Performing derivative and integral operations for optical waves with optical metamaterials

The graded refractive index waveguides can perform Fourier transform for an optical wave. According to this characteristic, simpler optical metamaterials with three waveguides are theoretically proposed, in which all of the waveguides are materials with a positive refractive index. By selecting the appropriate refractive index and structure size, the theory and simulations demonstrated that these metamaterials can perform mathematical operations for the outline of incident optical waves, including the first-order derivative, second-order derivative and the integral.