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Flexible Helices for Nonlinear Metamaterials

2013; Volume: 25; Issue: 25 Linguagem: Inglês

10.1002/adma.201300840

1521-4095

Alexey Slobozhanyuk, Mikhail Lapine, David A. Powell, Ilya V. Shadrivov, Yuri S. Kivshar, Ross C. McPhedran, Pavel A. Belov,

Antenna Design and Analysis

The successful fabrication and experimental verification of a novel metamaterial based on flexible metallic helices is reported. The helices undergo compression under the influence of incident radiation, demonstrating a nonlinear chiral electromagnetic response, associated with the power-dependent change in the helix pitch. This design is promising for application to power-dependent polarization rotation of propagating waves. After a decade of fruitful development, nonlinear metamaterials have received a new momentum with the introduction of alternative sources of nonlinearity, exploring a link between electromagnetism and other branches of physics, making use of thermal tuning1, 2 or mechanical coupling.3 An interesting opportunity to create nonlinearity which combines such effects, is offered by a chiral particle, a well-known helical spiral,4 which became popular in metamaterials design,5 in accordance with the growing interest in metamaterial chirality.6-11 The helix is a very attractive "meta-atom" to bring an optomechanical analogy to electromagnetic metamaterials: it demonstrates a unique duality being, at once, an electromagnetic resonator and a mechanical spring. An interplay between the two responses of different types is provided through the dependence of resonance parameters on the spring geometry, while the sensitivity to heat is expressed through thermal expansion and temperature-dependent resistance. With an increasing incident power, the spring undergoes compression forced by the attracting currents in the neighbouring windings, while the growing temperature leads to an overall increase in size. Both effects act in the same direction, changing the geometrical conformation and shifting the electromagnetic resonance down to a lower frequency. This provides a nonlinear feedback making self-tuning processes possible, and promises an interesting range of nonlinear phenomena,12 including a highly desirable reconfigurable chirality.13, 14 Previous theoretical analysis12 reached the conclusion that a fairly thin wire (with the wire radius being one hundred times smaller than the radius of the spring) is required in order to observe mechanical conformational changes. Accordingly, a preliminary experimental assessment of a single resonator12 resulted in a system where thermal effect dominates, significantly limiting the range of nonlinear processes. In this paper, we report an advanced design which enhances conformational self-tuning, making the latter stronger than the thermal contribution, and dramatically increasing the nonlinear response. With the improved manufacturing procedures, we are able to fabricate a large number of nearly identical elements for creating bulk metamaterials in the form of a lattice of helical meta-atoms (Figure 1). Our results open up a road to exploit the effect of nonlinear chirality for polarization conversion, beam splitting and modulation, and nonlinear chiral negative refraction, as well as nonlinear chiral optomechanics. Array of fabricated helical resonators. The scale bar of the ruler equals 1 mm. Large number of resonators are produced with nearly identical individual resonances, so that no significant resonance broadening is observed in the lattice. An alternative configuration (helical axes perpendicular to the surface) is also possible. To achieve this goal, we use compact multi-turn helices made of thin copper wire with closely spaced windings (Figure 2). High temperature annealing increases the mechanical stability of the helices and minimizes thermal effects, while the large number of turns enhances the mechanical response to electromagnetic excitation. Indeed, the helical element considered earlier12 was taken to be just a two-turn element for the purpose of precise analytical description. But for multi-turn helices, we may expect a more efficient current-induced compression as the compressing force increases through the interaction of multiple wire turns. Furthermore, the increase in the number of turns makes the entire helix less sensitive to possible fabrication inaccuracy, particularly to the variation of the total length of the wire. Artist's view of a single helical resonator from the lattice shown in Figure 1, having N = 9 turns, with the geometrical parameters used in the experimental design: helix radius r = 1.16 mm, helix pitch is ξr = 194 μm, and wire radius is wr = 90 μm. This expectation is confirmed with our experiments on a piece of metamaterial excited with magnetic field at various input power levels (Figure 3). With an increase of supplied power to nearly 1 W, the resonance was shifted by 24 MHz from the original value. For the experiment we have used 16 helices with practically identical resonant frequencies, and we arranged them into a two dimensional 4 × 4 lattice, with their axes parallel to each other and also parallel to the magnetic field created by an exciting loop antenna (the helices are placed in the plane of the exciting loop). We have controlled that the temperature of the helices did not increase by more than 80 °C, which would induce a frequency shift of about 2.7 MHz, implying that a possible thermal contribution in our metamaterial does not exceed 12% of the total effect. Experimental transmission spectra of the lattice of helical resonators observed at various levels of input power. The resonators are arranged in a 4 × 4 lattice, and placed in the centre of a loop antenna which is used for excitation. Input power is varying between 0 and 29 dBm as shown in the legend . We note that the particular polarization selected in our experiment is not crucial for the nonlinear behavior: as a chiral particle, the helix can be excited with either electric or magnetic field directed along its axis. We have tested with numerical simulations that a plane-wave incidence with either polarization leads to the induced magnetic (and electric) moments of comparable magnitude. This makes our design convenient for nonlinear wave propagation in large chiral arrays: regardless of the expected rotation of the polarization plane, the nonlinear response will not change except for an attenuation due to the dissipation. Also, in two-dimensional arrays, the mutual orientation of the helices may also vary (e.g., all the axes being perpendicular to the array plane, or lying in that plane); such variation leads to an overall shift of the resonance frequency due to modified mutual interaction, however this has no influence on the nonlinear behavior. Change of the helix pitch with power, recalculated from the experimental data on the resonance shift with power (for a lattice, these are shown in Figure 3). Blue circles represent the data obtained for a single resonator, and red squares for the lattice; the surrounding contours indicate the measurement errors. Green solid curve shows the corresponding dependence obtained with the Equation 4. The axis on the right indicates (γ − 1) as a measure of chirality . We note that implementation of the flexible helices is much easier at a larger scale, so the applications for radio and microwave and GHz frequencies are straightforward. For THz range, fabrication is more challenging, particularly because the helices would need to be made of rather thin wire, making them fragile. This problem may be solved by using a direct-laser writing technology5, 8 with less rigid materials and a subsequent thin metal coating10, 22 of the resulting helices. This would provide a sufficient conductivity (thanks to a strong skin-effect) and flexibility, while keeping wire radius comparably large. In the optical range, where metals are not suitable as conductors, a similar scheme can be realized by using high-permittivity dielectrics.23 We also note that, for the proof-of-principle experiments, we have studied an anisotropic array. For a quasi-isotropic performance, the same helices can be arranged with a 3D-checkerboard logic, having their axes aligned along the three dimensions, with a sequence of three different orientations periodically patterned in each direction. Finally, a deliberate distinction can be made between a chiral lattice and a non-chiral racemic mixture, with the latter retaining the same nonlinear response but having no chiral properties. In summary, we have presented the first experimental demonstration of conformationally nonlinear chiral metamaterial with the response governed by structural changes in its elements. Such nonlinear chirality can lead to interesting consequences when the operating frequencies lie near the resonance, especially above the resonance where negative effective permeability can be achieved. As we have shown, the effect obtained with a modest 1 W power is sufficient to move the resonance significantly over the resonance width, promising an efficient power-induced switching between positive and negative permeability along with chirality change. This will lead to interesting phenomena for wave propagation inside large metamaterial samples which can be easily manufactured. We believe that our work provides an encouraging implementation of metamaterials with conformational nonlinearity and paves a road towards optomechanical metamaterials. The helical resonators were fabricated by shaping a copper wire with 90 μm diameter. Two adjacent wires were tightly wound around the metal rod with ca. 2 mm diameter and were exposed to a moderate annealing by heating the metal rod, with the annealing optimized to provide best stability to the helix shape. The auxiliary wire was then wound off and the main helix was cut to produce a required number of turns. As a result, nine turn helical resonators with 1.16 mm ± 0.01 mm radius and 194 μm ± 1 μm pitch were selected. The measurements over a single resonator were performed using a loop antenna (inner loop radius 5.51 mm, wire radius 1 mm) producing a strong magnetic field parallel to the helix axis. An Agilent HP E8362C vector network analyzer was employed to generate signals in the GHz range and to measure the response. An Agilent HP 83020A amplifier was used for high-power measurements. The measurements with a 4 × 4 lattice were performed in a similar way but a larger loop antenna (inner loop radius 9.47 mm) was used. The array was positioned inside the antenna loop within the plane of the loop, with the resonators suspended horizontally on thin plastic wires (where the windings can slide with a minimal friction), with their axes being horizontal and parallel to the loop axis. For the array assembly, the resonance frequency was carefully measured to select the resonators with individual resonances matched within a 0.01% relative accuracy. Supporting Information is available from the Wiley Online Library or from the author. This work was supported by the Ministry of Education and Science of Russian Federation (Project 11.G34.31.0020,14.B37.21.1283, 14.B37.21.0942 and MD-6805.2013.2) and by the Australian Research Council (CUDOS Centre of Excellence CE110001018 and Discovery Projects). The authors are grateful to S. Maslovski for the useful advice on the experimental procedures, to D. Filonov for assistance with measurements and to S. Kosulnikov for help with numerical simulations. A.S. acknowledges support of the IEEE MTT-S Undergraduate Scholarship for Spring 2013. As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors. 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