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.
© 2013 IEEE
Bing Zou and Kin Seng Chiang, "Phase Retrieval From Transmission Spectrum for Long-Period Fiber Gratings," J. Lightwave Technol. 31, 2223-2229 (2013)