A single inverse-designed photonic structure that performs parallel computing

In the search for improved computational capabilities, conventional microelectronic computers are facing various problems arising from the miniaturization and concentration of active electronics devices (1-2). Therefore, researchers have been exploring several paths for the next generation of computing platforms, which could exploit various physical phenomena for solving mathematical problems at higher speeds and larger capacities. Among others, physical systems described by waves, such as photonic and quantum devices, have been utilized to compute the solution of mathematical problems (1-18). However, previous devices have not fully exploited the linearity of the wave equation, which as we show here, allows for the simultaneous parallel solution of several independent mathematical problems within the same device. In this Letter, we demonstrate, theoretically and experimentally, that a transmissive cavity filled with a judiciously tailored dielectric distribution and embedded in a multi-frequency feedback loop can calculate the solutions of an arbitrary number of mathematical problems simultaneously. We design, build, and test a computing structure at microwave frequencies that solves two independent integral equations with any two arbitrary inputs. We offer another design that can invert four arbitrary 5x5 matrices, confirming its functionality with numerical simulations. We believe our results presented here can provide "coincident computing" and pave the way for the design of low-power, ultrafast, parallel photonic analog computing devices for sensing and signal processing in embedded computing applications.