If you have had trouble with ordinary calculus, you may not be pleased to hear about “photonic calculus” — a recent idea from [Nader Engheta] of the University of Pennsylvania. The idea is that materials with certain properties could manipulate an electromagnetic wave in a way to solve a specific mathematical equation. [Engheta] proposed this idea back in 2014 and recently announced that he and his team have a demonstration device that proves the concept. The analog computer is about twice the size of an airplane’s tray table and made of CNC-shaped polystyrene. It solves Fredholm integral equations of the second kind.
The analog computer uses microwaves for the input and the polystyrene acts as a dielectric full of air holes. The team likens its structure to that of Swiss cheese. The shape is generated through an inverse design process which builds the shapes from known solutions to the equations. That means a particular set of shapes will do one specific equation. The equation could, for example, model the sound volume in a concert hall. You can encode certain parameters in the input wave and the output would specify the volume at different locations. However, a change to the actual equation would require a new set of plastic pieces.
The computation is very fast. Using microwaves, the answer comes out in a few hundred nanoseconds — a speed a conventional computer could not readily match. The team hopes to scale the system to use light which will speed the computation into the picosecond range. Creating a new optical analog computer could be similar to how we burn a CD or DVD today.