LEGO for photonics (Memphis B5&B6)
We have developed 2-D and 3-D linear embedding via Green’s operators (LEGO) modelling frameworks for photonics. Here, we consider a channel-drop filter as an elementary application. The channel-drop filter is a coupled waveguide configuration with a tunable resonant cavity. In the 2-D case, it is thought to consist of a homogeneous effective dielectric with circular empty holes. In 3-D, we consider a finite-size dielectric slab in free space with cylindrical holes.
Given a fixed complex 2-D environment, we performed local optimisation on a resonant cavity to maximise the signal transfer between the electromagnetic band-gap (EBG) waveguides. To provide matched EBG waveguide termination, we used tapered absorbing posts. In the 2-D case, we combined LEGO with the eigencurrent expansion method. For 3-D configurations, our order reduction strategy is based on adaptive cross approximation compression and the use of global Arnoldi basis functions.
Top down, the figures show the 3-D configuration, the electric field at the surface of the structure generated by a source at Port 1, and the field intensity in the 2-D configuration.