Analysis of the fiber Bragg gratings using the lattice filter model

We propose a new method for analyzing fiber Bragg gratings with an arbitrary index profile and an arbitrary individual grating length. The proposed method is based on the lattice filter model which is widely used in applications ranging from digital filtering to speech synthesis and explosive seismic signal processing. Lattice filter interpretation provides us with an accurate and simple tool for analyzing an arbitrary index profile and arbitrary aperiodic fiber grating structures, and gives us further insight into the understanding of fiber Bragg gratings. To verify the validity of the proposed model experimentally, 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 calculated transmission spectrum and the calculated reflectivity using our lattice filter model match very closely to the corresponding measured spectrum in the wavelength band of interest.