LAUSR

All-optical arbitrary-order temporal differentiators are demonstrated with phase-modulated fiber Bragg gratings (PM-FBGs) in transmission for the first time. The transmissive PM-FBGs are designed by employing a novel two-step nonlinear optimization method, which consists of unconstrained nonlinear optimization method step and constrained nonlinear optimization method step. Specifically, the first unconstrained nonlinear step is used to get appropriate parameters as input to the second step, while the second constrained nonlinear step is employed to generate more accurate result based on the output of the first step. The proposed method does not impose much restriction on the initial input parameters and also improves the result accuracy compared with previous one-step nonlinear optimization method. Examples of 0.5th-order, first-order, and second-order differentiators are designed and numerically simulated. The numerical results show that the designed PM-FBG differentiators are very accurate with a bandwidth up to 500 GHz. Moreover, the proposed method can be applied in designing arbitrary-order differentiators with the differentiation order n > 0.