the boundary between two different strained sections. This allows finding the true stress or temperature corresponded section.