Figure 3: Band diagram of a three-mode coupler with varying middle waveguide width W2.
From: Adiabatic elimination-based coupling control in densely packed subwavelength waveguides
The band diagram shows the electric field eigenvalues (blue curves) and eigenmodes (colour maps) of the system for TM polarization (for TE polarization, see Supplementary Fig. 4). (Inset I) All the three waveguides are identical, W1=W2=W3=220 nm and are mixed in the eigenmodes of the system. In this configuration, an input in one of the waveguides is projected necessarily on all the waveguides. (Inset II) AE regime. The AE is reached when W2 is larger and our sample (red circles, W2=275 nm) is in this regime. Here an eigenmode involving only the middle waveguide emerges and becomes less coupled, since the coupling is proportional to 1/Δn where 
, leading to the elimination of the middle waveguide. The two remaining eigenmodes are symmetric and antisymmetric superpositions of the outer waveguides as in a conventional two-mode coherent coupler. An input in either of the outer waveguides will be projected only onto those two eigenmodes, resulting in an effective two-waveguide system evolution, while the middle waveguide remains ‘dark’ along the propagation. On the other hand, an input injected in the middle waveguide is projected only onto the dark mode of the system and will stay ‘trapped’ in the middle waveguide without transferring energy to the adjacent ones.
