Neural Network Design of Multilayer Metamaterial for Temporal Differentiation

Controlling wave-matter interactions with metamaterials (MTMs) for the calculation of mathematical operations has become an important paradigm for analogue computing given their ability to dramatically increase computational processing speeds. Here, motivated by the importance of performing mathematical operations on temporal signals, multilayer MTMs with the ability to calculate the derivative of temporally modulated signals are proposed, designed, and studied. To do this, a neural network (NN) based algorithm is used to design the multilayer structures (alternating layers of indium tin oxide (ITO) and titanium dioxide (TiO2)) that can calculate the first temporal derivative of the envelope of an impinging electromagnetic signal modulated at telecom wavelengths (1550 nm). Different designs are presented using multiple incident temporal signals including a modulated Gaussian as well as modulated arbitrary functions, demonstrating an excellent agreement between the predicted results (NN results) and the theoretical (ideal) values. It is shown how the proposed NN-based algorithm can complete its search of the design space for the layer thicknesses of the multilayer MTM after just a few seconds, with a low mean square error in the order of (or below) 10(-4) when comparing the predicted results with the theoretical spectrum of the ideal temporal derivative.