However, physical limitations (such as quantum tunneling) imposed on the size and separation of individual transistors in semiconductor-based circuits means that performance gains may soon reach their maximum potential. [2] Additionally, parasitic capacitances appearing in these devices can lead to challenges in energy consumption and speed during the charging/discharging processes involved when using them as switching devices for computing. [3] While it is expected that semiconductor-based technology remains with us for many years to come and research is underway to overcome challenges and further improve its performance, ever-increasing demand for faster and more energy efficient computations therefore necessitates the introduction of alternative computing paradigms. Some notable examples that have been explored so far include quantum computing, [4] TEM pulse switching, [5][6][7][8] and computing with solitons, [9] to name a few. In this realm, analogue wave-based computing, as an alternative to current electronic-based computing systems, offers inherently parallel processing capabilities for fast, energy efficient computation on specialized tasks such as high throughput image processing, [10,11] equation solving, [12][13][14] and machine learning. [15] Another prominent area of research where this paradigm shift is taking off is in the field of metamaterials (MTMs)and metasurfaces (MTSs) as their 2D counterparts. [16,17] MTMs and MTSs are artificially engineered structures that enable enhanced and tailored wave-matter interactions both in space and time [18][19][20][21][22] with responses not easily available in nature such as epsilon near-zero or negative refractive index. [17,[23][24][25] For the past 2 decades, the scientific community has reported many interesting applications using MTMs across different branches of science and engineering. For example, MTM-based antennas for high gain 5G communications, [26] miniaturized optical neural networks (NNs) for real-time object recognition, [27] MTS-based sensors at terahertz frequencies [28] and invisibility cloaking devices, [29] to name a few. Recently, the concept of wave-based analogue computing with MTMs has also been introduced. [30] In this emerging branch of MTM research, the interactions between an incoming wave and the multiple metaatoms (scatterers) can be exploited to perform some mathematical operation of choice (e.g., differentiation, integration, 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 ...
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