  Optical differentiation and optical Hilbert transformation play important
roles in communications, computing, information processing and signal analysis
in optical domain which offering huge bandwidth. Meanwhile, silicon-based
photonic integrated circuits are preferable in all-optical signal processing
due to their intrinsic advantages of low power consumption, compact footprint
and ultra-high speed. In this study, we analyze the interrelation between
first-order optical differentiation and optical Hilbert transformation and then
experimentally demonstrate a feasible integrated scheme which can
simultaneously function as first-order optical differentiation and optical
Hilbert transformation based on a single microdisk resonator. This finding may
motivate the development of integrated optical signal processors.
