Studies about the Tolerance of Error of Fiber Length Difference in a FBG Based Sagnac Ring Filter

Abstract

In a FBG based Sagnac ring filter, the error of fiber length difference (Δ) is easy to be changed by environments and is crucial to the filter performances. But until now no relevant works have been found in open publications. In this paper, for this kind of filter we focus on studying the influence of Δ on the wavelength shift (Δ) in the transmission spectra. The theoretical models between Δ and Δ is established using Jones matrix theory and verified by Matlab numerical simulations. The simulation results show that with the increase of Δ , Δ will increase accordingly. When Δ = 100nm, insertion loss (L) will reach 8dB. This study can be used in the design and manufacture of a FBG based Sagnac filter.