Analysis of Optical Fibers with Long-Period Gratings

The topic of this paper is to study the transmittance of light in a long periodic fiber grating. By means of the couple characteristics of a light in the fiber, effect of Λ、n1、a1、a2、z、σ(z)n1 and phase shift of fiber to the transmittance frequency spectral is discussed.
About the couple characteristics of a light in the fiber, Maxwell’s equation is used to determine wave equation, and also by couple mode theory to get the couple equation of long periodic fiber grating. In order to analyze long periodic fiber grating conveniently, the couple equation is applied to find a general solution, and turn the general solution into the form of transfer matrix. According to this transfer matrix, the parameters is changed to simulate the variety of transmittance frequency spectrum and the phase shift of fiber grating to transmittance of light in a long periodic fiber grating. Finally, by means of the variety of transmission, bandwidth and resonant wavelength of fiber grating can be applied to design some instruments and devices.