We propose and demonstrate what we believe to be a new, simple, and compact all-fiber design for arbitrary-order ultrafast optical temporal differentiation. The proposed design allows us to implement any desired differentiation order using a maximum of two concatenated fiber gratings, both operating in transmission. A single specially apodized chirped fiber Bragg grating is required for implementing any even-order differentiator, whereas the immediately next odd-order differentiator can be implemented by concatenating a long-period fiber-grating first-order differentiator. Besides its simplicity, this scheme provides an optimized energetic efficiency. We experimentally demonstrate a set of high-order all-optical time differentiators (up to the fourth order) capable of accurately processing arbitrary optical waveforms with picosecond time features.
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