Optical Computing, Fourier Transform, Silicon Photonics, Signal Processing.
Using the property that exp(c1+c2) ​= exp(c1) exp(c2) for any two complex numbers c1​ and ​c2, this becomes: Performing the last two sums is equivalent to computing the optical Fourier transform of the array a​ʲ’ᵏ’. So, In this equation, the array indices are assumed to be periodic (with period