Computing with waves: from perfect splitting to routing and mathematical operations

Computing with electromagnetic waves has recently become an interesting paradigm for computing given its potential for high-speed computations. In this work, we will discuss our latest efforts in the field including perfect splitting of electromagnetic signals photonic valley crystals and interconnected rectangular waveguides exploiting evanescent coupling, as well as the solution of partial differential equations with waves and the potential of graphical modelling techniques to represent waves propagating within waveguide networks.