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Abstract
The divergence of orbital angular momentum (OAM) plays a crucial role in practical terahertz OAM applications. However, most of the existing research focuses on half-space configurations, which significantly limit the utilization of space and are not aligned with the future development of wireless communication. In this paper, we present the modeling and design of two broadband high-efficiency janus transmit-reflect metasurfaces (JTRMS). These metasurfaces enable the generation of quasi-non-diffracting terahertz beams carrying OAM in the forward transmission space (FTS), forward reflection space (FRS), and backward transmission space (BTS). The key difference lies in the polarization characteristics: TRMS1 produces a left-handed circularly polarized (LHCP) quasi-non-diffracting beam in both the FTS and FRS, while generating a right-handed circularly polarized (RHCP) beam in the BTS. On the other hand, TRMS2 generates a LHCP beam in the FTS and BTS, while producing a RHCP beam in the FRS. This design allows for flexible control of the polarization of the outgoing waves in different spaces. The proposed design strategy and the high-performance janus transmit-reflect metasurfaces hold promising application prospects in future communication systems that require large capacity and support multi-directional communication scenarios.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the exponential growth in the number of mobile users, spectrum resources are becoming increasingly scarce, leading to increased constraints on the capacity of wireless communication systems. It is widely recognized that millimeter waves and sub-terahertz beams have found their place in fifth-generation mobile communications. As a result, terahertz beams [1–4] in the unoccupied parts of the spectrum have emerged as the first choice for the next generation of mobile communications. In addition, the beams carrying orbital angular momentum (OAM) [5–9], also known as vortex beams, characterized by their doughnut-shaped intensity profiles and helical phase fronts, have the potential to generate a theoretically infinite number of orthogonal channels. As a result, OAM terahertz beams have become a focal point of research. In 2022, Liu et al. [10] proposed a metasurface, which can generate diagonal vortex beams, four vortex beams, and focused vortex beam for transmission mode at 1.26 Thz and reflection mode at 1.06 Thz by changing phase state of the VO2. In 2023, Liu et al. [11] proposed a transmissive metasurface, which can generate Thz vortex beams carrying OAM with different topological charges l = −1, −2, −3(l = +1, +2, +3) under left/right-handed circular polarization (CP) incidence at three different frequencies.
However, the practical application of OAM beams in long-range wireless communications is hampered by the gradual radial dispersion of the OAM beam in the transverse plane [12,13]. Henceforth, generating spatially stable Thz vortex waves carrying OAM in free space without changing their initial field distribution at any plane orthogonal to the direction of propagation becomes an urgent issue that merits further study. In 2021, He et al. [14] proposed a dielectric lens capable of generating quasi-non-diffracting off-axis OAM terahertz beams at a frequency of 0.14 Thz. In 2021, Wu et al. [15] proposed a novel 3-dimensional (3-D) printed discrete dielectric lenses for the generation of non-diffractive OAM beams operating at 0.3 Thz. In 2022, a quasi-non-diffracting OAM terahertz beam at 0.161 Thz was generated by Wu et al. [16] using a single-layer reflective metasurface. Both of these works were limited to half-space operation. The main reason for this limitation is the daunting task of designing a full space device with both high bandwidth and efficiency [17–21]. However, it has always been of interest to researchers to make full use of the space resources of the electric field to achieve more efficient signal transmission and processing.
In this paper, we present the design of two janus transmit-reflect metasurfaces (JTRMS), as shown in Fig. 1. Under forward incidence, JTRMS1 exhibits the ability to generate a LHCP quasi-non-diffraction beam with OAM mode l = +3 in the forward transmission space (FTS), as well as a LHCP quasi-non-diffraction beam with an off-angle of $45^\circ$ and OAM mode l = −1 in the forward reflection space (FRS). Similarly, JTRMS2 can produce a LHCP quasi-non-diffraction beam with OAM mode l = +3 in the FTS, and a RHCP quasi-non-diffraction beam with an off-angle of 45$^\circ$ and OAM mode l = −1 in the FRS. When it comes to backward incidence, JTRMS1 generates a RHCP quasi-non-diffracting beam with OAM mode l = +3 in the backward transmitted space (BTS), while not producing any reflected beam. On the other hand, JTRMS2 generates a LHCP quasi-non-diffracting beam with OAM mode l = +3 in the BTS, with no reflection occurring. The simulation results align with our expectations, validating the feasibility of the proposed concept. Overall, these two devices effectively utilize space resources and enable flexible beam control in complex transmission paths, leading to high integration and miniaturization of the devices. They hold significant practical applications, particularly in medium and short-distance communication scenarios.
Fig. 1. The proposed metasurfaces generate OAM topology number and polarization-tunable terahertz quasi-non-diffraction beams in different spaces
2. Meta-atom design
We have designed two janus transmit-reflect meta-atoms (JTRMA). JTRMA1 consists of three metal layers: the top layer comprises the transmitting antenna, the middle layer consists of the metal ground, and the bottom layer houses the receiving antenna, as shown in Fig. 2. Two identical dielectric layers separate these three metal layers. The material of metal layers is copper, and the material of the dielectric layer is acrylates ($\varepsilon _r=2.8, tan\delta =0.02$). Both the receiving and transmitting antennas share the same structural formula. They consist of circular metal patches with an oval groove etched at the center, while the middle metal layer features a circular hole, allowing the passage of metal vias to connect the receive and transmit antennas. Furthermore, the receiving and transmitting antennas are offset along the diagonal of the middle metal ground, making them sensitive to polarization. For forward incidence, when a RHCP beam is incident, the receiving antenna captures the incident beam and converts the energy into a guided wave signal, which is then transmitted to the transmitting antenna. The transmitting antenna converts the guided wave signal into a LHCP beam for emission. In the case of an incident LHCP beam, polarization mismatch leads to reflection, preventing transmission. Therefore, JTRMS1 enables control over both forward transmitted and reflected beams, operating effectively in the FTS ad FRS. The optimized size of the JTRMA1 is given by the equation: $p$ = 1.1 mm, $h_1$ = 0.035 mm, $h_2$ = 0.175 mm, $rl$ = 0.6 mm, $rw$ = 0.09 mm, $r_1$ = 0.325 mm, $d_1$ = 0.07 mm, $d_2$ = 0.14 mm, $sx$ = 0.13mm, $sy$ = 0.13 mm.
The scattering properties of the JTRMA1 were simulated using CST. For forward incidence, the top transmitting antenna is fixed while the bottom receiving antenna is rotated by a $\alpha$ degree. As the rotation angle increases, the magnitudes of transmission and reflection remain almost unchanged, but the phase of transmission advances by $\alpha$, while the phase of reflection lags by $2\alpha$, as depicted in Fig. 3. Next, the bottom receiving antenna is fixed, and only the top transmitting antenna is rotated by $\beta$ degrees. Under this rotation, the amplitudes of transmission and reflection show minimal change, while the phase of transmission advances by $\beta$, and the phase of reflection remains constant, as shown in Fig. 4. In summary, for forward incidence, the phase of the transmitted beam is jointly controlled by the rotation angles of the receiving and transmitting antennas, whereas the phase of the reflected beam is solely determined by the rotation angle of the receiving antenna. This can be expressed as follows:
Fig. 3. For forward incidence, changes in reflection amplitude, reflection phase, transmission amplitude, and transmission phase of JTRMA1 as the angle $\alpha$ changes.
Fig. 4. For forward incidence, changes in reflection amplitude, reflection phase, transmission amplitude, and transmission phase of JTRMA1 as the angle $\beta$ changes.
Therefore, by designing specific angles for the receiving and transmitting antennas, independent and simultaneous control of the forward-transmitted and forward-reflected beams throughout the space can be achieved, as shown in the following equation:
For backward incidence, a similar approach is followed. First, the top transmitting antenna is fixed, and the bottom receiving antenna is rotated by $\alpha$ degree. As the rotation angle of the receiving antenna increases, the magnitudes of transmission and reflection exhibit minimal change, while the phase of transmission advances by $\alpha$, and the phase of reflection remains unchanged, as shown in Fig. 5. Then, the bottom receiving antenna is fixed, and only the top transmitting antenna is rotated by $\beta$. As the rotation angle of the transmitting antenna increases, the magnitudes of transmission and reflection also show minimal change, while the phase of the transmitted beam advances by $\beta$, and the phase of the reflected beam lags by $2\beta$, as shown in Fig. 6. Therefore, for backward incidence, the phase of the transmitted beam is determined by both the receiving and transmitting antennas, while the phase of the reflected beam is solely determined by the rotation angle of the transmitting antenna, as expressed by the equations:
By combining Eq. (3), Eq. (4), Eq. (5), and Eq. (6), the transmitted and reflected phases during back incidence can be expressed in terms of those during forward incidence, as follows:
It can be observed that the phase of the backward-incidence transmitted beam is the same as that of the forward-incidence transmitted beam. However, the phase of the back-reflected wave is influenced by the phases of the forward-incidence transmitted and reflected beams and is generally unpredictable. It is important to highlight that the polarization of the transmitted and reflected beams of JTRMA1 is LHCP beams for forward incidence, while for backward incidence, the transmitted beam exhibits RHCP. Furthermore, the polarization of the outgoing wave can be adjusted simply by modifying the unit design. To demonstrate this concept, we have designed JTRMA2, which differs from JTRMA1 in that the $sy$ of the receiving antenna is changed to −0.13 mm, and $sx$, $sy$ of the transmitting antenna is changed to −0.13 mm. We have also conducted simulations using CST to analyze the scattering properties of JTRMA2. As shown in Fig. 7, Fig. 8, Fig. 9, and Fig. 10, the magnitudes of transmission and reflection remain nearly constant. Specifically, for forward incidence, the phase of the transmitted beam lags by $\alpha$ as the rotation angle of the receiving antenna increases and advances by $\beta$ as the rotation angle of the transmitting antenna increases, while the phase of the reflected beam advances by $2\alpha$ as the rotation angle of the transmitting antenna increases. This can be expressed as:
Fig. 5. For backward incidence, changes in reflection amplitude, reflection phase, transmission amplitude, and transmission phase of JTRMA1 as the angle $\alpha$ changes.
Fig. 6. For backward incidence, changes in reflection amplitude, reflection phase, transmission amplitude, and transmission phase of JTRMA1 as the angle $\beta$ changes.
Fig. 7. For forward incidence, changes in reflection amplitude, reflection phase, transmission amplitude, and transmission phase of JTRMA2 as the angle $\alpha$ changes.
Fig. 8. For forward incidence, changes in reflection amplitude, reflection phase, transmission amplitude, and transmission phase of JTRMA2 as the angle $\beta$ changes.
Fig. 9. For backward incidence, changes in reflection amplitude, reflection phase, transmission amplitude, and transmission phase of JTRMA2 as the angle $\alpha$ changes.
Fig. 10. For backward incidence, changes in reflection amplitude, reflection phase, transmission amplitude, and transmission phase of JTRMA2 as the angle $\beta$ changes.
For back incidence, the phase of the transmitted beam lags by $\alpha$ as the rotation angle of the receiving antenna increases, and advances by $\beta$ as the rotation angle of the transmitting antenna increases, while the phase of the reflected beam advances by $2\beta$ as the rotation angle of the transmitting antenna increases, as follows:
Thus, we can represent the phase of the backward outgoing beam using the phase of the forward outgoing beam:
Similar to JTRMA1, JTRMA2 also enables beam control throughout the space for forward incidence and the generation of a transmitted beam for back incidence. The main distinction is the change in the beam polarization. It is important to highlight that the polarization of the forward transmitted and backward transmitted beams of JTRMA2 is LHCP beams, while the forward transmitted beam exhibits RHCP.
3. Design and results of metasurfaces
The generation of full-space Thz quasi-non-diffraction OAM beams is demonstrated by utilizing JTRMAs to construct janus transmit-reflect metasurfaces (JTRMS). As shown in Fig. 11(a-b), the JTRMS1 consists of a grid of 22 $\times$ 22 JTRMA1, with an aperture size of 24.2 mm $\times$ 24.2 mm, corresponding to 9.7 wavelengths at a center frequency of 120GHz. The primary function of the JTRMS1 for forward incidence is to generate a quasi-non-diffracting LHCP transmitted beam with OAM mode l = +3. This beam exhibits a maximum non-diffracting distance of 40mm in the FTS. Simultaneously, the JTRMS1 produces a quasi-non-diffracting LHCP reflected beam in the FRS with OAM mode l = −1. This reflected beam is deflected at an angle of 45 degrees. To achieve these desired functionalities, the required phase compensation for transmission and reflection can be expressed as follows:
Fig. 11. (a) Top view of JTRMS1, (b) bottom view of JTRMS1, (c) rotation angle of JTRMS1 transmitting antenna, (d) rotation angle of JTRMS1 receiving antenna
The full-wave simulation of JTRMS1 was conducted using HFSS software. In the case of forward transmission, as depicted in Fig. 12(a), the electric field amplitude distribution of the LHCP beam along the propagation direction exhibits the characteristics of a vortex beam, with zero amplitude at the center depth of the beam. The main distribution of the electric field occurs within the maximum non-diffracting distance of 40 mm. Figure 12(b) shows the electric field amplitude and phase distribution on the propagation plane perpendicular to the beam at different distances. The amplitude distribution resembles a donut-shaped hollow ring. The phase distribution displays spiral arms, indicating the dominant polarization OAM mode l = +3.
Fig. 12. (a) The E-field amplitude of forward LHCP transmitted beam distributions along the beam’s direction, (b) the E-field amplitude and phase of forward LHCP transmitted beam distributions perpendicular to the beam’s direction.
In the case of forward reflection, as depicted in Fig. 13, the electric field amplitude distribution of the LHCP beam along the propagation direction (at an inclination angle of 45 degrees) is affected by the incident field, particularly near the JTRMS1. However, the amplitude still exhibits a hollow ring structure. The phase distribution clearly shows the main polarization OAM mode l = −1.
Fig. 13. (a) The E-field amplitude of forward LHCP reflected beam distributions along the beam’s direction, (b) the E-field amplitude and phase of forward LHCP reflected beam distributions perpendicular to the beam’s direction.
For back incidence, similar to the forward transmission, the function is consistent with that of the forward incidence transmitted wave, as shown in Fig. 14. However, the phase of the outgoing beam is RHCP.
Fig. 14. (a) The E-field amplitude of backward RHCP transmitted beam distributions along the beam’s direction, (b) the E-field amplitude and phase of backward RHCP transmitted beam distributions perpendicular to the beam’s direction.
Furthermore, to illustrate the non-diffractive nature of the OAM-carrying beam, Fig. 15 presents the main lobe (peak intensity) distribution along the propagation axis. It can be observed that the diameter of the diffractive OAM transverse energy ring increases linearly as the wave propagates, with higher OAM modes resulting in larger diameters. To sense the OAM information at the receiving end, a large electrical antenna is required. The beam generated by JTRMS1 overcomes the divergence effect of the vortex wave, maintaining a relatively constant diameter of the transverse energy ring throughout the non-diffraction propagation distance.
Fig. 15. Distribution of the main lobe (peak intensity of E) along the propagation axis for (a) forward-transmitted beam, (b) forward-reflected beam, (c) backward-transmitted beam.
The modulation efficiency at different transmission distances was investigated to further demonstrate the non-diffraction performance of the generated quasi non-diffraction vortex beam. The modulation efficiency is defined as the square root of the ratio of the power of quasi non-diffraction vortex beam to the power of quasi non-diffraction vortex beam in the reference plane, which can be expressed as
Sout and Sref are the observation planes used to study the power transformed into quasi non-diffraction vortex beam and the standard reference power, respectively. Here, the modulation efficiency depends on the selection of the observation plane Sout. In this paper, the observation plane Sout with an area of 24.2 mm $\times$ 24.2 mm is used, which is the design aperture area, to calculate the simulated output power. Sref is selected as a plane with an area of 24.2 mm $\times$ 24.2 mm perpendicular to the beam propagation direction at a beam propagation distance of 20 mm. Figure 16 depicts the variation of the modulation efficiency with the propagation distance of the beam. The modulation efficiency of the diffracted OAM beam decreases rapidly, with higher OAM modes experiencing faster divergence. However, the modulation efficiency of OAM generated by JTRMS1 exhibits a more gradual decrease within the non-diffraction distance, demonstrating its excellent non-diffraction properties. Beyond the non-diffraction distance, the reduction rate of the modulation efficiency increases significantly.
Fig. 16. Modulation efficiency along the propagation axis for (a) forward-transmitted beam, (b) forward-reflected beam, (c) backward-transmitted beam.
Lastly, the mode purity of the generated quasi-non-diffraction vortex beam at different transmission distances is analyzed using Fourier transform [14]. The OAM modes ranging from l = −4 to l = +4 are considered here. The mode purity remains nearly constant both within and outside the non-diffracting region. The unwanted OAM modal purity is lower than 0.2 for both forward transmission and back transmission cases. In the forward reflection case, it is affected by the incident beam and unwanted OAM mode purity is higher than 0.2. However, as the distance from the metasurface increases, the mode purity of unwanted OAM decreases, and the mode purity of the main mode is much higher than other modes, as shown in Fig. 17. This proves the successful generation of vortex beams in forward reflection space.
Fig. 17. Mode purity with a changing distance D for (a) forward-transmitted beam, (b) forward-reflected beam, (c) backward-transmitted beam.
Furthermore, to further illustrate the flexible control of electromagnetic wave polarization using this design method, JTRMS2 was developed based on JTRMA2. Figure 18(a-b) shows its top and bottom views, respectively. Figure 18(b-c) shows the rotation angles of the transmitting antenna and the receiving antenna, respectively. Its function is identical to that of JTRMS1, with the only difference being the polarization of the outgoing wave. The simulation of TRMS2 was also conducted using HFSS software.
Fig. 18. (a) Top view of JTRMS2, (b) bottom view of JTRMS2, (c) rotation angle of JTRMS2 transmitting antenna, (d) rotation angle of JTRMS2 receiving antenna
Figure 19, Fig. 20, and Fig. 21 depict the electric field amplitude distribution along the beam propagation direction and the electric field amplitude and phase distribution on the propagation plane perpendicular to the beam at various distances. It can be observed that the function of TRMS2 is similar to that of TRMS1, with changes in the polarization of the forward reflected beam and the backward transmitted beam. The distribution diagrams of the main lobe of the electric field and the modulation efficiency are also provided, demonstrating the excellent non-diffraction properties of the beams generated by JTRMS2, as shown in Fig. 22, and Fig. 23.
Fig. 19. (a) The E-field amplitude of forward LHCP transmitted beam distributions along the beam’s direction, (b) the E-field amplitude and phase of forward LHCP transmitted beam distributions perpendicular to the beam’s direction.
Fig. 20. (a) The E-field amplitude of forward RHCP reflected beam distributions along the beam’s direction, (b) the E-field amplitude and phase of forward RHCP reflected beam distributions perpendicular to the beam’s direction.
Fig. 21. (a) The E-field amplitude of backward LHCP transmitted beam distributions along the beam’s direction, (b) the E-field amplitude and phase of backward LHCP transmitted beam distributions perpendicular to the beam’s direction.
Fig. 22. Distribution of the main lobe (peak intensity of E) along the propagation axis for (a) forward-transmitted beam, (b) forward-reflected beam, (c) backward-transmitted beam.
Fig. 23. Modulation efficiency along the propagation axis for (a) forward-transmitted beam, (b) forward-reflected beam, (c) backward-transmitted beam.
The purity distribution of OAM mode under different conditions is shown in Fig. 24. Similar to TRMS1, the purity of the OAM in the reflected beam is influenced by the incident beam, resulting in a higher purity of unwanted OAM modes exceeding 0.2. However, the purity of the main mode remains significantly higher than other modes. The impact of the incident beam on the near-field reflected beam is inevitable, but oblique incidence can be employed to reduce its influence. In general, TRMS2 achieves the generation of quasi-non-diffracting beams with full-space terahertz OAM. Compared to TRMS1, it alters the polarization of the forward reflection beam to RHCP and the polarization of the back reflection beam to LHCP. The simulation results align with our expected design.
Fig. 24. Mode purity with a changing distance D for (a) forward-transmitted beam, (b) forward-reflected beam, (c) backward-transmitted beam.
4. Conclusion
In summary, we have presented a novel design strategy for polarization-dependent janus transmit-reflect meta-atoms. This strategy utilizes the PB phase, resulting in a wide operating bandwidth with transmission and reflection amplitudes exceeding 0.5 within the 0.1-0.14 Thz range, while maintaining a linear phase response. Based on this strategy, we have designed two janus transmit-reflect metasurfaces capable of generating quasi-non-diffracting terahertz vortex beams in the forward transmission space, forward reflection space, and back transmission space. This design overcomes the challenge of beam divergence in practical communication scenarios. Furthermore, by simply adjusting the design, JTRMS2 modifies the polarization of the forward-reflected beam and the backward-transmitted beam compared to JTRMS1. The strategy and devices significantly enhance the utilization of space, enabling miniaturization and integration of devices. These advancements have broad applications in future terahertz systems with multi-directional and high-capacity requirements, particularly in short and medium-distance communication scenarios.
Funding
Beijing Municipal Natural Science Foundation (L223030).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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