Wavelength-selective directional couplers with dissimilar waveguides are designed for ultrafast optical differentiation within the femtosecond regime (corresponding to processing bandwidths > 10 THz). The theoretically proposed coupler-based differentiators can be produced by wavelength matching of the propagation constants of two different waveguides in the coupler at the center wavelength. A single directional coupler can be designed to achieve either a 2nd-order differentiator or a 1st-order differentiator by properly fixing the product of coupling coefficient and coupling length of the coupler. We evaluated the differentiation errors (~2%) and energetic efficiency (~11% for 1st order differentiation) of the designed optical differentiators through numerical simulations. The proposed design has a strong potential to provide a feasible solution as an integrated differentiation unit device for ultrafast optical signal processing circuits.
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