1. Introduction

The light polarization rotation in quartz crystals was first discovered by F. J. Arago in 1811 [1]. This optical activity has subsequently been linked to intrinsically 3D-chiral molecules by Luis Pasteur since 1848 [2] and has been exploited in many disciplines of science including chemistry, physics, biology, and optics [3,4]. Although there exist some 3D chiral materials in nature, such as quartz crystals, DNA spirals, amino acids and sugars etc, the relatively weak optical activity and inflexible structure construction largely limit their widespread application. In comparison, the artificial 3D-chiral structures (also called chiral metamaterials) have been attracting much research interest due to their associated strong and controllable electro-magnetic coupling as well as optical activity through engineering their structures. Among them, the metallic helix is a typical and one of the most popular structures [5]. Comprehensive studies about the optical properties of different helix structures (such as single helix [6], multi-helix [7] and tapered helix [8] etc) have been performed and some distinct characteristics, such as strong optical activity, circular dichroism, circular transmission conversion and asymmetric transmission etc, have been successfully disclosed. As a result, the metallic helix structures have been treated as promising candidates for constructing circular polarizer [9,10] and polarization converter [11].

Various methods have been developed to fabricate the helix structures including laser direct writing [12,13], focused ion beam induced deposition [14,15], self-assembly [16] and multi-layer stacking [17,18] etc. Although exciting achievements have been extensively reported, these works require either expensive and/or non-standard equipments, or rather complicated process, making the fabrication with high efficiency and low cost impossible. More recently, Kan proposed a deformable 3D chiral structure based on Micro-electro-mechanical Systems (MEMS) technology [19,20]. In this case, the commonly used 2D planar process in semiconductor industry was adopted to fabricate a cantilever-like suspended 2D spiral structure. It was then deformed into a 3D form using the electrostatic and pneumatic force, respectively. This provided a brand new fabrication and tuning strategy for the 3D chiral metamaterial. Nevertheless, due to the residual stress in the chiral structure and the one end fixed condition, distinct structure deformation can be found after fabrication, resulting in a non-zero optical activity offset at initial status. Moreover, relatively complicated processes involving deep silicon etching and structure release with hydrofluoric acid vapor as well as rigorous process control are still needed. Most importantly, the system configuration especially the actuator lacks compact integration capability. Till now, to pursue a relatively simple and effective fabrication method for the 3D chiral metamaterial is a continuously ongoing development goal.

In this paper, aiming to develop a relatively simple yet effective solution for 3D chiral metamaterial fabrication, a 2D to 3D conversion mechanism based on our previously developed integrated pneumatic actuator technology [21–24] is proposed. In current case, the suspending membrane based pneumatic actuator integrated with microchannel network, which can be fabricated using well-known soft lithography process, is used, and a 2D planar metal chiral structure can be directly deposited onto the membrane using standard photolithography and lift-off process. Upon applying pressure, the deformed membrane will translate the attached 2D metal chiral structure into 3D format. With this translation, enantiomeric switching of the chiral structure can be obtained through controlling the pressure, thus giving rise to symmetric optical activity and circular dichroism tuning capability.

2. Structure and working principle

The proposed 2D to 3D convertible terahertz chiral metamaterial is schematically shown in Fig. 1. Its unit cell is a 150μm × 150μm square block consisting of two stacked layers. One is a polydimethylsiloxane (PDMS) substrate layer. At the center of which a cylindrical cavity with radius of 70μm and depth of 80μm is allocated and it is extended to the edges with four orthogonally arranged microchannels with rectangular cross section of 30μm width and 80μm height, also connecting all the unit cells together for synchronous actuation. The other layer is an 4μm thick elastomeric PDMS membrane with an Au Archimedean spiral structure being deposited onto its top surface (from the viewpoint of effective operation, only 200nm thick Au is enough considering skin effect, but in order to improve the computational efficiency during simulation, the thickness of Au is set to be 1μm in current case). The cavity substrate and the membrane can be firmly bonded together under the assistance of oxygen plasma activation, forming a sealed space for pneumatic actuation. Detailed fabrication process flow can be found in the appendix material.

 

Fig. 1 Schematic of the proposed 2D to 3D convertible terahertz chiral metamaterial.

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The Archimedean spiral is defined by $r\left(\phi \right)=b\left(\phi \right)$. “r” is the radial distance from the center, “φ” is the azimuth angle ranging from $\phi {}_1\left({\phi }_1=a/b\right)$ to ${\phi }_2\left({\phi }_2={\phi }_1+n\cdot 2\pi \right)$, where the parameter “a” represents the inner radius of the spiral, “b” is a scale factor, “n” is the spiral turn number. The schematic of the Archimedean spiral structure is also provided in Fig. 1. When observed from the Au-deposited side, the spiral is arranged along clockwise direction from margin to center. The inner radius, outer radius, the width, the turn spacing and the turn number of the spiral are designed to be 3μm, 60μm, 6μm, 6μm and 5, respectively. These parameters are determined with respect to the desired working frequency range from 0.5THz to 1.5THz.

During operation, this metal-dielectric structure will interact with the incident electromagnetic wave and its structure parameters will directly determine its optical transmission property. When introducing positive air pressure into the cavity via the microchannel network, the PDMS membrane together with the attached planar Au Archimedean spiral will be deformed upward. As a result, the initial 2D planar spiral will be transformed into a left-handed (LH) 3D tapered spiral as shown in Fig. 2. In comparison, if negative pressure is applied, downward membrane deformation will be obtained. In this case, the conversion from the planar Archimedean spiral into a right-handed (RH) 3D tapered spiral will be obtained instead. Obviously, with this design, not only the spiral structure parameters such as spiral height and pitch, but also its handedness, both can be controlled. At the same time, considering the nearly symmetric bi-directional actuation capability with this design, the resultant reversal in the spiral handedness can be used to achieve chirality switching whilst maintaining the enantiomeric symmetry.

 

Fig. 2 Schematic of the 2D to 3D conversion principle.

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3. Simulation results

To study the structure tunability as well as the induced optical property variation of the proposed chiral metamaterial associated with this 2D to 3D conversion, simulation using COMSOL Multiphysics was performed. For analyzing the structure conversion, the mechanical simulation was carried out, in which the membrane deformation as well as the resultant spiral structure change under pneumatic actuation with different applied pressures were studied. In this case, only the central circular PDMS membrane, being suspended on the cavity, and the attached Au structure on its surface were analyzed (the blue color regions as shown in Fig. 3(a)). During modeling, the circular edge of the PDMS membrane was set to be clamped boundary and a uniform pressure was applied onto the membrane. The Young’s modulus and Poisson’s ratio of the PDMS were set to be 300 kPa and 0.49, while those of the Au were 70 GPa and 0.44, respectively. Simulation results of the membrane deformation as well as the spiral change under pneumatic actuation were provided in Fig. 3(b). It can be found that with the increasing pneumatic pressure to 40kPa (far below the oxygen plasma activated bonding strength at the PDMS-PDMS interface), the membrane was blown up with its maximum deformation at the center being gradually increased to 31μm. Since the Au spiral was attached to the membrane, its structure will be changed along with the membrane deformation. As a result, it was finally pulled up into a LH 3D tapered spiral as shown in the inset. Meanwhile, nearly symmetric change tendency can be obtained in the case of downward actuation with negative pressure, in which the planar Au spiral was converted into a RH 3D tapered spiral instead.

 

Fig. 3 Mechanical simulation for the proposed structure (a) schematic of the model used in mechanical simulation (b) simulation results of the membrane deformation as a function of the applied pressure.

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In order to characterize the optical property of the proposed 2D to 3D convertible terahertz chiral metamaterial, the electromagnetic simulation was performed, during which the initial optical transmission through the 2D spiral structure without any actuation was firstly analyzed. In this case, the unit cell model as shown in Fig. 4 was built. The open boundary condition was set in the z direction, and the periodic boundary was set in the x and y directions, respectively. A linearly polarized plane wave was set normally incident onto the metamaterial surface with its electric field vector parallel to the x direction. The top Au spiral was modeled as lossy metal with electric conductivity σ = 4.56 × 10⁷ S/m. The PDMS membrane was modeled as lossy dielectric material with dielectric constant of 2.75 and loss tangent of 0.02. Subsequently, the unit cell model was refreshed with the deformed structures from the mechanical simulation above and the electromagnetic simulation was performed again to reveal the resultant optical property change.

 

Fig. 4 Schematic of the model used in electromagnetic simulation.

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During the electromagnetic simulation, two commonly used transmission parameters, namely the polarization azimuth rotation angle θ and the ellipticity angle η as calculated by Eq. (1) [25], were analyzed.

The frequency responses of the polarization azimuth rotation angle and the ellipticity angle of the transmission through the initial 2D spiral structure within the frequency range from 0.5 THz to 1.5THz were shown in Fig. 5. At the same time, those in the cases under pneumatic actuation were also provided, where pressures with the amplitude of 5kPa and 10kPa but opposite in direction were applied. From the results, distinct change with significant resonant characteristic can be found in all the spectrums, which was undoubtedly caused by the 2D to 3D conversion of the spiral structure under pneumatic actuation. As for the actuation with positive pressure namely upward deformation, the planar spiral structure was converted into the LH 3D tapered spiral and two positive peaks in the polarization azimuth rotation angle spectra can be obtained at 0.97THz and 1.33THz, respectively, and the amplitudes of which both were increased with the increasing pressure. Meanwhile, when considering the spectra of the ellipticity angle, an interesting phenomenon was observed that the ellipticity angle always showed a dispersive curve and crossed zero at both of these two frequencies irrespective of the applied pressure. This indicated that at these resonant frequencies the transmitted wave still kept linearly polarized except that the polarization plane was rotated by a certain extent, demonstrating a pure optical activity tuning. In comparison, two resonant peaks at 0.75THz and 1.46THz can be found in the ellipticity angle spectra, where the corresponding polarization azimuth rotation angle crossed zero. In these cases, the incident linearly polarized wave was converted into an elliptically polarized one instead after transmission with its main axis direction being kept aligning with the incident linear polarization direction, thus achieving a pure polarization conversion. Besides, nearly symmetric tuning in the downward actuation can be observed, which was mainly caused by the enantiomeric switching of the chiral structure from LH to RH under symmetric actuation.

 

Fig. 5 Simulation results of the spectrum of (a) polarization rotation angle and (b) ellipticity angle of the proposed structure under different statuses as well as the trend.

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In order to further study the optical properties tuning capability with current design, the changes of the polarization azimuth rotation angle and the ellipticity angle with respect to the applied pressure from −40kPa to 40kPa at particular frequencies were also provided as shown in Fig. 6. From the results, it can be seen that as for the interested frequency points of 0.97THz and 1.33THz, similar tuning range covering nearly −8° to 8° for the polarization azimuth rotation angle with symmetric characteristics can be obtained within the changing applied pressure from −40kPa to 40kPa. At the same time, under the same actuation conditions, a slightly larger tuning capability for the ellipticity angle can be found especially at the frequency of 0.75THz, where it can be changed from −10° to 10° through controlling the pressure.

 

Fig. 6 Simulation results of the optical property change with respect to the applied pressure at particular frequencies (a) polarization rotation angle and (b) ellipticity angle.

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4. Discussions

In order to explore the intrinsic mechanism for the tuning characteristic, detailed analysis especially at the individual resonant frequencies were performed. In optical analysis, the incident linearly polarized light can be treated as a superposition of a right circularly polarized (RCP) and a left circularly polarized (LCP) beams with equal amplitude and phase. It's obvious that if the phases of these two components become different after transmission, the polarization azimuth rotation will be induced. In addition, if the transmittance of these two components deviate from each other, a well-known phenomenon called circular dichroism (CD) will be generated, under the effect of which the linearly polarized incident will be transformed into an elliptically polarized one after transmission, resulting in the occurrence of ellipticity angle. With respect to these considerations, the status for the RCP and LCP lights after being transmitted through the proposed spiral structure under pneumatic actuation with ± 5kPa and ± 10kPa pressures were studied and their corresponding CD and phase difference ΔΦ are calculated by [26]

From the results shown in Fig. 7, it can be clearly seen that the RCP and LCP transmissions demonstrate the same phase but different amplitude (namely CD≠0) at the frequency points of 0.75THz and 1.46THz for all the cases. As a result, a linear to elliptic polarization conversion between the incident and the transmission can be achieved, in which the main axis direction of the elliptically polarized transmission was still kept aligning with the linear polarization direction of the incident. In contrast, the same transmittance (namely CD = 0) but different phase can be obtained between the RCP and LCP transmissions at 0.97THz and 1.33THz. From the analysis above it can be known that at these working frequencies, the transmissions maintained linear polarization status but deviated from the initial incident polarization direction by a certain angle. All the results agreed well with those observed in the spectrums of the polarization rotation angle and the ellipticity angle. Moreover, the ellipticity angle spectra demonstrated similar change tendency as that of the CD, whilst opposite tendency between the polarization rotation angle and the phase difference can be found instead. Therefore, the tuning capability was actually induced by the handedness dependent transmission for circularly polarized wave associated with the 3D helical structure.

 

Fig. 7 Simulation results of (a) circular dichroism and (b) phase difference between RCP and LCP transmissions.

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To further reveal the microscopic origin of the observed phenomenon, the current norm distributions generated on the LH spiral, which was induced by 5kPa applied pressure, for the incident circularly polarized light was intentionally studied. From the results shown in Fig. 8, it can be seen that the current generated by the LCP light was mainly concentrated within the inner spiral region, where the incident light first interacted with the spiral structure due to the upward deformation. In comparison, as for the case of the incident RCP light, most current was distributed among the outer spiral region. At the same time, the current generated by the LCP light was distinctly larger than that of the RCP light at 0.75THz, demonstrating stronger coupling between the incident and the spiral structure. In contrast, opposite condition can be found at the frequency of 1.46THz, in which the RCP light can induce more current than the LCP one instead. Considering the fact that the larger the current, the stronger the reflection, namely lower transmittance. As a result, positive and negative CD can be obtained at 0.75THz and 1.46THz, respectively. Meanwhile, nearly the same currents can be generated for both of the RCP and the LCP light at 0.97THz and 1.33THz, resulting in zero CD. Obviously, all of the results agreed well with the conditions provided in the CD spectra in Fig. 7. Moreover, the equivalent refractive indices indicated by the spiral structure for the RCP and LCP lights were also calculated from their corresponding transmission and reflection parameters [27,28], which can be found in the appendix document, any difference between them will cause transmission phase difference. It's clear that the spectra of the equivalent refractive index difference shown in Fig. 9 were consistent well with those of the transmission phase difference shown in Fig. 7.

 

Fig. 8 The current norm distributions on the LH spiral induced by 5kPa applied pressure for the incident circularly polarized light.

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Fig. 9 Simulation results of the equivalent refractive index difference between the RCP and the LCP lights.

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5. Conclusions

In summary, a 2D to 3D conversion mechanism based on integrated pneumatic actuator was proposed to provide a relatively simple yet effective solution for achieving tunable 3D chiral metamaterial. In this design, a suspending membrane based pneumatic actuator was integrated into the metal-dielectric based metamaterial structure, in which the top metal layer was patterned into the Archimedean spiral arrays and the membrane was also used as the dielectric layer. Upon actuation, the membrane will be deformed and the initial 2D spirals will be transformed into a 3D tapered helix, during which not only the structure parameters but also the chirality of the 3D tapered helix both can be controlled by the applied pressure. With the occurrence of this 2D to 3D conversion, the tuning capability demonstrating enantiomeric symmetry characteristic over some optical parameters such as the polarization azimuth rotation angle and ellipticity angle for the transmission of the linearly polarized incident has been obtained. Moreover, a pure optical activity tuning and a pure linear-to-elliptic polarization conversion both have also been successfully demonstrated at certain working frequency. With respect to our experience on the study of the pneumatic actuation before and considering the currently adopted structure parameter, the time that this pneumatic actuator takes to reach the steady state is around second range. In comparison, the most commonly used electrostatic actuation demonstrates a bit faster response around millisecond level. Nevertheless, the currently proposed pneumatic actuation still can be treated as an promising candidate for real applications considering its associated some distinct advantages such as relatively simpler structure fabrication, more compact system integration and dual-direction actuation capability over the electrostatic one.

Appendix

• 1. Detailed information about the fabrication and performance characterization for the proposed device are provided below.

Figure 10 shows the schematic of the fabrication process flow for the proposed device. As described in the section 2, the device consists of two stacked layers, they can be fabricated by step 1 and 2, respectively. In step 1, the process starts with a one-side polished silicon wafer. After standard cleaning processing, liquid PDMS prepolymer (Sylgard 184 silicone elastomer-a base and curing agent of Dow Corning Corp-mixed in a 10:1 weight ratio) will be spin-coated onto the surface followed by curing step to make a PDMS membrane (see Fig. 10(b)-1), the thickness of which can be controlling by the spin speed. Subsequently, a lift-off process will be used to deposit the desired metal pattern directly onto the membrane as shown in Fig. 10(c)-1. In step 2, one layer of SU-8 with 80μm thickness is spun onto the surface of another silicon wafer (see Fig. 10(b)-2). The patterns of the desired pneumatic actuator structures, including the cavity and the microchannel, are simultaneously transferred into this layer via standard photolithography process (Fig. 10(c)-2). This SU-8 structure will be used as the master mold for the following molding process, during which the liquid PDMS prepolymer will be poured onto the mold as shown in Fig. 10(d)-2. After complete curing in the furnace, the PDMS layer with inverse structures having been transferred from the SU-8 mold will be peeled from the mold substrate (see Fig. 10(e)-2). These two components will be aligned and bonded together using oxygen-plasma activation method so as to complete the device fabrication.

 

Fig. 10 Schematic of the fabrication process flow for the proposed device.

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Figure 11 shows the schematic of the performance characterization setup. During the operation, the device is put into a widely used standard terahertz time domain spectroscopy (THz-TDS) measurement system as shown in [29]. The microchannel of the device will be connected to external syringe pumping system via plastic pipe, through which the actuation pressure as well as the resultant structure change can be controlled. With this setup, the tuning capability for the optical property provided by the device can be obtained.

 

Fig. 11 Schematic of the performance characterization setup.

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• 2. Retrieval of equivalent material parameters

  It’s a most commonly used strategy to retrieve material parameters (such as refractive index n, wave impedance z, permittivity ε and permeability μ) from the corresponding S parameters (such as S₁₁ and S₂₁), which can be directly obtained/measured from the simulation/measurement. Detailed treatments are provided below, which can also be found in various references such as [30] and [31].

  (3)$$\{\begin{array}{l}n=\frac{1}{kd}{\cos }^{-1}\left[\frac{1}{2S_{21}}\left(1-S_{11}^2+S_{21}^2\right)\right]\hfill \\ z=\sqrt{\frac{{\left(1+S_{11}\right)}^2-S_{21}^2}{{\left(1-S_{11}\right)}^2-S_{21}^2}}\hfill \\ \epsilon =\frac{n}{z}\hfill \\ \mu =nz\hfill \end{array}$$

  where k is the wave number, d is the thickness of material.

Funding

Fundamental Research Funds for the Central Universities (2016JCTD112); Fundamental research fund from Shenzhen government (JCYJ20160414102014801).

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