Faezeh Bahrami Chenaghlou
Afshin Ahmadpour
Mahdi Sahafi
Amir Habibzadeh Sharif

Microring resonator (MRR)-based photonic fractional differ-entiators (DIFFs) play an important role in the on-chip integrated all-optical signal processors. One of the main challenges of these integratedcircuits is their physical size. In this paper, an ultra compact optical MRRis proposed to realize the concept of photonic-based fractional DIFF. Theoptical MRR is modeled as a rst order DIFF in its critically-coupledregime, while its under-coupled and over-coupled regimes are modeled asfractional DIFFs. By changing the coupling regime from under-coupled toover-coupled, the phase shift in the resonance frequency is changed fromless than to more than. This phase shift can be used to implement afractional order photonic DIFF with an order tunable from 0 to 2. Usingthe proposed ultra compact optical MRR, a Gaussian pulse with the fullwidth at half-maximum (FWHM) of 76 GHz is temporally di erentiatedwith orders of 1, 0.41 and 1.36. Simulation results obtained by the nite-di erence time-domain (FDTD) method for the presented MRR are in agood agreement with those of associated mathematical formulas.

Fractional di erentiator, Microring resonator, Optical processing