Spatial mode division de-multiplexing of optical signals has many real-world applications, such as quantum computing and both classical and quantum optical communication. In this context, it is crucial to develop devices able to efficiently sort optical signals according to the optical mode they belong to and route them on different paths. Depending on the mode selected, this problem can be very hard to tackle. Recently, researchers have proposed using multi-objective evolutionary algorithms (MOEAs) ---and NSGA-II in particular--- combined with Linkage Learning (LL) to automate the process of design mode sorter. However, given the very large-search scale of the problem, the existing evolutionary-based solutions have a very slow convergence rate. In this paper, we proposed a novel approach for mode sorter design that combines (1) stochastic linkage learning, (2) the adaptive geometry estimation-based MOEA (AGE-MOEA-II), and (3) an adaptive mutation operator. Our experiments with two- and three-objectives (beams) show that our approach is faster (better convergence rate) and produces better mode sorters (closer to the ideal solutions) than the state-of-the-art approach. A direct comparison with the vanilla NSGA-II and AGE-MOEA-II also further confirms the importance of adopting LL in this domain.@en

Spatial modes of light can be used as carriers of information in classical optical communication or as an alphabet in quantum optical communication. In order to exploit the spatial domain, it is required to (de)multiplex different modes from a shared input channel into different output ports. Mode sorters have been employed in free-space and fiber systems but to date have not been realized for planar guided waves. Here we present a general method for compact on-chip sorting of different planar beams with a micrometric footprint and nanometric thickness. The designs were generated using a linkage-tree-based genetic algorithm and were experimentally demonstrated on a surface plasmon polariton platform by sorting of Hermite-Gaussian beams. The method used here can be readily applied to optimize complex, large-scale optical devices involving beam propagation methods.

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