1. Introduction

Dynamic devices are widely used in terahertz systems [1–5]. According to the feeding forms of terahertz waves, the devices can be generally divided into two types. The first is the quasi-optics device, such as various meta-surfaces, in which the terahertz propagates in the free space and is modulated by resonances, Berry phase, and so on [6–10]. The second is the on-chip device, in which the terahertz propagates on the chip, and is modulated by the mechanisms of impendence matching, on-chip resonance, and so on [11–14].

In order to realize an easy system integration, more compact dynamic device, Spoof Surface Plasmon Polaritons (SSPPs) becomes a potential breakthrough point. SSPPs are electromagnetic slow waves that exist on the surface of periodic structures [15–18]. Due to its high localization and transmission robustness, it has great potential in wide applications of on-chip transmission line decoupling, parasitic parameter suppression, and chip miniaturization [19–23]. More importantly, the transmission characteristics of SSPPs are strongly dependent on the periodic structure design, which makes the dispersion reconfiguration by structure reconstructing to be a new degree for on-chip electromagnetic wave modulation [24,25]. Especially in the terahertz band, dispersion reconfiguration becomes a powerful means of breaking through the difficult problem of weak terahertz-matter interaction to achieve efficient terahertz modulation and has demonstrated great potential for amplitude modulation and high-precision shifting [26–29].

The typical routing of dispersion reconfiguration is to embed a phase transmission material into the periodic cell in a 2D grating, which adjusts the cut-off frequency of SSPPs to realize the amplitude modulation [30–34]. It is reported that modulation with more than 12 dB modulation depth and a minimum insertion loss of 5.5 dB in the frequency region from 0.22 to 0.28 THz is presented by adjusting the SSPPs with different duty cycles [35]. In 2020, Tiejun Cui's team investigated an integrated multi-mode digital modulator based on SSPPs. By introducing PIN diodes in SSPPs, reconfigurable cells are constructed to realize different modulation schemes such as ASK and FSK [36]. In addition, taking advantage of the high localization of SSPPs, Y. Liang et al. recently achieved a high-speed terahertz OOK modulation up to 13.5 Gbps by using SSPPs metal waveguides combined with SRR [37].

Nowadays, the developing terahertz communication demands higher data capacity, higher transmission rate, and higher integration, which poses new challenges for SSPPs-based modulation in terms of operating bandwidth and transmission group delay. However, the modulation based on the dispersion reconfiguration mainly comes from the variation of the cut-off frequency of SSPPs, it tends to present strong dispersion characteristics in this frequency range, which makes it difficult to achieve low group delay in a large bandwidth. On the other hand, due to the robustness of SSPPs, large spatial structural reconstructing is often required to achieve dispersive reconfiguration, which makes the regulation circuit more and more complex and inevitably introduces more parasitic parameters. These also make it difficult to be integrated on-chip.

In this paper, we propose a scheme to reconfigure the coupling process of SSPPs to achieve efficient modulation of terahertz waves. The coupling process of terahertz waves from on-chip quasi-TEM modes to SSPPs is regulated by the phase transmission of embedded VO₂, and a full-band, low group delay, low insertion loss, and high switching ratio terahertz dynamic transmission structure is realized. At the same time, the presented structure has a small reconfiguration area, which is easy to realize multi-device integration.

2. Mechanism of coupling reconfiguration

The schematic of the presented dynamic SSPPs transmission structure is shown in Fig. 1(a), in which a coplanar grating (CG) consisting of a two-dimensional symmetric groove with a signal wire loading is fabricated on a quartz substrate. Terahertz waves are fed from the coplanar waveguide (CPW), and propagate on the CG in the mode of SSPPs. To enable the dynamic transformation of terahertz waves from quasi-TEM mode to SSPPs, a coupling area with VO₂ film embedding is designed between the CPW and CG, as shown in Fig. 1(a). In this area, the gradually changed depth of the grooves provides the longitudinal electric fields and realizes the wave vector compensation to SSPPs.

 

Fig. 1. (a) The schematic of the proposed terahertz dynamic transmission structure; (b) The dispersion relation of the symmetrical mode of SSPPs, in which the thickness of the quartz substrate is 50 µm, dielectric permittivity is 4.5 (and tangent of loss angle is 0.0004), the structure is composed of 44 periodic structures with a duty cycle of 66µm, the width of the signal line is 20µm, the depth of the groove in the periodic structure is 60µm, and the distance from the middle signal line is 50µm.; (c) The current distribution at 529 GHz; (d) The current distribution at 220 GHz.

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To make sense of the mechanism of the dynamic transmission structure, the propagation characteristic of SSPPs on the CG is studied at first. Figure 1(b) illuminates the dispersion of the symmetric mode, which is defined by the E_z field of SSPPs on the CG, as shown in the inset of Fig. 1(b). It is found that a strong dispersion character appears near the cut-off frequency of SSPPs, and the induced currents are mainly concentrated on the profile of the grooves, such as that at 529 GHz shown in Fig. 1(c). This is because, in the cut-off frequency region, the shorter wavelength indicates the boundary conditions are mainly determined by the grooves. Then the fields are confined to the grooves, and the coupling in CG is dominated by that between the grooves (groove-groove coupling, G-G coupling). While in the lower frequency region, the boundary conditions are determined by both the grooves and the signal wire for the larger wavelength, and then the field distribution is dominated by the coupling between the grooves and the signal wire (groove-signal wire coupling, G-S coupling). Accordingly, the induced currents are concentrated on the signal wire, such as that at 220 GHz shown in Fig. 1 (d). In this case, the propagating waves are perturbated by the space harmonic waves induced by the grooves to slow down the phase velocity, but the induced current distribution is still kept as that of the quasi-TEM mode, which makes the phase velocity in the promotion to the frequency. This indicates a shorter wavelength than TEM mode and a low group delay due to the weak dispersion character, which benefits the transmission of high-speed data on a small size chip.

Here, a piece of vanadium dioxide (VO₂) is embedded into the signal wire in the transmission structure to modulate the terahertz waves, as shown in Fig. 1(a). For the physical states of VO₂ can be controlled by laser illumination, the induced currents on the signal wire are adjusted, which results in the transmission control of terahertz waves. In this paper, the VO₂ is described by the Drude model, whose parameters are adapted from Ref. [35,38,39]. And the geometry size is adjusted to match the impedance of VO₂ and the middle signal line.

Figure 2 demonstrates the physical process of modulation. For the case of metallic VO₂ shown in Fig. 2 (a), the conduction current propagates along the signal wire. In the coupling area, the gradually changed profile of the ground wires makes the current present a periodic perturbation, which induces the coupling between the grooves. Then the longitudinal electric fields are generated by the periodical current, and the wave vector is compensated between quasi-TEM and SSPPs modes. Thus, the terahertz waves are transformed into SSPPs modes and propagated along the grooves, corresponding to the “ON” state, as shown in Fig. 2(c).

 

Fig. 2. The physical process of modulation: (a) The enlarged fields distribution in the transition area at “ON” status; (b) The enlarged fields distribution in the transition area at “OFF” status; (c) to (d): The fields distribution at 220 GHz for different VO₂ conductivity

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When the embedded VO₂ is changed from metallic to dielectric, the conduction current is blocked gradually, and the induced charges are accumulated, which indicates that the transformation coupling is reconfigured by VO₂, as shown in Fig. 2 (b). On the one hand, the fields proposed to provide the longitudinal field and wave vector compensation, converge on the accumulated charges to form a quasi-static mode, which disables the phase matching between the terahertz waves and SSPPs. On the other hand, the variation of the physical state of VO₂ brings the change of boundary condition, which also blocks the propagation of SSPPs. Accordingly, the terahertz waves are switched off by the decreasing conductivity of VO₂, as shown in Fig. 2 (c) to(e).

3. Analysis of coupling reconfiguration

Based on the revealed mechanism of coupling reconfiguration, the SSPPs can be modulated in an ultra-wideband range that almost covers the whole region below the cut-off frequency. The S₂₁ parameters and the group delay of the dynamic CG in the region from 110 GHz to 400 GHz, which are commonly used in terahertz communication, are illuminated in Fig. 3. First, thanks to the long-range character of the asymmetrical mode SSPPs, the proposed CG presents a rather low insertion loss, which is as low as 0.8 dB at 140 GHz, 0.55 dB at 220 GHz and 0.5 dB at 340 GHz for the VO₂ with the conductivity of 2e5 S/m. Second, owing to the broadband characteristic of the generated quasi-static fields, the terahertz waves are switched off in a wide frequency range almost covering all the regions below the cut-off frequency. It is found in Fig. 3(a) that the CG is gradually switched off by the decreasing conductivity, and the switch ratio reaches 32 dB at 140 GHz, 29 dB at 220 GHz, and 17 dB at 340 GHz for 140 S/m. Furthermore, promising group delays, which are described by $- {{d({\arg ({{S_{21}}} )} )} / {d\omega }}$, are obtained for the weak dispersion. As shown in Fig. 3(b), the group delay difference appears within 1 ps in the frequency region from 110 to 170 GHz, within 2 ps from 170 to 260 GHz, and within 14 ps from 260 to 400 GHz, respectively. As a result, the characteristics of low insertion loss, high isolation, wide bandwidth, and low group delay difference indicate the promising potential for high data-rate transmission. It is also found that both the switch ratio and group delay deteriorated by the increasing frequency, this is because that the coupling reconfiguration is weakened due to the stronger and stronger G-G coupling.

 

Fig. 3. (a) The spectra of s₂₁ of the proposed dynamic transmission structure; (b) The group delay of the proposed dynamic transmission structure, and the symbol Δ is the difference of group delay.

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According to the presented mechanism, the dynamic CG is caused by the accumulation of induced charges, which are mainly determined by the structural spatial relation. Figure 4 presents the insertion loss and isolation for different lengths of VO₂ pieces. For the metallic state, because of the Ohm loss of VO₂, the conduction currents attenuate exponentially, which induces the increase of insertion loss with increasing VO₂ length, as shown in Fig. 4. For the dielectric state, with the increase of the VO₂ length, weaker fields are generated on the next part of the signal wire, according to a larger switching ratio, as shown in Fig. 4.

 

Fig. 4. The insertion loss and switch ratio for different lengths of VO₂ pieces.

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4. Conclusion

In this paper, a dynamic transmission based on SSPPs coupling reconfiguration in a 2D coplanar grating is proposed. The reconfiguration region is constructed by embedding a VO₂ film into the signal wire in the transitional region between the coplanar waveguide and gratings, and the coupling between the quasi-TEM waves and SSPPs is reconfigured by the phase transmission of the embedded VO₂ film. When the VO₂ is in the metallic state, the fed terahertz waves are coupled to the SSPPs mode through the coupling structure. When the VO₂ is in the dielectric state, quasi-static fields are excited between the grating structure and the signal line to realize the reconfiguration of the coupling process, which destroys the wave vector compensation of the SSPPs coupling and blocks the terahertz wave transmission. On the one hand, thanks to the broadband characteristics of the quasi-static field, the fed terahertz waves can be modulated in the entire region below the cut-off frequency of SSPPs. This not only provides a rather wide bandwidth but also benefits a promising group delay due to the weak dispersion character of SSPPs in the region much lower than the cut-off frequency. On the other hand, the mechanism of coupling reconfiguration indicates that the robustness of SSPPs can be broken by a dynamic material with a rather small action area, which greatly simplifies the auxiliary circuit for SSPPs reconfiguration, and presents a great potential for on-chip integration of terahertz devices. Thus, based on this mechanism, many other terahertz modulation devices can be explored, such as modulators, phase shifters by Schottky diodes, and high electron mobility transistors. Accordingly, the presented mechanism paves a promising way for a high-performance terahertz modulation device.