Resonant diffraction gratings for differentiation of optical signals in reflection and transmission

The propagation of an optical pulse through a diffraction grating with a resonance at the pulse's central frequency is considered. It is demonstrated that afore-mentioned gratings can perform time-domain differentiation of optical pulses in reflection and transmission. The correlation between the amplitude of the transformed pulse and the differentiation quality is investigated. A resonant grating intended for differentiation of picosecond pulses in reflection and transmission is computed.