Fig. 1. Graph representation of the possible connections in a seven-tile hexagonal waveguide mesh. The overall contour of the mesh is hexagonal, and the tiles are hexagons as well. There are 42 couplers. The hexagonal shape of the tiles is not completely straightforward but becomes apparent when one focuses on the six couplers making up the tile.

Fig. 2. Four studied architectures and the number of couplers that compose them organized in a square contour. (a) A mesh with triangular tiles: 45 couplers. (b) A mesh with square tiles: 24 couplers. (c) A mesh with hexagonal tiles: 56 couplers. (d) A mesh with ring-connected straight lines: 60 couplers.

Fig. 3. Mesh with a parallelogram contour with triangular tiles and two commodities with a shortest path. The leftmost path seems to be rather wasteful, needing three additional couplers for every coupler on the straight line from source to destination.

Fig. 4. Indicated structure adds an additional layer. If this is added to the entire outer layer, every two ports can be connected by a path, overcoming a serious limitation of the square/triangle tile shape and RCSL layout.

Fig. 5. Ratio of the actual path length compared to a straight line from source to destination. On the x-axis is the relative position of the source and destination node.

Fig. 6. Mesh with RCSL tiles and the appropriate coordinate system to easily calculate the analytical distance.

Fig. 7. Simplified representation of the different problem types. (a) Type I, (b) Type II, and (c) Type III.

Fig. 8. Average maximum number of commodities routable at the same time.

Fig. 9. Maximum number of commodities routable at the same time for the predefined patterns.

Fig. 10. Average length of a path.

Fig. 11. Average path length in the solution, with the average length of the shortest path marked with a dashed line.

Fig. 12. By smartly routing the green and brown commodities, one additional commodity can be routed.

Fig. 13. Comparison of the different ways a coupler can break. (a) Normal, (b) complete failure, (c) only bar mode, and (d) only cross mode.

Fig. 14. Impact of different types of coupler failure. Simultaneous—Dense is a subset of problems where there are many different paths and thus the mesh is densely used. (a) Damaged couplers are stuck in cross mode. (b) Damaged couplers are stuck in bar mode. (c) Damaged couplers have failed completely. (d) Half are stuck in cross mode and half have failed completely. (e) Damaged couplers are split in half cross mode and half bar mode. (f) One-third in cross mode, bar mode, and complete failure.

Fig. 15. Coordinate system used to describe an exact analytical distance.