THz wave is electromagnetic wave falling in the far-infrared band within the frequency ranging from 0.1 to 10 THz as a bridge between the millimeter and light waves in the electromagnetic spectrum [1,2]. With the development of information technology, the increase in the bandwidth and bit rate almost reaches the bottleneck. Moreover, the electronic circuits cannot meet the growing demand for practical applications [3]. The expansion from electronics to optics and photonics is essential. THz band is the new frontier of communications technology, and it has a great potential in developing next-generation, ultrahigh-speed communications [4,5].

Logic gates are one of the fundamental components in building THz signal processing systems and bridge the gap between electrical and optical computing. Good solid-state device compatibility, high transmission speed (light speed) endow THz waves with the capability of achieving high-speed information processing and electro-optical operation, which provides a promising solution for the fast data processing and advanced optical computing [[6], [7], [8], [9], [10], [11]]. THz logic gates play a pivotal role in THz signal processing systems and have been drawing significant attention. It is necessary to achieve efficient manipulation of THz waves. Unfortunately, conventional THz devices are usually have bulky sizes and low efficiencies due to weak interactions between natural materials and THz waves, and ultra compact active THz devices are even more lacking because of the low efficiencies of available dynamic-control approaches based on either electronic or photonic means [12,13]. MSs are two-dimensional metamaterials consisting of subwavelength planar microstructures (namely, meta-atoms), which possess customized electromagnetic wave responses and are arranged in particular global sequences, thus exhibiting extraordinary capabilities to control EM wavefronts [[14], [15], [16]]. It provides the basis for realizing a rich variety of applications such as invisibility cloaks [17,18], negative refraction [19], optical illusion [20] and epsilon near zero behaviors [21]. For the purpose of manipulating THz waves on a real-time basis, an efficient technique is to integrate standard MS with semiconductor or phase-change materials (PCM), for instance, graphene [22,23], liquid crystal [24,25], GST [26,27], and VO2 [[28], [29], [30], [31], [32], [33], [34]]. VO2 has attracted great interest as its intrinsic IMT is reversible through various external stimuli such as thermal heating [35] and optical pumping [36]. Such ability puts VO2 as a preferential candidate in electrically triggered and THz modulated hybrid MSs, and it is suitable as a photoelectric switch material. MSs embedded with VO2 may provide a new way to realize logic gates. By designing the MSs, precise control and processing of the input electromagnetic waves can be achieved, thus implementing the logical functions required for logical operations.

Recently, many MS logic gates for THz bands have been proposed, such as a reconfigurable MEMS Fano resonant MS performing THz logic gate operations. Electrical inputs present XOR and XNOR operations in the far field and NAND operation in the near-field [37]. In addition, NOR and OR Boolean operations have been shown in an all-optical THz logic gate constructed from a semiconductor-metal hybrid MS [38]. Further, THz logic gates have likewise been presented in MSs founded on spoof plasmons, within externally excited tunable MSs, and in graphene-based MSs or the MS of other integrated semiconductor materials [[39], [40], [41], [42]]. VO2-integrated MS have also received attention from some scholars and have been designed with logic functions. Ref. [43] proposed a hybrid THz MS consisting of VO2 and germanium. The AND and OR logic operations are respectively achieved at two adjacent frequency bands by weighing normalized transmission amplitude. Ref. [44] proposed an approach utilizing polarization-sensitive graphene-VO2 MS to realize a controlled-NOT logic gate. The proposed controlled-NOT logic gate enables multi-input and multi-output functionality through a dual-parameter control system. However, most of them are only confined to the construction of basic logic gates. In order to meet the needs of more complex logic operations, further research is imperative.

Motivated by the previous researches, here we propose and demonstrate a THz full-adder strategy based on electrically controlled VO2-integrated cascaded MSs. Three different structural designs of MSs are used. Coupling intensity between THz wave and each MS can be dynamically manipulated by electrically triggering the insulator-to-metal-transition (IMT) of the VO2, resulting in changes in the transmittance at 0.66 THz and thus realizing the logical operation. With a specific configuration of the input electrodes, each MS can individually realize XOR or AND logic gate operations. By cascading MSs, we can also achieve half-adder operation. By combining the THz output signals with the help of THz beam splitter (BS) and mirrors, and then calculating and comparing the normalized wave transmittance values, a complex full-adder operation is finally realized with a contrast ratio of 15.5 dB. This new configuration of THz complex combinational logic gates shows the potential for application in fields such as optoelectrical switching, THz communication, and photonics computing.