Birefringence-induced frequency shift error estimation for Brillouin dynamic grating reflected spectra

Abstract

To investigate the error in temperature and strain simultaneous measurement based on Brillouin scattering and Brillouin dynamic grating (BDG), the error estimation for birefringence-induced frequency shift in BDG reflected spectra is systematically investigated. In view of the validity of characterization of the BDG reflected spectra by the coupled-wave equations and estimation of birefringence-induced frequency shift by Gaussian model, the BDG reflected spectra with different values of frequency sweep span, signal-to-noise ratio (SNR), linewidth and number of sweeps are numerically generated based on solving of the coupled-wave equations. The birefringence-induced frequency shift is estimated by fitting the Gaussian model to the numerically generated spectra. The relationship between the error in the birefringence-induced frequency shift and the above factors is obtained by the least-squares fit. The results reveal that the birefringence-induced frequency shift error decreases exponentially with increasing SNR. The error is approximately proportional to linewidth. The error decreases as a power of the number of sweeps and the exponent is −0.5. Too narrow or wide frequency sweep span corresponds to a large error. The frequency sweep span is suggested to be set to one linewidth. An estimation formula for birefringence-induced frequency shift error in BDG reflected spectra is proposed based on a large number of generated spectra.