Abstract
Optical temporal differentiators (DIFFs) based on on-chip all-pass microring resonators (APMRRs) are the fundamental all-optical signal processing blocks for differentiation of the complex envelope of optical pulses. This paper presents, for the first time to our knowledge, an accurate full-wave analysis for the ultra-compact APMRR-based optical fractional-order temporal DIFFs. The intensity transmission and phase response of the APMRR, and normalized intensity in the output of the temporal DIFFs for ultra-fast optical pulses have been obtained numerically with a high accuracy compared with those of mathematical model. The critically coupled, under-coupled and over-coupled APMRRs have been modelled as mathematical DIFFs. Key factors such as inverse phase response behaviour of the over-coupling regime, time-delay and time-reversal characteristics, finite slope of the phase response in the under and over-coupling regimes, and dependence of the differentiation order to the input pulse full-width at half-maximum (FWHM) have been analysed in detail.
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