Theory of Fiber Optical Bragg Grating: Revisited

The reflected signature of an optical fiber Bragg grating is analyzed using the transfer function method. This approach is capable to cast all relevant quantities into proper places and provides a better physical understanding. The relationship between reflected signal, number of periods, index of refraction, and reflected wave phase is elucidated. The condition for which the maximum reflectivity is achieved is fully examined. We also have derived an expression to predict the reflectivity minima accurately when the reflected wave is detuned. Furthermore, using the segmented potential approach, this model can handle arbitrary index of refraction profiles and compare the strength of optical reflectivity of different profiles. The condition of a non-uniform grating is also addressed.