## Introduction

Driven by the global demand for high-data-rate communication links, the use of terahertz (THz) radiation1 (with frequencies spanning the range between 0.1 and 10 THz) to carry data-streams will soon become unavoidable2. Despite the recent dramatic push towards THz wireless communications3,4,5, THz waveguides serve as an indispensable alternative when a free-space propagation approach is unfeasible6,7,8. In general, THz waveguides that can preserve both the broad bandwidth and low dispersion of a free-space link are desirable. Metal waveguides that support transverse electromagnetic (TEM) modes, such as parallel-plate waveguides9 (PPWGs) and two-wire waveguides10 (TWWGs), are promising candidates due to their capabilities to support the low-loss and low-dispersion propagation of broadband THz pulses. In particular, compared to the large footprints of PPWGs, TWWGs have several distinct advantages, including structural simplicity11, tolerance to bending12, and affinity to cables for efficient and straightforward connections13. Besides the efficient guiding of broadband THz pulses, these waveguides are expected to provide a number of options for versatile signal processing14,15. However, in contrast to the recent advances in PPWG-based signal-processing devices, such as power splitters16, multiplexers/demultiplexers17,18, and add-drop filters19, few signal-processing functionalities have been realized in TWWGs. The underlying reason is that the modal energy is tightly confined in the wavelength-scale space between the two wires10, which limits the possible ways to manipulate the propagating THz waves. While Bragg gratings, considered among the most fundamental processing units, have been realized in TWWGs, they typically rely on a hybrid approach that requires inserting standalone metalized papers20,21 or dielectric gratings22 into the waveguides. This, in turn, severely hampers the realization of more sophisticated devices and complex processing functionalities.

Here, we introduce a universal approach for the realization of broadband THz signal processing in metal-wire waveguides by engineering the wire surfaces, in turn leading to the realization of Bragg gratings directly on the metal-wires without the need of introducing additional materials. This is because the THz guidance in metal-wire waveguides is based on the propagation of THz surface plasmon polaritons (SPPs) along the metal-air interface, which is extremely sensitive to the metal surface conditions. Such an approach can be incorporated into innovative waveguide designs, further allowing for the realization of more complex signal-processing functionalities. As a proof-of-concept, we propose a versatile metal-wire waveguide topology, namely a four-wire waveguide (FWWG), which is capable of sustaining two independent and orthogonally polarized fundamental modes, thus acting as a broadband polarization-division multiplexer. By integrating Bragg gratings on metal-wires into such a component, we demonstrate the independent manipulation of polarization-division multiplexed THz signals. The proposed device enables polarization-division multiplexing in waveguides with remarkable structural simplicity, while featuring unprecedented capabilities towards processing multiplexed signals over a broad THz frequency range.

## Results

### Directly engraving of multiscale-structured Bragg gratings on metal-wires

When a periodic array of grooves is engraved on the metal surface, surface states behaving like SPPs, so-called spoof SPPs, can be supported23. Depending on the spatial period, a subwavelength-scale (sub-λ) periodic structure can be treated as an effective medium, while a wavelength-scale periodic structure behaves as a Bragg grating24. Figure 1a shows a sub-λ periodic array of grooves in a TWWG. The dispersion relation of such a structure (Fig. 1c) is not linear and the group velocity vg of the spoof SPPs decreases as the frequency increases. In addition, a cut-off frequency fc occurs at ~1.2 THz, indicating that the spoof SPPs at such a frequency are inhibited25 and the frequencies above fc cannot be guided (Fig. 1d). The propagation characteristics (i.e., vg and fc) of the spoof SPPs can be tailored by engineering the depth of the grooves d and the duty cycle w/p25 (see Supplementary Note 1). When the geometry of the grooves is adjusted to the wavelength scale, fc will accordingly shift to a lower frequency range, in turn narrowing the operating bandwidth of the waveguide. In addition, from a practical viewpoint, fabricating trenches with a wavelength-scale geometry on metal-wires is simply not feasible, since it would greatly lower the robustness of the wires, thus potentially leading to their fracture when tension is applied. More importantly, by engraving grooves with a single periodicity on the metal-wires, it is impossible to achieve a Bragg resonance spanning the operating THz bandwidth.

To overcome this issue, while maintaining the operating bandwidth and the wire robustness, we introduce in the THz domain the concept of multiscale structures (Fig. 1b), realized by superimposing a wavelength-scale periodic modulation of T = 280 µm onto the sub-λ periodic grooves (see Supplementary Note 1). The dispersion relation of the multiscale grooves (Fig. 1c) indicates the existence of a Bragg bandgap at 0.53 THz, given by fBragg = c/(2T)26, where c is the speed of light. The THz electric field distributions also confirm the occurrence of a notch frequency at 0.53 THz (Fig. 1e), consistent with the Bragg condition, and the local trapping of the THz energy at 1.0 THz (Fig. 1f). We fabricate a TWWG with integrated Bragg gratings (see Methods) by directly engraving the multiscale grooves along one of the two wires. As shown in Fig. 1g, the experimental transmission spectrum exhibits a Bragg resonance at ~0.53 THz with a notch depth of ~25 dB, which matches the simulated transmission spectrum quite well. The achieved linewidth of such a Bragg resonance (with a Q-factor of ~479.5) is remarkably narrow, due to the application of a large number of periods (150 periods). By varying the wavelength-scale modulation T, the location of the Bragg resonance can be easily tuned over a broad frequency range within 1 THz.

### Polarization-division multiplexing of THz pulses within FWWGs

Building on the concept of TWWG, we introduce the FWWG platform, which features excellent capabilities in terms of signal transporting (see Supplementary Note 2). The FWWG consists of four identical copper wires (radius r = 127 µm) equally separated by an air gap (g = 300 µm), arranged into a square geometry, as depicted in Fig. 2a. Its two fundamental modes, TEMx (Fig. 2b) and TEMy (Fig. 2c), exhibit symmetric field profiles, which are equally divided into two identical portions along the axes. Notably, each portion of the field distribution is mainly confined in-between the two corresponding wires and shows a similar profile to that of the TWWG, thus indicating that the FWWG can also be efficiently accessed by a linearly polarized THz beam. Specifically, TEMx is excited within the FWWG by an x-polarized THz beam, while TEMy is excited by a y-polarized THz beam. Remarkably, the FWWG is capable of guiding linearly-polarized THz signals with arbitrary polarization directions. This is because an arbitrary linearly-polarized THz beam coupled into the FWWG is decomposed into the two orthogonal polarization states, which then propagate independently in terms of its fundamental TEM modes. Experimental results detailed in Supplementary Note 2 extensively prove the ability of the FWWG to couple and transmit broadband THz pulses with arbitrary linear polarization directions in a low-loss and low-dispersion manner. It is worth mentioning that, in contrast to all the other existing THz waveguides27, this is a unique characteristic of the FWWG.

In particular, based on its two fundamental TEM modes, the FWWG is able to support the independent propagation of two THz pulses multiplexed along the two different polarization axes. For the experimental demonstration, we employ a customized THz time-domain spectroscopy (TDS) system (Fig. 3) with two transmitters (Tx1 and Tx2, generating the x- and y-polarized beams, respectively) and a single receiver (configured as Rx1 or Rx2 depending on the selected polarization direction). We compare the signals detected via Rx1 and Rx2, under different ON/OFF configurations of Tx1 and Tx2, as shown in Fig. 4. When Tx1 is ON and Tx2 is OFF, the signal from Tx1 is detected via Rx1 and exhibits a single-cycle shape, indicating that the propagation in the FWWG is nearly dispersion-less; when Tx1 is OFF but Tx2 is ON, no significant signal from Tx2 is detected via Rx1, and the corresponding spectra demonstrate an extinction ratio exceeding 20 dB. Concerning the scheme adopted for polarization-division multiplexing, when both Tx1 and Tx2 are ON, the overall signal retrieved via Rx1 and its spectrum is almost identical to those observed when only Tx1 is ON, indicating a negligible contribution from Tx2. When the receiver is switched to Rx2, the results obtained under various ON/OFF configurations exhibit a behavior consistent with the Rx1 configuration (see Fig. 4c, d). Our observations demonstrate that the FWWG can provide the low-loss, almost dispersion-free, and independent propagation of two broadband THz pulses with orthogonal polarization states, and as such, it can be operated as a broadband polarization-division multiplexer.

### Independent manipulation of polarization-division multiplexed THz pulses

Finally, we integrate the Bragg gratings on metal-wires into the FWWG, in turn allowing us to realize the independent manipulation of two polarization-division multiplexed broadband THz pulses. We fabricate a FWWG with integrated Bragg gratings by engraving the designed multiscale grooves along the two wires on one side of the FWWG (see Fig. 5a). The transmission spectra of the FWWG with Bragg gratings engraved on different wires are investigated in Supplementary Note 3. Since the grooves are cut along the y-direction (in turn making them face along the x-direction) and they are relatively shallow (only 40 µm in depth), they mainly interact with the x-polarized THz beam and barely influence the y-polarized THz beam in the FWWG (see Supplementary Note 5). As a result, this device should ideally feature a notch filter at 0.53 THz for the x-polarized THz beam, while behaving as an all-pass filter for the y-polarized THz beam. We perform the experimental characterization using the system in Fig. 3 when both Tx1 and Tx2 are ON. As shown in Fig. 5c, compared to the reference (i.e., no grooves), the signal received via Rx1 is attenuated in amplitude and delayed in time. In particular, a long-lasting ringing signal is observed corresponding to the strong Bragg resonance in the frequency domain. In contrast, the signal detected via Rx2 displays the same pulse shape, yet with a slightly lower peak than that of the reference, demonstrating the practically negligible influence of the grooves on the y-polarized THz beam.

We investigate the transmission spectra of this device, as shown in Fig. 5d. For Rx1, the experimental transmission spectrum clearly exhibits a Bragg resonance at ~0.53 THz with a notch depth exceeding 20 dB as expected. We note that limited by the fabrication precision of periodic grooves, the Bragg resonance frequencies realized on the two different wires may not exhibit exactly the same value. In addition, due to the imperfect control over the tension manually applied onto the wires, a slight, yet unequal stretch of the periods affects both the sub-λ and wavelength-scale structures hosted on different wires. As a result, the overlap of two slightly shifted Bragg resonances leads to the formation of a seemingly single resonance with a wider linewidth. This fact may explain why the Q-factor of the observed Bragg resonance (which is ~105.2) is smaller than what we predict in our simulations. Moreover, a non-Bragg bandgap occurs at 0.59 THz in the simulated transmission spectrum. In fact, the origin of this non-Bragg bandgap is attributed to a half-wavelength delay28 between the THz electric fields propagating along the asymmetric structure. Figure 5e reveals that the electric field propagating on the side containing the grooves is out of phase with respect to the field propagating on the unetched side. Both location and notch depth of the non-Bragg bandgap are affected by the shifts between the grooves on the two wires, where the notch depth reaches a maximum when the grooves are perfectly aligned (see Supplementary Note 4). In the experiments, due to the uneven tightening of the wires, the shifts between the grooves on different wires are non-consistent, as observed in Fig. 4b. This explains why we cannot identify the non-Bragg bandgap, but rather observe an additional ~6 dB loss across the range from 0.6 to 0.9 THz. Nevertheless, these shifts have no impact on the Bragg resonance (see Supplementary Note 4), and thus do not influence the designed filtering function. For Rx2, the experimental transmission spectrum exhibits an all-pass response as predicted in our simulations, except for a slight loss (<5 dB) in the low frequency range. Such scattering loss is due to the existence of cutting burrs, unintentionally created around the groove edges during the fabrication process (see Methods).

To summarize, we have introduced a universal approach for the realization of broadband THz signal processing in metal-wire waveguides by directly engineering the wire surfaces. The concept of engraving grooves with multiscale structures, combining the merits of photonic crystals and metamaterials, offers additional degrees of freedom to tailor the spectral response of the entire structures. This paves the way for the realization of versatile signal-processing functionalities, including custom-engineered filtering29, time differentiation and integration30, as well as modulation/demodulation. In parallel, we have experimentally demonstrated the FWWG topology, which provides two independent fundamental modes with orthogonal polarization states for the low-loss and nearly dispersion-free propagation of polarization-division multiplexed THz pulses. By judiciously incorporating the multiscale-structured Bragg gratings into the FWWG, we have demonstrated a unique platform, featuring significant potential towards the independent manipulation of signal channels multiplexed in both frequency (due to its inherent broadband nature) and polarization. Such a platform is anticipated to dramatically enhance THz systems’ capacity and eventually achieve data-rates of ~Tb/s in future THz networks. We envision that the proposed platform can be widely applied in novel application scenarios2,31,32, such as multi-channel transmission of uncompressed ultra-high-definition videos, ultra-high-speed short-distance data transfer between THz network elements, as well as chip-to-chip communications.

## Methods

### Simulations

Based on a finite-element-method (FEM) approach, the simulation results presented in Fig. 2 were obtained by means of the COMSOL Multiphysics mode solver. The frequency dependent relative permittivity $$\varepsilon (\omega )$$ of copper at THz frequencies were modeled according to the Drude model33:

$$\varepsilon (\omega )=1-\frac{{\omega }_{p}^{2}}{{\omega }^{2}+{{{{{\rm{i}}}}}}\omega \varGamma }\mathop{\approx }\limits_{THz}-\frac{{\omega }_{p}^{2}}{{\varGamma }^{2}}+{{i}}\frac{{\sigma }_{0}}{{\varepsilon }_{0}\omega };\,{\sigma }_{0}\mathop{\approx }\limits_{{{THz}}}\frac{{\varepsilon }_{0}{\omega }_{p}^{2}}{\varGamma },$$
(1)

where $${\varepsilon }_{0}$$ is the free-space permittivity, $$\omega$$ is the angular frequency, $${\omega }_{p}$$ is the angular plasma frequency, and $$\varGamma$$ is the electron scattering rate. In the THz frequency range, the Drude model is especially simple as it assumes a frequency independent real part of the relative permittivity $${\varepsilon }_{r}=-1.7\times {10}^{5}$$ and a frequency independent conductivity $${\sigma }_{0}$$=5.96 × 107 S/m. Therefore, the frequency-dependent relative permittivity $$\varepsilon (\omega )$$ of copper at THz frequencies can be modeled as33: $$\varepsilon (\nu )=-1.7\times {10}^{5}+{{i}}1.1\times {10}^{6}{\nu }^{-1}$$, where $$\nu =\omega /2\pi$$ in THz. Scattering boundary conditions were used in the simulations. The THz response of the sub-λ and wavelength-scale periodic grooves in metal-wire waveguides was numerically investigated via finite-difference-time-domain (FDTD) simulations. The numerical results in Figs. 1 and  5 were obtained using the FDTD module of Lumerical. A perfect electric conductor was used for the waveguide, whereas 16 standard perfectly matched layers were employed to absorb spurious reflections coming from the domain edges. To excite the waveguide, we used a broadband signal with a center frequency of 0.5 THz and a 1-THz-bandwidth, carried by a Gaussian beam profile focused down to a waist size of 600 µm at the center of the FWWG input gap. The FDTD simulations were evaluated in a time window of 460 ps with a time resolution of 0.02 ps.

### Experiments

The experiments were performed using the setup illustrated in Fig. 3, which is a customized THz-TDS system with two independent broadband transmitters and a single receiver. The system was driven by an ultrafast near-infrared pulse train (800 nm, 120 fs, 80 MHz) generated by a Ti:Sapphire laser oscillator. The pump and probe beams were obtained by means of a 90/10 beam splitter (BS1). The pump beam was further divided by a 50/50 beam splitter (BS2) to excite the two transmitters. Two identical PCAs (iPCA-21-05-300-800-h, BATOP) served as the transmitters. THz pulses were produced by exciting the PCAs with an average optical power of 500 mW. A bipolar square-wave bias voltage, oscillating at 5 kHz and with a peak-to-peak amplitude of 12 V, was generated by a low-noise function generator and applied to the PCAs. A THz TPX lens (BATOP) with a diameter of 25.4 mm and a focal length of 10 mm was used to focus the THz pulses into the waveguide. Such a lens allowed us to focus the THz beam down to a waist diameter of 400 µm at 0.5 THz. The THz pulses were detected by carrying out the electro-optic sampling technique in a 3 mm-thick ZnTe <110> crystal. The use of such a thick crystal allowed us to achieve a larger temporal window in the measurements, which was necessary to acquire the long-lasting THz transient as modulated by the multiscale grooves. Each recorded THz waveform was centered in a time window of 100 ps with a time resolution of 0.05 ps.

### Fabrications

The fabrication process of the grooves on the bare copper wires was performed at the LMN laboratory at the INRS-EMT, Canada. First, the wires were kept as straight and flat as possible and were glued on a quartz plate. Then the quartz plate with the wires was installed on the base of an automatic dicing saw. The thickness of the employed diamond blade was 35 µm, which determines the width of the grooves. The grooves along the wires were fabricated by utilizing the three-dimensional motor control of the dicing saw. Deviations in the depth were mainly induced by the blade wearing over several cuts. The width of the grooves was constant with the exception of a few burrs at the edge of the cuts. To mount the wires22, two PMMA slabs with holes were used to hold and support them. The diameter of the holes was set to 1037 µm in order to guarantee that the gap size between wires was 300 µm in each direction. Screws on the slabs were used to apply tension to the wires, so as to maintain a uniform gap all along the waveguide.