Multifield-Controlled Terahertz Hybrid Metasurface for Switches and Logic Operations

Terahertz (THz) meta-devices are considered to be a promising framework for constructing integrated photonic circuitry, which is significant for processing the upsurge of data brought about by next-generation telecommunications. However, present active metasurfaces are typically restricted by a single external driving field, a single modulated frequency, fixed switching speed, and deficiency in logical operation functions which prevents devices from further practical applications. Here, to overcome these limitations, we propose a hybrid THz metasurface consisting of vanadium dioxide (VO2) and germanium (Ge) that enables electrical and optical tuning methods individually or simultaneously and theoretically investigate its performance. Each of the two materials is arranged in the meta-atom to dominate the resonance strength of toroidal or magnetic dipoles. Controlled by either or both of the external excitations, the device can switch on or off at four different frequencies, possessing two temporal degrees of freedom in terms of manipulation when considering the nonvolatility of VO2 and ultrafast photogenerated carriers of Ge. Furthermore, the “AND” and “OR” logic operations are respectively achieved at two adjacent frequency bands by weighing normalized transmission amplitude. This work may provide an auspicious paradigm of THz components, such as dynamic filters, multiband switches, and logical modulators, potentially promoting the design and implementation of multifunctional electro-optical devices in future THz computing and communication.


Introduction
The terahertz (THz) spectral region, bridging the infrared and microwave band at 0.1-1 THz, has become one of the candidate spectra for upcoming prospective next-generation communication technology owing to its advantages of superior penetration, outstanding security and confidentiality, and high data rate with low latency [1][2][3][4][5]. To handle the imminent increase in wireless data traffic brought about by further development of societal informatization and intellectualization, there is an urgent requirement for efficient photonics and electronics devices capable of dynamically manipulating THz signals [5][6][7][8]. However, most of the natural materials are not suitable for direct THz wave modulation, which seriously hinders the applications of THz devices. Metasurfaces, favored for their customizable abilities regarding the tailoring of the amplitude, phase, and polarization of electromagnetic waves through artificially elaborated two-dimensional structures, are considered to be an effective avenue for compensating for the portability, flexibility, and reliability generally Figure 1a demonstrates the working principle of the electrically and optically controlled hybrid metasurface that consists of four materials (gold (Au), VO 2 , Ge, and sapphire). Considering the excellent chemical stability and electrical conductivity, Au was utilized to constitute electrodes and metal parts of resonant units. Four gold split-ring resonators (SRRs) were located symmetrically on the upper surface, with the middle two called SRR I and SRR II and the outer two called SRR III and SRR IV . In the common long side of SRR I and SRR II , an embedded VO 2 bridge was precisely connected to the electrodes and resonators, which could undergo a reversible phase transition triggered by the heat generated from external currents. The dielectric permittivity of VO 2 can be described using a Drude model [51]:

Materials and Methods
where ε ∞ and γ are usually assumed to be 12 and 5.75 × 10 13 rad/s, plasma frequency ω 2 p (σ) is dependent on conductivity, and σ is proportional to the free carrier density [44,52]. Additionally, to properly manipulate resonance intensity, semiconductor layers made of Ge were selected to wrap SRR III and SRR IV . The entire structure was constructed based on a sapphire substrate with excellent light transmittance. Figure 1b,c illustrate the single unit cell and its geometrical dimensions, while the detail parameters which stem from an overall consideration of the bandwidth, operating frequency, modulation depth, sensitivity, and stability of the device are listed in Table 1. The fabrication process of the device is discussed in S1 (Supplementary Material). communication, and photonics computing. Figure 1a demonstrates the working principle of the electrically and optically co trolled hybrid metasurface that consists of four materials (gold (Au), VO2, Ge, and sa phire). Considering the excellent chemical stability and electrical conductivity, Au w utilized to constitute electrodes and metal parts of resonant units. Four gold split-ri resonators (SRRs) were located symmetrically on the upper surface, with the middle tw called SRR Ⅰ and SRR Ⅱ and the outer two called SRR Ⅲ and SRR Ⅳ . In the common long si of SRR Ⅰ and SRR Ⅱ , an embedded VO2 bridge was precisely connected to the electrodes a resonators, which could undergo a reversible phase transition triggered by the heat ge erated from external currents. The dielectric permittivity of VO2 can be described usin Drude model [51]:

Materials and Methods
where ε ∞ and γ are usually assumed to be 12 and 5.75 × 10 13 rad/s, plasma frequen ω p 2 (σ) is dependent on conductivity, and σ is proportional to the free carrier dens [44,52]. Additionally, to properly manipulate resonance intensity, semiconductor lay made of Ge were selected to wrap SRR Ⅲ and SRR Ⅳ . The entire structure was construct based on a sapphire substrate with excellent light transmittance. Figure 1b,c illustrate t single unit cell and its geometrical dimensions, while the detail parameters which ste from an overall consideration of the bandwidth, operating frequency, modulation dep sensitivity, and stability of the device are listed in Table 1. The fabrication process of t device is discussed in S1 (Supplementary Material).   The proposed metasurface's performance was numerically investigated based on the time-domain solver of the full-wave electromagnetic software CST Microwave Studio 2019. Periodical boundaries were assumed to X and Y directions, and open boundaries were applied in the Z direction. The linear plane waves are normally incident with Y polarization along the negative Z direction. To imitate the phase transition of VO 2 induced by electrical voltage, conductivity was varied from 2 × 10 2 to 2 × 10 5 S/m [50,52,53]. Similarly, the conductivity of Ge was varied from 1 to 4 × 10 3 S/m to simulate the influence of optical pump irradiation [49,54]. It is essential to mention that a 400 nm optical pump (3.1 eV) is typically used to activate the photoinduced carriers in Ge (0.66 eV), and the pump frequency enables the Ge conductivity change to 4 × 10 3 S/m that only leads to a slight alteration in undoped VO 2 conductivity, thus ensuring independence between the two modulation approaches [52,[55][56][57]. The normalized transmission spectra were calculated via the formula: |T(ω)| = |E s (ω)/E r (ω)| with E s (ω) and E r (ω) representing the amplitude of THz waves transmitted through the device and the thickness of bare sapphire, respectively [58]. Figure 2a indicates the behaviors of the current directions and magnetic field (H-field) when VO 2 bridges are in the metal phase and Ge layers are unexcited, at which time strong resonances occur at the SRRs. Transmission spectra of the proposed metasurface for two materials with or without excitation are plotted in Figure 2b. To examine the working mechanism of the proposed hybrid metasurface, we separately simulated the two parts of the units, and the surface currents are shown in Figure 2c,e. Considering the nonvolatility of VO 2 , currents can flow through metal phase VO 2 bridges after excitation for a certain period, resulting in opposite current loops on SRR I and SRR II surfaces. Such a current distribution motivates a circular closure of the oscillating H-field that rotates around the two SRRs, which characterizes the appearance of the toroidal dipole and vector T in the space [16]. In the absence of optical pump influence, the conductivity of Ge is approximately equal to 1 S/m, and the current distribution on the surfaces of SRR III and SRR IV manifests an obvious magnetic dipole type. Figure 2d,f show the simulated transmission spectra for the two different types of resonance modulation. Due to the influence of contrary direction currents flowing on Au electrodes, the resonance intensity of the toroidal dipole is weaker in terms of transmission dip value.

Simulation of Electrically Tuned VO2 Bridges
We firstly investigated the electrical tuning properties of the hybrid metasurface by simply varying the conductivity of VO2 bridges in the simulation, and the normalized transmission spectra without or with the optical pump irradiation are depicted in Figure  3a,j, respectively. In the absence of external stimuli, Figure 3a presents a transmission dip of 0.02 located at 0.362 THz, accompanied by a peak of 0.95 appearing at 0.518 THz. With the increase in VO2 conductivity, the transmission valley constantly grew while the peak kept dropping. By fixing the VO2 conductivity at 2 × 10 5 S/m to imitate the ultimate outcome achieved by electrical stimulation, the transmission amplitude at 0.362 THz reached a maximum of 0.81. Meanwhile, a new dip valued at 0.26 occurred at 0.481 THz. Similarly, supposing Ge conductivity of 4 × 10 3 S/m, Figure 3j displays transmission amplitudes rising from 0.03 to 0.80 at 0.362 THz, and a peak of 0.86 at 0.508 THz is replaced by the new dip of 0.33 at 0.483 THz alongside the phase transition of VO2. To explain the modifications to transmission spectra, we modeled the alterations to the H-field transmitted through the surface by simply enhancing the VO2 conductivity and fixing the Ge conductivity to 1 S/m at 0.362 THz and 4 × 10 3 S/m at 0.483 THz, as shown in Figure 3b-i. As observed, the dip nearby 0.362 THz is caused by the strong resonance on both sides of the gold electrodes, where the H-field gathers when VO2 is in the insulator phase. Increasing the conductivity of VO2 bridges gradually permitted the flux of currents, thus resulting in

Simulation of Electrically Tuned VO 2 Bridges
We firstly investigated the electrical tuning properties of the hybrid metasurface by simply varying the conductivity of VO 2 bridges in the simulation, and the normalized transmission spectra without or with the optical pump irradiation are depicted in Figure 3a,j, respectively. In the absence of external stimuli, Figure 3a presents a transmission dip of 0.02 located at 0.362 THz, accompanied by a peak of 0.95 appearing at 0.518 THz. With the increase in VO 2 conductivity, the transmission valley constantly grew while the peak kept dropping. By fixing the VO 2 conductivity at 2 × 10 5 S/m to imitate the ultimate outcome achieved by electrical stimulation, the transmission amplitude at 0.362 THz reached a maximum of 0.81. Meanwhile, a new dip valued at 0.26 occurred at 0.481 THz. Similarly, supposing Ge conductivity of 4 × 10 3 S/m, Figure 3j displays transmission amplitudes rising from 0.03 to 0.80 at 0.362 THz, and a peak of 0.86 at 0.508 THz is replaced by the new dip of 0.33 at 0.483 THz alongside the phase transition of VO 2 . To explain the modifications to transmission spectra, we modeled the alterations to the H-field transmitted through the surface by simply enhancing the VO 2 conductivity and fixing the Ge conductivity to 1 S/m at 0.362 THz and 4 × 10 3 S/m at 0.483 THz, as shown in Figure 3b-i. As observed, the dip nearby 0.362 THz is caused by the strong resonance on both sides of the gold electrodes, where the H-field gathers when VO 2 is in the insulator phase. Increasing the conductivity of VO 2 bridges gradually permitted the flux of currents, thus resulting in a toroidal resonance that affected SRR I and SRR II . This was followed by a certain coupling resonance with SRR III and SRR IV , signified by the transmitted H-field inside. Finally, as VO 2 conductivity was set to 2 × 10 5 S/m, the magnetic field surrounding the electrodes tended to vanish, and a toroidal resonance impacted SRR I and SRR II thereby leading to a transmission dip near 0.483 THz.
Nanomaterials 2022, 12, x FOR PEER REVIEW 6 of 12 a toroidal resonance that affected SRR Ⅰ and SRR Ⅱ . This was followed by a certain coupling resonance with SRR Ⅲ and SRR Ⅳ , signified by the transmitted H-field inside. Finally, as VO2 conductivity was set to 2 × 10 5 S/m, the magnetic field surrounding the electrodes tended to vanish, and a toroidal resonance impacted SRR Ⅰ and SRR Ⅱ thereby leading to a transmission dip near 0.483 THz. To quantitatively analyze the effect of electrical tuning, we adopted modulation depth (MD) to measure the switching ability of the device when dynamically manipulating the transmission of THz waves. For the purpose of precisely unveiling the conversion degree, MD is defined as: where Ton or Toff represents the transmission amplitude when the device is on or off, respectively. By fixing the conductivity of Ge layers at 1 S/m, Figure 4a  To quantitatively analyze the effect of electrical tuning, we adopted modulation depth (MD) to measure the switching ability of the device when dynamically manipulating the transmission of THz waves. For the purpose of precisely unveiling the conversion degree, MD is defined as: where T on or T off represents the transmission amplitude when the device is on or off, respectively. By fixing the conductivity of Ge layers at 1 S/m, Figure 4a

Simulation of Optically Tuned Ge Layers
The optical tuning properties of the proposed hybrid metasurface were investigated by simply varying the conductivity of Ge layers in the simulation, and the normalized transmission spectra without and with the electrical voltage excitation are depicted in Figure 5a,j. It was noticed that the transmission valley kept elevating with the increase in the conductivity of Ge layers. Independent of external stimuli, a transmission dip of 0.11 emerged at 0.565 THz, which then gradually rose to 0.469 as the conductivity of Ge layers was set to 4 × 10 3 S/m. Identically, by fixing VO2 conductivity to 2 × 10 5 S/m, a transmission dip of 0.285 occurred at 0.585 THz, which finally rose to 0.654 with the enhancement to the conductivity of Ge layers. Supposing VO2 conductivity of 2 × 10 2 and 2 × 10 5 S/m, changes in the transmitted H-field with the increase in Ge conductivity at 0.565 and 0.585 THz were observed, as shown in Figure 5b-i. Without optical pumping, the H-field was concentrated inside SRR Ⅲ and SRR Ⅳ , indicating the predominant position of magnetic dipole resonance in the transmission dip generation. As the Ge layer conductivity elevates, the gradual convergence of the magnetic field toward the electrodes and inside SRR Ⅰ and SRR Ⅱ manifests the dropped proportion of the magnetic dipole in the suppressed transmission. Meanwhile, the alternations in the H-field also disclose that other resonance modes are induced due to the interactions with SRR Ⅲ , SRR Ⅳ , and nearby unit structures. Overall, the resonance strength of the whole unit tends to decline, resulting in improvements in the transmitted H-field and the consequent amelioration of transmission amplitude.

Simulation of Optically Tuned Ge Layers
The optical tuning properties of the proposed hybrid metasurface were investigated by simply varying the conductivity of Ge layers in the simulation, and the normalized transmission spectra without and with the electrical voltage excitation are depicted in Figure 5a,j. It was noticed that the transmission valley kept elevating with the increase in the conductivity of Ge layers. Independent of external stimuli, a transmission dip of 0.11 emerged at 0.565 THz, which then gradually rose to 0.469 as the conductivity of Ge layers was set to 4 × 10 3 S/m. Identically, by fixing VO 2 conductivity to 2 × 10 5 S/m, a transmission dip of 0.285 occurred at 0.585 THz, which finally rose to 0.654 with the enhancement to the conductivity of Ge layers. Supposing VO 2 conductivity of 2 × 10 2 and 2 × 10 5 S/m, changes in the transmitted H-field with the increase in Ge conductivity at 0.565 and 0.585 THz were observed, as shown in Figure 5b-i. Without optical pumping, the H-field was concentrated inside SRR III and SRR IV , indicating the predominant position of magnetic dipole resonance in the transmission dip generation. As the Ge layer conductivity elevates, the gradual convergence of the magnetic field toward the electrodes and inside SRR I and SRR II manifests the dropped proportion of the magnetic dipole in the suppressed transmission. Meanwhile, the alternations in the H-field also disclose that other resonance modes are induced due to the interactions with SRR III , SRR IV , and nearby unit structures. Overall, the resonance strength of the whole unit tends to decline, resulting in improvements in the transmitted H-field and the consequent amelioration of transmission amplitude. The MD of the metasurface controlled by the optical stimulation was also calculated, as shown in Figure 6a,b. As the conductivity of Ge layers reached 4 × 10 3 S/m, the maximum MD reached 77.08% at 0.565 THz and 56.36% at 0.585 THz for two different states of VO2 bridges. The reason for the difference can be interpreted by the changing resonance modes between the gold electrodes and SRRⅠ and SRRⅡ, which in turn leads to disparate coupling strengths with the adjacent SRRⅢ and SRRⅣ.  The MD of the metasurface controlled by the optical stimulation was also calculated, as shown in Figure 6a,b. As the conductivity of Ge layers reached 4 × 10 3 S/m, the maximum MD reached 77.08% at 0.565 THz and 56.36% at 0.585 THz for two different states of VO 2 bridges. The reason for the difference can be interpreted by the changing resonance modes between the gold electrodes and SRR I and SRR II , which in turn leads to disparate coupling strengths with the adjacent SRR III and SRR IV . The MD of the metasurface controlled by the optical stimulation was also calculated, as shown in Figure 6a,b. As the conductivity of Ge layers reached 4 × 10 3 S/m, the maximum MD reached 77.08% at 0.565 THz and 56.36% at 0.585 THz for two different states of VO2 bridges. The reason for the difference can be interpreted by the changing resonance modes between the gold electrodes and SRR Ⅰ and SRR Ⅱ , which in turn leads to disparate coupling strengths with the adjacent SRR Ⅲ and SRR Ⅳ .

Logic Operation Controlled by a Multifield
The proposed hybrid metasurface could find wide application. For instance, we further extended our design to realize the logic operation function. Two external input signals were configured as the voltage and optical pump, and the defined "0" and "1" input conditions with or without an external stimulus were respectively imitated by assigning the conductivity of VO 2 bridges to 2 × 10 2 S/m or 2 × 10 5 S/m and Ge layers to 1 S/m or 4 × 10 3 S/m. Notably, the output signals were contingent on weighing the normalized amplitude of transmitted THz waves through standardization of the transmission spectrum of the minimum valley in the frequency range. By exploiting the performance of the device controlled by the electrical and optical methods at 0.56-0.57 THz and 0.58-0.59 THz, the logical operation of two different gates can be independently realized, as depicted in Figure 7.

Logic Operation Controlled by a Multifield
The proposed hybrid metasurface could find wide application. For instance, we further extended our design to realize the logic operation function. Two external input signals were configured as the voltage and optical pump, and the defined "0" and "1" input conditions with or without an external stimulus were respectively imitated by assigning the conductivity of VO2 bridges to 2 × 10 2 S/m or 2 × 10 5 S/m and Ge layers to 1 S/m or 4 × 10 3 S/m. Notably, the output signals were contingent on weighing the normalized amplitude of transmitted THz waves through standardization of the transmission spectrum of the minimum valley in the frequency range. By exploiting the performance of the device controlled by the electrical and optical methods at 0.56-0.57 THz and 0.58-0.59 THz, the logical operation of two different gates can be independently realized, as depicted in Figure 7. The data in Figure 7a illustrate the "OR" logic gate executed by the metasurface. Here, the transmission spectrum when applying no external excitation (whereby VO2 conductivity was 2 × 10 2 S/m and Ge conductivity was 1 S/m) was assumed to have the criterion value of 1. The other normalized amplitudes are observed to be more than four times greater in the range of 0.56-0.57 THz. Therefore, the output of amplitude can be considered as "0" in the absence of stimuli and "1" when modulated by either one or both of the approaches. Figure 7b illustrates the "AND" logic gate in the range of 0.58-0.59 THz, where the transmission spectrum was assumed to be the criterion at the VO2 conductivity of 2 × 10 5 S/m and the Ge conductivity of 1 S/m. Except for the output tuned by both methods, which was taken as "1" for its amplitude being more than double that of others, the remainders were taken as "0" (for simply one or no stimulus).
From the above analysis, the basic but critical "OR" and "AND" logic operation gates can be implemented, which greatly expands the application of the device. These logic gates are intended not only for simple numerical calculations, but also for functional operations applicable to many scenarios, such as read-erase-write manipulation of information that needs a clear amplitude difference from "1" and "0" output. Considering the "AND" logic gate, the device can output a "1" by individually modulating either VO2 or Ge, thus supplying two degrees of output timing freedom. From the "OR" logic gate, both materials need to be excited together to output a "1". However, due to the memory property of VO2, it is possible to stimulate Ge at a certain frequency during the phase transition The data in Figure 7a illustrate the "OR" logic gate executed by the metasurface. Here, the transmission spectrum when applying no external excitation (whereby VO 2 conductivity was 2 × 10 2 S/m and Ge conductivity was 1 S/m) was assumed to have the criterion value of 1. The other normalized amplitudes are observed to be more than four times greater in the range of 0.56-0.57 THz. Therefore, the output of amplitude can be considered as "0" in the absence of stimuli and "1" when modulated by either one or both of the approaches. Figure 7b illustrates the "AND" logic gate in the range of 0.58-0.59 THz, where the transmission spectrum was assumed to be the criterion at the VO 2 conductivity of 2 × 10 5 S/m and the Ge conductivity of 1 S/m. Except for the output tuned by both methods, which was taken as "1" for its amplitude being more than double that of others, the remainders were taken as "0" (for simply one or no stimulus).
From the above analysis, the basic but critical "OR" and "AND" logic operation gates can be implemented, which greatly expands the application of the device. These logic gates are intended not only for simple numerical calculations, but also for functional operations applicable to many scenarios, such as read-erase-write manipulation of information that needs a clear amplitude difference from "1" and "0" output. Considering the "AND" logic gate, the device can output a "1" by individually modulating either VO 2 or Ge, thus supplying two degrees of output timing freedom. From the "OR" logic gate, both materials need to be excited together to output a "1". However, due to the memory property of VO 2 , it is possible to stimulate Ge at a certain frequency during the phase transition after the excitation of VO 2 , thereby achieving a continuous ultrafast output of "1". Therefore, the device we propose possesses some similar functions, such as time-controlled readerase-write operations. It also has simple time-manipulated information encryption and decryption capabilities when information is being read or written, which undoubtedly enhances the capability of contemporary VO 2 -or Ge-based information processing.

Conclusions
In summary, we have theoretically demonstrated a VO 2 and Ge hybrid metasurface that supports electrical and optical control methods individually or simultaneously. To reveal the working mechanism of the designed device, the surface current and transmitted H-field were simulated, which testifies to the dominant role of the toroidal and magnetic dipole resonance strength respectively occupied by the two kinds of material components arranged in the meta-atoms. The switch on-off behaviors and modulation capability at four different frequencies were then investigated. Considering the distinct properties of modulated materials and tuning methods, the four switches possess nonvolatile or temporary on-off speeds to capture two kinds of temporal degrees of freedom. Furthermore, upon active excitation by two stimuli, the device manifests the logical operation functions of "AND" or "OR" gates in two frequency bands, which was confirmed by weighing normalized transmission amplitude. By integrating VO 2 and Ge in one device, we have attained a THz metasurface with performance far beyond that of devices equipped with only one single material. Looking forward, such a hybrid metasurface with multiple functions and modulatory degrees of freedom could hold potential for THz photonic and electric meta-device design, which may greatly facilitate applications in data storage, ultrahigh-speed wireless communication, and optic-electric digital processing.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/nano12213765/s1, S1: Discussion of available fabrication process of the proposed device.