Asymmetric Wavelength-Selective Directional Couplers as Fractional-Order Optical Differentiators

In this paper, the asymmetric wavelength-selective directional coupler (DC) is designed as a fractional-order optical differentiator. It is shown that the order of the optical differentiator is determined by the coupling coefficient and the propagation constant difference between the two waveguides in the coupler. The relation between the order of differentiator and the structure parameters of DC is analyzed. Optical differentiators with fractional orders of 0.47, 0.78, and 1.1 based on the asymmetric wavelength-selective DC are designed and analyzed, of which the processing errors are 10.04%, 6.11%, and 22.24%, and the energetic efficiencies are 20.61%, 19.62%, and 20.39%, respectively. The proposed design provides a competitive way for the fractional-order optical differentiator.