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Yang Zhao, Jinwei Shi, Liuyang Sun, Xiaoqin Li, and Andrea Alù* Metamaterials are formed by engineered subwavelength structural elements, or meta-atoms[1] that provide exotic electromagnetic bulk properties, not available in natural materials. Due to their anomalous features they have attracted significant attention and research interest in the past decade. Their fascinating properties do not stem from the average composition, as for conventional mixtures, but are instead based on the specific arrangement and geometry of the structural elements of which they are composed. Their popularity is associated with the possibility to tune the operation frequency and functionality by tailoring the geometry of these constituent meta-atoms, providing functionalities such as negative refraction,[2–6] extrinsic chirality and giant optical activity,[7–14] among many others. With the critical dimensions of the constituent inclusions shrinking as we push up the operation frequency, optical metamaterials are particularly challenging to realize, due to the lack of suitable nanofabrication techniques. Complex three-dimensional (3D) fabrication procedures face significant challenges due to their inherently limited spatial resolution, combined with an equally limited overall area of the realizable metamaterial devices.[15] Compared to 3D fabrication, two-dimensional (2D) lithographic processes are better established and can provide much higher resolution and in many cases very large footprints, as in the case of nano-imprint lithography.[16] For this reason, there has been significant recent interest in realizing 3D optical metamaterials by combining stacks of planarized 2D structures, such as densely packed metasurfaces,[17] realized with high-resolution planar lithography combined with spin-on spacer for planarization and vertical stacking.[18,19] Similar methods have also been employed to fabricate negative index metamaterials.[20–22] In these previous experiments, the proposed functionality inherently relies on the precise alignment of the inclusions from one metasurface to the next, which raises significant challenges and causes delays in the fabrication process, especially if methods like the membrane transfer technique[23] need to be employed for large area production. Y. Zhao, Prof. A. Alù Department of Electrical and Computer Engineering The University of Texas at Austin Austin, TX 78712, USA E-mail: [email protected] Dr. J. Shi, L. Sun, Prof. X. Li Department of Physics and Center for Complex Quantum Systems The University of Texas at Austin Austin, TX 78712, USA Dr. J. Shi Applied Optics Beijing Area Major Laboratory Department of Physics Beijing Normal University Beijing, 100875, China
DOI: 10.1002/adma.201304379
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In a recent paper,[24] we have proposed that by stacking a number of metasurface layers with proper choice of spacing between them can provide a significant broadening of the operational bandwidth of the metamaterial as a bulk material, compared to a single metasurface, as they can essentially open a continuous eigen-modal band of propagation. This design, however, is difficult to realize if lateral alignment between successive layers is required. We have speculated in Ref. [24] that, under certain conditions, alignment may not be an issue, since the eigen-modal excitation along the stack is based on the zero-th order Floquet mode coupling between neighboring metasurfaces. The scope of this study is to systematically prove these claims with a theoretical and experimental study of layered metamaterials, generalizing this concept also to other metamaterial functionalities. In the following, we determine the criteria for which it may be possible to relax the alignment requirements in general metamaterials formed by stacked metasurfaces while keeping the anomalous wave interaction properties. For this purpose, we study the field interaction between closely spaced metasurfaces using fully vectorial numerical simulations, and study the influence of higher-order Floquet modes on this interaction, showing under what conditions the coupling between neighboring layers may be kept strong, but robust to misalignment. Our analysis, applicable to arbitrary metasurface designs to realize multilayered 3D metamaterials for a variety of purposes, is validated with the fabrication of various two-layer metamaterial samples with different levels of registration and distance between metasurfaces. We conclude this study by applying our design principle to experimentally realize alignment-free metamaterials for large, broadband, circularly polarized asymmetric transmission, showing how our concept may provide new opportunities to realize large-scale 3D metamaterials for various practical applications of interest. In all the following examples we consider one of the most basic meta-atoms, a gold nanorod with dimensions 250 nm × 60 nm × 50 nm (length×width×thickness), which supports its fundamental resonance in the near-IR regime. Our full-wave simulations model the gold permittivity using values obtained from Ref. [25]. We first consider periodic planar metasurfaces with two different lattice arrangements: rectangular and hexagonal arrangements of nanorods in the transverse plane. We consider a periodicity much smaller than the wavelength of interest, ensuring that, within the metasurface plane (z = 0 plane), we can safely homogenize the array to describe its farfield interaction.[26,27] As a first application of these metasurfaces, we explore their use to realize 3D chiral metamaterials, formed by stacking two or more of these elements with a distance d between consecutive ones, and further introducing an arbitrary in-plane rotation angle θ between one metasurface and the next. This sequential rotation of the meta-atoms in consecutive planes has been
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Alignment-Free Three-Dimensional Optical Metamaterials
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shown to provide[24] a large and broadband structural chirality. Specifically, we have shown that an optimal choice of the design parameters d and θ can significantly increase the bandwidth and overall chiral response of the metamaterial, while retaining a planarized low-profile geometry. In the following, we analyze in detail the effect of misalignment Δ of these multilayered metamaterials on their overall performance. First, we analyze how the packing density and lattice geometry of each metasurface influences the coupling between closely spaced elements. A metasurface by definition has a transverse periodicity much smaller than the wavelength, ensuring that closely spaced meta-atoms experience collective and coherent excitation. Consequently, only the fundamental Floquet mode (zero-th order) is propagative and sustains farfield radiation, while higher-order harmonics are all evanescent and exponentially decay away from the metasurface. Therefore, it is expected that only when two metasurfaces are in close proximity can they strongly couple through higher-order Floquet harmonics. This coupling can be visualized by exciting the metasurface with the dominant Floquet harmonic and monitoring the amount of coupling into higher-order modes at a distance d. This is studied in Figure 1 using full wave numerical simulations:[28] in each panel we vary the distance d of the observation plane from the metasurface center and we evaluate | An | 2, where An are the northe coupling coefficient C = n≠0 malized amplitudes of the higher-order Floquet harmonics. We consider in all panels a circularly polarized excitation, which is of interest for the following discussions, but similar results may be obtained for linear excitation. Due to the intrinsic symmetries of a single ultrathin metasurface, our results are independent of whether the excitation is left-handed (LCP) or
right-handed (RCP). The larger the coupling coefficient C is, the more important the relative lateral misalignment is expected to be when stacking a second metasurface at a distance d; and for a negligible C the metasurface is ‘seen’ as a uniform impedance sheet, as it interacts only through the dominant zero-th order Floquet mode. Under this condition the alignment issue would not matter. Figure 1b–d show simulation results for metasurfaces with square lattice in the transverse plane (Figure 1a), varying the transverse period from 300 nm (Figure 1b), 400 nm (Figure 1c), to 500 nm (Figure 1d). Each panel shows a resonant peak, corresponding to the metasurface resonance, for which increased coupling to higher-order harmonics is found due to the stronger wave interaction with the metasurface. By increasing the period, the resonance becomes sharper and the coupling coefficient peak grows, which is reflected in a decrease in the decay rate for all higher-order Floquet modes.[29] Monitoring the fields farther away from the surface, i.e., for increased d, the peak decays exponentially, as expected. Panels f–h show similar calculations for hexagonal lattice metasurfaces (illustrated in Figure 1e. We consider in each panel the same level of packing density (P.D.), as detailed in each column of Figure 1, which is defined as the filling ratio for each unit cell. In Figure 1i we summarize these results, plotting the coupling coefficient at the resonant peak for each curve in the previous panels. We notice that the peak decays exponentially with d as expected, and is generally lower for more densely packed arrays. This is consistent with Floquet’s propagation constant inverse proportionality with the periodicity within the surface (directly related to the density of the array), which affects the decay rate away from the surface. The coupling with higher-order harmonics is
Figure 1. Simulated results for the coupling coefficient to higher-order Floquet modes for circularly polarized plane waves for gold nanorod arrays with 60 nm (width) x 250 nm (length) x 50 nm (thickness). The distance away from the metasurface is varied from 30 to 100 nm, with an interval of 5 nm. Two transverse lattice geometries are considered: (a) square and (e) hexagonal lattices. The periodicity for square lattices varies from (b) 300, (c) 400, to (d) 500 nm. For hexagonal lattices, (f) shows the same packing density (P.D. = 16.7%) as (b); (g) P.D. = 9.4% as (c); and (h) P.D. = 6% as (d). (i) Peak coupling coefficient for all previous panels as a function of the observation distance. The solid symbols refer to hexagonal lattices, void symbols to square lattices.
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COMMUNICATION Figure 2. Simulated results for the mean deviation in the transmission spectra of twisted metamaterials comparing perfectly aligned metasurfaces with misaligned metasurfaces. The mean deviation is defined as the mean of the Euclidean distance between spectra as schematically shown in the shaded region in (a) and (b). LCP and RCP denote the excitation polarizations, which are consistent for each column. No analyzer is included in the simulation, so the transmission represents the total transmitted power, without differentiating the polarization of transmitted fields. (c) and (d) consider misalignment along one axis in the transverse plane for the two impinging polarizations, with √ an accumulated total shift L/2, where L is the transverse periodicity. (e) and (f) consider misalignments along both axes with a total misalignment 2/2L.
hardly affected by the lattice geometry, and it is mainly determined by the packing density and observation distance. The coupling coefficient rapidly decays away from the surface, even for distances significantly smaller than the transverse period. Notice that the metasurface itself has a finite thickness of 50 nm, so the distance d is 25 nm offset from the exit surface. This plot serves as a useful chart to determine the required period and minimum center-to-center distance from neighboring metasurfaces of a 3D multilayered array in order to keep the coupling coefficient below a given threshold. After having established this general trend, and confirmed that the lattice arrangement does not affect the sensitivity to misalignment for densely packed arrays, we analyze its effect on the response of a 3D multilayered twisted metamaterial.[24] We consider the geometry originally introduced in Ref. [24], formed by a series of metasurfaces as in Figure 1a stacked with an arbitrary sequential rotation between neighboring metasurfaces, which produces giant, broadband chirality around the nanorod resonance. In Ref. [24] it was qualitatively argued that this proposed geometry and functionality is robust to misalignment, and indeed the measurement from a large-area sample,
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realized without strictly forcing the lateral alignment between neighboring layers, produced consistent results. In the following, we specifically study how the misalignment between layers affects the transmission spectra for different distances between consecutive layers. To quantify this change, in Figure 2 we evaluate the mean value of the Euclidean distance, defined as the mean absolute deviation, between the spectra obtained for perfectly aligned and misaligned metasurfaces, considering normally incident circularly polarized plane waves. We consider different numbers of layers, and various distances between neighboring surfaces. For each example, we chose a lateral misL alignment = 2(N−1) , where L is the transverse period and N is the total number of layers in the stack, to ensure that the total misalignment from entrance to exit of the metamaterial slab is fixed at L/2. Figures 2a and b show the simulated power transmission spectra for a pair of square-lattice metasurfaces with a period L = 300 nm (as in Figure 1b), a distance d = 100 nm between them and a relative rotation θ = 60°. It is seen how LCP waves (Figure 2a) are poorly transmitted by the pair around the nanorod resonance, which is quite different from
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RCP excitation (Figure 2b), realizing a structural chirality effect. The panels compare the case of perfectly aligned metasurfaces (black solid lines) with the case of misalignment Δ along one of the lattice axis x (dotted lines) and in both axes x and y (dashed), essentially misaligning √ the lattice in the 45° direction by an amount equal to 2 . The shaded regions in each panel highlight the effect of misalignment, and clarify how we calculate the Euclidean distance between the two curves by integrating the shaded area. The mean deviation is a good indication of the effect of misalignment between neighboring layers, and it indicates how the near-field coupling is affected by higher-order Floquet harmonics. Figures 2c and d report this quantity for different metasurface pairs (black solid squares) and larger number of layers as a function of the distance d between adjacent layers with square lattices, considering only misalignments along x, while Figures 2e and f take into account shifts in both directions. In each case, the panel on the left refers to LCP excitation, the one on the right to RCP. The two hollow squares in each panel specifically highlight the mean deviation for a 2-layer stack with d = 100 nm and d = 200 nm, respectively, which are experimentally analyzed in the following. In both Figure 1 and Figure 2, all metasurfaces are embedded in vacuum; in our experiments in the following, however, we consider a dielectric spacer and adhesion layers, which produce a red-shift in their resonant operation.[30] Overall, Figure 2 shows that the effect of misalignment decreases exponentially with d, consistent with Figure 1i, and that a larger number of metasurfaces is more robust, as the total misalignment is distributed over more layers. For metasurface stacks with d < 70 nm, for which the metasurfaces are almost touching (recall the finite thickness of 50 nm), the trend is not necessarily as clear cut, suggesting that
in this case the large coupling to higher-order harmonics builds up with a larger number of metasurfaces. Even in these cases, however, the mean deviation is surprisingly low, always below 10%. This small mean deviation indicates that the operation of twisted metamaterials is inherently robust to misalignment. This analysis confirms that structural lattice chirality produced by rotated stacks of metasurfaces is mainly associated with the zero-th diffraction order, and the effect from higher-order harmonics can be safely neglected as d increases.[24] To validate our theoretical results, we experimentally realized several metasurface stacks for different levels of misalignment Δ and separation distance d. We used a dedicated etch-back approach to achieve planarization and multilayered fabrication. The fabrication procedure is discussed in details in the Experimental section. In total, six samples of two-layer metasurface stacks were fabricated with three levels of misalignment registrations and two separation distances, as shown in Figure 3 with SEM images and corresponding illustrations of the three alignment configurations: no misalignment (Figure 3a,d) misalignment only along one lattice axis (Figure 3b,e), and same misalignment along both lattice axes (Figure 3c,f). Figures 3g–i refer to the samples with d = 100 nm, Figures 3j–l to d = 200 nm. Figure 4a,b show the transmittance measurements through the six samples; the corresponding full-wave numerical simulations are shown in Figure 4c and d. In the abovementioned theoretical study we considered vacuum as the background material, which represents the worst-case scenario in terms of coupling to higher-order Floquet harmonics for fixed distance d compared to any other dielectric substrate supporting a shorter wavelength. In these simulations, on the other hand, we consider a silicon dioxide spacer and an adhesive Ti layer to more precisely model our experimental setup. The measured
Figure 3. Illustration of different alignment registrations and corresponding SEM images for experimentally realized two-metasurface stacks with separation distance (g-i) d = 100 nm and (j-l) d = 200 nm. Perspective views of the two-metasurface stacks with (a) no misalignment, (b) lateral misalignment along one lattice axis, (c) lateral misalignment along both lattice axes. (d)-(f) are the corresponding top view images for these configurations.
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response when the distance between metasurfaces is released to d = 200 nm. To quantify the robustness of this effect, we extracted the previously defined mean deviation over a wavelength range from 650 nm to 1150 nm. The simulated mean deviations, compared with experimental measurements, are summarized in Table 1. Although the measured deviations are slightly bigger than what predicted in Figure 2, the overall trend is well confirmed in our experiments. After having theoretically and experimentally verified that the concept of alignmentfree metamaterials may provide a robust way to realize broadband chiral planarized ultrathin devices, and having explored the general necessary and sufficient conditions on the separation between neighboring metasurfaces to minimize the influence of higherFigure 4. Comparison of measurements and numerical simulations for different misalign- order Floquet harmonics, we apply this conments, consistent with the configurations in Figure 3 (a), (b) and (c), as indicated in the cept to a different metamaterial effect that legends. (a) Measurement for d = 100 nm, (b) measurement for d = 200 nm. (c) and (d) are has raised significant interest in the recent the corresponding numerical simulations. Solid curves are corresponding to RCP excitation, literature. More specifically, in Figure 5 we dotted curves are for LCP excitation. realize an alignment-free layered metamaterial providing large, broadband asymmetric transmission, with the goal of assessing the general relevance transmittance curves match qualitatively well the simulation of our findings. The concept is illustrated in Figure 5b, and results, despite some disagreement due to the practical chalit implies the possibility of transmitting mostly RCP waves lenges in realizing the metamaterial samples. Overall, it is eviwhen excited from one side of the stack, and mostly LCP waves dent that each realized stack can robustly differentiate between when excited from the other side. Since the device is linear and RCP and LCP excitation. The curves for RCP excitation (solid) nonmagnetic, it indeed satisfies the general conditions of Lorappear to match slightly better the simulation results than for entz reciprocity theorem, implying that its response is strictly LCP (dotted), mainly because the stack interacts more strongly reciprocal. However, large asymmetries may be induced for with LCP waves and reflects the large majority of the impinging different impinging polarizations, originating from the differpower for this excitation. Therefore, fabrication imperfecence between the transmittance of cross-polarization terms tions, such as local thickness and shape variations, affect more (TLR and TRL),[31] when excited from the two sides of the strucstrongly this excitation. Since we proved that higher-order Floture. This asymmetric transmission can be similarly observed quet harmonics have an inherently larger effect for shorter with linearly polarized excitation.[32] It has been recently sugdistances, the effect of misalignment for d = 100 nm appears gested to realize this interesting effect using single[31,33–35] even more pronounced in our experiments than in simulations, and stacked[32,36] metasurfaces, but these structures have been due to the additional excitation of these harmonics arisen from usually characterized by narrow bandwidths and small extincthe disorder and imperfections in the realized samples. These tion ratios. We propose here a design based on the previous effects are amplified when misalignment is introduced. On the theoretical results to obtain a robust, broadband metasurface contrary, both experiments and simulations confirm a robust stack with large extinction ratios, totally free of alignment requirements. Table 1. Comparison of Experimentally Measured and Simulated Mean Figure 5a shows the SEM images of our optimized twoDeviation. layer metasurface stack, in which the second layer is composed of zigzag patterns, while the first layer is made of horizontal Experiment Simulation Distance (d) Excitation Lateral Shift (Δ) nanorods (see inset for further details on the geometry). The [nm] Polarization fabrication is conducted following a similar procedure as in 100 LCP One direction 7.1% 2.8% the previous example, described in the Experimental section. Both directions 9.1% 4.2% Based on previous conclusions, we do not require alignment RCP One direction 5.7% 2.9% between the two layers in realizing this structure. Broadband Both directions 8.6% 3.0% asymmetric transmission is indeed observed for the realized configuration (see Figure 5c,d) for excitation from opposite 200 LCP One direction 2.5% 0.2% directions, confirmed by full-wave simulations assuming perBoth directions 1.0% 0.7% fect alignment and periodicity (Figure 5e,f). The effect is someRCP One direction 1.7% 0.4% what similar to the one recently reported in[37] using two layers Both directions 0.7% 0.4% of chiral molecules with achiral absorbing dyes. Our design,
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Figure 5. Two-layered metasurface stack composed of horizontal achiral nanorods, and a zigzag patterned second layer. (a) SEM images of the stacked layers. The bottom layer is composed of horizontal nanorods with 300 nm periodicity, and dimensions of 250 nm × 60 nm × 50 nm, with two layer separation of d = 150 nm. The top layer is a zigzag metasurface, and the dimensions are marked on the inset of panel (a). (b) Schematic illustration of the asymmetric transmission effect. (c) Experimental measurements for excitation from top, and (d) from bottom. (e) and (f) Simulation results correspond to (c) and (d), respectively.
however, is based on purely achiral inclusions that weakly absorb below 15% of the impinging power over the operational bandwidth, and the effect in this case is simply based on symmetry breaking. When excited from opposite sides, a strong asymmetry in transmission for the same input handedness can be observed,[38] confirming the possibility of realizing a robust ultrathin metamaterial with broadband asymmetric response. More importantly, the design is totally free of alignment issues, which is confirmed by the fact that our experimental results have been measured on a sample realized without constraints on alignment. In addition, our full-wave simulations confirm an estimated mean deviation between perfectly aligned and largely misaligned metasurfaces of less than 1% within the wavelength range from 650 nm to 1150 nm. In conclusion, we have presented the concept, analysis, design, and experimental validation of multilayered 3D metamaterials robust to misalignment, which can be achieved by controlling the coupling to higher-order Floquet modes by regulating the packing density and separation distance between neighboring metasurfaces. The robustness to misalignment has been validated experimentally by measuring a set of twolayer metasurface stacks with different alignment registrations, which confirmed our theoretical results and numerical simulations. Finally, our concept has been applied to a metamaterial
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bilayer to realize large, broadband asymmetric transmission in the visible range. We expect that our results may provide more degrees of freedom to design and fabricate multilayered metamaterials over large scales, without worrying about alignment issues. The principle of shift invariant metamaterials may have broader impact on devices involving metamaterials that are characterized by sheer forces, such as stretchable electronic devices, for which alignment may be affected during their operation.
Experimental Section Device Fabrication: All chemicals have been used as received. All fabrication procedures were performed in a class 100 clean room. The structure was fabricated on an optical flat glass substrate (Corning 1737–0107 from Delta Technologies). Before the first layer fabrication, a global alignment mark was fabricated on the substrate using a 100 nm thick gold, then a thick silicon dioxide layer was deposited on the substrate using electron beam evaporation to ensure same conditions for each subsequent layer. All patterns were written using electronbeam lithography. The e-beam resist was a positive tone resist ZEP 520a, prepared with dilution (2:3) using e-beam resist thinner (Anisole). Adhesion issues for the e-beam resist are commonly encountered on silica surface, therefore surface treatment was conducted before applying the resist to maintain repeatability. The substrate was soaked in piranha
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Acknowledgements This work is supported by the ONR MURI grant No. N00014–10–1– 0942, the U.S. AFOSR YIP award No. FA9550–11–1–0009, AFOSR FA9550–10–1–0022, the ARO grant No. ARO W911NF-11–1–0447, the Norman Hackerman Advanced Research Program and the Welch foundation grant No. F-1662. Received: August 31, 2013 Published online: December 5, 2013
[1] Y. M. Liu, X. Zhang, Chem. Soc. Rev. 2011, 40, 2494. [2] R. A. Shelby, D. R. Smith, S. Schultz, Science 2001, 292, 77.
Adv. Mater. 2014, 26, 1439–1445
[3] V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, A. V. Kildishev, Opt. Lett. 2005, 30, 3356. [4] S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, S. R. J. Brueck, Phys. Rev. Lett. 2005, 95, 137404. [5] C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, Phys. Rev. Lett. 2003, 90, 107401. [6] J. F. Zhou, J. F. Dong, B. N. Wang, T. Koschny, M. Kafesaki, C. M. Soukoulis, Phys. Rev. B 2009, 79, 121104. [7] A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, Phys. Rev. Lett. 2006, 97, 177401. [8] M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, Y. Svirko, Phys. Rev. Lett. 2005, 95, 227401. [9] B. Bai, Y. Svirko, J. Turunen, T. Vallius, Phys. Rev. A 2007, 76, 023811. [10] Y. Q. Ye, S. He, Appl. Phys. Lett. 2010, 96, 203501. [11] Z. F. Li, K. B. Alici, E. Colak, E. Ozbay, Appl. Phys. Lett. 2011, 98, 161907. [12] M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, M. Wegener, Opt. Lett. 2009, 34, 2501. [13] J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, M. Wegener, Science 2009, 325, 1513. [14] M. X. Ren, E. Plum, J. J. Xu, N. I. Zheludev, Nat. Commun. 2012, 3, 833. [15] C.M. Soukoulis, M. Wegener, Nat. Photon. 2011, 5, 523. [16] S. Y. Chou, P. R. Krauss, P. J. Renstrom, Science 1996, 272, 85. [17] C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, D. R. Smith, IEEE Antenn. Propag. M. 2012, 54, 10. [18] N. Liu, H. Giessen, Opt. Express 2008, 16, 21233. [19] N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, H. Giessen, Nat. Mater. 2008, 7, 31. [20] S. Zhang, Y. S. Park, J. S. Li, X. C. Lu, W. L. Zhang, X. Zhang, Phys. Rev. Lett. 2009, 102, 023901. [21] E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, Y. Chen, Appl. Phys. Lett. 2007, 90, 223113. [22] B. N. Wang, J. F. Zhou, T. Koschny, C. M. Soukoulis, Appl. Phys. Lett. 2009, 94, 151112. [23] D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, J. A. Rogers, Nat. Nanotechnol. 2011, 6, 402. [24] Y. Zhao, M. A. Belkin, A. Alù, Nat. Commun. 2012, 3, 870. [25] P. B. Johnson, R. W. Christy, Phys. Rev. B 1972, 6, 4370. [26] Y. Zhao, N. Engheta, A. Alù, Metamaterials 2011, 5, 90. [27] A. Alù, N. Engheta, in Structured Surfaces as Optical Metamaterials (Ed: A. A. Maradudin), Cambridge University Press, United Kingdom 2011, Ch. 3. [28] CST Microwave Studio 2011, www.cst.com. [29] A. Alexopoulos, Phys. Rev. E 2010, 81, 046607. [30] Y. Zhao, A. Alù, Phys. Rev. B 2011, 84, 205428. [31] E. Plum, V. A. Fedotov, N. I. Zheludev, J. Opt. 2011, 13, 024006. [32] C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, F. Lederer, Phys. Rev. Lett. 2010, 104, 253902. [33] V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, N. I. Zheludev, Phys. Rev. Lett. 2006, 97, 167401. [34] V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, Nano Lett. 2007, 7, 1996. [35] R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, N. I. Zheludev, Phys. Rev. B 2009, 80, 153104. [36] C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E. B. Kley, A. Tunnermann, F. Lederer, T. Pertsch, Nano Lett. 2011, 11, 4400. [37] S. Tomita, Y. Kosaka, H. Yanagi, K. Sawada, Phys. Rev. B 2013, 87, 041404. [38] Z. Y. Wang, Z. Wang, J. Y. Wang, B. Zhang, J. T. Huangfu, J. D. Joannopoulos, M. Soljacic, L. X. Ran, P. Natl. Acad. Sci. USA 2012, 109, 13194. [39] B. A. Sexton, B. N. Feltis, T. J. Davis, Sens. Actuator A-Phys. 2008, 141, 471.
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solution before each e-beam writing to remove any organic residues and also for adding hydroxyl groups to the surface to promote adhesion. After drying, the surface-treated silica substrate was immediately coated with HMDS primer at a spin speed of 2000 rpm and baked for 2 minutes on a hot plate at a temperature of 120 °C. After cooling down to room temperature, the prepared e-beam resist was spun onto the substrate at a speed of 4000 rpm and baked for 2 minutes at 180 °C to achieve a final thickness of 105 ± 5 nm. A JOEL 6000 JBX electron beam aligner with an accelerating voltage of 50k was used in the patterning, the exposure current was tuned to 100 pA. After exposure, the sample was developed in ZED-N50 (Emyl Acetate) for 2 minutes. To achieve multilayered fabrication, one of the most critical issues is the surface flatness before each layer deposition. To ensure a flat surface, we applied a special etch back process to first etch trenches into the silicon dioxide layer using the e-beam resist as an etch mask under a timed reactive ion etching (RIE). The CF4/He (3:1) gas mixture was calibrated so that it usually consumed the e-beam resist and silicon dioxide at around a one to one ratio. A 55 nm thickness of silicon dioxide was etched off in the RIE procedure, which resulted in an etched trench that maintained the aspect ratio between depth to minimum width of two to one to avoid shadow effects during metal deposition and to ensure enough thickness of e-beam resist left to perform liftoff. After anisotropic etching, a sequential deposition of 5 nm of Titanium (Ti) and 50 nm of Gold (Au) using ebeam evaporation was performed to fill the trench. Ti was chosen other than Chromium (Cr) for the adhesive layer due to the fact that Cr usually diffuses faster into the Au layer and forms an oxide on the surface, which affects the plasmon resonance of Au inclusions and increases the nonradiative damping loss.[39] After lifting off in N-methyl2-pyroridone the first layer fabrication was completed with the nanorod inclusions embedded in the silicon dioxide substrate with a flat surface finish. A 100 nm thick silicon dioxide layer is then deposited on top to serve as a dielectric spacer. The subsequent layers are fabricated using the same procedure, and the global alignment mark serves to ensure the correct rotation angle for subsequent layers. Measurements: The transmission spectrum was measured using a home-built setup. A Tungsten Halogen lamp (Ocean Optics) was employed as a white light source. By passing light through a linear polarizer (Newport 05P109AR16) and a quarter wave-plate (Special Optics 8–0912–1/4) we obtained either left- or right -handed circularly polarized light. The incident light was focused onto the sample at normal direction with a 10X objective (NA = 0.28, Mitutoyo). The excitation spot size was around 0.5 mm in diameter, which covered the entire sample area (200 μm by 200 μm). The transmitted light was collected via a 100X (NA = 0.70, Mitutoyo) objective followed by an imaging lens with a focal length of 200 mm (Thorlabs AC254–200-B-ML). We then selected a small area of the magnified image using the entrance slit (about 3.5 mm by 0.35 mm) of a spectrograph, which corresponds to an area of 35 μm × 3.5 μm on the sample. The transmitted signal was then dispersed by a grating (150 g/mm) onto a nitrogen-cooled, Si CCD (Princeton Instruments) where the spectrum was recorded.
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Yang Zhao, Jinwei Shi, Liuyang Sun, Xiaoqin Li, and Andrea Alù* Metamaterials are formed by engineered subwavelength structural elements, or meta-atoms[1] that provide exotic electromagnetic bulk properties, not available in natural materials. Due to their anomalous features they have attracted significant attention and research interest in the past decade. Their fascinating properties do not stem from the average composition, as for conventional mixtures, but are instead based on the specific arrangement and geometry of the structural elements of which they are composed. Their popularity is associated with the possibility to tune the operation frequency and functionality by tailoring the geometry of these constituent meta-atoms, providing functionalities such as negative refraction,[2–6] extrinsic chirality and giant optical activity,[7–14] among many others. With the critical dimensions of the constituent inclusions shrinking as we push up the operation frequency, optical metamaterials are particularly challenging to realize, due to the lack of suitable nanofabrication techniques. Complex three-dimensional (3D) fabrication procedures face significant challenges due to their inherently limited spatial resolution, combined with an equally limited overall area of the realizable metamaterial devices.[15] Compared to 3D fabrication, two-dimensional (2D) lithographic processes are better established and can provide much higher resolution and in many cases very large footprints, as in the case of nano-imprint lithography.[16] For this reason, there has been significant recent interest in realizing 3D optical metamaterials by combining stacks of planarized 2D structures, such as densely packed metasurfaces,[17] realized with high-resolution planar lithography combined with spin-on spacer for planarization and vertical stacking.[18,19] Similar methods have also been employed to fabricate negative index metamaterials.[20–22] In these previous experiments, the proposed functionality inherently relies on the precise alignment of the inclusions from one metasurface to the next, which raises significant challenges and causes delays in the fabrication process, especially if methods like the membrane transfer technique[23] need to be employed for large area production. Y. Zhao, Prof. A. Alù Department of Electrical and Computer Engineering The University of Texas at Austin Austin, TX 78712, USA E-mail: [email protected] Dr. J. Shi, L. Sun, Prof. X. Li Department of Physics and Center for Complex Quantum Systems The University of Texas at Austin Austin, TX 78712, USA Dr. J. Shi Applied Optics Beijing Area Major Laboratory Department of Physics Beijing Normal University Beijing, 100875, China
DOI: 10.1002/adma.201304379
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In a recent paper,[24] we have proposed that by stacking a number of metasurface layers with proper choice of spacing between them can provide a significant broadening of the operational bandwidth of the metamaterial as a bulk material, compared to a single metasurface, as they can essentially open a continuous eigen-modal band of propagation. This design, however, is difficult to realize if lateral alignment between successive layers is required. We have speculated in Ref. [24] that, under certain conditions, alignment may not be an issue, since the eigen-modal excitation along the stack is based on the zero-th order Floquet mode coupling between neighboring metasurfaces. The scope of this study is to systematically prove these claims with a theoretical and experimental study of layered metamaterials, generalizing this concept also to other metamaterial functionalities. In the following, we determine the criteria for which it may be possible to relax the alignment requirements in general metamaterials formed by stacked metasurfaces while keeping the anomalous wave interaction properties. For this purpose, we study the field interaction between closely spaced metasurfaces using fully vectorial numerical simulations, and study the influence of higher-order Floquet modes on this interaction, showing under what conditions the coupling between neighboring layers may be kept strong, but robust to misalignment. Our analysis, applicable to arbitrary metasurface designs to realize multilayered 3D metamaterials for a variety of purposes, is validated with the fabrication of various two-layer metamaterial samples with different levels of registration and distance between metasurfaces. We conclude this study by applying our design principle to experimentally realize alignment-free metamaterials for large, broadband, circularly polarized asymmetric transmission, showing how our concept may provide new opportunities to realize large-scale 3D metamaterials for various practical applications of interest. In all the following examples we consider one of the most basic meta-atoms, a gold nanorod with dimensions 250 nm × 60 nm × 50 nm (length×width×thickness), which supports its fundamental resonance in the near-IR regime. Our full-wave simulations model the gold permittivity using values obtained from Ref. [25]. We first consider periodic planar metasurfaces with two different lattice arrangements: rectangular and hexagonal arrangements of nanorods in the transverse plane. We consider a periodicity much smaller than the wavelength of interest, ensuring that, within the metasurface plane (z = 0 plane), we can safely homogenize the array to describe its farfield interaction.[26,27] As a first application of these metasurfaces, we explore their use to realize 3D chiral metamaterials, formed by stacking two or more of these elements with a distance d between consecutive ones, and further introducing an arbitrary in-plane rotation angle θ between one metasurface and the next. This sequential rotation of the meta-atoms in consecutive planes has been
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Alignment-Free Three-Dimensional Optical Metamaterials
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shown to provide[24] a large and broadband structural chirality. Specifically, we have shown that an optimal choice of the design parameters d and θ can significantly increase the bandwidth and overall chiral response of the metamaterial, while retaining a planarized low-profile geometry. In the following, we analyze in detail the effect of misalignment Δ of these multilayered metamaterials on their overall performance. First, we analyze how the packing density and lattice geometry of each metasurface influences the coupling between closely spaced elements. A metasurface by definition has a transverse periodicity much smaller than the wavelength, ensuring that closely spaced meta-atoms experience collective and coherent excitation. Consequently, only the fundamental Floquet mode (zero-th order) is propagative and sustains farfield radiation, while higher-order harmonics are all evanescent and exponentially decay away from the metasurface. Therefore, it is expected that only when two metasurfaces are in close proximity can they strongly couple through higher-order Floquet harmonics. This coupling can be visualized by exciting the metasurface with the dominant Floquet harmonic and monitoring the amount of coupling into higher-order modes at a distance d. This is studied in Figure 1 using full wave numerical simulations:[28] in each panel we vary the distance d of the observation plane from the metasurface center and we evaluate | An | 2, where An are the northe coupling coefficient C = n≠0 malized amplitudes of the higher-order Floquet harmonics. We consider in all panels a circularly polarized excitation, which is of interest for the following discussions, but similar results may be obtained for linear excitation. Due to the intrinsic symmetries of a single ultrathin metasurface, our results are independent of whether the excitation is left-handed (LCP) or
right-handed (RCP). The larger the coupling coefficient C is, the more important the relative lateral misalignment is expected to be when stacking a second metasurface at a distance d; and for a negligible C the metasurface is ‘seen’ as a uniform impedance sheet, as it interacts only through the dominant zero-th order Floquet mode. Under this condition the alignment issue would not matter. Figure 1b–d show simulation results for metasurfaces with square lattice in the transverse plane (Figure 1a), varying the transverse period from 300 nm (Figure 1b), 400 nm (Figure 1c), to 500 nm (Figure 1d). Each panel shows a resonant peak, corresponding to the metasurface resonance, for which increased coupling to higher-order harmonics is found due to the stronger wave interaction with the metasurface. By increasing the period, the resonance becomes sharper and the coupling coefficient peak grows, which is reflected in a decrease in the decay rate for all higher-order Floquet modes.[29] Monitoring the fields farther away from the surface, i.e., for increased d, the peak decays exponentially, as expected. Panels f–h show similar calculations for hexagonal lattice metasurfaces (illustrated in Figure 1e. We consider in each panel the same level of packing density (P.D.), as detailed in each column of Figure 1, which is defined as the filling ratio for each unit cell. In Figure 1i we summarize these results, plotting the coupling coefficient at the resonant peak for each curve in the previous panels. We notice that the peak decays exponentially with d as expected, and is generally lower for more densely packed arrays. This is consistent with Floquet’s propagation constant inverse proportionality with the periodicity within the surface (directly related to the density of the array), which affects the decay rate away from the surface. The coupling with higher-order harmonics is
Figure 1. Simulated results for the coupling coefficient to higher-order Floquet modes for circularly polarized plane waves for gold nanorod arrays with 60 nm (width) x 250 nm (length) x 50 nm (thickness). The distance away from the metasurface is varied from 30 to 100 nm, with an interval of 5 nm. Two transverse lattice geometries are considered: (a) square and (e) hexagonal lattices. The periodicity for square lattices varies from (b) 300, (c) 400, to (d) 500 nm. For hexagonal lattices, (f) shows the same packing density (P.D. = 16.7%) as (b); (g) P.D. = 9.4% as (c); and (h) P.D. = 6% as (d). (i) Peak coupling coefficient for all previous panels as a function of the observation distance. The solid symbols refer to hexagonal lattices, void symbols to square lattices.
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hardly affected by the lattice geometry, and it is mainly determined by the packing density and observation distance. The coupling coefficient rapidly decays away from the surface, even for distances significantly smaller than the transverse period. Notice that the metasurface itself has a finite thickness of 50 nm, so the distance d is 25 nm offset from the exit surface. This plot serves as a useful chart to determine the required period and minimum center-to-center distance from neighboring metasurfaces of a 3D multilayered array in order to keep the coupling coefficient below a given threshold. After having established this general trend, and confirmed that the lattice arrangement does not affect the sensitivity to misalignment for densely packed arrays, we analyze its effect on the response of a 3D multilayered twisted metamaterial.[24] We consider the geometry originally introduced in Ref. [24], formed by a series of metasurfaces as in Figure 1a stacked with an arbitrary sequential rotation between neighboring metasurfaces, which produces giant, broadband chirality around the nanorod resonance. In Ref. [24] it was qualitatively argued that this proposed geometry and functionality is robust to misalignment, and indeed the measurement from a large-area sample,
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realized without strictly forcing the lateral alignment between neighboring layers, produced consistent results. In the following, we specifically study how the misalignment between layers affects the transmission spectra for different distances between consecutive layers. To quantify this change, in Figure 2 we evaluate the mean value of the Euclidean distance, defined as the mean absolute deviation, between the spectra obtained for perfectly aligned and misaligned metasurfaces, considering normally incident circularly polarized plane waves. We consider different numbers of layers, and various distances between neighboring surfaces. For each example, we chose a lateral misL alignment = 2(N−1) , where L is the transverse period and N is the total number of layers in the stack, to ensure that the total misalignment from entrance to exit of the metamaterial slab is fixed at L/2. Figures 2a and b show the simulated power transmission spectra for a pair of square-lattice metasurfaces with a period L = 300 nm (as in Figure 1b), a distance d = 100 nm between them and a relative rotation θ = 60°. It is seen how LCP waves (Figure 2a) are poorly transmitted by the pair around the nanorod resonance, which is quite different from
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RCP excitation (Figure 2b), realizing a structural chirality effect. The panels compare the case of perfectly aligned metasurfaces (black solid lines) with the case of misalignment Δ along one of the lattice axis x (dotted lines) and in both axes x and y (dashed), essentially misaligning √ the lattice in the 45° direction by an amount equal to 2 . The shaded regions in each panel highlight the effect of misalignment, and clarify how we calculate the Euclidean distance between the two curves by integrating the shaded area. The mean deviation is a good indication of the effect of misalignment between neighboring layers, and it indicates how the near-field coupling is affected by higher-order Floquet harmonics. Figures 2c and d report this quantity for different metasurface pairs (black solid squares) and larger number of layers as a function of the distance d between adjacent layers with square lattices, considering only misalignments along x, while Figures 2e and f take into account shifts in both directions. In each case, the panel on the left refers to LCP excitation, the one on the right to RCP. The two hollow squares in each panel specifically highlight the mean deviation for a 2-layer stack with d = 100 nm and d = 200 nm, respectively, which are experimentally analyzed in the following. In both Figure 1 and Figure 2, all metasurfaces are embedded in vacuum; in our experiments in the following, however, we consider a dielectric spacer and adhesion layers, which produce a red-shift in their resonant operation.[30] Overall, Figure 2 shows that the effect of misalignment decreases exponentially with d, consistent with Figure 1i, and that a larger number of metasurfaces is more robust, as the total misalignment is distributed over more layers. For metasurface stacks with d < 70 nm, for which the metasurfaces are almost touching (recall the finite thickness of 50 nm), the trend is not necessarily as clear cut, suggesting that
in this case the large coupling to higher-order harmonics builds up with a larger number of metasurfaces. Even in these cases, however, the mean deviation is surprisingly low, always below 10%. This small mean deviation indicates that the operation of twisted metamaterials is inherently robust to misalignment. This analysis confirms that structural lattice chirality produced by rotated stacks of metasurfaces is mainly associated with the zero-th diffraction order, and the effect from higher-order harmonics can be safely neglected as d increases.[24] To validate our theoretical results, we experimentally realized several metasurface stacks for different levels of misalignment Δ and separation distance d. We used a dedicated etch-back approach to achieve planarization and multilayered fabrication. The fabrication procedure is discussed in details in the Experimental section. In total, six samples of two-layer metasurface stacks were fabricated with three levels of misalignment registrations and two separation distances, as shown in Figure 3 with SEM images and corresponding illustrations of the three alignment configurations: no misalignment (Figure 3a,d) misalignment only along one lattice axis (Figure 3b,e), and same misalignment along both lattice axes (Figure 3c,f). Figures 3g–i refer to the samples with d = 100 nm, Figures 3j–l to d = 200 nm. Figure 4a,b show the transmittance measurements through the six samples; the corresponding full-wave numerical simulations are shown in Figure 4c and d. In the abovementioned theoretical study we considered vacuum as the background material, which represents the worst-case scenario in terms of coupling to higher-order Floquet harmonics for fixed distance d compared to any other dielectric substrate supporting a shorter wavelength. In these simulations, on the other hand, we consider a silicon dioxide spacer and an adhesive Ti layer to more precisely model our experimental setup. The measured
Figure 3. Illustration of different alignment registrations and corresponding SEM images for experimentally realized two-metasurface stacks with separation distance (g-i) d = 100 nm and (j-l) d = 200 nm. Perspective views of the two-metasurface stacks with (a) no misalignment, (b) lateral misalignment along one lattice axis, (c) lateral misalignment along both lattice axes. (d)-(f) are the corresponding top view images for these configurations.
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response when the distance between metasurfaces is released to d = 200 nm. To quantify the robustness of this effect, we extracted the previously defined mean deviation over a wavelength range from 650 nm to 1150 nm. The simulated mean deviations, compared with experimental measurements, are summarized in Table 1. Although the measured deviations are slightly bigger than what predicted in Figure 2, the overall trend is well confirmed in our experiments. After having theoretically and experimentally verified that the concept of alignmentfree metamaterials may provide a robust way to realize broadband chiral planarized ultrathin devices, and having explored the general necessary and sufficient conditions on the separation between neighboring metasurfaces to minimize the influence of higherFigure 4. Comparison of measurements and numerical simulations for different misalign- order Floquet harmonics, we apply this conments, consistent with the configurations in Figure 3 (a), (b) and (c), as indicated in the cept to a different metamaterial effect that legends. (a) Measurement for d = 100 nm, (b) measurement for d = 200 nm. (c) and (d) are has raised significant interest in the recent the corresponding numerical simulations. Solid curves are corresponding to RCP excitation, literature. More specifically, in Figure 5 we dotted curves are for LCP excitation. realize an alignment-free layered metamaterial providing large, broadband asymmetric transmission, with the goal of assessing the general relevance transmittance curves match qualitatively well the simulation of our findings. The concept is illustrated in Figure 5b, and results, despite some disagreement due to the practical chalit implies the possibility of transmitting mostly RCP waves lenges in realizing the metamaterial samples. Overall, it is eviwhen excited from one side of the stack, and mostly LCP waves dent that each realized stack can robustly differentiate between when excited from the other side. Since the device is linear and RCP and LCP excitation. The curves for RCP excitation (solid) nonmagnetic, it indeed satisfies the general conditions of Lorappear to match slightly better the simulation results than for entz reciprocity theorem, implying that its response is strictly LCP (dotted), mainly because the stack interacts more strongly reciprocal. However, large asymmetries may be induced for with LCP waves and reflects the large majority of the impinging different impinging polarizations, originating from the differpower for this excitation. Therefore, fabrication imperfecence between the transmittance of cross-polarization terms tions, such as local thickness and shape variations, affect more (TLR and TRL),[31] when excited from the two sides of the strucstrongly this excitation. Since we proved that higher-order Floture. This asymmetric transmission can be similarly observed quet harmonics have an inherently larger effect for shorter with linearly polarized excitation.[32] It has been recently sugdistances, the effect of misalignment for d = 100 nm appears gested to realize this interesting effect using single[31,33–35] even more pronounced in our experiments than in simulations, and stacked[32,36] metasurfaces, but these structures have been due to the additional excitation of these harmonics arisen from usually characterized by narrow bandwidths and small extincthe disorder and imperfections in the realized samples. These tion ratios. We propose here a design based on the previous effects are amplified when misalignment is introduced. On the theoretical results to obtain a robust, broadband metasurface contrary, both experiments and simulations confirm a robust stack with large extinction ratios, totally free of alignment requirements. Table 1. Comparison of Experimentally Measured and Simulated Mean Figure 5a shows the SEM images of our optimized twoDeviation. layer metasurface stack, in which the second layer is composed of zigzag patterns, while the first layer is made of horizontal Experiment Simulation Distance (d) Excitation Lateral Shift (Δ) nanorods (see inset for further details on the geometry). The [nm] Polarization fabrication is conducted following a similar procedure as in 100 LCP One direction 7.1% 2.8% the previous example, described in the Experimental section. Both directions 9.1% 4.2% Based on previous conclusions, we do not require alignment RCP One direction 5.7% 2.9% between the two layers in realizing this structure. Broadband Both directions 8.6% 3.0% asymmetric transmission is indeed observed for the realized configuration (see Figure 5c,d) for excitation from opposite 200 LCP One direction 2.5% 0.2% directions, confirmed by full-wave simulations assuming perBoth directions 1.0% 0.7% fect alignment and periodicity (Figure 5e,f). The effect is someRCP One direction 1.7% 0.4% what similar to the one recently reported in[37] using two layers Both directions 0.7% 0.4% of chiral molecules with achiral absorbing dyes. Our design,
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Figure 5. Two-layered metasurface stack composed of horizontal achiral nanorods, and a zigzag patterned second layer. (a) SEM images of the stacked layers. The bottom layer is composed of horizontal nanorods with 300 nm periodicity, and dimensions of 250 nm × 60 nm × 50 nm, with two layer separation of d = 150 nm. The top layer is a zigzag metasurface, and the dimensions are marked on the inset of panel (a). (b) Schematic illustration of the asymmetric transmission effect. (c) Experimental measurements for excitation from top, and (d) from bottom. (e) and (f) Simulation results correspond to (c) and (d), respectively.
however, is based on purely achiral inclusions that weakly absorb below 15% of the impinging power over the operational bandwidth, and the effect in this case is simply based on symmetry breaking. When excited from opposite sides, a strong asymmetry in transmission for the same input handedness can be observed,[38] confirming the possibility of realizing a robust ultrathin metamaterial with broadband asymmetric response. More importantly, the design is totally free of alignment issues, which is confirmed by the fact that our experimental results have been measured on a sample realized without constraints on alignment. In addition, our full-wave simulations confirm an estimated mean deviation between perfectly aligned and largely misaligned metasurfaces of less than 1% within the wavelength range from 650 nm to 1150 nm. In conclusion, we have presented the concept, analysis, design, and experimental validation of multilayered 3D metamaterials robust to misalignment, which can be achieved by controlling the coupling to higher-order Floquet modes by regulating the packing density and separation distance between neighboring metasurfaces. The robustness to misalignment has been validated experimentally by measuring a set of twolayer metasurface stacks with different alignment registrations, which confirmed our theoretical results and numerical simulations. Finally, our concept has been applied to a metamaterial
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bilayer to realize large, broadband asymmetric transmission in the visible range. We expect that our results may provide more degrees of freedom to design and fabricate multilayered metamaterials over large scales, without worrying about alignment issues. The principle of shift invariant metamaterials may have broader impact on devices involving metamaterials that are characterized by sheer forces, such as stretchable electronic devices, for which alignment may be affected during their operation.
Experimental Section Device Fabrication: All chemicals have been used as received. All fabrication procedures were performed in a class 100 clean room. The structure was fabricated on an optical flat glass substrate (Corning 1737–0107 from Delta Technologies). Before the first layer fabrication, a global alignment mark was fabricated on the substrate using a 100 nm thick gold, then a thick silicon dioxide layer was deposited on the substrate using electron beam evaporation to ensure same conditions for each subsequent layer. All patterns were written using electronbeam lithography. The e-beam resist was a positive tone resist ZEP 520a, prepared with dilution (2:3) using e-beam resist thinner (Anisole). Adhesion issues for the e-beam resist are commonly encountered on silica surface, therefore surface treatment was conducted before applying the resist to maintain repeatability. The substrate was soaked in piranha
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Acknowledgements This work is supported by the ONR MURI grant No. N00014–10–1– 0942, the U.S. AFOSR YIP award No. FA9550–11–1–0009, AFOSR FA9550–10–1–0022, the ARO grant No. ARO W911NF-11–1–0447, the Norman Hackerman Advanced Research Program and the Welch foundation grant No. F-1662. Received: August 31, 2013 Published online: December 5, 2013
[1] Y. M. Liu, X. Zhang, Chem. Soc. Rev. 2011, 40, 2494. [2] R. A. Shelby, D. R. Smith, S. Schultz, Science 2001, 292, 77.
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[3] V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, A. V. Kildishev, Opt. Lett. 2005, 30, 3356. [4] S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, S. R. J. Brueck, Phys. Rev. Lett. 2005, 95, 137404. [5] C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, Phys. Rev. Lett. 2003, 90, 107401. [6] J. F. Zhou, J. F. Dong, B. N. Wang, T. Koschny, M. Kafesaki, C. M. Soukoulis, Phys. Rev. B 2009, 79, 121104. [7] A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, Phys. Rev. Lett. 2006, 97, 177401. [8] M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, Y. Svirko, Phys. Rev. Lett. 2005, 95, 227401. [9] B. Bai, Y. Svirko, J. Turunen, T. Vallius, Phys. Rev. A 2007, 76, 023811. [10] Y. Q. Ye, S. He, Appl. Phys. Lett. 2010, 96, 203501. [11] Z. F. Li, K. B. Alici, E. Colak, E. Ozbay, Appl. Phys. Lett. 2011, 98, 161907. [12] M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, M. Wegener, Opt. Lett. 2009, 34, 2501. [13] J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, M. Wegener, Science 2009, 325, 1513. [14] M. X. Ren, E. Plum, J. J. Xu, N. I. Zheludev, Nat. Commun. 2012, 3, 833. [15] C.M. Soukoulis, M. Wegener, Nat. Photon. 2011, 5, 523. [16] S. Y. Chou, P. R. Krauss, P. J. Renstrom, Science 1996, 272, 85. [17] C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, D. R. Smith, IEEE Antenn. Propag. M. 2012, 54, 10. [18] N. Liu, H. Giessen, Opt. Express 2008, 16, 21233. [19] N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, H. Giessen, Nat. Mater. 2008, 7, 31. [20] S. Zhang, Y. S. Park, J. S. Li, X. C. Lu, W. L. Zhang, X. Zhang, Phys. Rev. Lett. 2009, 102, 023901. [21] E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, Y. Chen, Appl. Phys. Lett. 2007, 90, 223113. [22] B. N. Wang, J. F. Zhou, T. Koschny, C. M. Soukoulis, Appl. Phys. Lett. 2009, 94, 151112. [23] D. Chanda, K. Shigeta, S. Gupta, T. Cain, A. Carlson, A. Mihi, A. J. Baca, G. R. Bogart, P. Braun, J. A. Rogers, Nat. Nanotechnol. 2011, 6, 402. [24] Y. Zhao, M. A. Belkin, A. Alù, Nat. Commun. 2012, 3, 870. [25] P. B. Johnson, R. W. Christy, Phys. Rev. B 1972, 6, 4370. [26] Y. Zhao, N. Engheta, A. Alù, Metamaterials 2011, 5, 90. [27] A. Alù, N. Engheta, in Structured Surfaces as Optical Metamaterials (Ed: A. A. Maradudin), Cambridge University Press, United Kingdom 2011, Ch. 3. [28] CST Microwave Studio 2011, www.cst.com. [29] A. Alexopoulos, Phys. Rev. E 2010, 81, 046607. [30] Y. Zhao, A. Alù, Phys. Rev. B 2011, 84, 205428. [31] E. Plum, V. A. Fedotov, N. I. Zheludev, J. Opt. 2011, 13, 024006. [32] C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, F. Lederer, Phys. Rev. Lett. 2010, 104, 253902. [33] V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, N. I. Zheludev, Phys. Rev. Lett. 2006, 97, 167401. [34] V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, S. L. Prosvirnin, Nano Lett. 2007, 7, 1996. [35] R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, N. I. Zheludev, Phys. Rev. B 2009, 80, 153104. [36] C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E. B. Kley, A. Tunnermann, F. Lederer, T. Pertsch, Nano Lett. 2011, 11, 4400. [37] S. Tomita, Y. Kosaka, H. Yanagi, K. Sawada, Phys. Rev. B 2013, 87, 041404. [38] Z. Y. Wang, Z. Wang, J. Y. Wang, B. Zhang, J. T. Huangfu, J. D. Joannopoulos, M. Soljacic, L. X. Ran, P. Natl. Acad. Sci. USA 2012, 109, 13194. [39] B. A. Sexton, B. N. Feltis, T. J. Davis, Sens. Actuator A-Phys. 2008, 141, 471.
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solution before each e-beam writing to remove any organic residues and also for adding hydroxyl groups to the surface to promote adhesion. After drying, the surface-treated silica substrate was immediately coated with HMDS primer at a spin speed of 2000 rpm and baked for 2 minutes on a hot plate at a temperature of 120 °C. After cooling down to room temperature, the prepared e-beam resist was spun onto the substrate at a speed of 4000 rpm and baked for 2 minutes at 180 °C to achieve a final thickness of 105 ± 5 nm. A JOEL 6000 JBX electron beam aligner with an accelerating voltage of 50k was used in the patterning, the exposure current was tuned to 100 pA. After exposure, the sample was developed in ZED-N50 (Emyl Acetate) for 2 minutes. To achieve multilayered fabrication, one of the most critical issues is the surface flatness before each layer deposition. To ensure a flat surface, we applied a special etch back process to first etch trenches into the silicon dioxide layer using the e-beam resist as an etch mask under a timed reactive ion etching (RIE). The CF4/He (3:1) gas mixture was calibrated so that it usually consumed the e-beam resist and silicon dioxide at around a one to one ratio. A 55 nm thickness of silicon dioxide was etched off in the RIE procedure, which resulted in an etched trench that maintained the aspect ratio between depth to minimum width of two to one to avoid shadow effects during metal deposition and to ensure enough thickness of e-beam resist left to perform liftoff. After anisotropic etching, a sequential deposition of 5 nm of Titanium (Ti) and 50 nm of Gold (Au) using ebeam evaporation was performed to fill the trench. Ti was chosen other than Chromium (Cr) for the adhesive layer due to the fact that Cr usually diffuses faster into the Au layer and forms an oxide on the surface, which affects the plasmon resonance of Au inclusions and increases the nonradiative damping loss.[39] After lifting off in N-methyl2-pyroridone the first layer fabrication was completed with the nanorod inclusions embedded in the silicon dioxide substrate with a flat surface finish. A 100 nm thick silicon dioxide layer is then deposited on top to serve as a dielectric spacer. The subsequent layers are fabricated using the same procedure, and the global alignment mark serves to ensure the correct rotation angle for subsequent layers. Measurements: The transmission spectrum was measured using a home-built setup. A Tungsten Halogen lamp (Ocean Optics) was employed as a white light source. By passing light through a linear polarizer (Newport 05P109AR16) and a quarter wave-plate (Special Optics 8–0912–1/4) we obtained either left- or right -handed circularly polarized light. The incident light was focused onto the sample at normal direction with a 10X objective (NA = 0.28, Mitutoyo). The excitation spot size was around 0.5 mm in diameter, which covered the entire sample area (200 μm by 200 μm). The transmitted light was collected via a 100X (NA = 0.70, Mitutoyo) objective followed by an imaging lens with a focal length of 200 mm (Thorlabs AC254–200-B-ML). We then selected a small area of the magnified image using the entrance slit (about 3.5 mm by 0.35 mm) of a spectrograph, which corresponds to an area of 35 μm × 3.5 μm on the sample. The transmitted signal was then dispersed by a grating (150 g/mm) onto a nitrogen-cooled, Si CCD (Princeton Instruments) where the spectrum was recorded.
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