Design of ultracompact tunable fractional-order temporal differentiators based on hybrid-plasmonic phase-shifted Bragg gratings

The design and the simulation of tunable fractional-order temporal differentiators based on Si-hybrid plasmonic phase-shifted Bragg gratings are proposed in this paper, where strong light confinement in the hybrid plasmonic waveguide is employed to significantly reduce the overall length of the differentiators. According to 2D- and 3D-FDTD simulation results, the proposed structures with overall lengths of less than 8 μm can provide arbitrary differentiation order and differentiation bandwidths as high as 1.6 THz. The differentiation order and the bandwidth of the proposed structures can be tuned in relatively wide ranges by changing the geometrical parameters of the structures. For example, the differentiation order can be changed from 0.57 to 0.97 by changing the number of the Bragg grating periods in a 3D differentiator structure. Furthermore, it is shown that using an electro-optical polymer as the low-index material of the hybrid plasmonic waveguide, the differentiation order and the central frequency of the proposed differentiators can be actively tuned through applying a proper actuating electrical field (voltage) to the structure. This property, along with the ultracompact footprint and wide bandwidth of the proposed differentiators, suggest their application in ultrafast all-optical signal-processing systems.