Synthesis of Fiber Bragg Gratings With Arbitrary Stationary Power/Field Distribution

A method to synthesize a fiber Bragg grating (FBG) providing a desired, arbitrary stationary power/field distribution along the grating length is proposed and numerically demonstrated. In the proposed method, starting from the desired stationary power/field distribution or its differential at the Bragg wavelength, the forward and the backward propagation modes are derived for a uniform-period FBG consisting of a prescribed number of grating sections. Using the transfer matrix method, the local reflection coefficient (i.e., ρ_k) is calculated from the two derived propagation modes, and this information is subsequently employed to obtain the corresponding local coupling coefficient (i.e., q_k) and the associated refractive index modulation (i.e., FBG profile) along the grating length. The proposed synthesis method is first numerically verified when two stationary power distributions from a uniform and a Gaussian-apodized FBGs are chosen as the target, showing an excellent agreement between the reconstructed refractive index modulations and those of the original FBGs. Next, several FBG profiles providing user-defined stationary power distributions, including a flat-top shape, a sharp peak, a saddle shape, or multiple peaks in the power distribution differential, are successfully synthesized. In addition, the proposed method is also shown to be suitable for the synthesis of integrated-waveguide Bragg gratings with arbitrary stationary power/field distributions.