Terahertz (THz) technology has the potential to transform high-rate communications, high-precision radar, and high-resolution imaging applications [1–5]. THz communication systems using digitally coded modulation can provide ultra-high data rates for future wireless communication [6–9]. The demand for THz systems has made effective dynamic control of the phase and amplitude a global research focus, whose conventional strategies rely on dynamic metasurfaces employing tunable materials [10–12]. Since the first work of THz phase manipulation using a doped-semiconductor metasurface in 2009 [13], numerous types of THz phase modulation metasurfaces have emerged [14–17]. However, this method typically performs phase modulation near the resonance frequency, where the amplitude and phase change drastically, exhibiting undesirable amplitude fluctuations and limited phase shift accuracy (minimum step of the phase shift) [18–20]. Moreover, all of these devices operate with free-space THz beams making them bulky.

Modulating THz waves in the guided-wave mode has proven effective in overcoming the existing limitations, enabling superior performance such as high-speed amplitude modulation, high-precision phase shifting, and high power handling [21–23]. Moreover, wide-range high-precision guided-THz-wave phase manipulation enables low-error calibration for terahertz measurement systems and terahertz coherent-demodulation communication links. However, the on-chip THz phase shifter still faces challenges in achieving both high phase shift precision and wide phase shift range simultaneously [24–26]. Furthermore, Cui et al. proposed information metamaterials, which consist of coded metamaterials digitized as “0” or “1” to achieve complex functions [27–31]. We believe introducing information metamaterials into a guided-wave system with special array design and digital coding can break through the precision limitation of independent meta-units. This approach is analogous to super-resolution imaging, which uses meta-lens and digital processing to break the limitation of the lens diameter on imaging resolution, so we termed this approach “super-resolution precision phase modulation.” Our previous work preliminarily verified this strategy by achieving a high phase shift accuracy of 2° using a coding unit array, while each unit exhibited a phase shift of ∼10°. However, our previous device still suffers from a small phase shift range [22].

In this paper, we employ a new waveguide-inserted needle meta-structure to realize super-resolution precision phase manipulation. As illustrated in Fig. 1(a), the proposed strategy consists of a rectangular waveguide and a digitally coding needle meta-chip. THz waves are efficiently coupled to the meta-chip through the charge aggregation effect of the needle tips, and then the electronic transport characteristics of Schottky diodes are regulated to control the charge accumulation amount in each part [Fig. 1(b)]. The charge distribution can affect the THz resonance strength, yielding the phase shifts. More importantly, in the array shown in Fig. 1(a), a large charge accumulates on the needle tips with sub-λ/10 spacing, resulting in near-field coupling between tips. This near-field intercoupling resonance from different coding voltages yields nonlinear phase superposition, revolutionizing previous coding phase manipulation mechanisms to enable superior performance. Leveraging 8-bit phase shift units with ∼20° per unit, we achieve a total of 256 coding states through nonlinear phase superposition, thereby forming a marvelous phase shift database with a phase shift accuracy of up to 3°. Ultimately, a phase shift exceeding 170° is achieved at 213.2 GHz, with a 3° precision and a mean absolute error of only 0.642°, demonstrating super-resolution precision phase modulation capabilities.

As shown in Fig. 1, this needle meta-structure unit is grown on 50-μm-thick quartz, featuring a gapped needle-shaped metal strip, an enhancing-branch, a grounding structure, a feed structure, and a GaAs Schottky diode. Here, the GaAs Schottky diode is flipped and embedded in the gap of the needle-shaped metal strip, with the grounding structure next to the diode’s cathode and the feed structure behind the diode’s anode. The needle tip of the meta-structure unit is inserted into the rectangular waveguide through a small hole in the Y–Z plane. The THz waves propagate in the Z direction along the rectangular waveguide. Figure 1(b) illustrates the connection between the GaAs Schottky diode and the needle meta-structure (detailed model in Appendix A.1). When the Schottky diode switches from the off state to the on state, it becomes an electron transport channel; hence, the current on the diode transitions from an induced current to a conduction current. In turn, the charge distribution of the meta-structure is altered, resulting in resonance strength modulation and phase shifting. Notably, the enhance-branch can increase the resonance strength and phase shifting range.

When the external bias voltage is 0 V, the Schottky diode acts as a capacitor. At this point, the meta-structure unit couples with the THz wave, and the anode and cathode of the Schottky diode trap massive charge, resulting in a strong LC resonance as shown in Fig. 2. Eventually, it enhances the induced current shown in Figs. 2(d) and 2(e), causing the current to be transmitted over the entire surface of the diode. Furthermore, the strong current causes a large charge accumulation at the tip and generates a strong electric field [Figs. 2(c) and 2(d)], which we call the “1” state. Upon application of a 1 V bias voltage, the Schottky diode becomes a charge transport channel, at which time the strong resonance peak weakens and red shifts from 190 to 170 GHz. The diode no longer enhances the induced current of the coupled THz wave, so the current transport concentrates on the line [Figs. 2(d) and 2(e)]. Consequently, the charge on the needle tip decreases, and the electric field (E-field) becomes weak in Fig. 2(c), which is called the “0” state.

The switching from strong to weak resonance caused by the state-changing brings about drastic amplitude fluctuations and phase jumps [Figs. 2(a) and 2(b)], rendering them unsuitable for phase modulation. However, phase modulation with reduced amplitude fluctuations can be achieved outside the resonance region, specifically in the 210–230 GHz range. Furthermore, Figs. 2(a) and 2(b) show that the enhancing-branch strengthens the strong resonance peak, achieving an increase in phase shift from 15° to 20.3° at 220 GHz. This indicates that the enhancing-branch placed right next to the diode’s cathode also traps the charge and boosts the induced current of the coupled THz wave [Figs. 2(d) and 2(e)]. Therefore, in the same “1” state, the E-field at the tip is slightly weaker without the enhancing-branch than with it, as depicted in Fig. 2(c). To summarize, in combination with the enhancing-branch, the amplitude curves appear to intersect at 215.5 GHz when the diode switches states within the 213–227 GHz range, exhibiting a maximum transmission loss of 2.1 dB. Meanwhile, state transitions result in a phase shift of about 20.3°. In our further investigation of the single unit, adjusting the distance from the needle tip to the waveguide center and the distance from the diode anode to the center allows us to tailor the amplitude and phase shift, thereby obtaining a broadened operation band.

As mentioned above, the charges are trapped in different parts of the meta-structure (tip, anode, cathode, and enhancing-branch), producing resonances and phase shifts. Due to the massive current flowing towards the tip of the needle, the accumulated charge is immense. When two tips are placed symmetrically at a distance of 90 μm (0.06λ), as shown in Figs. 3(a) and 3(b), an odd-mode charge distribution is exhibited while generating a strong odd-mode intercoupled E-field. This means that when multiple needle meta-structures are present, the THz resonance generated by a single unit will be affected by the others.

Here, we placed four centrally symmetric needle meta-structure units on a quartz substrate, each of which can be independently set to either the “0” state or the “1” state. Figures 3(c)–3(f) show that we encoded four needle meta-structure units in sequences “0000,” “0101,” “1100,” and “0110.” The sequence “0000” is the reference, and the other three sequences similarly have two units in the “1” state, encompassing all possible coding sequences under centrosymmetric space. Under coding “0000,” the E-fields on the tips of all four metal needles are negligible without interfering with each other. However, Fig. 3(d) shows that under code “0101,” the strong resonant state and the weak resonant state are opposite in the X direction, resulting in energy interferences between two tips. At coding “1100,” the two tips with strong resonant states are side-by-side in the Z direction, and besides the E-field interferences between the strong and weak states, the strong-strong electric field interferences are even more intense [Fig. 3(e)]. In addition, under the coding “0110,” dramatic intercoupling occurs between the E-fields of the opposing strong resonances in the X-direction inducing a large insertion loss, whereas the weak-strong E-field interference disappears due to the distant separation of the tips in the Z-direction [Figs. 3(f) and 3(g)]. Even if the voltage of one unit is constant, its E-field distribution is influenced and varied by the other units, which clearly indicates the nonlinear interactions within the needle’s meta-structure unit array.

Figures 3(g) and 3(h) further illustrate the nonlinear interactions by presenting amplitude and phase variations for the coding sequences. Naturally, the coding “0000” features a single resonance peak at 170 GHz due to the superposition of four weak resonances. Notably, although all three other coding sequences contain two “1” states, their resonance peaks are completely different, corresponding to different phase jump frequencies. Figure 3(h) shows that the phase shifts of these coding sequences are separated into three curves in terms of “0000,” meaning different output phase shifts and a nonlinear phase superposition of the array. Figures 3(f) and 3(g) indicate that strong intercoupling increases energy dissipation in the diode series resistance (Rs); hence, reducing Rs can mitigate amplitude fluctuations. Additionally, due to the nonlinearity of the near-field coupling, adjusting the tip-tip distance to design resonance points and phase shifts facilitates better performance for wider bandwidth.

We further exploit this nonlinearity to provide a richer selection of different phase shifts by determining all phase shifts for each frequency, similar to a coded phase database. Figure 4 presents the database simulation results for an 8-unit meta-chip consistent with Fig. 1. With 256 coded sequences, the simulation results demonstrate phase modulation over a 180° range with an S21 parameter greater than −11dB in the 213–227 GHz range. Thanks to the optimized phase shift coding sequences from the database, the high insertion loss situations (such as the “0110”) can be avoided to realize lower amplitude fluctuations. More prospectively, by combining our 180° super-resolution precision phase shifting with a 0°–180° fixed phase shifting (1-bit inverter), full 360° phase shift coverage can be effectively achieved for a wider range of applications. This approach preserves the accuracy of the phase shift (minimum step of 3°) while maintaining a low coding complexity of 512 coding sequences.

To demonstrate the super-resolution precision phase shifting using the digitally coding needle meta-chip [Figs. 5(b) and 5(c)], we fabricated the meta-structure on the quartz substrate, flip-flopped the Schottky diode, and assembled the meta-chip in a metal cavity. The RT-5880 circuit (Rogers Corporation) enables external voltage inputs for digital phase manipulation (see Appendix A.2 for device processing). Figure 5(a) illustrates that we acquired the experimental amplitude and phase data by utilizing a terahertz vector network analyzer (THZ-VNA) and the external coding voltages (refer to Appendix A.3 for details). The experimental results for all 256 possible coding sequences in the 213–227 GHz range are shown in Figs. 5(d) and 5(e). The experimental phase shifts exceed 180° and even reach 210° at 213 GHz with a <15dB insertion loss. The nonlinear superposition results are in good agreement with the simulation results in Fig. 4.

Furthermore, by applying the phase shift database, the optimized coding sequences can achieve the desired performance, such as ultra-precision phase shift with low amplitude fluctuations. As shown in Fig. 6, the meta-chip realizes phase shift accuracies of 11.25°, 5.625°, and 3°. At 213.2 GHz, the phase shift accuracy of 11.25° (>200° shift range, <14dB insertion loss) is demonstrated in Fig. 6(a). As the number of encodings increases, the phase shift accuracies of 5.625° and 3° are achieved at 213.2 GHz in Figs. 6(b) and 6(c), with maximum phase shifts of 180° and 171°, respectively. At the 3° phase shift accuracy, its mean absolute error (MAE) is only 0.642°, demonstrating a wide range of phase shifts with extremely high precision and low error.

Figures 6(d)–6(f) present remarkable results at 220 GHz, where a 180° phase shift is achieved with 11.25° accuracy and an MAE of only 0.5528°. Meanwhile, the amplitude varies in a small range of 7.8–10.5 dB. When the phase shift is 180° (5.625° accuracy) and 156° (3° accuracy), the amplitude fluctuation is also small, with an MAE of 0.403° and 0.623°, respectively. Figures 6(g)–6(i) further validate the wide phase shift range with ultra-high precision at 226.7 GHz. The meta-structure unit offers a phase shift of 20°; however, the array achieves an ultra-high precision phase shift of 3°, realizing super-resolution precision phase modulation. In addition, the diode cutoff frequency fc=1/(2π×Rs×Cj) estimated from the Rs and Cj (0 V) is about 1.061 THz, and our previous studies [4,32] of amplitude modulators using similar diodes demonstrated modulation rates exceeding 30 GHz. These results indicate the potential for high modulation rates in our device.

In summary, our digitally coding needle meta-chip employs the nonlinear phase shift superposition within needle meta-structure array to realize super-resolution precision phase shifting, which is a new method of terahertz ultra-high precision modulation. This nonlinear phase superposition from the near-field intercoupling resonance revolutionizes previous coding phase manipulation mechanisms, enabling outstanding performance. Upon independent 256 coding sequences, it can achieve a total phase shift exceeding 180° in the 213–227 GHz range. Following optimized coding, the meta-chip enables a 3° precision phase shift with a phase shift range of up to 171° at 213 GHz, with an MAE of only 0.642°. At 220 GHz, the MAEs of phase shifts at 11.25°, 5.625°, and 3° accuracies are all lower than 0.623°, with an amplitude fluctuation of only 2.7 dB. Our meta-chip exhibits remarkable advantages in phase shift range, accuracy, and amplitude fluctuation, making it an ideal device for future THz high-precision applications.