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First-order loss-less differentiators using long period gratings made in Er-doped fibers.

An active-fiber-based all-optical first-order temporal differentiator with power efficiency surpassing 100% is demonstrated experimentally. It is based on a long-period fiber grating (LPFG) inscribed into a piece of highly-doped Erbium-doped fiber (EDF). The performed theoretical analysis considers effects like relative position of the LPFG with respect to the input end of the EDF and influence of the input signal power. In the design, parameters like noise characteristics and level of non-linear interaction are taken into account. The advantages of such an implementation over the setup using concatenation of a passive LPFG with an amplifier lies in reducing the unwanted nonlinearities and reducing the amplified spontaneous emission (ASE).