Solution box: SOLBOX-19: Nano-optical diodes

The design and analysis of nano-optical structures involving nanoparticles has been discussed several times in previous issues of this column, e.g., see SOLBOX-08 [1] and SOLBOX-16 [2] for nano-optical couplers, and SOLBOX-13 [3] for nano-arrays. Given a grid of nanoparticles, the general aim is to reach a configuration by keeping/deleting nanoparticles such that the final structure operates as desired. In the case of nano-optical couplers, the designed configurations provide efficient transmission of electromagnetic waves through sharp bends and corners, while they also allow for diverse transmission options at junctions. Despite their geometric simplicity, such couplers can hence enable the construction of complex nano-optical networks. In the case of nano-arrays, similar nanoparticle configurations are used for beam shaping, particularly to obtain directional radiation from isotropic sources. On the other hand, in all these cases easy-to-define geometrical properties and design specifications turn out to be remarkably challenging computational problems. Using surface integral equations, the numbers of unknowns can be maintained at reasonable levels; however, large numbers of possible configurations make it impossible to test each candidate design to find the best design. For this reason, an in-house implementation of genetic algorithms was used in [1–3] to limit the number of simulations, while reaching satisfactory results. It was shown that successful coupler and array designs can be obtained via several thousands (instead of billions) of trials per optimization.