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Abstract
In this article, we explore a mechanically tunable metasurface on an elastic polydimethylsiloxane (PDMS) membrane operating at Terahertz (THz) frequencies synthesized using a “pattern and peel fabrication” technique. The tunability of the metasurface is based on the change of physical dimensions of the individual micro-structures due to the strain caused by mechanical stretching. The novelty of this technique is the ability to use high resolution e-beam patterning in contrast to established screen-printing techniques reported in the literature. The metasurface studied in this article is a periodic lattice of split-ring structures resonant at THz frequencies. The effect of mechanical stretching on the response of the metasurface is investigated thoroughly through experiments and numerical simulations. The response of the metamaterial to stretching manifests as a shift in the higher order mode by ∼ 12% for an applied strain of ∼ 25%. This tunability of the spectral response with macroscopic strain is not only substantial for the given structure, but also follows a linear behavior. This device can have potential applications in communications technology, remote strain sensing, chemical and biological sensing.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Interest in structured composite media known as metamaterials has changed the paradigm of light-matter interaction due to their immense applications such as negative refractive index materials, perfect lensing, and invisibility cloaking [1, 2] and in controlling the propagation of electromagnetic radiation [3–15]. The response of metamaterials are based on resonant structuring of matter and is controlled by the size and geometry of the structures. Thus they can be used to modify the radiation at specific frequency bands, which makes it very attractive for many interesting applications. A variety of metasurfaces operating at THz frequencies have been demonstrated with a lot of interesting applications [16–18]. However, a drawback of conventional metamaterials arises from the fact that their response is fixed once the structure is fabricated with the designed geometrical parameters. This essentially means that a particular metasurface fabricated for a particular frequency band can have a totally contradictory response in the adjoining band of frequencies. Nevertheless, many applications such as modulators, switches, filters, molecular sensors, and absorbers require materials to have a similar response tunable over a relatively broad frequency range. Recently, control of metamaterial response has been demonstrated, by both passive and dynamical methods [19–27].
In this work, we exhibit a mechanically tunable metasurface operating in the THz band, which comprises gold microstructures on an elastomeric substrate. The substrate selected is polydimethylsiloxane (PDMS), a biocompatible silicone-based elastomer. PDMS films are stretchable and have shown the potential for high flexibility, even at length scales as low as 10 nm [28]. Recently, work on tunable metamaterials has been reported using PDMS substrates. In these studies, researchers used liquid metal microstructures in the metamaterial, or created solid patterns by gold evaporation and photolithography. For example, Kim et al. have reported the fabrication of a metamaterial comprising of layered PDMS microchannels injected with EGaIn liquid metal [29]. There are several other reports on stretchable substrates made by photo-lithography [30–34]. While Lee et. al. show no apparent spectral shift, Li et. al. show very weak shift in resonance with stretching [30,31]. Owing to the fabrication techniques, the resolution of the resonant structures under investigation was not very high.
Our fabrication method utilizes electron beam lithography to create high resolution gold patterns for the metamaterial. Since PDMS is normally not suited to the sputtering and e-beam lithography environments, a “pattern and peel” fabrication technique was developed by us, in which the gold micropattern is first written on a sacrificial surface, and the PDMS layer is thereafter formed on top. It should be noted here that PDMS-gold adhesion under normal conditions is poor, and it is customary to use a thin (∼10 nm) chromium or titanium layer to improve the adhesion. However, these additional layers affect the optical performance of the metamaterial, and have been found to shift, broaden and/or weaken resonances [35, 36]. Therefore, we used a monomolecular adhesive layer of (3-mercaptopropyl)trimethoxysilane (MPTMS) which has been shown to demonstrate excellent adhesion properties between gold and PDMS [37,38]. Finally, the sacrificial layer was dissolved to yield the free-floating PDMS membrane with gold micropatterns. Pryce et al. have shown tunable metasurface on PDMS in the infrared regime with electron beam patterning [39]. However, they etched out the bottom Si-substrate with a very low DC bias SF6 plasma to create a free-standing stretchable metasurface. This is not only challenging and time-consuming due to the presence of the PDMS but also not sustainable as the substrate is not reusable. In our technique, the use of sacrificial layer allows a very fast, easy, clean and repeatable extraction of the free-standing stretchable metasurface on PDMS. It also avoids etching of the thick substrate.
Having fabricated gold SRR structures on PDMS films, we studied the THz transmission spectrum of the sample using Time Domain Spectroscopy (TDS) with various degrees of stretching, up to strains as high as 25%. We observe a near-linear tunability of the higher order resonant mode with mechanical stretching. We further show numerical simulations and models to elucidate the results. These observations render the investigated device highly promising from an application point of view.
2. Design and fabrication
The Split Ring Resonator (SRR) is a well-studied structure in the literature, with narrow, well-defined resonant modes [40]. We have therefore chosen this structure to study the mechanical tunability of our metamaterial in the THz regime. In order to obtain resonances in the frequency band of 0.5 THz to 3.0 THz, the dimensions of the SRR structures were as follows: side length L = 60 μm, period P = 70 μm, width of gold bars w = 10 μm and gold thickness t = 100 nm. The period was chosen such that, the effect of the lattice i.e. the Rayleigh anomaly does not lie in the spectral range of interest. The gap in the SRR was 5 μm in length. Figure 1(a) shows the schematic of the lattice of the SRRs on a substrate while the inset shows the optical microscope image of the SRR array on PDMS. Figure 1(b) shows the optical microscope images of the 3 SRRs under different applied external strain values (S = 0, 0.1, 0.2). It is to be noted that the SRR as a whole does not expand uniformly with the applied stretch, rather deforms with expanding gap of the split-end. This is due to the fact that although the substrate (PDMS) is elastic, the SRRs are not. So the distortive effect due to the strain is due to the lack of symmetry in the structure. Figure 1(c) shows a photograph of the SRR array on the PDMS clearly demonstrating the flexible nature of the metasurface. Figure 1(d) shows the specially designed sample holder with two plastic clamps to hold the metasurface. This device is equipped with two perpendicularly attached micrometer stages which allow for stretching and also alignment of the film on the cradle, perpendicular to the stretching axis. These are fitted on an aluminum plate with a circular aperture in line with the metamaterial to allow for transmission mode measurements.
Fig. 1 (a) Schematic of the metasurface consisting gold SRRs on PDMS substrate. Inset shows the optical microscope image of the SRR array on the PDMS surface. (b) Processed optical microscope images of the SRRs structure under different applied strain values (S = 0, 0.1, 0.2). (c) A photograph showing the metasurface on the flexible PDMS substrate and, (d) shows the photograph of the custom-made cradle on the sample holder for mounting the stretchable metasurface for transmission measurements. The red arrows indicate the movements of the micrometer stage for stretching the metasurface, while the green arrows indicate the movement of the other micrometer stage for proper alignment of the film on the cradle.
The fabrication process began with spin-coating a ∼800 nm sacrificial PMMA layer (MicroChem 950 PMMA A7) onto a 2.5 cm × 2.5 cm glass slide (2000 rpm) for 45 seconds followed by baking at 170°C for 120 seconds). It is easily removable but inert enough to withstand the fabrication process. Thereafter, in line with the idea of “pattern and peel” fabrication technique mentioned above, a 100 nm layer of gold was directly sputtered onto the sacrificial layer by DC sputtering. Next, the desired pattern was made on the gold layer by electron beam lithography with AR-N 7520 resist. E-beam lithography allowed us to attain very small feature sizes with excellent resolution compared to other techniques such as photolithography and screen printing which are currently used for making elastic metamaterials. This was followed by argon (Ar) plasma etching of the gold and oxygen plasma etching of the e-beam resist to yield the gold SRR array on PMMA.
To improve the adhesion between these gold microstructures and the PDMS membrane, MPTMS was deposited on the gold. A monolayer of MPTMS works as a molecular adhesive due to its different terminal groups: The methoxy (-OCH3) groups bond to oxide surfaces in PDMS, and the thiol (-SH) bonds with the metal surface. While many techniques of MPTMS deposition are available [37, 38], vapour-phase deposition for four hours (less than an hour with heating upto 90° C) in a vacuum chamber was chosen since it is possible to obtain a self-assembled monolayer of the chemical on gold, and because it eliminates the need for other solvents, cleaners, etc. which could chemically interfere with our sample. This completes the preparation of the gold pattern for PDMS casting.
PDMS was made by mixing the monomer (Dow Corning Sylgard Silicone Elastomer 184) and hardener (curing agent) in a 10:1 (w/w) ratio and mixing for a few minutes. The mixture was placed in a vacuum desiccator to degas until all the bubbles have been expelled from the mixture (which typically takes around 3 hours). The PDMS thus obtained was spin-coated onto the prepared slide at 500 rpm for 5 minutes for a 44 μm thick layer. It was then cured for 2 hours at 70°C and left overnight. The complete metamaterial film is extracted by dissolving the sacrificial layer in MicroChem Remover PG, which allows the membrane with gold to be released from the glass slide. This entire process is shown schematically in Fig. 2.
Fig. 2 Schematic of the entire fabrication process starting from bottom left to bottom right in a clockwise fashion. The inset shows the molecular structure of the MPTMS monolayer (shown in purple) which works as an molecular adhesive between the gold (shown in yellow) and PDMS layer (shown in grey). The green spheres represent Silicon atoms, blue represents Carbon, yellow for Sulphur, red for Oxygen and grey represents Hydrogen atoms.
3. Results
THz time domain spectroscopy (TDS) using ultrashort pulses of duration 10 fs, wavelength centered at 800 nm and a repetition rate of 78 MHz using a mode locked Ti:Sapphire laser (Femtosource Synergy) was done to obtain the transmission spectrum of the fabricated metamaterial structure on PDMS film. The THz wave from the emitter was first collimated and then focused onto the center of the sample with a beam diameter of approximately 2 mm.
The metamaterial film was mounted on the custom made sample holder as shown in Fig. 1(d). The THz radiation is transmitted through the metamaterial with the polarizations both parallel and perpendicular to the gaps in the split rings. When a stretching force is applied along the direction of the split of the SRR, the macroscopic deformation results in an expansion in the gap width of the resonators. The stretching was applied up to a maximum of 0.5 cm, corresponding to 25% strain of the film having an effective length of 2 cm. This macroscopic deformation is responsible for a change in the response of the SRR array manifested by modulation of THz transmission spectra. The transmission spectra for polarization of THz and mechanical strain, both parallel to the split of the SRRs for different mechanical strains (s = 0 for unstretched, s = 0.5 to 0.25 for different stretching) are shown in Fig. 3(a). Figure 3(b) shows the transmission spectra for THz polarization perpendicular to the split of the SRR, however, the mechanical strain parallel to the split. The individual spectra are vertically shifted with respect to each other by a constant for clarity. The general nature of the spectra shown in Fig. 3(a) indicates the formation of two resonance dips (the green transparent rectangles indicate the resonant frequencies for s=0). The first dip is similar to a λ/2 mode of a dipolar antenna, whereas, the second dip is similar to 3λ/2 mode for the same SRR. The physical origin of the resonant dips are discussed in the next section with the help of numerical FDTD simulations. Similarly, the single resonant dip in transmission shown in Fig. 3(b) indicates the λ mode of the SRR (the green transparent rectangle indicates the spectral position for the λ resonance for s=0).
Fig. 3 (a) Shows the measured THz transmission spectra of the SRR array for different applied strains, indicated by S = 0 to 0.25, with the THz electric field polarization parallel to the gap between the split ends of the SRRs. (b) Shows the measured THz transmission spectra of the SRR array for different applied strains with the THz electric field polarization perpendicular to the gap between the split ends of the SRRs. The applied strain in both the cases is parallel to the split of the SRR. The spectra are numerically shifted vertically with respect to each other by 0.3 with increasing values of strain (black: S = 0, red: S = 0.05, blue: S = 0.1, magenta: S = 0.15, green: S = 0.2 and dark blue: S = 0.25). The green transparent vertical rectangles indicates the position of the resonances of the SRR in the un-stretched condition.
It can be appreciated that the 3λ/2 dip, as seen in Fig. 3(a), blue-shifts with increasing values of strain. The λ/2 resonant dip blue shifts for small values of applied strain on the metamaterial. However, for very large values of strains, the λ/2 splits into two distinct modes. This effect is seen to be replicated for the λ mode as well, as shown in Fig. 3(b). While the origin of the splitting due to elastic deformation needs further studies, we concentrate on the mechanically tunable resonance in the following. Figure 4 shows the relative shift of the 3λ/2 resonance frequency as a function of applied strain. The behavior of the relative shift seems to follow a linear trend with applied strains. The upper inset of the figure shows the FDTD simulation results for the strain-induced shift of resonance. A clear linear shift matching the experimental data is apparent. It should be noted that the simulations were performed with the actual images of the SRRs under stretching. The lower inset in the same figure shows the relative shift of the 3λ/2 resonance frequency as a function of applied strain for a second sample with thicker substrate thickness. This results indicate that the linear trend is not limited by substrate. However, the absolute values of the shifts are different owing to the difference in the effective strain in the SRRs due to difference in thickness in the substrate for the same applied external strain. The physical origins of these observed results are discussed in the following section.
Fig. 4 Illustrates the tunability of the 3λ/2 resonance dip (around 1.65 THz) with applied strain. The black squares indicated the measured data points extracted from Fig. 3(a), while the red solid line is a linear fit to the data points. Positive values in the vertical axis indicate blue-shift of resonance. Upper inset shows the simulation results for strain-induced shift of resonance. The green triangles are simulated data points while the black line is a linear fit. Lower inset shows similar data from a second sample with a thicker substrate thickness. Black squares are experimental data points while red line is linear fit.
4. Discussions
To elucidate the physical origin of the resonant dips in the transmission spectra as seen in Fig. 3, we have performed numerical FDTD simulations of the gold SRRs on PDMS in Lumerical with THz polarization parallel to the split. Figure 5(a), (b) and (c) shows the out of plane magnetic field component and the corresponding surface currents (green arrows indicates the simulated vectors, while black arrows indicates the approximate resultant) in the vicinity of the SRR under a strain of S = 0.1 for frequencies 0.6, 1, 1.65 THz. These values were chosen due to distinctive features in the transmission spectra at these frequencies. The qualitative explanation of the measured features in the transmission spectra follows from the understanding of the surface currents in the vicinity of the structures, as shown in Fig. 5(a), (b) and (c). These modes have been modelled in the literature as being equivalent to the response of an LC element in a LCR circuit [41,42]. The current in Fig. 5(a) indicates that the first or the fundamental resonance (λ/2) due to the charge density oscillations at 0.6 THz is a result of a circulating current (i1) throughout the length of the SRR structure. The frequency of the fundamental mode is highly dependent on the effective length of the SRR, which does not change appreciably with stretching, as shown by the microscope images in Fig. 1(b). Hence, this mode shows a very small blue shift for small values of applied strain, due to the reduction of capacitive coupling between the two split ends. For larger values of strain (greater than 0.1), the mode splits into two distinctive levels (at 0.45 THz and 0.85 THz), as seen in Fig. 6, with a high modulation of transmission, by more than 40% (with associated change in the mode quality factors) and a splitting of ∼0.4 THz at the position of the fundamental resonance, as seen in Fig. 6, due to the high mechanical strain induced elastic deformation in the SRR structure. It would be interesting to note the distinct stretching-induced response of the SRR. At low stretching, one can observe electromagnetically induced transparency like behavior, with transmission increasing with strain [15, 43–45]. However, at large strain (>0.15), we can see splitting similar to Autler-Townes splitting observed in atomic systems in strong coupling regime [46–48].
Fig. 5 Finite difference in time domain (FDTD) simulations of out-of-plane magnetic field amplitudes at (a) 0.6 THz, (b) 1 THz and (c) 1.65 THz in the vicinity of SRRs with incident electric field polarizations parallel to the gap between the split ends of the resonators. The green arrows are the simulated surface current vectors due to the charge density oscillations caused by THz excitation, while the black curves indicate the approximate current flow, for the ease of interpretation.
Near 1 THz, the high transmission with parallel polarization is a result of current component oscillations (i2) shown in Fig. 5(b). This is similar to a λ resonance in an antenna. Here, a quadrupolar nature of the charge density oscillations is observed which is a non-radiative channel and hence, has a very low effective coupling to the incident field polarized along the split. However, it couples with the perpendicular polarization, which results in a resonant dip, as shown in Fig. 3(b). A careful study of the λ mode reveals a non-linear trend in the shift of the resonance position with increasing values of applied strain. Analysis of this behavior is not straightforward when the polarization is orthogonal to the applied strain as the change of resistance and inductance values associated with the distortions in the structures affect the resonance position. Furthermore, this additional mode can arise from scattering induced orthogonal states [49]. The 3λ/2 resonance dip at 1.65 THz for the co-polarized THz is the result of non-zero surface current (i4) parallel to the field polarization thereby, introducing a radiative dipole-like channel with high coupling to the incident field. This mode is highly dependent on the capacitive coupling between the split-ends of the resonators by the simple proportionality [41,42],
where, νres is the resonant frequency of the second dip in the transmission spectra, C is the capacitance of the gap between the split ends of the SRR. The response is thus, equivalent to that of a capacitive element in the equivalent LCR circuit. The value of the capacitance, C, is approximately inversely proportional to the gap (l) between the split ends of the SRR [41]. This implies, For applied strains, the gap, l can be shown to approximately scale linearly with applied strains. Therefore, differentiating the above equation, i.e. the relative shift of resonance scales linearly with small values of applied strain. This relation (Eq. (2)) explains the linear shift seen in Fig. 4. It can be seen that for higher values of strain the fit deviates from linearity, which is understandable due to the small strain approximation in Eq. (2). For larger values a square root dependence can be expected. Also, the assumption that the gap length is linear in nature with applied strain is not valid for higher values of strain.Fig. 6 Demonstrates the observed splitting of the λ/2 and the λ modes of the SRR structure with increasing values of applied strain. The blue inverted triangles, and green triangles represents the position of the resonant frequency of the λ mode whereas, the red circles and black squares indicate the same for the λ/2 mode.
5. Conclusion
We have developed and demonstrated a novel method for fabricating an elastic, tunable metamaterial filter using a stretchable PDMS membrane. The “pattern and peel” fabrication process allows a quick and clean extraction of the metasurface from the substrate and the use of techniques such as electron-beam lithography and DC sputtering, which are improvements on most processes used currently for stretchable metamaterial fabrication. Further, using MPTMS as a molecular adhesive eliminates the need for using chromium or titanium adhesion layers. We have fabricated and characterized a THz split-ring metasurface using this process, and report a near-linear relative tunability in the higher order resonant mode of over 12%, for 25% stretching of the material. This tunability of the spectral response of the metasurface was found to be very repeatable due to the high elasticity of the PDMS layer. With a mask made in solid substrate, highly repeatable bulk fabrication of nanostructures is possible with this technique. Therefore, this technique can prove to be highly promising for real life applications in fields such as communications, remote sensing and biosensors. Furthermore, the demonstrated fabrication technique is not limited to micro-structures as shown in this article, rather can be easily used to fabricate tunable metamaterials in different frequency regimes.
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