On a density criterion for universal interlaced unitary photonic architectures*

Programmable photonic integrated circuits represent an emerging technology for light-based information processing at high speeds and low power consumption, providing a flexible and reconfigurable platform to perform multiple tasks, thereby holding great promise for revolutionizing future optical networks. Indeed, matrix-vector multiplication is one of the most fundamental information-processing operations. Unitary matrices are particularly interesting since they describe lossless processes and serve as the building blocks of more general operations.

 

This talk focuses on a universal unitary architecture based on layers of diagonal matrices and specific interlacing unitary matrices. Numerical evidence brings evidence that such an interlacing matrix can have a random pattern as long as it fulfills the required density properties. In this regard, Haar-generated random matrices are suitable candidates that lead to suitable interlacing matrices in most outcomes. To distinguish the efficacy of the random matrix in question, a density criterion has been introduced as an a priori condition to ensure the validity of the interlacing matrix in question, reducing the computational workload due to heavy numerical optimization to classify them.

 

This approach is beneficial for two reasons. Firstly, it allows for more possibilities for further interlacing matrices beyond particular waveguide arrays. Secondly, the random nature of the interlacing matrix provides resilience due to manufacturing defects. These results are illustrated by means of some realistic photonic realizable examples.