1. Introduction

THz waves offer significant advantages in terms of penetration, water absorption and high resolution, making them widely used in spectroscopy, imaging, nondestructive testing and other fields. Additionally, electromagnetic waves carrying OAM offer significant advantages in improving communication capacity and spectral efficiency. OAM can be quantified as different states in coaxial propagation and orthogonal to each other, making it a new transmission multiplexing degree of freedom after frequency, time, space, polarization [1,2], etc. This greatly improves its data capacity, making it an important field of study for researchers. OAM beams have been widely used in particle capture [3], beam focusing [4], holographic imaging [5,6], etc.

There are several commonly used methods for generating vortex beams carrying OAM, including the spiral phase plate [7], array antenna [8], photonic crystal fiber (PCF) [9] and metasurface [10,11]. However, the spiral phase plate has a relatively complex structure and large volume, which is not conducive to device integration and miniaturization. Additionally, the angle difference between the incident electromagnetic wave and the spiral phase plate can greatly reduce reflection magnitude, resulting in low efficiency [12]. The array antenna requires a complex feeding network, which can cause larger losses and hinder miniaturization. Moreover, when high-order OAM beams require more antenna elements, the complex feeding network will significantly increase design difficulty and production technology complexity [13]. In the pursuit of OAM wave generation, PCF have been utilized by some researchers [14,15]. While PCF can support more OAM modes with large bandwidth and flat dispersion variations, the processing technology can be relatively complex. In recent years, the use of metasurfaces for OAM wave generation has garnered great interest among researchers [16–18]. As a synthetic material, metasurfaces offer significant advantages in component integration and miniaturization, and enable phase and amplitude modulation of electromagnetic waves to be realized through structural design [19]. Accordingly, the design of vortex beam generators based on metasurfaces holds great promise for a variety of applications. Additionally, reflecting metasurfaces can achieve high reflection efficiency, which is essential for avoiding the low reflection efficiency problem associated with spiral phase plates [20]. Overall, metasurface-based approaches offer a promising avenue for further research into OAM wave generation and its practical applications.

The metasurface-based vortex beam generator fulfills the requirements of device miniaturization and easy integration, significantly reducing manufacturing complexity. For a long time, THz applications were limited to imaging and sensing due to the scarcity of efficient THz devices. However, the rapid development of THz technologies has drawn attention to the THz gap (between 100 GHz and 10 THz), which can be used in several applications related to security, astronomical observation, and localization. Presently, the generation of vortex beams using metasurfaces has mainly been studied in the microwave [21,22] and visible bands [23], whereas few studies have been conducted in the THz low-frequency range. Generating THz OAM beams can provide many benefits in terms of improving bandwidth, channel capacity, and spectral efficiency, especially considering the vast bandwidth of the THz band and the additional degree of freedom provided by the OAM beams. It is important to note that, at short wavelengths, beam divergence decreases, resulting in reduced OAM beam divergence at higher frequencies. Additionally, the short wavelengths of THz frequencies can help minimize the size of structures, enabling hundreds of antennas to be packed together and contributing to reducing the divergence problem of OAM waves. Furthermore, this integration can improve both security and integrated sensing and communications.

Therefore, in this paper, an ultra-wideband multimodal vortex wave THz generator based on reflection type is proposed. The designed reflective metasurface has high polarization conversion efficiency and phase control ability in a wide frequency range, which can transform the polarization beam into a high quality vortex beam.

The article presents a comprehensive design process and simulation results. The remainder of the paper is organized as follows: the characteristics analysis of the encoding element is depicted in Section II. Then, coding element array design and performance analysis are given in Section III. Next, a conclusion is given in Section IV.

2. Characteristics analysis of the encoding element

In this study, a metal metasurface is used to design the low THz band ultra-wideband OAM generator, and the generator unit is extracted by 3-bit coding. As shown in Fig. 1, the metasurface is composed of three layers of metal-medium-metal structure: the metal metasurface is located on the upper surface of the medium substrate supported by the metal stratum, so as to realize the reflective metasurface unit design. The thickness of the metal layers is all 0.2 $\mu$m. The dielectric substrate material is F4B with a relative dielectric constant of 2.65, and its loss tangent angle is 0.001. The optimized structural parameters are as follows: $p=98$ $\mu$m, $l=75.6$ $\mu$m, $a=20$ $\mu$m, $b=20$ $\mu$m, $w_1=10$ $\mu$m, $w_2=2.8$ $\mu$m, $h=42$ $\mu$m.

 

Fig. 1. Schematic diagram of element structure. (a) and (b) are: top view. (c) side view.

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Compared to dielectric metasurfaces, metal metasurfaces offer significant advantages in terms of device integration, processing ease, and manufacturing. In this study, a low THz band ultra-wideband OAM generator is designed using a metal metasurface, and the generator unit is extracted by 3-bit coding. According to the simulation results obtained using the high-frequency simulation software CST, the metasurface with identical parameters exhibited a 90$^{\circ }$ rotation over time, as depicted in Fig. 1(a) and (b). Furthermore, the unit cell boundary and Floquet port were utilized to simulate the periodic boundary conditions. As Fig. 1(c) demonstrates, the metasurface element comprises three layers of a metal-medium-metal structure where the metal metasurface is located on the upper surface of the dielectric substrate, supported by the metal stratum, enabling the design of reflective metasurface units. The thickness of the metal layers is 0.2um each. The dielectric substrate material used is barium flint glass, with a refractive index of 1.63 and a loss tangent angle of 0.001. The optimized structural parameters obtained by parameter sweep are as follows: $p=98$ $\mu$m, $l=75.6$ $\mu$m, $a=20$ $\mu$m, $b=20$ $\mu$m, $w_1=10$ $\mu$m, $w_2=2.8$ $\mu$m, $h=42$ $\mu$m. As for $g_1$ and $g_2$, the selection of metasurface elements is achieved by controlling the sizes of $g_1$ and $g_2$. The fabrication technique involves depositing a metal layer onto the substrate through sputtering, followed by using laser etching to create the desired pattern.

Figure 2 illustrates that when a Y-polarized wave is incident vertically into two element respectively, the cross-polarized reflection amplitude response of the element remains consistent within the frequency range of 0.6THz-1.4THz, while the phase response difference is close to 180$^{\circ }$. As a result, the required number of phase controls of coding units can be reduced by using rotating elements.

 

Fig. 2. Amplitude and phase of cross-reflection of two elements, with parameters as $g_1$ = $g_2$ =43.9um.

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The 3-bit coded metasurface is composed of $2^3$ fundamental element structures with reflective phase intervals of approximately 45$^{\circ }$, which are represented by eight base codes: 000, 001, 010, 011, 100, 101, 110, 111. By arranging and combining these eight types of reflection elements, the electromagnetic regulation of the encoded metasurface can be realized. The selection of metasurface elements with a difference of approximately 45$^{\circ }$ is achieved by controlling the sizes of $g_1$ and $g_2$, as described before.

In Fig. 3, the first four curves (coded as 000,001,010,011) correspond to $g_1$ sizes of 59.8$\mu$m, 43.9$\mu$m, 26.1$\mu$m and 10.3$\mu$m, respectively, while the following four curves (coded as 100,101,111) correspond to $g_2$ sizes of 59.8$\mu$m, 43.9$\mu$m, 26.1$\mu$m and 10.3$\mu$m, respectively.

 

Fig. 3. Performance analysis of coding element. (a) Cross-polarized reflection phase. (b) Cross-polarized reflection amplitude.

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As indicated in Fig. 3(a), the difference between adjacent units is approximately 45$^{\circ }$ in the frequency range of 0.6THz-1.4THz. Therefore, the metasurface elements capable of realizing 3-bit coding exhibit excellent broadband characteristics and can be utilized in the design of ultra-wideband vortex wave generator. The corresponding cross-polarization reflection amplitudes of the coding units are shown in Fig. 3(b). Within the frequency range of 0.60THz-1.3THz, the corresponding reflection amplitudes of the coding elements all exceed 0.85, which is sufficient for designing reflective metasurfaces.

3. Coding element array design and performance analysis

To generate a vortex electromagnetic beam, the coding elements can be arranged in arrays using the expression of the field distribution of a vortex beam, which should have a phase factor exp($-jl\phi$). The phase distribution of the OAM beam metasurface array generated by the vortex beam should follow the following formula [24]:

In this paper, the coding element is utilized to design an ultra-wideband OAM generator based on Eq. (1), and the full-wave simulation software CST is used to simulate and analyze the performance of the designed metasurface OAM generator. Equation (1) is used to design the metasurface of the OAM generator, and its metasurface array layout is presented in Fig. 4, where $L_m=1568$ $\mu$m and $W_m=1568$ $\mu$m. A 3D far-field scattering pattern of OAM vortex beams obtained by simulation based on this structure is shown in Fig. 5.

 

Fig. 4. The structure of the proposed metasurface.

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Fig. 5. The simulated 3D far-field pattern of the OAM beam.

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The phase distribution of the reflection exhibits helical properties, and there are clear singularities in the center of all amplitude planes. The designed OAM generator also has the phase helix property at other operating frequency points. The electromagnetic wave purity of the designed OAM generator is evaluated by means of mode spectrum analysis, where the mode purity is defined as the ratio of the power in the dominant mode to the total power distributed in all modes, as shown in Eq. (2), where $A_i$ is the power of the $i$th mode.

In Fig. 6(a) and (b), the phase distribution and coding element distribution for a single-beam orbital angular momentum mode $l$=+1 are depicted, respectively. Eight coding elements sequentially correspond to each other, and there is a phase variation of 2$\pi$ around the array center. Figure 6(c) and (d) demonstrate the phase distribution and coding unit distribution for the single-beam orbital angular momentum mode $l$ =+2, respectively. The array layout selects four coding units with a 90$^{\circ }$ difference among the eight coding elements, and the phase variation is 4$\pi$ around the array center. The phase and amplitude of the reflection at 3000$\mu$m above the metasurface of the generator at typical frequencies of 0.6THz, 0.8THz, and 1.2THz are shown in Fig. 7 and Fig. 8.

 

Fig. 6. (a) Ideal phase diagram of OAM beam when $l$ =+1. (b) OAM beam array coding unit layout when $l$ =+1. (c) Ideal phase diagram of OAM beam when $l$ =+2. (d) OAM beam array coding unit layout when $l$ =+2.

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Fig. 7. The electric field phase, amplitude and mode spectrum results of OAM beam when $l$=+1 is generated at different frequencies :(a) and (b) are 0.6THz, (c) and (d) are 0.8THz, (e) and (f) are 1.2THz.

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Fig. 8. The electric field phase, amplitude and mode spectrum results of OAM beam when $l$=+2 is generated at different frequencies :(a) and (b) are 0.6THz, (c) and (d) are 0.8THz, (e) and (f) are 1.2THz.

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Figure 7 shows the reflection phase, amplitude and mode purity values of the generator at 3000 $\mu$m from the center of the encoded metasurface when $l$=+1. The generator achieves the phase helix 2$\pi$ difference at 0.6THz, 0.8THz and 1.2THz, and obtains the dark energy region at the center of the metasurface. The purity of main modes of OAM are 74.2$\%$, 79.0$\%$, and 76.0$\%$, respectively. For comparison, Fig. 8 shows the reflection phase, amplitude and mode purity values of the generator at 3000$\mu$m from the center of the coded metasurface when $l$=+2. At 0.6THz, 0.8THz and 1.2THz, the helical difference is 4$\pi$, the electric field amplitude distribution is about the central zero of the plane, and the main modes of OAM account for 68.2$\%$, 67.9$\%$ and 69.4$\%$, respectively. Therefore, the generator can achieve high purity OAM beam in the range of 0.6THz-1.3THz, with a fractional working bandwidth of 75$\%$, while other studies have either focused solely on maximum bandwidth or best performance in the same frequency band [11,25].

4. Conclusion

This paper presents and simulates a novel cross-polarized wideband reflective metasurface. The simulation results demonstrate that the 3-bit element structure can achieve equal phase distribution intervals of $\pi$/4 with large reflection amplitude over a wide wavelength range. By combining the 3-bit metasurface elements in an array, linearly polarized waves can be effectively converted into vortex beams within the frequency band of 0.6THz-1.3THz. The proposed metasurface structure is simple to implement and can be easily integrated with printed circuit boards and photoelectric circuits. Moreover, it can generate OAM with different topological change values, making it a promising candidate for terahertz field and OAM transmission applications.