Increasing the Number of Inputs for Hadamard Transform Using Two-Dimensional Multimode Interference Couplers

In this letter, a Hadamard transform based on two-dimensional multimode interference (2DMMI) couplers is proposed. Due to the nature of the Hadamard transform, the 2DMMI structure can increase the number of inputs from
N
to
N
²
in comparison to the one-dimensional (1-D) case. This method, which extends the 1-D structure to 2-D, can be used to optimize all kinds of optical Hadamard transformers.