Design of short fiber Bragg gratings by use of optimization.

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Abstract
We demonstrate an optimization approach for designing fiber Bragg gratings. A layer-peeling inverse-scattering algorithm is used to produce an initial solution, which is optimized numerically with an iterative optimization method. To avoid problems with local minima, we use merit functions that are zero for wavelengths for which the predefined demands (acceptance limits) are fulfilled, making it possible to alter the local minima under the optimization process without disturbing the global minimum. Because short gratings are difficult to design with inverse scattering, and because the time consume of the optimization increases rapidly with the grating length, the method is particularly useful for designing short gratings. The method is also useful when the demands are complex and difficult to handle with inverse-scattering methods. Design examples are given, including a dispersionless bandpass filter suitable for dense wavelength-division multiplexing and a filter with linear reflectivity.