Analysis of apodized phase-shifted long-period fiber gratings

We present a detailed theoretical analysis of the transmission spectra of apodized phase-shifted long-period fiber gratings (LPFGs). Simple analytical formulas are derived to provide insights into the characteristics of the gratings and facilitate their designs for specific applications. In particular, we focus on the achievement of zero or complete transmission at the resonance wavelength with zero- or π-phase-shifted gratings. The effects of index apodization and length apodization on the transmission spectra of the LPFGs are studied in detail. A number of numerical examples are given to illustrate the features of various kinds of LPFG designs.