Electronic waves with a frequency range of 0.1∼10 THz are known as terahertz (THz) waves. These waves have a wide range of potential uses in non-destructive testing, security monitoring, 6G communications, and space situational awareness [1]. THz waves fall in between photonics and electronics. There is a “terahertz gap” in the electromagnetic spectrum as a result of the limited development of THz functional devices caused by the difficulty of producing efficient THz responses in natural materials [2, 3]. Metasurfaces are two-dimensional metamaterials that are made by arranging sub-wavelength artificial electromagnetic structural units in a certain pattern. They have unique electromagnetic property control capabilities for electromagnetic waves [4] and can achieve a variety of electromagnetic control functions such as wave absorption [5–7], superlenses [8, 9], asymmetric transmission [10, 11], polarization conversion [12], vortex waves [13]. The cross-integration of metamaterials and THz frequency provides an important way to solve the bottleneck of conventional THz technology. A common geometric feature found in structures like proteins and DNA double helix molecules is chirality [14]. In the electromagnetic environment, chiral structures can generate circular dichroism (CD) [15] and circular birefringence optical rotation effects [16], as well as distinct reactions to left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) electromagnetic waves. Artificially designed metamaterials/metasurfaces can achieve chiral effects far greater than those of natural materials [17]. Chiral metamaterials/metasurfaces have been applied in electromagnetic wave amplitude and phase regulation and polarization conversion. Some scholars have proposed using chiral metasurfaces to absorb circularly polarized waves [18]. When LCP/RCP waves are incident on chiral metasurfaces, only one type of electromagnetic wave is efficiently absorbed. Reflecting or transmitting orthogonally polarized electromagnetic waves exhibits circular dichroism [19–22]. The authors in [23] proposed the generalized Snell’s law, which laid a theoretical foundation for the design of phase-controlled metasurfaces. Through resonant phase units [24] and geometric (Pancharatnam-Berry) phase units [25], electromagnetic control of abnormal reflection and abnormal refraction of electromagnetic waves can be achieved. Among them, geometric phase is an important means for metasurfaces to control THz circularly polarized waves. By rotating the unit, the reflected or transmitted circularly polarized wave can produce a phase difference of two times the rotation angle, thereby achieving abnormal reflection or transmission of circularly polarized waves [26, 27].

The authors in [28] proposed using a V-shaped unit structure to form a single-layer new artificial electromagnetic surface. By changing the angle of the V-shaped unit structure, the phase wavefront of the electromagnetic wave can be controlled to generate a vortex beam. The authors in [29] proposed a metasurface based on graphene materials. By changing the chemical potential of the graphene unit, a modally tunable OAM beam can be achieved in the range of 4.2–5.6 THz. The authors in [30] proposed a metasurface based on VO₂ materials. By driving the change from the insulating state to the metallic state of VO₂ by temperature change, an OAM beam with reconfigurable modes and beam steering angle can be achieved in the range of 0.69–0.79 THz. In [31], the research group further proposed to use VO₂ to convert THz incident waves into outgoing beams with different modes or frequencies in a tunable THz operating frequency band. The authors in [32] used the temperature control properties of InSb materials and based on the geometric phase principle to produce a modally reconfigurable metasurface in the frequency range of 1.8–4.5 THz.

At present, the design of THz chiral metasurfaces is mainly for a single function or a single frequency band, and the research on THz multi-band multifunctional chiral metasurfaces needs to be deepened.

This paper proposes a novel dual-frequency THz wave absorbing and anomalous reflecting circular-polarized chiral metasurface. The main contributions are as follows.

1) This metasurface can adjust the amplitude and phase of circularly polarized waves according to their rotation direction, and realize the dual-function integration of circularly polarized wave absorbing and abnormal reflection.

The remainder of this paper is organized as follows. In Section 2, the theoretical analysis of the metasurface is performed. In Section 3, the absorption performance is evaluated. In Section 4, the metasurface array design and performance is discussed. In Section 5, the conclusion is discussed.

The dual-frequency THz circularly polarized wave absorption and abnormal reflection chiral metasurface array proposed in this paper can realize the control of the amplitude, phase, and polarization of circularly polarized waves in dual frequency bands [33–35]. The function is shown in Figure 1a. It absorbs the incident waves of LCP and RCP at the low frequency of 2.53 THz and high frequency of 3.43 THz, and realizes the chiral anomalous reflection of −26° and +19° for the orthogonal circularly polarized waves (low frequency and high frequency) in the 2 THz frequency bands. Figure 1b shows the top view and side view of the metasurface unit structure.

The unit is a metal-dielectric-metal “sandwich” structure [36–38]. The top pattern and the floor material are made of gold with a conductivity of 4.56 × 10⁷ S/m and a thickness of 200 nm. The middle dielectric layer is made of polyimide with a dielectric constant of 3.5 and a loss tangent of 0.0027 [28]. The unit can be regarded as a meta-molecule composed of a meta-atom I and a meta-atom II with a period of p. Among them, the meta-atom I is a chiral rectangular resonant ring with asymmetric openings on the top and bottom [37, 38]. The Meta-atom II is a chiral circular resonant ring with openings at different angles on the top and bottom. The nested meta-molecule is a two-dimensional chiral structure with neither rotational symmetry nor mirror symmetry.

The specific values of the unit size parameters are shown in Table 1.

According to the theory of rotation-selective absorption and reflection [29], the Jones matrix is used to evaluate the circular dichroism of a two-dimensional chiral metasurface unit [39–41]. The connection between a linearly polarized electromagnetic wave’s incident and reflected electric fields in the Cartesian coordinate system can be written as in Equation 1: E R x E R y = r x x r y x   r x y r y y E I x E I y = R E I x E I y (1)

Among them, the reflected and incident electric fields are denoted by the letters E R and E I , respectively. The reflection coefficient is denoted by r , and the linear polarization direction is denoted by its superscript and subscript, x and y [42–44]. The reflection coefficient makes up the reflection matrix R . The circular polarization basis reflection matrix R circ is created by transforming the linear polarization basis reflection matrix R via matrix transformation which is expressed by Equation 2: R circ = r L R r R R   r L L r R L = Λ − 1 R Λ = 1 2   r x x + r y y + i r x y − r y x r x x − r y y + i r x y + r y x   r x x − r y y − i r x y + r y x r x x + r y y − i r x y − r y x (2)

Among them, Λ = 1 / 2 1 i   1 − i   denotes the transformation matrix, r L L and r R R are the coefficients of the co-polarization reflection; r R L and r L R represents the coefficients of cross-polarization reflection [45–47]. The subscripts “ L ” and “ R ” represent left-hand circular polarization (LCP) and right-hand circular polarization (RCP) in the direction of the wave, respectively.

Due to the presence of the underlying metal, the absorption performance of the unit is only related to the reflected field [48–50]. Considering the cross-polarization of the chiral unit, the left-handed absorption coefficient ALCP and the right-handed absorption coefficient ARCP of the unit can be expressed as in Equations 3, 4: A LCP = 1 − r L L 2 − r R L 2 (3) A RCP = 1 − r R R 2 − r L R 2 (4)

Equations 3, 4 show that the key to achieving efficient wave absorption is to make the co-polarization and cross-polarization reflection coefficients close to 0 at the same time.

The difference between left-handed and right-handed wave absorption by a metasurface unit is measured by the circular dichroism (CD), which is defined in Equation 5: CD = A LCP − A RCP (5)

The value of CD can be positive or negative, indicating the selective absorption of the rotation direction of LCP waves or RCP waves.

The CST Microwave Studio simulator is used to analyze meta-atom I, meta-atom II and meta-molecule. These chiral unit structures’ distinctive properties, including their circular dichroism, wave absorption rate, and reflection coefficient, are primarily determined [51–53]. Using vertically incident LCP and RCP waves as excitation, Figure 2 illustrates the simulation results of the reflection coefficient, wave absorption rate, and circular dichroism of the three structures. The results of Figures 2a,b show that, the meta-atom I can efficiently absorb LCP waves at 2.59 THz, while reflecting RCP waves and keeping their chirality unchanged. The absorption rate of LCP waves reaches 99.3%, while the absorption rate of RCP waves is only 8.6%, and the circular dichroism reaches 0.9 [54–56]. This is because meta-atom I can achieve cross-polarization reflection below 0.3 and co-polarization reflection above 0.9 in the frequency band of 2.4∼3.8 THz, and resonate at 2.59 THz, making r LL close to 0. The results of Figures 2c,d show that at 3.49 THz, the absorption rate of the meta-atom II for RCP wave is 54.6%, the absorption rate for LCP wave is 17.1%, and the circular dichroism is −0.37.

The excellent cross-polarization suppression performance of meta-atom I in a wide frequency band provides space for expanding the second chiral resonance point. The characteristic size of meta-atom II can be reasonably optimized to make its chiral resonance frequency just near the frequency point with the strongest cross-polarization suppression of meta-atom I, thereby realizing dual-frequency circular dichroism recombination [57–59]. Figures 2e, f show the performance of the meta-molecule after recombination. At the two frequencies of 2.53 THz and 3.43 THz, the meta-molecule has strong chiral absorption for LCP waves and RCP waves, respectively, and can achieve efficient chiral reflection for circularly polarized waves of the other hand direction. At 2.53 THz, the absorption rate of the meta-molecule for LCP waves is 96.3%, and the absorption rate for RCP waves is only 11.2%, and the circular dichroism reaches 0.85. The absorption rate of the meta-molecule for LCP waves is 14.1% at 3.43 THz. The absorption rate for RCP waves is 90.9%. The circular dichroism is −0.77. That is to say, the meta-molecule achieves opposite strong circular dichroism in two frequency bands [60–62]. It is possible to determine from observation that the meta-molecule’s two chiral resonance frequency points are near to those of meta-atoms I and II.

The simulation results in Figure 2 show that the design scheme integrating two chiral resonant rings can improve the high-frequency chiral resonant response of meta-atom II while inheriting the low-frequency strong circular dichroism of meta-atom I. The reason is that the introduction of a chiral rectangular ring outside the chiral circular ring can significantly enhance the chiral characteristics of the structure and strengthen the coupling effect between adjacent metal structures.

To further evaluate the physical mechanism of chiral wave absorption of meta-molecular units, the surface current distribution of metamolecular units at 2.53 THz and 3.43 THz is simulated [63–65]. Figure 3 shows the surface current distribution of the unit at two resonance points when the LCP/RCP wave is incident.

As shown in Figures 3a,b, the LCP wave will excite a pair of antiparallel currents with approximately equal amplitudes on both sides of the rectangular ring at 2.53 THz. A magnetic moment perpendicular to the metasurface unit is produced by the circular magnetic dipole formed by these two current oscillations. To achieve the absorption of the LCP wave, this magnetic dipole mode will bind electromagnetic energy on the unit surface. The electromagnetic energy will then be dissipated by the metal’s ohmic loss effect and the polyimide medium’s absorption effect. The RCP wave can be effectively reflected since it stimulates a weak current [66–68]. The results of Figures 3c,d show that at 3.43 THz, the RCP wave will excite a pair of strong currents flowing in opposite directions on the right side of the rectangular and circular rings. The circular magnetic dipole formed by it can also achieve strong absorption of the RCP wave, while the LCP wave can only excite a weak surface current, so it is efficiently reflected.

The impact of the geometric parameters of the metasurface unit on the circular dichroism is shown in Figure 4. According to the analysis of the results of Figures 2, 3, the characteristic sizes of meta-atom I and meta-atom II can be adjusted respectively to achieve independent manipulation of the low-frequency and high-frequency circular dichroism working frequencies [69–71]. The results of Figure 4a show that when the size parameter k 1 changes in the range of 8∼10 μm, the low-frequency circular dichroism of the meta-molecule always maintains a strong circular dichroism characteristic higher than 0.6, and the low-frequency chiral resonance frequency can be adjusted in the range of 2.48∼2.58 THz. The high-frequency circular dichroism of the unit is almost unaffected by the size parameter k 1 . The results in Figure 4b show that when the size parameter β increases from 5° to 17°, the high-frequency of chiral meta-molecule can be adjusted between 3.43 and 3.76 THz, and always maintains a strong circular dichroism higher than −0.7, and the low-frequency circular dichroism of the unit is almost unaffected by the size parameter β. Furthermore, the scaling method may be used to modify the structural size of the unit while controlling the two chiral resonance spots to broaden the spectrum, in accordance with the scalability of Maxwell’s equations.

Figure 5 shows the absorption rates of LCP and RCP of the metasurface unit under different incident angles θ [72]. Because the designed metasurface unit is an anisotropic structure, the situation will be different at different azimuth angles of oblique incidence. Therefore, this paper studies the two oblique incidence situations when the wave vector is restricted to the xOz plane and the yOz plane. When the wave vector is restricted to the xOz plane, it can be seen from Figure 5a that as the incident angle θ increases to 45°, the LCP absorption rate remains at 74.4%, accompanied by a slight blue shift phenomenon [73]. In Figure 5b, the RCP absorption peak hardly changes with the increase of the incident angle θ, and still has an RCP absorption rate of 83.9% when θ increases to 45°.

When the wave vector is limited to the yOz plane, the results of Figure 5c show that when θ is increased to 45°, the absorption rate of the unit to LCP waves is 76.1%. The results of Figure 5d show that when the RCP absorption peak increases with the incident angle θ to 45°, the absorption rate of the unit to RCP is greater than 80.1%.

It should be noted that when the wave vector is limited to the x-z plane, the unit will produce an RCP absorption band of approximately 28% near 2.6 THz when θ is close to 45°. The frequency of this RCP absorption band is close to the frequency of the LCP absorption band, which will affect the CD of the unit considering this oblique incidence condition. Figure 6a intuitively shows this influence. As the incident angle θ in the x-z plane increases, the circular dichroism of the unit at 2.53 THz is weakened and blue-shifted. When θ = 45°, the circular dichroism will be reduced to 0.45. The circular dichroism of the unit near 3.43 THz is less affected by the incident angle, the operating frequency is almost not shifted, and it still has a strong circular dichroism of −0.72 when θ = 45° [74]. When the wave vector is confined to the yOz plane, the asymmetry of the unit structure is more reduced compared with the first oblique incidence case, so the performance of circular dichroism deteriorates more seriously. The results in Figure 6b show that when the incident angle θ in the yOz plane increases to 45°, the dual-frequency circular dichroism of the unit will drop to 0.42 and −0.51 respectively. Therefore, the hand-selective absorption performance of the structure under this oblique incidence is not stable, and this problem needs to be paid attention to in practical applications.

Figure 7 shows the relationship between the circular dichroism of the unit and the simulation frequency, and the inset is an illustration of the rotation angle φ of the pattern. As φ increases, the unit can still maintain the characteristics of having opposite strong circular dichroism at two frequency points [75]. The outer rectangular ring structure responsible for low-frequency circular dichroism has a strong coupling with the adjacent unit, and the working frequency of positive circular dichroism fluctuates periodically with φ in the range of 2.53∼2.65 THz. The inner ring structure responsible for high-frequency negative circular dichroism has very little coupling with the adjacent unit, so for any rotation angle φ , the unit can maintain a strong circular dichroism of −0.77 at 3.43 THz.

Only the unit rotation angle can govern the extra phase shift produced by the metasurface. According to theory, this phase control technique has a broad bandwidth [30], allowing the total rotation unit pattern to simultaneously control the dual-frequency reflection phase. In order to overcome the periodic change of the working frequency of the circular dichroism when the unit rotates, this paper selects four units with φ of 22.5°, 67.5°, 112.5° and 157.5° for separate simulation verification. The phase and amplitude of the co-polarization reflection coefficient of the four units are shown in Figure 8. At the two resonance points of 2.53 THz and 3.43 THz, as the rotation angle increases, the reflection phase of the four units appears to be faulted. This is because the chiral wave absorption characteristics of the unit at the resonance point blur the phase change.

The LCP wave’s reflection phase progressively diminishes as the rotation angle grows at the non-resonant frequency, whereas the RCP wave’s reflection phase gradually increases as the rotation angle increases [76–78]. The phase change trends are exactly opposite, and both can achieve a phase coverage of nearly 360°. Further observation also shows that the absolute value of the reflection phase difference between adjacent units is about 90°, which is exactly twice the rotation angle increment of 45°, and this phase change is dispersion-free, which conforms to the geometric phase theory. The co-polarization reflection amplitude of the four units is constant over the broad frequency range of 2.2∼3.8 THz, and it has a greater reflection amplitude at the non-resonant point, according to the reflection coefficient’s amplitude. Based on this excellent reflection coefficient dispersion-free performance, these four meta-molecular units can be used to design circularly polarized wave absorbing and abnormal reflection metasurface arrays.

For the above four meta-molecular units with a reflection phase difference of 90°, digital coding can be used to represent their phase response to design a reasonable coding strategy [31, 32]. This paper uses the numbers “0”, “1”, “2” and “3” to represent these four units, and uses the coding strategy of reflection phase gradient arrangement to construct a 2-bit strong circular dichroism circular polarization amplitude-phase control metasurface, in order to simultaneously realize the three functions of dual-frequency circular polarization chiral absorption, circular polarization conversion and abnormal reflection. The metasurface coding arrangement strategy is shown in Figure 9a. In the x direction, the four units form a superstructure unit cell with a period of L = 8 × p in the encoding mode of “00112233”, and extend with a period of L in the x direction. In the y direction, the superstructure unit cell extends with a period of p. The final constructed 16 × 16 supersurface array is shown in Figure 9b.

The metasurface with gradient phase can change the reflection direction of electromagnetic waves, that is, realize the abnormal reflection of electromagnetic waves [79, 80]. The reflection angle θ r of the abnormal reflection is obtained by the generalized form of Snell’s law: θ r = ± ⁡ sin − 1 sin ⁡ θ i + λ 0 / L (6) where θ i represents the angle of incidence, λ 0 is the wavelength of the signal, and L denotes the period length of the metastructure unit cell. In the proposed metasurface array, θ i is fixed to 0° and L = 268 μm. The sign of the reflection angle is specified as follows: “+” for LCP waves and “−” for RCP waves. Using Equation 6, the theoretical LCP/RCP reflection angles at the two resonance points of 2.53 THz and 3.43 THz are calculated to be −26° and +19° respectively.

The full-wave simulation was performed by using LCP/RCP plane waves to excite the metasurface at vertical incidence. Figure 10 displays the metasurface array’s one-dimensional normalized far-field pattern, with the three-dimensional far-field pattern inset. The RCP wave experiences hand-preserving anomalous reflection with a reflection angle of −26° at 2.53 THz, whereas the LCP wave is heavily absorbed. The LCP wave experiences hand-preserving anomalous reflection with a reflection angle of +19° at 3.43 THz, while the RCP wave is heavily absorbed. The experimental results are consistent with the theoretical analysis. The simulation results show that the metasurface array has two functions of circularly polarized chiral absorption and chiral anomalous reflection in two frequency bands, it is able to control the amplitude and phase of the CP waves at the same time.

The further validate the effectiveness of the proposed metasurface, Figure 11 compares the performance of the LCP and RCP wave in terms of phase angle. As can be seen from Figure 11, the phase angle variation is considerable for covering the desired spectrum.

Figure 12 compares the simulated and measured gain of the metasurface under increasing rotation angle.

As can be seen that, the simulated and measured gain are consistent and effective.

Figure 13 evaluates the surface current of the RCP and LCP waves with different values of phase angles. As can be seen from Figure 13, asymmetric electric field is created to generate resonant phase delay between both sides of the metasurface.

Figure 14 compares the OAM mode purity performance. It can be seen from Figure 14, the mode purity level at desired mode number is higher which is desirable for designing the metasuface generating OAM waves. This also enables to generates waves at specific mode.

Table 2 lists the comparison between the proposed metasurface design the existing works. Currently, most THz chiral metasurfaces with strong circular dichroism can usually only work in a single frequency band. From Table 2, it is evident that the suggested metasurface offers benefits in dual-frequency circular dichroism peak and multifunctional integration in addition to extending the operating frequency range to two.

This paper uses Jones matrix theory and geometric phase control principle to design a dual-frequency THz circularly polarized wave absorption and abnormal reflection chiral metasurface array. The metasurface realizes opposite circular dichroism in 2 THz frequency bands. Compared with ordinary metal plates, it can perform hand-preserving reflection of circularly polarized waves of specific rotation direction and has good circular polarization conversion ability. At the same time, the proposed metaruface has the ability of geometric phase control, and can realize the abnormal reflection of circularly polarized waves at a given angle through gradient phase arrangement. It explains the circular polarization absorption mechanism of chiral metasurface units by analyzing the surface current distribution of metasurface units. Through phase gradient arrangement, a chiral metasurface integrated array with chiral absorption, polarization conversion and abnormal reflection functions is designed, which realizes the absorption of circularly polarized waves of specific rotation direction at two working frequencies, and makes the orthogonal circularly polarized waves have chiral-preserving abnormal reflections at −26° and +19° respectively. In the future, it will promote its application in THz energy collection, polarization conversion, sensing, imaging and other fields.