Single-resonance diffraction gratings for time-domain pulse transformations: integration of optical signals.

A general transformation of the optical pulse envelope implemented by a single-resonance diffraction grating is studied. The particular cases considered include optical pulse integration and differentiation implemented by the grating in the Wood anomalies and the fractional integration and differentiation of order 1/2 implemented in the Rayleigh-Wood anomalies. The extraordinary-optical-transmission plasmonic gratings are shown to be well suited for the integration in the transmission. Diffraction gratings to perform the integration and semi-integration of optical pulses with temporal features in the picosecond range are designed. Numerical simulations based on the rigorous coupled-wave analysis of Maxwell's equations are in good agreement with presented theoretical analysis.