In this way, different mathematical operations (spatial differentiation, integration, or convolution) can be realized as electromagnetic (EM) waves propagate through the metamaterial layer. brought the analog computations back to the competition as “computational metamaterials” to overcome the speed and energy limitations as well as data conversion loss of digital techniques. Relying on a decade of fruitful development and the recent breakthrough in the seemingly unrelated field of metamaterials, Silva et al. Due to having large sizes and slow responses, such analog computing devices were then totally overshadowed by the emergence of faster and more efficient digital integrated circuits in the second half of the twentieth century, where a far superior performance for real-time analysis or processing applications was demanded. The history of analog computation comes from several electronic and mechanical computing machines developed to implement simple mathematical operations. Keywords: signal processing space-time digital metasurfaces spatial differentiation and integration 1 Introduction This time-varying wave-based computing system can set the direction for future developments of programmable metasurfaces with highly promising applications in ultrafast equation solving, real-time and continuous signal processing, and imaging. Proof-of-principle simulations are also reported to demonstrate the successful realization of image processing functions like edge detection. Unlike the recent proposals based on the Green’s function (GF) method, the designed time-modulated signal processor effectively operates for input signals containing wide spatial frequency bandwidths with an acceptable gain level. Several illustrative examples are demonstrated to show that the proposed multifunctional calculus metasurface is capable of implementing a large class of useful mathematical operators, including 1st- and 2nd-order spatial differentiation, 1st-order spatial integration, and integro-differential equation solving accompanied by frequency conversions. Exploiting space-time coding strategy enables local, independent, and real-time engineering of not only amplitude but also phase profile of the contributing reflective digital meta-atoms at both central and harmonic frequencies. In the quest to realize analog signal processing using subwavelength metasurfaces, in this paper, we present the first demonstration of programmable time-modulated metasurface processors based on the key properties of spatial Fourier transformation.

Analog signal