THz science and technology are experiencing rapid developments owing to the advent of efficient THz sources and detectors. These advancements have unveiled numerous promising applications in imaging, sensing, and communications^[1–4]. Consequently, there is an urgent need for high-performance devices capable of modulating THz waves to realize these application goals including polarization modulators and absorbers^[5–9]. However, the optical response of most natural materials is not strong enough to THz waves^[10], and traditional THz polarization modulators face limitations in terms of thickness, profile, and operating distance, prompting the exploration of metamaterials for their unconventional electromagnetic properties^[11].

Metamaterials are artificially structured materials with subwavelength periodicities, enabling them to exhibit exotic electromagnetic responses^[12,13]. Numerous polarization modulators have been designed using metamaterials because THz sources often generate waves with uncontrolled polarization. Additionally, THz applications may require specific polarization states for optimal performance. Polarization converters (PCs) address these challenges by enabling polarization manipulation of THz waves. These PCs enable control over the direction of the electric field within the THz wave, leading to improved functionalities in THz devices^[14–16]. Similarly, metamaterial absorbers in the THz regime offer near-perfect absorption at specific frequencies, making them valuable for applications like THz imaging with enhanced sensitivity^[17,18]. In this regard, switchable metamaterials between a PC and an absorber have been investigated by researchers, showcasing dynamical polarization modulation as well as absorption, by altering the electromagnetic response of the metamaterial with the help of functional phase-change materials^[19–21].

Reconfigurable and switchable multifunctional metamaterial devices based on phase-change materials, such as ${\mathrm{VO}}_2$, GST, and GeTe, are research hotspots because they provide a controllable degree of freedom in light–matter interaction and information processing^[22]. Recently, bi-functional and multifunctional switchable metamaterial devices that can be used as a PC and an absorber have been proposed^[23–27]. However, the proposed structures were composed of six or more layers, in which some layers were responsible for polarization conversion while others were responsible for absorption. The multi-layer structure raised the difficulty of device realization in experiments. In addition, thermal modulation of phase-change materials limited their practical implications. The experimental realization of multifunctional switchable metamaterial in the THz regimes is still one of the challenging aspects and needs to be addressed more in the scientific community.

In this regard, we proposed a flexible and bendable metamaterial that can be switched between a PC and an absorber based on laser-induced graphene (LIG). LIG is a porous graphene material that was found in 2014 by Lin et al. via direct laser ablation of commercial polyimide (PI) films^[28]. It has good electrical and thermal conductivities and the advantages of low cost and quick fabrication of patterned structures without a clean environment. LIG was also found to have a high reflection of THz waves. Thus, LIG meta-structures can be realized^[29,30]. In this work, utilizing the flexibility of LIG, a bending switchable LIG metamaterial is designed and fabricated by a 532 nm $\mathrm{Nd}:{\mathrm{YVO}}_4$ solid-state laser. The device works as a THz linear polarization converter (LPC) and a circular polarization converter (CPC) when it is in a flat shape, while as an absorber after it is bent.

Figure 1 illustrates the unit cell and working schematic of the proposed LIG-based metamaterial in the reflection mode. It comprises three parts from bottom to top: an Aluminum (Al) reflector, a PI substrate, and a LIG antenna. Figure 1(a) depicts the front side of the unit cell in which $P=200\mathrm{\mu m}$ represents the period of the unit cell. The circular resonator is made of LIG having a thickness of 30 µm. Two gaps on the main diagonal are created having a dimension of $D=50\mathrm{\mu m}$. In this manner, the circular shape is converted to a double C-shaped resonator. The width of the LIG is taken as $W=30\mathrm{\mu m}$. The refractive index of the LIG is from the measured results of our previous work^[29]. The radius of the circular resonator is $R=50\mathrm{\mu m}$. A PI with a refractive index of 3.5 and tangent loss of 0.0027 is the precursor for generating the LIG, which is also used as a dielectric spacer, having a thickness of 80 µm^[31].

To investigate the optical properties of the design, an $X$-polarized (TE) field $E_{xi}{\widehat{e}}_x$ is incident on the metamaterial, using a commercially available CST microwave studio with Floquet unit cell boundaries. Unit cell boundary conditions are applied along the $x$- and $y$-directions while open boundaries are assigned along the $z$-direction. The optical responses for the two modes (TE, TM) are the same due to the structure anisotropy. Thus, the response for the two modes (TE, TM) was found to be the same. The reflected response can be mathematically written as, ${\overrightarrow{E}}_{\mathrm{ref}}=E_{xi}(R_{xx}{e}^{i{\delta }_{xx}}{\widehat{e}}_x+R_{yx}{e}^{i{\delta }_{yx}}{\widehat{e}}_y)$, where ${\delta }_{xx}$ and ${\delta }_{yx}$ are the phases of the co- and cross-polarizations. $R_{xx}$ and $R_{yx}$ are the reflection coefficients of the transverse electric (TE) mode. When the structure was excited by the two modes, the four reflected Jones matrix coefficients corresponding to the TE and transverse magnetic (TM) modes concerning the incident and reflected beams would be written as$$\left(\begin{array}{c}{E}_{xr}\\ E_{yr}\end{array}\right)=\left(\begin{array}{cc}{R}_{xx}& R_{xy}\\ R_{yx}& R_{yy}\end{array}\right)\left(\begin{array}{c}{E}_{xi}\\ E_{yi}\end{array}\right).$$(1)

The polarization conversion ratio (PCR) is usually defined as the ratio of power reflected in the cross-polarization to the sum of the co-polarization and cross-polarization^[32], $$\mathrm{PCR}=\frac{R_{yx}^2}{R_{yx}^2+R_{xx}^2}.$$(2)

The reflection coefficients were first numerically obtained for the TE mode incident on the metamaterial from the $Z_{\max }$ port, which is shown in Fig. 2(a). It is found that the cross-polarization component becomes stronger than the co-polarization component when the frequency is larger than 0.20 THz. The maximum amplitude of the cross-polarization reaches 0.83 at the frequency of 0.35 THz. The PCR spectrum calculated by Eq. (2) is depicted in Fig. 2(b). It can be seen that the polarization of the incident plane wave is converted to its cross-polarization from 0.27 to 0.41 THz with a PCR larger than 90%, which is indicated by the pink-shaded region. Therefore, the metamaterial acts as a linear polarization converter with a bandwidth of 0.12 THz. In addition, if the co- and cross-polarization coefficients have the same magnitude but have a phase difference of $\mathrm{\Delta }\phi ={\delta }_{yx}-{\delta }_{xx}=2n\pi \pm 0.5\pi$, the reflected wave will be circularly polarized. In Fig. 2(c), it is observed that the phase difference between the co- and cross-polarization components is approximately 88°–92° indicated by the green region. From Fig. 2(a), it can be found that the magnitude of the co- and cross-polarization components is almost equal from 0.48 to 0.62 THz, which is denoted by the shaded rectangle.

Considering both the reflection magnitude and phase difference, a linear polarized THz wave in this region is able to be converted into a circular polarization wave. To further investigate the circular polarization function, we calculate the axial ratio response of the metamaterial. An axial ratio below 3 decibels can be considered as a circularly polarized wave, which is defined as^[32]$$\text{Axial ratio}=10\log \left\{\tan \left[\frac{1}{2}\arcsin \left(\frac{S_3}{S_0}\right)\right]\right\},$$(3)$$S_0={|R_{xx}|}^2+{|R_{yx}|}^2,$$(4)$$S_3=2|R_{xx}||R_{yx}|\sin (\mathrm{\Delta }\phi ),$$(5)where $S_3$ and $S_0$ are the Stokes parameters, $\mathrm{\Delta }\phi$ is the phase difference between the co- and cross-polarization components, $S_0$ is the relative output electric field intensity or total reflection, and $S_3$ represents the circular polarization of the reflected wave. Figure 2(d) shows the axial ratio of the reflected wave in units of decibels. It can be seen that from 0.48 to 0.62 THz, the magnitude of the axial ratio is less than 3 decibels, indicating the conversion of linear polarization to circular polarization.

To elucidate the physical mechanism of the polarization conversion, we checked the $u–v$ analysis in which the incident $y$-polarized wave can be decomposed orthogonally into two components along the $u$-axis and the $v$-axis. This new coordinate basis $(u,v)$ is formed by rotating the original coordinates $(x,y)$ basis by 45°. In the simulation, this can be achieved by changing the polarization angle to 45°. The reflection coefficients in the new basis of the reflected wave are given in Fig. 3(a). The magnitudes of the co-polarized components are high compared to those of the cross-polarization components. If the phase difference of the co-polarized components between the incident wave and reflected wave is $\pm 180°$, the reflected polarization will be deflected 90° relative to the incident wave. If the phase difference is $\pm 90°$ or $\pm 270°$, the reflected polarization will be a left or right circularly polarized. From the phase difference shown in Fig. 3(b), we can see that from 0.27 to 0.41 THz, the phase difference is $-180°$ as indicated by the green strip, while at 0.48 to 0.62 THz, it is approaching $+90°$ as shown by the blue strip, indicating the polarization conversion from linear to cross polarization and linear to circular polarization conversion in these two bands, respectively. We also studied the current distributions on the top layer resonator and the bottom layer reflector at the resonance frequencies of 0.3 and 0.55 THz, where both the co- and cross-polarization components vary with equal magnitudes, which is depicted in Figs. 3(c) and 3(d), respectively. It is found in Fig. 3(c) that the currents on the resonator and the reflector are anti-parallel, resulting in a strong magnetic resonance. Therefore, a magnetic dipole moment is induced in the dielectric layer, leading to a strong coupling with the incident field. This electromagnetic coupling regulates the phase and amplitude of the reflected wave and causes a cross-polarization conversion. Similarly, at 0.55 THz, the current in the resonator can be differentiated into four different regions, as shown in Fig. 3(d). The currents in regions 1 and 3 are parallel, and the currents in regions 2 and 4 are anti-parallel to the current in the reflector, resulting in strong electric and magnetic dipole moments inside the dielectric layer. These strong electric and magnetic dipole moments are mainly responsible for linear to circular polarization conversion.

Instead of using a phase-change material, the optical response of the metamaterial is designed to be changed by convex shape bending. The structure was bent in a convex shape with the help of a cylinder having a radius ($r$) equal to the width of the $10\times 10$ array of the unit cell in the simulation and 1 cm in the experiment with $50\times 50$ array of the unit cell. In both cases, the bending angle around the cylinder is 57° or 1 rad, as shown in Fig. 4(a). The results suggest that when the structure was bent, the meta-atom resonator gradually lost the geometry that was responsible for the polarization conversion and in response reduced the cross-polarization component amplitude. The simulation results are depicted in Fig. 4(a), indicating that the optical response of the proposed design can be tuned from a PC to a low-absorbing material for various THz frequencies and thus can act as an on/off switch for the PC.

The absorption spectrum indicated by the blue line in Fig. 4(a) suggests that the metamaterial absorbed 75% to 95% of the incident THz wave. Thus, the metamaterial switches to a THz absorber from a PC in the process of the structure bending. The absorption of a THz wave by a metamaterial as it transitions from free space into the metamaterial can be comprehensively quantified by considering the reflection coefficients corresponding to both co- and cross-polarization components. This absorption, encapsulated in the formula $A=1-{|R_{xx}|}^2-{|R_{yx}|}^2$, delineates the reduction in reflectance achieved by the metamaterial through special boundary conditions under impedance matching theory. Fundamentally, this calculation is grounded in the relative impedance ($Z_r$), defined as the ratio of the effective impedance of the metamaterial $z_1=\sqrt{{\mu }_1/{\epsilon }_1}$ to the free space impedance $z_0=\sqrt{{\mu }_0/{\epsilon }_0}$, where ${\mu }_0$ and ${\epsilon }_0$ represent the permeability and permittivity of the free space, while ${\mu }_1$ and ${\epsilon }_1$ correspond to the metamaterial optical properties. This intricate interplay between reflection coefficients and impedance characteristics underpins the metamaterial efficacy in minimizing reflectance and maximizing absorption, facilitating the passage of the electromagnetic field into the metamaterial. The relative impedance in terms of the S-parameters is defined as$$Z_r=\pm \sqrt{\frac{{(1+S_{11})}^2-S_{21}^2}{{(1-S_{11})}^2-S_{21}^2}}.$$(6)

The real and imaginary parts of the relative impedance for both flat and bent structures are shown in Fig. 4(c). For the flat surface, the imaginary and real curves indicate a complete mismatch from the standard value of the relative impedance, which should be $+1$ for the real part and 0 for the imaginary part. For the bent structure, the real part of the relative impedance is $+1$ for the maximum band of the THz wave while the imaginary part is approaching 0. Thus, efficient absorption is achieved by the bent structure.

We prepared the double C-shaped metamaterial using a laboratory-built fabrication system^[29]. It consists of a $\mathrm{Nd}:{\mathrm{YVO}}_4$ nanosecond solid-state laser with an adjustable repetition rate (pulse width) of 15 ns and an output wavelength of 532 nm; a beam expander; a telecentric scan lens, which has a 60 mm focal length; and a matching scanning system that consists of two scanning mirrors used to tilt the laser beam toward the $x$- and $y$-directions, respectively, as shown in Fig. 5(a). A Kapton PI type with a thickness of 80 µm was used as a substrate. The reflector used is a 1-mm-thick aluminum tape, which can make the metamaterial flexible so that it can be bent easily. By controlling the system, the focused laser beam scans in a 2D plane to generate LIG patterns, as shown in Fig. 5(b). The fabrication of the double C-shaped metasurface with a size of $1\mathrm{cm}\times 1\mathrm{cm}$ was printed in 11 s. The power of the laser was ${153\mathrm{J}\mathrm{cm}}^{-2}$ for induction. The structure was analyzed by an optical microscope to visualize the array periodicity and parameters, as shown in Figs. 5(c) and 5(e). A reflective THz time-domain spectroscopy (TDS) system setup, as shown in Fig. 5(d), was used to measure the optical response of the proposed metamaterial. This involved positioning the metamaterial on the sample stage, with a THz wave emitted by a photoconductive antenna (PCA) incident normally, while the reflected THz wave was detected by the receiver using a semitransparent lens. The obtained results are shown in Fig. 6(a) for the co- and cross-polarization components and their respective PCRs. The PCR in this case is broadened and attains a bandwidth of 0.24 THz with a frequency shift towards higher THz frequencies, i.e., from 0.38 to 0.62 THz with an efficiency greater than 90%.

The broadening of the PCR spectra can be attributed to the geometrical errors in the fabrication process as the structure is highly sensitive to geometrical parameters. However, the experimental results show that the device can be used as a broadband and efficient PC.

Using the same apparatus, we measured the optical response of the bent structure in which a significant amount of decrease in cross-polarization intensity was observed, as shown in Fig. 6(b). The absorption spectra show 75% to 88% absorption for the whole bandwidth, demonstrating that the metamaterial becomes an absorbing THz material. From the above findings, it was confirmed that the metamaterial structure can be switched or reconfigured without the use of phase-change materials.

In summary, a single-layered low-cost bendable metamaterial based on LIG in the THz regime was investigated and showed a multifunctional ability, predominantly linear to cross and linear to circular polarization conversion, for a wide range of THz frequencies in the reflection mode. It could be used as a half-wave plate and a quarter-wave plate. The measured results were found to be consistent with the simulated results. It is anticipated that the design would open a new avenue for switchable THz devices with low cost and easy manufacturing.