We show analytically and numerically that a practically realizable phase-shift fiber Bragg grating (PS-FBG) can function as a temporal first-order optical differentiator and a temporal first-order optical integrator at the same time. The PS-FBG working in reflection implements the differentiation and working in transmission implements the integration. We provide both the generalized conditions for a PS-FBG functioning as a first-order optical differentiator and a first-order optical integrator. The proposed PS-FBG can perform the time differential and integral of the complex envelope of an arbitrary input optical signal with high accuracy, respectively.
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Funding: National Natural Science Foundation of China (NSFC) (61775074), Natural Science Foundation of Guangdong Province, China (2015A030313633), Key Project of Department of Education of Guangdong Province (2014KTSCX153) and Fundamental Research Funds of Foshan University (2014042).
- Fiber gratings
- ultrafast devices
- pulse shaping