Terahertz cascaded metasurfaces for both spin-symmetric and asymmetric beam diffractions with active power distribution

Electromagnetic waves in the frequency band of 0.1–10 THz (1 THz = 10¹² Hz) are defined as Terahertz (THz) waves. Due to its important applications in wireless communication,^1,2 radar monitoring,³ imaging,⁴ and sensing,^5,6 THz technology has attracted considerable attention recently. In addition to the vital THz sources⁷ and detectors,^8,9 efficient THz manipulation technologies, including beam focusing, deflection, steering, and polarization conversion, are also highly desired in these applications.^10–12 For conventional THz deflection devices, active angle scanning and energy distribution are hard to realize, which limits the degree of freedom of beam control. Moreover, their bulky size and low efficiency also cannot meet the needs of ultra-compact devices.¹³ 

The rapid development of metasurfaces provides an effective solution for ultra-compact and high-efficiency THz wavefront manipulation devices.^14–16 Metasurfaces are constituted of prearranged artificial unit cells or so-called meta-atoms with sub-wavelength size, the meta-atoms are capable of generating abrupt phase changes over the scale of the wavelength.^17–19 By constructing meta-atoms to form certain predesigned phase profiles, versatile beam manipulation effects can be demonstrated, such as anomalous deflection,^20–22 polarization manipulation,^23,24 and holograms.^25–27 

Pancharatnam–Berry (PB) metasurfaces, which are composed of half-wave-plate (HWP) meta-atoms with the spatial rotation axis, exhibit interesting properties in manipulating right-handed circularly polarized (RCP) states and left-handed circularly polarized (LCP) states with conjugated spatial phase distribution.^28–30 PB metasurfaces have been proposed for various functions, such as special beam generation,^31–33 metalens,³⁴ hologram,^35,36 and anomalous reflection.^37–39 To break the spin-conjugated symmetry of the geometric phase, a strategy is proposed to manipulate independent phase profiles by introducing additional dynamic phases. This kind of metasurface is also known as a spin-decoupled metasurface.^40–42 For example, Li et al.⁴³ proposed a metasurface with these two types of phases, broke the conjugated characteristic of the PB phase simultaneously, and achieved the longitudinal focusing and transverse shifting of different spin states.

However, the fixed structure cannot meet the requirements of dynamic manipulation of THz beam deflection, and the active control of power distribution is also difficult to achieve for the traditional PB or decoupled metasurfaces. Therefore, different kinds of fabrication processes and materials have been introduced into the metasurface devices for efficient diffraction and active functions. For example, PB metasurfaces integrated with magneto-optical materials,⁴⁴ graphene,⁴⁵ and liquid crystals⁴⁶ have been demonstrated recently. Kim et al.⁴⁵ proposed a gate-controlled THz PB metasurface that combined graphene to modulate the intensity of anomalous refracted waves, but the modulation depth was limited to 28%. Moreover, the rise of semiconductor materials has effectively improved the speed of beam modulation.^47,48 For example, Lan et al.⁴⁷ recently demonstrated a reconfigurable metasurface based on GaN technology, achieving wide-angle beam scanning with a high speed of 100 MHz. However, an active THz beam deflection device with high modulation depth is still a challenge, and the flexibility in high-order diffraction, large-angle deflection, spin conversion, and order transformation is limited by a single metasurface. Cascading two or more metasurfaces may greatly enrich the function of beam manipulation.

In this work, we propose an all-dielectric cascaded metasurface that integrates a decoupled metasurface and a PB metasurface. The conjugated characteristic of the PB phase for two photonic spin states is broken by efficient high-order diffractions through the wave vector superposition of the cascaded metasurfaces. Moreover, the spin-asymmetric transmission for spin-locked states (RR state and LL state) and the spin-symmetric transmission for spin–flip states (RL state and LR state) are obtained in different frequency bands based on the differences in metasurface bandwidth designing. By changing the incident polarization state, the active power distribution between the deflection beams has been confirmed. The unique method of manipulating the deflection of spin photons may have a significant impact on the design of ultra-compact multifunctional devices and spin photonics devices.

The cascaded metasurface is composed of a decoupled metasurface and a PB metasurface. Both the two metasurfaces were fabricated by a photolithography process and reactive ion beam etching on a high-resistance Si substrate of >10 kΩ cm with a thickness of 1 mm. The detailed fabrication process and geometric parameters can be found in Sec. A of the supplementary material. As shown in Fig. 1(a), the THz wave passes through the decoupled metasurface first. A supercell of decoupled metasurface consists of three rectangular silicon column meta-atoms with different lengths (l), widths (w), and orientations (θ). Different from the decoupled metasurface, a PB supercell is composed of four meta-atoms with the same length and width but different orientation angles with a step of Δθ_PB = 45° along the x-axis. The scanning electron microscope (SEM) photographs of two metasurfaces are shown in the inset in Fig. 1(a). The two metasurface layers are tightly attached with no separated air gap, and only a layer of Si substrate is separated between the spin-decoupled microstructures and the PB microstructures. The size of both metasurfaces is 1.5 × 1.5 cm², so there are 17 supercells in the x-direction for the PB metasurface and 26 supercells in the x-direction for the decoupled metasurface.

The working frequency band in which the metasurface has good spin state conversion and beam deflection performance is worthy of our attention. In the simulation, we get the frequency-dependent far-field diffraction distribution of two metasurfaces as shown in Fig. 1(b). For incident conjugated spin states, a decoupled metasurface can achieve asymmetric transmission. This means when an RCP state is incident, the beam will deflect toward the negative angle side in the range of Δf_DC = 0.6–0.85 THz, while the beam will not deflect when an LCP state is incident. However, outside this frequency range, there are still plenty of directly transmitted components that exist at 0° when the RCP state is incident, indicating that the spin-decoupling effect fails. In contrast, the PB metasurface can realize symmetrical deflection transmission with high diffraction efficiency in a broader frequency range of over 0.5–1.05 THz than the decoupled metasurface in the simulation.

Whereas, outside the frequency range Δf_DC, there are plenty of directly transmitted components with φ₁ = 0° after the THz beam passes through the decoupled metasurface. In this case, the spin conversion and spatial phase of the decoupled meta-atoms will disappear, so the transmission matrix of the cascaded metasurface is consistent with that of the PB meta-atoms as shown in Eq. (1).

We utilized an angle-resolved THz time-domain polarization spectroscopy (AR-THz-TDPS) system as shown in Fig 1(c). The femtosecond laser used is a fiber-based femtosecond laser (CFL-10RFF from Carmel Laser Company). It works at 780 nm with a repetition rate of 80 MHz and a pulse width of 86 fs. All experiments were carried out at room temperature (20 ± 2 °C) and relative humidity <30%. The laser beam is divided into two optical paths by a beam splitter, and both laser beams illuminate on THz GaAs photoconductive antenna (PCA), respectively. One is used to excite the THz wave, and the other is used to detect the THz signal.

The excited THz wave polarizes along the y-axis direction, and the parabolic mirror collimates the THz wave into a parallel beam with a diameter of 2 cm. The metasurface is placed at the center of a rotating table. As shown in Fig. 1(d), after the beam passes through the first polarizer and the metasurface, it is deflected with a diffraction angle φ and incident into the detector after passing through the second rotatable polarizer. The deflected parallel beam is focused on the PCA probe by a silicon lens located at the front of the detector. The angle-adjustable module has an angle resolution of 0.25°. Compared with the traditional THz-TDS system, we add a pair of THz polarizers before and after the metasurface for the generation and detection of orthogonal linearly polarized (LP) states. The THz polarizers are composed of double-layer metallic wire grids. The polarizers have more than 99.7% polarization degree in a range of 0.3 to 2.0 THz.

When the decoupled metasurface realizes good performance in spin conversion and beam deflection, it exhibits decoupled transmission properties for different photonic spin states as shown in Fig. 2(a). At this point, both metasurfaces can achieve the conversion of spin states. Therefore, the beam will retain its initial spin state after passing through the cascaded metasurface, that is, the spin-locked states RR and LL.

Next, we discuss the wave vector matching process of the spin-asymmetric transmission as shown in Fig. 2(b). As discussed in Sec. II B, the decoupled metasurface forms a negative phase gradient profile only for the incident RCP state, so the metasurface vector K_DC = 2π/A_DC is negative along the x-axis for the incident RCP state, and K_DC = 0 for the incident LCP state. Consequently, the RCP state can be converted to the LCP state and diffracted to −1st order (m₁ = 1) with the diffraction angle φ₁ = arcsin(−λ/A_DC) calculated by Eq. (4). While the LCP state is converted to the RCP state and still stays at 0°. Since the PB metasurface forms conjugated gradient phases for different spin states, the vectors K_PB = 2π/A_PB have opposite directions along the x-axis for the two spin states, respectively. For the above outgoing wave vector k₁ along the z-axis direction, when it is superposed with the vector K_PB, +1st order (m₂ = 1) diffraction can be obtained, and the RCP state is converted to the LCP state.

In this case, according to Eq. (5), the diffraction angle of the cascaded metasurface is φ_LL = arcsin[+c/(fA_PB)] when the RCP state is incident, and φ_RR = arcsin[−c/(fA_DC) + 3c/(fA_PB)] when the LCP state is incident. The results show that the two spin-locked states RR and LL are deflected to the same side with different diffraction angles. We use the beam diffraction order: +1st and +3rd orders through the PB metasurface to distinguish the two deflected beams.

In the simulation, we get the frequency-dependent diffraction distribution of two spin-locked states as shown in Fig. 2(c). The results show that both spin-locked states LL and RR are diffracted to a positive angle with different diffraction orders. The diffraction angles φ_LL and φ_RR satisfy the frequency-angle correspondence of the +1st order and +3rd order, respectively. The diffraction frequency range of the +1st order is wider than that of the +3rd order, which is related to the critical angle for total internal reflection. The diffraction intensity of the +1st order is also stronger than that of the +3rd order.

We scanned the diffraction angles in the experiment and obtained the diffraction efficiency of the cascaded metasurface as shown in Fig. 2(d). For the LL state, the +1st diffraction order covers the frequency range over 0.52–1 THz, corresponding to the diffraction angle range over 22°–46°. While for the RR state, the +3rd order covers the frequency range over 0.6–0.87 THz, corresponding to a larger diffraction angle over 41°–72°. The intensity of both diffraction orders reaches its maximum at 0.72 THz, and the diffraction intensity of the +1st order is also stronger than that of the +3rd order in the experiment. As a consequence, the spin-asymmetric transmission between the two spin-locked states RR and LL can be achieved by the cascaded metasurface in the frequency band 0.6–0.87 THz.

When the beam frequency is outside the operating frequency band Δf_DC of the decoupled metasurface, there are plenty of directly transmitted components that maintain the original spin states at φ₁ = 0° after the THz beam passes through the decoupled metasurface as shown in Fig. 3(a). At this point, the vectors K_DC for the two spin states are always equal to 0, resulting in the outgoing wave vector k₁ remaining in the z-axis direction without deflection as shown in Fig. 3(b). The vectors K_PB = 2π/A_PB still have opposite directions along the x-axis for the two spin states, respectively. In this case, the cascaded metasurface will degenerate into a PB metasurface with the functions of spin conversion and spin-symmetric transmission. When the outgoing wave vector k₁ is superposed with the vector K_PB, +1st order and −1st order diffraction (m₂ = 1) can be obtained for the two spin states, respectively. The diffraction angle of the cascaded metasurface becomes φ_LR = arcsin[+c/(fA_PB)] when the RCP state is incident, and φ_RL = arcsin[−c/(fA_PB)] when the LCP state is incident. Consequently, the two spin–flip states RL and LR are deflected to different sides in the x-direction with the same diffraction angles.

Similarly, we verified the theory in the simulation and experiment, and the frequency-dependent diffraction distributions of two spin–flip states are shown in Figs. 3(c) and 3(d). The simulated results reveal that the diffraction distributions of the two spin–flip states RL and LR are symmetric to 0°, and the beams have essentially equal power at ±1st order. In the experiment, we scanned the diffraction angles and obtained a symmetric diffraction distribution for RL and LR states in a frequency band of 0.42–0.67 and 0.85–1.05 THz, corresponding to a diffraction angle of 34°–63° and 21°–26°. There are some deviations between the simulation and experimental results in terms of diffraction efficiency and bandwidth, which are mainly caused by the imperfections in the actual fabrication process. Fortunately, a larger bandwidth was obtained in the experiments. Therefore, the spin-symmetric transmission between the two spin–flip states RL and LR can be achieved by the cascaded metasurface in the frequency bands 0.42–0.67 and 0.85–1.05 THz.

In the simulation, the QWP is modeled as a medium with uniaxial anisotropy, a detailed simulation of the QWP can be found in Sec. D of the supplementary material. We selected the incident wave sources with frequencies of 0.7 and 0.45 THz, respectively, and obtained far-field transmittance spectra to verify the power distribution function as shown in Figs. 4(b) and 4(c). When the wave is incident with a frequency of 0.7 THz, the beam can be diffracted to +32.5° and +54.5° diffraction angles, respectively, corresponding to the diffraction angles of the +1st and +3rd orders in the frequency band Δf_DC. It can be seen that the beam power can be actively distributed from +3rd order to +1st order with the increase of the rotation angle α. Whereas, when the wave is incident with a frequency of 0.45 THz, the beam can be diffracted to ±56.5° diffraction angles symmetrically, corresponding to the diffraction angles of the ±1st orders outside the frequency range Δf_DC, and the power is dynamically tuned between ±56.5° diffraction angles as the rotation angle changes. Therefore, the rotation of the QWP can be regarded as an efficient strategy to actively distribute the power between the diffraction beams.

We carry out the experiments in the AR-THz-TDPS system. The diffraction angles measured in the experiment are calculated by substituting the selected frequencies of 0.7, 0.8, and 0.45 THz into the diffraction angle equation for different diffraction orders. The actual measurement frequencies were 0.69, 0.78, and 0.45 THz due to the mechanical error introduced by the instrument. As discussed in Secs. III A and III B, spin-asymmetric transmission can be achieved theoretically by cascading metasurface at 0.69 and 0.78 THz, while spin-symmetric transmission can be achieved at 0.45 THz. The results at these three frequencies are shown in Figs. 5(a)–5(c). At 0.69 THz, when α is rotated from 45° to 135°, beam power is gradually distributed from 54.5° (+3rd) diffraction angle to 32.5° (+1st) diffraction angle. At the same time, two diffraction beams have opposite spin states. Similar results are found at 0.78 THz. While at 0.45 THz, the beam power is distributed between 56.5° (±1st) diffraction angles on different sides, and two diffraction beams also have opposite spin states. In addition, there is a residual signal for the LCP transmission at 54.5° and 45.5° diffraction angles. The reason is that under the oblique incidence condition, the PB phase matching condition in high-order diffraction is no longer perfectly satisfied, but this residual peak below 15% only causes a small negative impact on the overall performance of the device.

The angular resolution of the diffractive beam is determined by the number of metasurface supercells and working frequency, which have been given in Sec. II A. The larger the aperture of the metasurfaces, the narrower the beam angle width will be. According to the dependence between frequency and diffraction angle, the full width at half maximum (FWHM) of the transmission peak in the experiment can also reflect the diffraction angle width. The experimental results in Fig. 5 reveal that the FWHM is in the range of 28–48 GHz.

We define the power modulation ratio (PMR): R_α = (T_max − T_α)/T_max to characterize the performance of active power distribution between the diffraction beams, where T_α is the intensity transmittance at different QWP rotation angles, and T_max is the maximum intensity transmittance at the corresponding diffraction angles. The results are shown in Figs. 6(a) and 6(b). At 0.78 THz, the PMR of the two diffraction orders reaches 99.3% and 95.1%, respectively, indicating that the energy is allocated to the other diffraction beam with the rotation of QWP. At 0.45 THz, the PMR of the two diffraction orders also reaches 88.2% and 92.8%, respectively. The experimental results show that no matter the spin-asymmetric transmission or the spin-symmetric transmission, the beam power can be actively distributed between the two diffraction beams depending on the rotation of QWP. In the actual device, the PMR is affected by the spin conversion efficiency of the decoupled metasurface and the PB metasurface. Moreover, when the frequency of the deflected beam deviates from the center frequency of QWP, the modulation efficiency will also be reduced. Consequently, the modulation depth is determined by the matching degree of the bandwidth and center frequency of these three components.

Finally, this controllable beam steering and power distribution method is expected to show great potential applications. For example, in a point-to-point THz communication network, when the network link is blocked, active beam steering can effectively establish a new link without mechanical movement to realize the function of fast anti-shielding interference. Active beam manipulation with large deflection angles and a wide scanning range can also effectively realize multi-azimuth target monitoring in radar monitoring. It should be pointed out that mechanically rotating the QWP is only intended to demonstrate the physical process of device modulation in the simplest way by changing the incident polarization states. Other active modulation mechanisms for the metasurfaces excited by the electric, optical, and magnetic fields are more practical options,^44–48 but this issue is not the main focus of this work.

In summary, we demonstrated an all-dielectric cascaded metasurface consisting of a decoupled metasurface and a PB metasurface for THz beam manipulation. Spin-asymmetric and spin-symmetric diffraction transmission is realized in different frequency bands for two conjugate photonic spin states, and active power distribution between the diffraction beams of the same frequency is achieved by the rotation of QWP. Some conclusions can be drawn: (1) In a frequency band of 0.6–0.87 THz, the cascaded metasurface can induce the +1st and +3rd order diffraction for the two spin-locked states RR and LL, respectively, realizing the spin-asymmetric transmission. (2) In a frequency band of 0.42–0.67 and 0.85–1.05 THz, the cascaded metasurface degenerates to the PB metasurface, which can induce the +1st and −1st order diffraction for the two spin–flip states RL and LR, respectively, thus achieving a spin-symmetric transmission. (3) Relying on the polarization conversion characteristic of the QWP, the active power distribution between the diffraction beams is realized. The experimental results show that the power modulation ratio of the two diffraction orders at 0.78 THz reaches 99.3% and 95.1%, respectively. Therefore, this work provides a scheme of active THz manipulation and realizes controllable wavelength division multiplexing, spin separation, conversion, and power distribution. The proposed metasurface has a significant impact on designing ultra-compact multifunctional devices and has certain application potential in terahertz wireless communication, radar, and imaging.

See the supplementary material for further details on metasurface structure and fabrication, metasurface design, transmission matrix derivation, simulation modeling, and a discussion of the distance between two metasurfaces.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62371258, 62335012, 61971242, 61831012, 62205160) and the National Key Research and Development Program of China (Grant No. 2017YFA0701000).

The authors have no conflicts to disclose.

Jiayue Liu: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Methodology (lead); Resources (equal); Validation (lead); Visualization (lead); Writing – original draft (lead). Fei Fan: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal); Methodology (supporting); Resources (equal); Visualization (supporting); Writing – review & editing (equal). Zhiyu Tan: Resources (equal); Writing – review & editing (equal). Huijun Zhao: Methodology (supporting); Visualization (supporting); Writing – review & editing (equal). Jierong Cheng: Methodology (supporting); Resources (equal). Shengjiang Chang: Funding acquisition (equal); Resources (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.