We present a theoretical study of a new application of a simple π-phase-shifted fiber Bragg grating (PSFBG) in transmission mode as a high-speed optical temporal integrator. The PSFBG consists of two concatenated identical uniform FBGs with a π phase shift between them. When the reflectivities of the FBGs are extremely close to 100%, the transmissive PSFBG can perform the time integral of the complex envelope of an arbitrary input optical signal with high accuracy. As an example, the integrator is numerically shown to be able to convert an input Gaussian pulse into an optical step signal.
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