All-Optical Discrete Sine Transform and Discrete Cosine Transform Based on Multimode Interference Couplers

In this letter, a novel method to realize all-optical discrete sine transform (DST) and discrete cosine transform (DCT) is proposed. The approach requires only one multimode interference (MMI) coupler and several phase shifters at the input and output ports. By properly arranging the length of the MMI coupler and adjusting the phase shifters, the DST can be directly realized all-optically. Meanwhile, the DCT is related to the DST with a simple formula. By changing the input phase and relabeling the output ports, it can also be realized on the MMI structure. The proposed methodology has no limit on the number of the inputs.