Modelling of linearly chirped fiber Bragg gratings by the method of single expression

To model chirped fiber Bragg gratings (FBGs) for dispersion compensation in optical fibers a novel method of single expression (MSE) is used. The reformulation of Helmholtz’s equation in the MSE to the full set of first-order differential equations leads to dealing with the electric field amplitude,...

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Bibliographic Details
Published in:Optical and quantum electronics 2002-05, Vol.34 (5-6), p.481-492
Main Authors: BAGHDASARYAN, H. V, KNYAZYAN, T. M
Format: Article
Language:English
Subjects:
Apodization
Applied sciences
Bragg gratings
Chirp
Circuit properties
Derivatives
Differential equations
Dispersion
Electric fields
Electric, optical and optoelectronic circuits
Electronics
Exact sciences and technology
Integrated optics. Optical fibers and wave guides
Mathematical models
Optical and optoelectronic circuits
Optical fibers
Phase distribution
Power flow
Self-similarity
Sidelobe reduction
Sidelobes
Spectra
Time lag
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Summary:To model chirped fiber Bragg gratings (FBGs) for dispersion compensation in optical fibers a novel method of single expression (MSE) is used. The reformulation of Helmholtz’s equation in the MSE to the full set of first-order differential equations leads to dealing with the electric field amplitude, its derivative, power flow density and phase distributions in any aperiodic media. The phase derivative obtained numerically permits to compute the dispersion slope in the time delay of investigated chirped gratings. Reflective and time delay spectra of linearly chirped gratings of different lengths and chirp coefficients are computed. A self-similarity law for the gratings of the same strength but different lengths and chirp coefficients is revealed. The apodization of gratings is applied to reduce sidelobes in gratings’ reflection spectra and eliminate oscillations in the time delay characteristics.
ISSN:0306-8919
1572-817X
DOI:10.1007/BF02892612