Speaker: Tony (Hai) Jin, Mathematics
Title:
Time: 3:30 PM, Thursday, 03/3/05
Place: Guggenheim Room 408d
Abstract:
Inverse problem of fiber Bragg gratings (FBG) comes from fiber optics. An impulsive probe is applied at the input end of the FBG, two counterpropagating waves, the transmission and the reflection, move along the fiber length, and the ensuing reflection spectra is measured. The problem of recovering the coupling potential of the grating from the measured (or prescribed) data is the inverse problem of FBG. We set up the problem mathematically as an inverse problem for a first order 2 2 hyperbolic system in the space-time domain, give a quick review of our theoretical results, and then concentrate on the discrete inverse problem. We prove similar results for the discrete model, derive two inversion algorithms (the Downward Continuation algorithm and the Levinson recursion algorithm), and give a characterization or realisability condition.
Everyone welcome!