Abstract
We demonstrate a method to retrieve the phase spectrum of a long-period fiber grating (LPFG) from its transmission spectrum. The method is based on the Hilbert transform that relates the minimum phase and the amplitude spectrum of a linear system, and is applicable to under-coupled LPFGs with arbitrary grating profiles. We verify the method with numerical examples and experiments. The method provides a simple and effective way to obtain the phase characteristics of LPFGs and thus complement the measured transmission spectra of the gratings.
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