Terahertz wave is an electromagnetic wave with a frequency range located between microwave and mid-infrared. It has unique applications in security [1], molecule identification [2], industrial quality control [3], the study of light—matter interaction [4], etc., because of the unique fingerprint properties of materials in the terahertz frequency range [5]. However, terahertz optics are usually composed of either large dielectric lenses or bulky metal mirrors. This limits the implementation of terahertz-wave technologies. Particularly, traditional terahertz-wave quarter-wave plates (QWPs) are usually thick plates of up to few centimeters, because of the small birefringence property of natural materials such as crystalline quartz [6]. A new technique is required for the development of thin terahertz-wave QWPs.

Metamaterials have shown promise for device application in the terahertz frequency band, as they allow for direct tuning of material optical properties. This has been exploited in filters [7], modulators [8], and polarizers [9]. Metamaterials have been used to demonstrate terahertz-wave QWPs based on the artificial birefringence property. Reference [10] describes a double-layer metallic grating structure for a terahertz-wave QWP and demonstrates the max transmittance of 0.6. Reference [11] uses metal slits with different dimensions in orthometric directions to introduce different dipole resonance modes to achieve the birefringence for the QWP. Other designs using cut wire [12], menderlines [13], and electric split ring resonators (SRRs) [13] have also been demonstrated for terahertz-wave QWPs, either with a single layer or multilayers. Dynamical controls of the metamaterial artificial birefringence for terahertz-wave QWPs have also been reported [14,15]. However, although the ellipticity of the converted circular polarization is close to 1, all these works suffer from a common issue of low transmittance, which is also a general issue for other transmission-type terahertz-wave devices based on metamaterials [16–19]. Reflection-type terahertz-wave QWPs are also reported from the artificial birefringence of metamaterials [20,21]. Nonetheless, a transmission-type device is usually requested in terahertz optics. Therefore, a novel metamaterial design concept is desired to solve the above issue for a high-transmission device, and it shall still be able to manipulate the terahertz-wave phase shift or phase front for functionalities such as for a terahertz-wave QWP.

In this Letter, we demonstrate a novel metamaterial design by employing off-resoannce and in-resoance excitation for a high-transmission terahertz-wave QWP. The device is demonstrated with a thin film metamaterial with double-layer SRRs of rectangular shapes as the metamaterial unit. We design, fabricate, and measure the film metamaterial device which shows excellent agreement between the simulation and the experiment. Our terahertz-wave QWP achieves a transmittance of 0.8 and ellipticity of 0.99 at 0.98 THz, from the experiment.

Figure 1(a) schematically presents the metamaterial unit structure for the terahertz-wave QWP. We use double-layer SRRs for the metallic patterns. The SRRs at the top and bottom of the metamaterial unit have identical structures, which is anisotropic and holds a two-fold symmetry. The SRR expresses different resonance modes, depending on the polarization of the incident wave. Specifically, it introduces inductor-capacitor (LC) resonance in the TE mode (polarization of the incident terahertz wave along the $y$-axis) and dipole resonance in the TM mode (polarization of the incident terahertz wave along the $x$-axis). Consequently, the polarization-dependent resonances produce the birefringence property to form an essential factor for a wave plate. In order to obtain high transmission for a terahertz-wave QWP, double-layer SRRs with a certain distance designed between the layers is proposed. Double-layer SRRs enable the device to choose the working frequency off from LC resonance with weak electromagnetic interaction for the TE mode, while in dipole resonance with a strong interaction for TM mode. The off-resonance and in-resonance provide high transmission for the proposed QWP.

 

Fig. 1. (a) Schematic of the metamaterial unit structure with double-layer SRRs. (b) Developed film metamaterial device. (c) Zoom-in figure. The details of the SRRs are shown with a visible light microscope image.

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The SRR metallic patterns uses aluminum (Al), and the substrate uses a polymer bisbenzocyclobutene (BCB) to accommodate the SRRs. The distance between the double-layer SRRs is 32 μm. The lattice of the metamaterial unit structure uses a square shape with a length of 64 μm, but the SRR metallic pattern has a rectangular shape with a dimension of $40\mathrm{\mu m}\times 48\mathrm{\mu m}$. The rectangular shape of the SRR presents the benefit of controlling the frequencies of the LC and dipole resonances, as well as the resonant strength, which will be discussed later. The line width is 4 μm. The gap separating the two hammers in the lattice center is 2 μm.

In Fig. 1(a), additional polymer layers are added on both the top (9 μm) and the bottom (6.5 μm) of the SRR metallic patterns, which are for the device fabrication process in regards to the film releasement [22]. The two polymer layers are also considered for the electromagnetic performance in the metamaterial unit structure, where the major influence lies in the LC resonance, rather than the dipole resonance because of the different resonant mechanisms. The polymer layers added on the top and bottom have different thicknesses; however, this is still a reciprocal metamaterial device. Consequently, the transmission behaviors are the same, regardless of the direction of the terahertz incidence along the $z$-axis.

The film metamaterial device was developed by using photolithography and metal wet patterning techniques. The details of the process are reported elsewhere [22]. The developed film metamaterial device is shown in Figs. 1(b) and 1(c). The zoom-in figure of Fig. 1(c) shows the details of the SRRs with a visible light microscope image taken from the top view. Because of the thin thickness around 48 μm, the film expresses flexibility, as presented in Fig. 1(b).

We conducted a numerical simulation with the commercial software high-frequency structure simulator (HFSS [23]) on the double-layer SRRs to investigate the electromagnetic performance. Periodic boundary conditions were used on the metamaterial unit to simulate an infinite array. The material parameters used in the simulation are metal with conductivity of $4.7\times {10}^7\mathrm{S}/\mathrm{m}$, polymer with a relative dielectric constant of 2.45 and a loss tangent of 0.01. Dispersion was excluded for the material parameters, because it is negligible for the materials Al and BCB used in the device at frequencies of 0.6–1.2 THz. Figure 2 presents the simulation results with the dashed lines. The TE and TM modes represent the polarization of the incident terahertz wave, where the detected terahertz-wave polarization is coincident with the incidence for each mode.

 

Fig. 2. Spectral performance of the thin film metamaterial terahertz-wave QWP. (a) Transmission coefficient for both TE and TM modes. It shows high transmission for the two modes in the frequency band of the gray area. (b) Phase shift using air (phase shift is 0) as the reference. (c) Phase difference between TE and TM modes. The gray area shows the estimated bandwidth of 0.12 THz for the terahertz-wave QWP. Solid line, measurement; dashed line, simulation.

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The film metamaterial device was measured using terahertz-time-domain spectroscopy (THz-TDS, Advantest TAS7500, Advantest Corp.). The solid lines in Fig. 2 present the measurement results for the amplitude, the phase shift, and the phase difference between the TE and TM modes. Both the measurement and the simulation are normalized by a reference of an air slab, which has a thickness 47.5 μm from the design, similar to that of the film device 48 μm. The phase shift for the air slab is set to be zero for convenience, and the phase shift for the film metamaterial device is referred to this air slab. Being the same as the simulation, the incident and detected terahertz waves have coincident polarization for the measurement of TE and TM modes.

Under the TE mode, the double-layer SRRs express an LC resonance, as shown from the transmission coefficient dip in the spectra. The LC resonance causes a reversed phase change among the resonant frequency band, first phase delay and then phase ahead along the spectra. By contrast, under the TM mode, the double-layer SRRs respond in a dipole resonance, which leads to a transmission coefficient peak in the spectra; afterwards, the transmission slopes down. The corresponding phase delay is also apparent.

In general, in order to obtain a QWP, one needs the TE and TM modes to have similar transmission, but with a phase difference of 90 deg. For the spectra presented in Fig. 2(a), both the TE and TM modes show high-transmission coefficients with similar values in the frequency band highlighted in gray in the spectra. The phase difference between the two modes $\varphi =({\varphi }_{\mathrm{TE}}-{\varphi }_{\mathrm{TM}})$ in Fig. 2(c) shows a value around 90 deg at the same frequency band. Therefore, a terahertz-wave QWP is obtained with the double-layer SRR film metamaterial. Figure 2 also presents an excellent match between the measurement and simulation results.

The phase difference is caused by the phase responses from the LC resonance under the TE mode and the dipole resonance under the TM mode [Fig. 2(b)]. Herein, for the QWP, for the TE mode, we choose the frequency band off from the transmission dip of LC resonance, but its neighbor frequency band with high transmission (gray area in Fig. 2). For the TM mode, the double-layer SRRs enable the spectra to maintain high transmission at the same frequency band. The bandwidth of the terahertz-wave QWP is estimated as 0.12 THz. The terahertz-wave QWP works under terahertz-wave normal incidence to the metamaterial device with polarization along the diagonal direction of the square lattice.

To assess the polarization conversion performance of the terahertz-wave QWP quantitatively, we calculated the Stokes parameters [24] from both the simulated and measured spectral data. As described above, the terahertz-wave QWP works under the terahertz wave at normal incidence to the device, while the polarization has an angle of $\theta =45\mathrm{deg}$ to the $x$-axis. The simulated and measured spectra are from the linear polarized terahertz wave of the TE and TM modes, where the transmission coefficient ($T_{\mathrm{TE}}$, $T_{\mathrm{TM}}$) can be used to describe the two components of the transmission of the normal incident terahertz wave, as $\overrightarrow{E}=\overrightarrow{E_x}+\overrightarrow{E_y}=T_{\mathrm{TE}}\cos \theta \overrightarrow{i_x}+T_{\mathrm{TM}}\sin \theta \overrightarrow{i_y}$. Therefore, the Stokes parameters are calculated using the following equations:

We plot $S_0$ and $\chi$ in Figs. 3(a) and 3(b), respectively. Ellipticity $\chi$ keeps almost 0.99 between 0.92 and 1.04 THz, while the transmittance ($S_0$) still remains higher than 0.62. This is higher than for devices using designs of metal slits [11] or menderlines [13]. At a frequency of 0.98 THz, the device shows transmittance of 0.8 and ellipticity of 0.99. Therefore, a high-performance terahertz-wave QWP is demonstrated. The subwavelength film thickness of 48 μm ($\sim 0.15\lambda$) of the QWP enables its easy integration with other terahertz-wave devices.

 

Fig. 3. Polarization conversion performance of the terahertz-wave QWP. (a) Calculated Stokes parameter $S_0$ from the obtained spectra data. (b) Ellipticity $\chi$. A high-performance terahertz-wave QWP is obtained with transmittance of 0.8 and ellipticity of 0.99 at 0.98 THz. Solid line, measurement; dashed line, simulation.

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In the following, we discuss the potential reasons leading to the high transmittance for the terahertz-wave QWP. Metamaterials are well known to have large loss at resonant frequencies because of the joule loss from finite conductivity of metal and the dielectric loss from substrate. The loss usually affects the transmission of the device. In this Letter, however, we avoid using the resonant frequency of LC resonance for the TE mode for the metamaterial-based QWP. Instead, the neighbor frequency band of higher frequency is chosen for the device. Consequently, the loss is reduced. Meanwhile, because the frequency band is off from the LC resonance, the incident terahertz wave does not have as much interaction with the SRRs as that in the LC resonant frequency. Thus, the spectra result in a high transmission at this frequency band. The electric field distribution (not shown) at 0.98 THz of off from LC resonance for the TE mode also indicates the high transmission.

Apart from the high transmission, the phase of the transmitted wave is also changed correspondingly. At the LC resonance under the TE mode, in the ideal case of lossless, the phase would have a 180 deg phase reversal; however, because of the unavoidable material loss, it cannot achieve this ideal value. Nonetheless, phase reversal is still found with the metamaterial in this Letter. In the frequency band at the neighbor of the LC resonance, the phase shift has also been influenced from the phase reversal of the LC resonance.

For the TM mode, usually one-layer SRR metamaterial has a transmission dip at the frequency of dipole resonance. However, here we use double-layer SRRs with a distance designed between the double layers for the metamaterial unit to have a transmsission peak. The transmission peak results from the impedance match from the dipole resonance. The anti-parallel currents (not shown) of the dipole resonance enables the magnetic reponse, which combines with the electric resposne to achieve the impednace match between air and the film metamateiral [22]. In dipole resonance, the joule loss due to the finite metal conductivity and the dielectric loss are higher than off resonance, but the reflection is low because of the impedance match. Therefore, high transmission appears with the double-layer SRRs.

The phase shift is also associated with the dipole resonance in the TM mode. By considering with the phase shift influenced from the LC resonance for the TE mode, there is a phase difference around 90 deg between the TE and TM modes at the frequency band of the gray area in Fig. 2. Therefore, a high transmission terahertz-wave QWP is obtained.

One might notice that for both the top and bottom SRR structures, a rectangular design for the SRR frame is used, instead of a usual square shape in the literature [25–27]. The rectangular design presents flexibility to tune the phase difference between the TE and TM modes but, meanwhile, still enables high transmission for both. For a TE mode with the LC resonance, the shape of the SRR does not matter to the resonant frequency, but the area of the SRR dominates its performance. However, for a TM mode with dipole resonance, the effective length of the dipole current determines the resonant frequency, which further determines the spectral transmission and phase shift. Usually, the effective length of the dipole current lies in the physical structure for a specific polarization wave incidence. Consequently, a rectangular SRR design enables us to tune the physical length of the SRR structure for the TM mode and, meanwhile, still keep the area of the SRR unchanged for the TE mode.

The distance between the double-layer SRRs plays an important role for the high transmision of the terahertz-wave QWP. In the case of the TE mode, the distance influence is small because of the working frequency off from LC resonance. An interference model can be used to explain the double-layer patterns [28,29]. On the other hand, for the TM mode, the transmission is sensitive to the distance variation due to the dipole resonance. From the anti-parellel currents on the double-layer SRRs, a model related with magnetic response is applied [30], where the distance serves as a key parameter in the resonance.

We demonstrate a thin terahertz-wave QWP with high transmission by a novel metamaterial design employing off-resonance and in-resonance excitation with double-layer SRRs. The experiment shows high transmittance of 0.8 and ellipticity of 0.99 at 0.98 THz. We discuss the mechanism of the high transmission from both the TE and TM modes, which lies in the off from LC resonance for TE mode and in-dipole-resonance for TM mode, respectively. The bandwidth of the device is 0.12 THz.