Analytic expression of the chirped sampled function used to produce the equal chirp in the specific reflection channel in uniform period fiber Bragg gratings

The general analytic expression of the chirped sampled function is derived based on coupled mode theory. This function can be used to describe how to use uniform period fiber Bragg grating to produce the equal chirp at will in the specific reflection channel. As an example, the exact sampled function expression that produces a linear chirped at the +4 channel is given. The simulation results by using the transfer-matrix show that the theory is correct.