The worst-case error amplification factor in reconstructing a grating from its complex reflection spectrum is shown to be of the order 1/T(min), where T(min) is the minimum transmissivity through the grating. For a uniform grating with coupling coefficient-length product kappaL, the error amplification is exp(2kappaL). The exponential dependence on the grating strength shows that spatial characterization of gratings from a measured reflection spectrum is impossible if the grating is sufficiently strong. For moderately strong gratings, a simple regularization technique is proposed to stabilize the solution of the inverse-scattering problem of computing the grating structure from the reflection spectrum.
This paper studies the influence of random phase and amplitude fabrication errors on the performance of optical filters based on fiber Bragg gratings (FBG'sj. In particular, we analyze two effects of particular importance for optical communications: the excess crosstalk induced in apodiaed gratings commonly used in wavelength-division-multiplexing (WDM) systems, and the time-delay fluctuations that appear in chirped gratings employed tu compensate the fiber dispersion. A statistical model is presented to explain these effects in terms of the coherence length of the grating fabricatiun procedure.
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