Design and characterization of finite-length fiber gratings

A rigorous analysis of the response of fiber Bragg gratings of finite length is presented. For the discrete grating model, we find necessary and sufficient conditions for the response to be realizable as a grating of finite length. These conditions are used to develop a general method for designing...

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Bibliographic Details
Published in:IEEE journal of quantum electronics 2003-10, Vol.39 (10), p.1238-1245
Main Authors: Skaar, J., Waagaard, O.H.
Format: Article
Language:English
Subjects:
Applied sciences
Bragg gratings
Circuit properties
Design engineering
Design methodology
Diffraction gratings
Electric, optical and optoelectronic circuits
Electronics
Exact sciences and technology
Fiber gratings
Fibers
Finite impulse response filter
Fourier transforms
Gratings (spectra)
Impulse response
Integral equations
Integrated optics. Optical fibers and wave guides
Inverse problems
Mathematical analysis
Mathematical models
Optical and optoelectronic circuits
Other fiber-optical devices
Reflection
Sufficient conditions
Wavelength division multiplexing
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Summary:A rigorous analysis of the response of fiber Bragg gratings of finite length is presented. For the discrete grating model, we find necessary and sufficient conditions for the response to be realizable as a grating of finite length. These conditions are used to develop a general method for designing gratings with a prescribed length. The design process is divided into two parts. First, we find a realizable reflection spectrum which approximates the target spectrum. Once the spectrum is found, one can determine the associated grating profile by straightforward layer-peeling inverse-scattering or transfer matrix factorization methods. As an example, a dispersionless bandpass filter is designed and compared to the results when the layer-peeling algorithm is applied directly to a windowed impulse response. We also discuss potential applications to grating characterization including regularization and finding the absolute reflection spectrum from a measured, normalized version.
ISSN:0018-9197
1558-1713
DOI:10.1109/JQE.2003.817581