Broadband metamaterial polarizers with high extinction ratio for high-precision terahertz spectroscopic polarimetry

(a) Selective absorption of unpolarized light in a polarizer. (b) Schematic design of the single- and double-layer gold MPs placed on the PI substrate. (c) Schematic side view of (top) SL, (middle) ADL, and (bottom) CDL MPs. The metal structure was patterned with gold, and polyimide was used as a substrate and spacer between the upper and lower layers.

To obtain the optimized geometrical parameters of the MPs, we compared the transmittance in the perpendicular (T_⊥) and parallel (T_∥) polarizations to the three MP designs using a commercial finite element method solver, CST microwave studio [Figs. 2(a)–2(c)]. Here, we fixed the lattice constant L = 7 µm and varied the gap width, g, from 2 to 6 µm. The simulation results show that for all three MP designs, as the gap width g decreases, T_⊥ varies insignificantly over ∼5 dB, whereas T_∥ decreases substantially. In addition, with an increase in the number of grating layers, T_∥ decreases markedly. It can be observed that CDL has the lowest T_∥ below −80 dB compared to SL and even ALD. The effectiveness of the polarizers in filtering T_∥ directly influenced the ER, indicating a critical dependency on the design parameters of the MPs. Here, the ER is the ratio T_⊥ of T_∥ and can be defined as $ER (dB) = 10 \log (T_{⊥} / T_{‖})$ ⁠. Figure 2(d) shows the calculated ER for optimized parameters of g = 2 µm and d = 3 µm. The simulation results of the CDL MP show that more than 80 dB of ER is achieved in the wide frequency range from 0.2 to 2.5 THz. In comparison, the ADL MP achieves ER levels ranging from 70 to 80 dB, while the SL MP demonstrates lower ER levels, between 40 and 60 dB. To investigate why CDL maintains EOT for the perpendicular polarization component while more effectively blocking the parallel polarization component, we compared the numerically calculated electric field distributions of the three MP designs. Figures 2(e) and 2(f) show the perpendicular component of the electric field E_⊥ and the parallel component of the electric field E_||. When the THz wave is incident with perpendicular polarization, as seen in the electric field distribution of E_⊥, there is a strong field concentration around the gaps in all cases, resulting in high EOT [Fig. 2(e)]. For both ADL and CDL, the re-radiation of SPPs from the bottom plane of the upper layer couples effectively to the SPPs in the lower layer. Despite the overlapping structure of CDL, at the lower layer, this coupling induces EOT and maintains a comparable level of EOT with minimal transmission loss compared to SL. On the other hand, for the incidence of parallel polarization, as with SL and ADL, the blocking mechanism is attributed to absorption and reflection via the Drude response of metallic wire. To investigate the differences in the values of T_|| for each MP in more detail, we plotted with a reduced scale of E_|| [Fig. 2(f)]. Most of the E_|| is reflected and absorbed by the metallic wire, allowing only a very small amount to be transmitted. Due to the overlapping structure of the CDL, the small amount of transmission in the upper layer is more effectively blocked in the lower layer, resulting in significantly higher attenuation compared to SL and ADL designs, as seen in the field distribution.

FIG. 2.

(a)–(c) Numerically calculated transmittance T_⊥ and T_|| for (a) SL, (b) ADL, and (c) CDL MPs with a variation in metal width w. (d) Calculated ER for SL (black line), ADL (blue line), and CDL (red line). Electric field distributions for (e) T_⊥ and (f) T_|| in SL, ADL, and CDL MPs.

III. FABRICATION AND EXPERIMENTAL SETUP

A. Fabrication process for proposed metamaterial polarizer

The proposed MPs are fabricated using a conventional microelectromechanical systems (MEMS) process [Fig. 3(a)]. First, the PI solution (PI-2610, HD MicroSystems) was applied to a sacrificial silicon wafer using spin-coating to achieve a target thickness of 3 µm. A 200-nm-thick layer of gold was deposited on a negative photoresist (AZ nLOF2035, MicroChemicals) with a 20-nm-thick chromium adhesion layer used for adhesion, followed by patterning via photolithography. In the double-layer polarizers, the manufacturing process was repeated in the same manner. The separation between the upper and lower layers was achieved using the same PI curing process, resulting in a thickness of 3 µm. Then, the thin and flexible MPs were peeled off from the silicon substrate and mounted on a custom 3D-printed holder [Fig. 3(b)]. The overall sample size is 2.5 by 2.5 cm². The film is mounted flatly without any critical wrinkles or deformation. Although slight wrinkles may form during the taping process, the total thickness of the sample is very thin at 3 µm. Given that the wavelength at 1 THz is 300 µm, this minimal deformation has a negligible impact on the measured results from the fabricated sample. Figure 3(c) shows the microscope images of the fabricated MPs, demonstrating that the upper and lower layers of the double-layered structure are well aligned.

FIG. 3.

(a) Schematic representation of fabrication process for MPs. PI is used as a flexible substrate, and the separation between the upper and lower layers is achieved with a narrow space. (b) Mounted CDLs MP on a custom 3D-printed holder and (c) microscopic image of fabricated three MPs. The overall sample size is 2.5 by 2.5 cm².

B. Polarization-resolved THz TDS Setup

The MPs are characterized using a commercial THz time-domain spectroscopy system (TOPTICA TeraFlash Pro). As illustrated in Fig. 4(a), the experimental setup consists of a photoconductive emitter generating the polarized THz wave, which is then focused onto the sample through two parabolic mirrors. Two SL MPs were placed both behind the THz emitter and in front of the detector to establish and detect linear polarization of the generated THz waves. SL1 defines the polarization of the incident THz electric field in the x-direction, and SL2 is configured to block the y-component of the THz field before detection. To characterize the performance, the polarizer is rotated by 90° to align with either a perpendicular or parallel orientation, and the corresponding transmittance is measured. Then, the THz wave transmitted through the polarizer is subsequently detected and measured by a photoconductive detector.

FIG. 4.

(a) Schematic illustration of THz time-domain spectroscopy. Measured THz time-domain signal for three MPs with (b) perpendicular and (c) parallel polarizations. Fourier-transformed THz frequency-domain spectroscopy of (d) T_⊥, (e) T_∥, and (f) ER (solid lines) for the three MPs. The measured results are compared with simulation results (dashed lines).

IV. CHARACTERIZATIONS OF METAMATERIALS POLARIZER

We start by measuring the polarized and blocked time-domain signals in the parallel and perpendicular directions to a metal wire in the MPs, respectively. As shown in Fig. 4(b), all three MPs allow most of the incident perpendicularly polarized THz waves (E_⊥) to pass through. Moreover, the subwavelength thickness and minimal dispersion of the designed polarizers allow the THz pulse to be maintained without multiple internal reflections. However, for incidence of parallel polarization (E_||), while the SL MP does not completely block the parallel component, the ALD and CLS MPs block it to the level of noise [Fig. 4(c)]. Through Fourier transformation, the T_⊥ and T_∥ spectra were obtained (solid lines) and compared with the simulation results (dotted lines) for the three MPs in the frequency range of 0.2–2.5 THz, as shown in Figs. 4(d) and 4(e). For T_⊥ spectra [Fig. 4(d)], the ALD (red line) and CLD (blue line) MPs are lower than that of the SL MP (black line), and all polarizers transmit more than 40% of the THz wave in the broad frequency range from 0.2 to 2.5 THz [Fig. 4(d)]. In the case of ALD and CLD MPs, the insertion loss remains very low up to about 1.0 THz, and there is almost no difference in transmission. However, for T_∥, the CDL is about 10 dB lower than the ADL [Fig. 4(e)], indicating that the CDL effectively shields the parallel polarized electric field, as previously shown in the electric field distribution simulation results. As a result, the CDL MP shows ER ∼10 dB higher than the ADL MP across the entire frequency range. In particular, the maximum ER for the CDL MP is measured to be about 90 dB at 0.7 THz with T_⊥ of more than 90%. In Table I, we compared the performance of polarizers in the THz region from existing studies, including commercial products. The comparison covers key parameters such as the number of layers, fabrication methods, transmission efficiency, ER, and operating bandwidth. Compared to conventional single- and multi-layered polarizers, our study demonstrates notable advantages in terms of simplicity and ease of fabrication while still delivering superior broadband performance and a high ER.

TABLE I.

Performance comparison of recent research and this work on highly efficient broadband THz polarizers.

Layer	Material	Fabrication	Transmission efficiency (%)	Extinction ratio (dB)		Bandwidth (THz)	References
1	Au	Photolithography	>70	Avg	∼40	0.1–1.0	24
1	SiO₂	Lif-off	>70	Max	48@0.2 THz	0.1–1.0	24
2	AI	Photolithography	∼80.5	Avg	>55	0.1–2.0	25
	PI	Deposition		Max	70@0.1 THz
	PI	Wet etching		Max	70@0.1 THz
2	Au	Photolithography	∼50	Avg	∼60	0.5–2.0	26
	Si₃N₄	Deposition		Max	87@1.06 THz
	Si	Wet etching		Max	87@1.06 THz
2	Au	Photolithography	>90	Avg	>50	0.2–1.1	27
	SiO₂	Deposition		M > 90ax	65@0.3 THz
	Si	Wet etching		M > 90ax
2	Au	Photolithography	∼40	Avg	∼69.9	0.6–3.0	28
	Si	E beam evaporation		Max	84.9@1.67 THz
		Ion etching		Max
1	AI	Photolithography	>90	Avg	<30	0.3–2.5	29
	COP	E beam evaporation		Max	45@0.3 THz
		Wet etching		Max
1	ITO	Photolithography	>80	Avg	∼20	0.1–2.5	30
1	PET film	RF sputtering deposition	>80	Max	25@0.6 THz	0.1–2.5	30
1	Au	Photolithography	>95	Avg	∼40	0.4–2.0	31
	AI₂O₃	Atomic layer deposition	>95	Max	55@1.0 THz
	SI	Atomic layer deposition			55@1.0 THz
1	Tungsten wires	w/o substrate	>92	Avg	>30	0.2–2.0	Tydex (commercial)
1	Tungsten wires	w/o substrate	>92	Max	50@0.2 THz	0.2–2.0	Tydex (commercial)
2	Au	Photolithography	∼40	Avg	>60	0.2–2.5	This work (CDLs)
	PI	Deposition	>90@0.2–1 THz	Max	>92@0.7 THz
	PI	Lift-off	>90@0.2–1 THz	Max	>92@0.7 THz

Layer	Material	Fabrication	Transmission efficiency (%)	Extinction ratio (dB)		Bandwidth (THz)	References
1	Au	Photolithography	>70	Avg	∼40	0.1–1.0	24
1	SiO₂	Lif-off	>70	Max	48@0.2 THz	0.1–1.0	24
2	AI	Photolithography	∼80.5	Avg	>55	0.1–2.0	25
	PI	Deposition		Max	70@0.1 THz
	PI	Wet etching		Max	70@0.1 THz
2	Au	Photolithography	∼50	Avg	∼60	0.5–2.0	26
	Si₃N₄	Deposition		Max	87@1.06 THz
	Si	Wet etching		Max	87@1.06 THz
2	Au	Photolithography	>90	Avg	>50	0.2–1.1	27
	SiO₂	Deposition		M > 90ax	65@0.3 THz
	Si	Wet etching		M > 90ax
2	Au	Photolithography	∼40	Avg	∼69.9	0.6–3.0	28
	Si	E beam evaporation		Max	84.9@1.67 THz
		Ion etching		Max
1	AI	Photolithography	>90	Avg	<30	0.3–2.5	29
	COP	E beam evaporation		Max	45@0.3 THz
		Wet etching		Max
1	ITO	Photolithography	>80	Avg	∼20	0.1–2.5	30
1	PET film	RF sputtering deposition	>80	Max	25@0.6 THz	0.1–2.5	30
1	Au	Photolithography	>95	Avg	∼40	0.4–2.0	31
	AI₂O₃	Atomic layer deposition	>95	Max	55@1.0 THz
	SI	Atomic layer deposition			55@1.0 THz
1	Tungsten wires	w/o substrate	>92	Avg	>30	0.2–2.0	Tydex (commercial)
1	Tungsten wires	w/o substrate	>92	Max	50@0.2 THz	0.2–2.0	Tydex (commercial)
2	Au	Photolithography	∼40	Avg	>60	0.2–2.5	This work (CDLs)
	PI	Deposition	>90@0.2–1 THz	Max	>92@0.7 THz
	PI	Lift-off	>90@0.2–1 THz	Max	>92@0.7 THz

V. IMPACT OF EXTINCTION RATIO ON POLARIZATION MEASUREMENT ACCURACY

In this section, we quantitively examine the impact of ER with the proposed MPs on THz polarimetry. The polarization-dependent transmission coefficient after passing through a series of optical elements as illustrated in Fig. 5(a) can be efficiently calculated by Jones matrix formalism. Our proposed MPs are represented by the 2 × 2 Jones matrices

J_{x} = [10; 0 η]

and

J_{y} = [η 0; 01]

⁠, where η is the inverse of the ER. We start by considering the materials with optical anisotropy simply described by Jones matrix

M_{lin} = [t_{x x} t_{y x}; t_{x y} t_{y y}]

⁠, where the transmission coefficient t_ij represents the transmission of i-polarized light into j-polarized transmitted light. Assuming a fixed polarization direction of both the THz source and detector

(|E_{s}⟩ = |E_{d}⟩ = (0; 1)

⁠) and neglecting other experimental errors except for the polarizer’s ER, the measured transmission coefficient t_m,ij in the Jones matrix M_lin of target materials with two polarizers in the THz polarimetry setup [Fig. 5(a)] can be derived as

t_{m, i j} = a R (- \frac{π}{4}) J_{i} M_{lin} J_{j} R (\frac{π}{4}) ⟨ E_{d} | E_{s} ⟩,

(1)

where i, j = x, y and

a = 1 / \sqrt{1 + η^{2}}

⁠. The rotation matrix

R (π / 4)

transforms the laboratory coordinates of the source and detection into the sample coordinates, while

R (- π / 4)

converts the sample coordinates back to the laboratory coordinates. This indicates that the x and y axes in the sample coordinates are rotated by π/4 with respect to the laboratory coordinates. Compared to sample Jones matrix M_lin, the measured Jones matrix M_m,lin of sample in linear polarization basis is given by

M_{m, l i n} = (\begin{matrix} t_{m, x x} & t_{m, x y} \\ t_{m, y x} & t_{m, y y} \end{matrix}) = \frac{a}{2} (\begin{matrix} η^{2} t_{y y} + η (t_{y x} + t_{y x}) + t_{x x} & η^{2} t_{y x} + η (t_{y y} + t_{x x}) + t_{x y} \\ η^{2} t_{x y} + η (t_{y y} + t_{x x}) + t_{y x} & η^{2} t_{x x} + η (t_{y x} + t_{x y}) + t_{y y} \end{matrix}) .

(2)

As η ≪ 1, M_m,lin can be approximated as

M_{m, l i n} \approx (\begin{matrix} η (t_{y x} + t_{y x}) + t_{x x} & η (t_{y y} + t_{x x}) + t_{x y} \\ η (t_{y y} + t_{x x}) + t_{y x} & η (t_{y x} + t_{x y}) + t_{y y} \end{matrix}) .

(3)

FIG. 5.

https://doi.org/10.1038/nmat708

(a) Schematic illustration of THz polarimetry setup and NH metasurfaces with two orthogonally oriented SRRs. Dimensions are set to L_y1 = L_y2 = 30, L_x1 = 55, L_x2 = 80, d₁ = 10, d₂ = 50. The thickness of the silicon substrate is 525. All units are in μm. Calculated (b) transmittance and (c) phase and measured (d) transmittance and (e) phase in the circular polarization basis.

While the diagonal terms depend on the sum of cross-polarization terms (t_yx + t_xy), the off-diagonal elements are influenced by the sum of diagonal terms (t_yy + t_xx) weighted by η. In other words, as η decreases (ER increases), the impact on each element diminishes, which means that a high ER of a polarizer is closer to a perfect polarizer (η = 0). Furthermore, when the optical system defined with x and y eigen polarization states is characterized, we can measure the co-polarization component (t_m,xx, t_m,yy) nearly accurately and the off-diagonal term (t_m,xy, t_m,yx) does not need to be measured due to the negligible cross-polarization component. However, when the optical system with non-orthogonal eigen polarization states is characterized, all components of the Jones matrix need to be measured to accurately define materials’ optical properties and the dependence of measured optical properties on η becomes significant. In addition, the effects of the polarizer’s ER on polarimetry can also be revealed through the investigation of the circular polarization basis. Here, the Jones matrix of materials in a circular polarization basis is defined by

M_{cir} = [t_{l l} t_{l r}; t_{r l} t_{r r}]

⁠, and then we can calculate the measured one M_m,lin as

M_{m, c i r} = \frac{1}{2} (\begin{matrix} - 2 η i (t_{r l} - t_{l r}) + t_{l l} & t_{l r} - 2 η i (t_{r r} + t_{l l}) \\ t_{r l} + 2 η i (t_{r r} + t_{l l}) & - 2 η i (t_{r l} - t_{l r}) + t r r \end{matrix}) .

(4)

In most optical materials, the co-polarization transmission (t_ll, t_rr) is higher than the cross-polarization transmission (t_rl, t_lr). This difference can lead to an increased error due to ER when measuring the cross-polarization component, as can be seen in Eq. . This dependence of the measured cross-polarized transmission (t_rl, t_lr) on η is numerically validated by calculating the Jones matrix for the designed MPs with different ER values in this work and target materials.

To examine the effect of ER on polarimetry measurements, particularly in cross-polarization transmission in a circular polarization basis, we consider a NH metasurface composed of two orthogonally oriented split ring resonators (SRRs) [Fig. 5(a)] with a chiral exceptional point (EP) that exhibits identical co-polarized transmission but differences in cross-polarized transmission.²¹ Furthermore, the co-polarized transmission is higher than the cross-polarized transmission, meaning that the measurement of cross-polarized transmission is easily influenced by η. Similarly, the SL MPs were placed behind the THz emitter and in front of the detector to achieve and detect linear polarization in the x-axis direction of the generated THz waves. In our analysis, the numerically calculated Jones matrix of the NH metasurface is represented by matrix M_lin, with the numerically acquired Jones matrix polarizers for x and y directions denoted by J_x and J_y, respectively. Using Eq. (1), we can derive each component of the Jones matrix measured with the polarizers. This formulation allows us to numerically analyze the effect of polarizers with different ER on the measurement accuracy of the Jones matrix components for the NH metasurfaces. Figures 5(b) and 5(c) show the numerically calculated transmittance and phase of all the elements in circular polarization bases with SL (purple), ADL (red), CDL (blue), and without polarizer (green). The effect of the ER of the polarizer on polarimetry can be determined by how well the results with the polarizer match the calculations without the polarizer. The transmittance and phase of the co-polarized wave (t_rr and t_ll) are identical regardless of the presence of a polarizer but the ER significantly affects the cross-polarization, especially t_rl (when left-handed circular polarization converts to right-handed circular polarization) due to the strong resonance caused by the chiral EP. The simulation results show that the higher the ER of the MP, the more closely the transmittance matches the ideal results (without polarizer, green line). For the highly sensitive phase case, an abrupt jump can occur depending on the ER, leading to completely different results.

To experimentally validate the effectiveness of our high-performance polarizers, we also performed fabrication and characterization of the polarization-dependent transmission properties of the NH metasurface as designed in numerical simulation. The sample consisted of the NH metasurface on a silicon substrate, as shown in Fig. 5(a). The experimental setup for THz time-domain spectroscopic polarimetry involved placing the MPs both in front of (MP1) and behind (MP2) the sample. These polarizers were rotated by +45° or −45° to measure co- and cross-polarization in the linear basis components of t_xx, t_yy, t_xy, and t_yx. These measured transmission components were then transformed into transmission components in the circular polarization basis as follows:

(\begin{matrix} t_{l l} & t_{l r} \\ t_{r l} & t_{r r} \end{matrix}) = \frac{1}{2} (\begin{matrix} (t_{x x} + t_{y y}) + i (t_{x y} - t_{y x}) & (t_{x x} - t_{y y}) - i (t_{x y} + t_{y x}) \\ (t_{x x} - t_{y y}) + i (t_{x y} + t_{y x}) & (t_{x x} + t_{y y}) - i (t_{x y} - t_{y x}) \end{matrix}) .

(5)

As shown in Figs. 5(d) and 5(e), the measured results confirm distinct differences in transmittance and phase for t_rl depending on the ER values of the MPs, which show good agreement with the simulation results. By examining the measured transmittance of t_rl, we observe that the result with CDL is nearly close to zero, indicating proximity to the chiral EP. The measured phase of t_rl with CDL and ADL demonstrates nearly identical phase gradients, while that of SL, with a relatively smaller ER, exhibits a phase flip, indicating that this measured result is relatively farther from the EP. This reveals the relationship between the ER of the MPs and their effectiveness in accurately measuring cross-polarized transmission. This simulated and measured t_rl with different values of ER highlight the importance of using high-ER polarizers for precise polarization-dependent characterization of complex optical materials with cross-polarized transmission components, such as metasurfaces with Pancharatnam-Berry (PB) phase and asymmetric transmission, and materials with hall conductivity.

VI. CONCLUSION

Our study introduces a transformative approach to THz spectroscopic polarimetry through the development of high ER MPs. These MPs significantly improve the analysis of polarization-dependent optical properties. The precision of measuring cross-polarized transmission is crucial for characterizing materials such as those exhibiting Faraday and Kerr rotations, the anomalous and quantum Hall effects in condensed matter, and in-plane mirror symmetry-breaking metasurfaces. Future work will focus on scaling the production and further enhancing the design to cover a broader range of THz frequencies. By incorporating these high ER polarizers, our approach promises substantial advancements in polarization analysis and chiral sensing in THz systems, paving the way for new discoveries in material science and beyond.

ACKNOWLEDGMENTS

This work was supported by the National Research Foundation of Korea (NRF) through the government of Korea (Grant Nos. NRF-2021R1C1C100631612 and NRF-RS-2024-00411969) and the Electronics and Telecommunications Research Institute (ETRI) (Grant No. ETRI-2011-2024-00011).

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

H. Park: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). H. Park: Formal analysis (supporting); Software (supporting). J. Lee: Investigation (supporting); Methodology (supporting). J. Shim: Investigation (supporting); Methodology (supporting). H. Son: Validation (supporting); Visualization (equal). J. Park: Formal analysis (supporting). S. Baek: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). T.-T. Kim: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal).

DATA AVAILABILITY

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

DATA AVAILABILITY

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

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