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Pneumatically Actuated Tunable Terahertz Metamaterial Absorber With Dual-Side Tuning Capability Volume 9, Number 4, August 2017 Feng Chuhuan Shi Fan Shao Jian Li Qi Yu Hongbin

DOI: 10.1109/JPHOT.2017.2713805 1943-0655 © 2017 IEEE

IEEE Photonics Journal

Pneumatically Actuated Tunable Terahertz Metamaterial

Pneumatically Actuated Tunable Terahertz Metamaterial Absorber With Dual-Side Tuning Capability Feng Chuhuan, Shi Fan, Shao Jian, Li Qi, and Yu Hongbin School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China DOI:10.1109/JPHOT.2017.2713805 C 2017 IEEE. Translations and content mining are permitted for academic research only. 1943-0655 Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received April 6, 2017; revised June 2, 2017; accepted June 6, 2017. Date of publication June 8, 2017; date of current version June 23, 2017. This work was supported by the Fundamental Research Funds for the Central Universities (2016JCTD112) and fundamental research fund from Shenzhen government (JCYJ20160414102014801). Corresponding author: Yu Hongbin (e-mail: [email protected]).

Abstract: Aiming to achieve dual-side postfabrication performance tuning capability, a new tunable terahertz metamaterial absorber design with built-in pneumatic actuation mechanism was proposed, in which a circular split ring resonator with double-slit was adopted. Using multiphysics simulation, including electromagnetic and mechanical, the desired dualside tuning on absorption peak has been successfully demonstrated by simply changing the direction as well as the amplitude of the applied pressure, agreeing well with theoretical expectation. In addition, detailed discussion about the design optimization strategy for the radius of the split ring resonator from the consideration on improving tuning range was also provided. Index Terms: Metamaterials, pneumatic actuators.

1. Introduction Metamaterials are a group of artificially constructed materials. They usually consist of periodic subwavelength microstructures with particularly designed geometry [1]–[3]. Through the interaction between these structures and the incident electromagnetic wave, unique properties that are unavailable in nature, including negative refractive index [4], [5], cloaking behavior [6], [7], subwavelength focusing [8], [9] and perfect absorption [10]–[13] etc, can be achieved. In recent years, the terahertz metamaterial absorber (MMA) has attracted much interest due to its wide application perspective in detecting [14], [15], sensing [16], [17] and imaging [18], [19]. Considering the working principle of MMA, the relatively high absorption is achieved via the electrical or/and magnetic resonance. As a result, the absorption curve usually demonstrates a sharp peak with small full width at half maximum(FWHM) in the frequency spectrum. In order to broaden its working range, various methods have been reported to achieve dual-band [20], multi-band [21] and broadband [22] MMA. However, in most cases, the absorption performance will be fixed given its as-fabricated structure geometry. From the application point of view, the capability with post-fabrication performance tuning will be much more desired since it can be used to extend the operation range further and initiate new applications such as multispectral imaging. A lot of endeavors have been paid on the post-fabrication tuning strategy, such as mechanical stretch [23]–[25], photo excitation [26], [27], electrical excitation [28], [29], and MEMS (Micro-electro-mechanical Systems) actuation [30]–[34],

Vol. 9, No. 4, August 2017

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Fig. 1. Schematic of the pneumatically actuated tunable terahertz metamaterial absorber.

but till now, most of them can only provide one-side tuning capability, namely the absorption peak frequency can be tuned toward monolithically increasing or decreasing direction. In comparison, the much favored dual-side tuning capability around the original status is still under exploration. In this paper, a new strategy aiming to achieve dual-side absorption peak tuning was proposed. Different from conventional mechanical tuning methods (e.g., external stretching or bending), a more convenient tuning mechanism with build-in pneumatic actuator was adopted, in which the suspending membrane based pneumatic actuation mechanism integrated with microchannel network was designed, through which geometry of the metal structure sitting on the membrane (constructing the unit cell of MMA) can be changed. With respect to the applied positive or negative pressure, the opposite membrane deflection as well as the induced geometry change in the metal structure can be obtained, thus achieving dual-side absorption peak tuning.

2. Device Design and Working Principle The proposed tunable terahertz MMA was schematically shown in Fig. 1. Its unit cell was a 100 μm × 100 μm square block consisting of two stacked layers. One was a polydimethylsiloxane (PDMS) substrate layer, in which a cylindrical cavity with radius of 25 μm was allocated at the center and it was extended to the edges with four orthogonally arranged microchannels, also connecting all the unit cells together. The other layer was an 4 μm thick elastomeric PDMS membrane, which was sandwiched between a top patterned Au structure and a bottom continuous Au film (the thicknesses of them both are 200 nm). The cavity was covered by the membrane, forming a sealed space for pneumatic actuation. In this paper, the top patterned Au was designed into a circular split ring resonator (SRR) with double-slit, detailed structure parameters of which were shown in Fig. 1 They were determined with respect to the designed absorption peak around 4.5∼5 THz. During operation, this metal-dielectric-metal structure interacted with the incident electromagnetic wave and its structure parameters determined the original absorption performance of the MMA. When introducing positive air pressure into the cavity via the microchannel network, the membrane will be deformed upward and the SRR structure sitting on which will be stretched by the resultant tensile stress, thus expanding the slit gap as well as reducing the capacitance at this region. As a result, a blueshift of the absorption peak can be achieved. In comparison, as for the applied negative pressure, downward membrane deformation and shrinked slit gap can be found, and the absorption peak would be shifted to lower frequency (redshift) instead as shown in Fig. 2. Detailed analysis about the absorption peak tuning will be provided in the following content.

3. Simulation Results To study the performance of the tunable terahertz MMA and validate its dual-side tuning capability, simulation using COMSOL Multiphysics was performed. The initial MMA absorption performance in frequency domain was firstly analyzed using the electromagnetic simulation. In this case, the


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Fig. 2. Schematic of the working principle of the proposed device.

Fig. 3. Schematic of the model used in (a) electromagnetic and (b)mechanical simulation.

unit cell model as shown in Fig. 3(a) 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 plane wave was set normally incident onto the MMA surface with its electric field vector polarized parallel to the slit gap (namely x direction). The top and bottom Au structures were modeled as lossy metal with electric conductivity σ = 4.6 × 107 S · m−1 . The PDMS membrane was modeled as lossy dielectric material with dielectric constant of 2.75 and loss tangent of 0.02. Subsequently, mechanical simulation was carried out, in which the membrane deformation as well as the resultant slit gap change of the Au SRR under pneumatic actuation with different applied pressures were studied. In this situation, only the central circular PDMS membrane, suspending on the cavity, and the attached Au structures were analyzed [as shown in Fig. 3(b)], in which 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 Au were set to be 70 GPa and 0.44, while those of the PDMS were 300 kPa and 0.49, respectively. Finally, the unit cell model was refreshed with the deformed structures using moving mesh method and the electromagnetic simulation was performed again to reveal the performance change. From the original absorption spectrum shown in Fig. 4(a), a distinct absorption peak at 4.77 THz can be observed. To further explore its intrinsic mechanism, the electric field as well as the surface current distributions on the Au SRR and the bottom Au film at this peak frequency were analyzed as shown in Fig. 4(b). It can be seen that electric currents running along the electric field direction can be found in both of the two arms of SRR. At the same time, anti-parallel currents can be observed in the corresponding regions of the bottom Au film. As a result, an equivalent circular current loop was formed between the top and bottom Au layers, demonstrating a remarkable characteristic associated with magnetic response. The equivalent LC circuit model of the MMA was provided in Fig. 4(c), and its impedance Z can be expressed as

Z =


jωL ·

jωL +

1 jωC t 1 jωC t

+ +

1 jωC t

1 jωC t

·2+

1 jωC s l i t

(1)

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Fig. 4. Electromagnetic simulation results of MMA. (a) Original absorption spectrum; (b) Electric field and surface current distribution at 4.77 THz; (c) Equivalent LC circuit model.

Fig. 5. Resultant membrane deformation and slit gap change as a function of the applied pressure.

where C s l i t is the capacitance locating at the SRR slit region with gap of g, which is inversely proportional to g. C t is the effective capacitance existing between the top SRR and the bottom Au film. The effective inductance L is dependent on the length, width as well as the thickness of Au SRR. When letting the imaginary part of the impedance to zero, the resonant peak can be determined by 2 1 (2) f = √ C + 4C s l i t 2π L t In comparison, the corresponding electric field as well as the surface current distributions on the Au SRR and the bottom Au film at the neighboring two small peaks were also provided in Fig. 4(a), from which weak magnetic response and electrical response can be found at 3.95 THz and 5.6 THz, respectively. Simulation results about pneumatic actuation were provided in Fig. 5. It can be seen that with the increasing positive air pressure to 60 kPa (far below the oxygen plasma activated bonding strength at the PDMS-PDMS interface), the membrane was forced to deflect upward and its maximum deformation at the membrane center was gradually increased to 0.82 μm. Under the effect of tensile stress caused by the membrane deformation, positive strain was generated at the slit region of SRR structure, as a result, the slit gap was expanded from original 1 μm to 1.09 μm. In contrast, in the case of applied negative pressure, opposite phenomenon can be found, in which the membrane


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Fig. 6. Absorption peak tuning under pneumatic actuation. (a) Absorption spectrum under different working conditions; (b) Resultant absorption peak change as a function of the applied pressure.

deformation was deflected downward instead and the slit gap was shrunk to 0.89 μm under the effect of the resultant compressive stress when −60 kPa was applied. Fig. 6 showed the absorption peak tuning under pneumatic actuation. In the case of pneumatic actuation with positive pressure, the absorption peak was monolithically shifted to higher frequency (namely blueshift) with the increase of applied pressure, while redshift of the absorption peak was observed when using negative pressure for actuation. Obviously, the desired double-side tuning was successfully achieved. In addition, smaller tuning range under positive pressure can be found when compared with that of the negative case. From (2), the frequency shift under the effect of the gap change can be calculated by df dC s l i t −1 2 2 dC s l i t df = = (3) √ dg dC s l i t dg 2π L C t + 4C s l i t C t + 4C s l i t dg Since C s l i t is inversely proportional to the slit gap g, given certain gap change dg, the resultant frequency shift can be expressed as 1 2 2 1 df ∝ dg (4) √ 2π L C t + 4C s l i t C t + 4C s l i t g 2 From the simulated membrane deformation results shown in Fig. 5, it can be seen that when applying positive and negative pressure, expanded and shrinked slit gap can be obtained, respectively. At the same time, given the same pressure amplitude, slightly smaller gap change was also found in the case of positive pressure when compared with that of the negative one. As a result, considering (4), it can be estimated that the tuning range of the absorption peak under positive pressure will be smaller than that under negative pressure due to the increased g as well as the reduced dg, which agrees with the simulation results shown in Fig. 6(b).

4. Discussion From the theoretical analysis above, it can be concluded that the resonant absorption peak of the MMA was inversely proportional to the square root of its effective capacitance (2), while it was dependent on the slit gap. Considering the fact that the expanding slit gap under the effect of applied positive pressure would result in reduced capacitance, therefore blueshifting the resonant peak. Similarly, in the case of negative pressure actuation, redshift of the resonant peak was mainly caused by the increased capacitance due to the slit gap shrinkage.


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Fig. 7. Slit gap change as a function of the SRR radius.

Combining the theoretical analysis and the simulation results, it is clear that the MMA peak tuning performance was actually dependent on the capacitance change at the slit region, which was in turn determined by the deformation induced slit gap variation. Obviously, the larger the gap change, the wider the tuning range. In order to achieve larger gap tuning, SRRs with the same original slit gap but different in radius were studied, in which the membrane radius was fixed at 25 μm. Fig. 7 showed the gap change as a function of the radius of SRR structure under the applied pressure of 60 kPa and -60 kPa, respectively. It can be seen that the change tendencies for both of the positive and negative applied pressure cases were nearly the same, during which the gap change amplitude increased with the increasing SRR radius in initial status and reached the maximum at the radius around 17 um (68% of the membrane radius). After that, with further increase of the SRR radius, the gap change decreased instead. Considering the classic plate theory, the deformation of a membrane with clamped boundary under the uniformly applied pressure was govern by [35] p d 4 w (r ) 2d 3 w (r ) d 2 w (r ) d 2 w (r ) = (5) + − 2 2 + 3 4 3 dr r dr r dr r dr D where w(r) is the membrane deformation at the position with a distance of r to the center, p is the applied pressure and D is the flexural rigidity of membrane, D =

E · h3 12 1 − ν2

(6)

where h is the membrane thickness, E and v are the Young’s modulus and Poisson’s ratio of membrane material (namely PDMS), respectively. Under deformation, stresses were generated in the membrane along both of the radial and tangent directions [36]. (7) σr adi al (r ) ∝ (1 + ν) · a 2 − (3 + ν) · r 2 · p (8) σtangent (r ) ∝ (1 + ν) · a 2 − (1 + 3ν) · r 2 · p where a is the membrane radius. It can be seen that both of the tangent and radial stress were tensile at the position close to the membrane center when positive pressure was applied. Both of them decreased with the increasing distance away from the center and the declining rate of the radial stress was faster than that of the tangent one. At the position of around 65% of the membrane radius, the radial stress reached zero and began to change into compressive stress. In comparison, as for the case of the tangent one, its transition point between the tensile and compressive stresses appeared at the position of 77% of the membrane radius. In the case of negative pressure, similar phenomenon can be


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Fig. 8. Schematic of the object deformation under the effect of external stress. (a) Stress is applied along the interested direction; (b) Stress is applied vertically to the interested direction.

found except that the stress would be gradually changed from compressive into tensile with the increased distance from the center. Whatever the actuation status, both of the tangent and radial stress contributed to the slit gap change. With respect to the classic mechanics, when subjected to external stress σ, object will be forced to deform accordingly. Fig. 8 shows two typical cases. When stress is applied horizontally as shown in Fig. 8(a), the resultant deformation along this interested direction can be described by l// σl = σ ⇒ l// = (9) l E is the resultant strain along the stress direction, namely horizontal direction in current E ε// = σ ⇒ E

where ε// case. Similarly, as for the case of the stress applied vertically, the resultant deformation along the vertical direction can be expressed as

σl (10) E In comparison, the resultant deformation along the interested horizontal direction in this case can be calculated by − εε//⊥ = ν (11) ⇒ l⊥ = −l// · ν ε⊥ = ll ⊥ l// =

where ε⊥ is the resultant strain along direction vertical to that of the stress, namely horizontal direction in this case. Considering the fact that for the currently used PDMS membrane, its Poisson’s ratio ν is 0.49, as a result, smaller deformation along the horizontal direction can be induced if the same stress is applied vertically rather than horizontally. From above analysis it can be concluded that although both of the tangent and radial stress contribute to the slit gap change, the contribution weight factor of the tangent stress was actually a bit larger than that of the radial one since its direction was rightly aligned with the slit gap width as well as its change direction. From mechanical analysis it is well known that the tensile stress in tangent direction would stretch the slit gap, while it would be shrunk by the compressive tangent stress correspondingly. On the contrary, considering the positive Poisson’s ratio of PDMS membrane, the tensile and compressive radial stress (orthogonal to the slit width direction) would compress and stretch the slit gap instead, respectively. As a result, when the membrane was deformed upward, at the position close to the membrane center, the relatively large tensile stress in both of the tangent and radial directions would strongly counteract with each other, resulting in smaller slit gap extension. With the increasing distance from the center, due to the faster decrease rate of the radial stress than that of the tangent one, the increased net effect helped to increase the gap extension. After passing the transition point of the radial stress, the effect of the compressive radial stress would be positively superimposed with that of the tensile tangent stress, further increasing the gap extension. After passing the maximum, the slit gap extension would begin to reduce with approaching tangent stress to zero. Thereafter, with the change of the tangent stress into compressive, counteracting effect would appear again, as


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a result, reducing the slit gap extension further. The analysis for downward membrane deformation was similar except that the slit gap was shrunk rather than extended.

5. Conclusion In summary, a new pneumatically actuated tunable terahertz metamaterial absorber was proposed. In this design, a suspending membrane based pneumatic actuator was integrated into the metaldielectric-metal based MMA structure, in which the top metal was patterned into the circular SRR with double-slit and the membrane was also used as the dielectric layer. Upon actuation, the membrane will be deformed and the slit gap of SRR will be changed accordingly, thus shifting the absorption peak associated with LC resonance. Through controlling the applied pressure as well as the resultant membrane deformation direction, the extension or shrinkage of the slit gap can be observed, and the dual-side tuning capability can be eventually achieved. The working principle and the design optimization for improving tuning performance were also discussed.

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