Analysis of the fiber Bragg gratings using the lattice filter model

We propose a new method for analyzing fiber Bragg gratings having an arbitrary index profile and an arbitrary individual grating length. The proposed method is based on the lattice filter model which are widely used in the signal processing community ranging from digital filtering to speech synthesis and explosive seismic signal processing applications. Lattice filter interpretation provides us with an accurate and simple tool for analyzing arbitrary aperiodic fiber grating structures, and gives us further insight to the understanding of the fiber Bragg gratings. To verify the validity of the proposed model, we have fabricated two grating structures; the short period (periodic) fiber Bragg grating structure and the chirped fiber Bragg grating structure. We have observed that the predicted transmission spectrum and the predicted reflectivity using the lattice filter model match very closely to the corresponding measured spectrum curves in the band of the wavelength of our interest.