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A stacked metal-dielectric hole array (SHA) containing rectangular holes whose shape gradually varies in-plane is proposed as a means of achieving wavefront control. The dependence of the transmitted phase on the frequency can be tuned by the hole shape, in particular the length of the sides that are normal to the incident polarization. The combination of periodic holes along the polarization direction and the gradual change in hole shape normal to the polarization direction produce an inclined wavefront for 1-dimensional beam steering. An in-plane phase difference of 0.6π using an SHA with a thickness of one-sixth of the wavelength has been experimentally demonstrated.
© 2013 Optical Society of America
1. Introduction
Passage of light through a single metallic hole array or a stacked metal-dielectric hole array (SHA) [1, 2] gives rise to extraordinary optical transmission (EOT) [3] and a negative refractive index for fishnet metamaterials [4, 5]. Transmission through such SHA films has been explained [6, 7] mainly in terms of two types of laterally propagating surface plasmon polaritons (SPPs) [8]. One is an outer SPP whose electromagnetic field is localized at the metal-dielectric interface, and the other is a gap SPP whose electromagnetic field is confined between the metal films [9]. Transmission through an SHA is now recognized as a combination of laterally propagating SPPs excited by the periodic hole array and localized hole resonances [10, 11].
Although SHAs have so far only been applied to spectral filtering [12, 13] and negative index prisms [2, 14], they could also be used to control the phase of transmitted light, because coupling between the light and laterally and resonantly propagating waves leads to a phase shift. While prisms are attractive structures to prove a negative refractive index [2, 14], they are difficult to fabricate and are not ideal for applications such as flat light-emitting diodes. Recently, Yu et al. reported a flat phase-control element using a V-shaped nano-antenna [15]. Using this approach, phase control in the range 0 to 2π was successfully achieved, which suggests a wide range of potential applications [16]. We also reported a transmission-phase-control element using an SHA with a two-dimensional geometric design [17], in which the resonance frequency is determined by the periodicity of the hole array, and the dispersion of the transmission phase is controlled by the hole shape. Based on this concept, an inclined wavefront was created for beam steering using a flat SHA in which the hole shape was gradually changed from circular to square.
Stacked metal-dielectric structures for radio frequency (RF) range have been reported on phase control applications, such as ultra-thin [18], composite left/right-handed design [19], and steerable antennas [20, 21]. In optical regime, however, the metals behave not as good conductors but as dielectrics with negative permittivity and large loss component, i.e. plasmonic materials. Thus, the device has to be designed to work with displacement current, with extreme care on ohmic loss. Additionally, device structure has to be enough simple such that present nano-machining technologies can fabricate.
The problem with our beam-steering element [17] is that the phase difference between the circular and square hole regions is only 0.1π. This value is insufficient; however unlike Ref. [15], refraction is only achieved in one direction, without the presence of ordinary refraction. Therefore, it is important to consider the type of hole shapes that can produce the largest phase difference in order to realize a realistic flat beam-steering element. In order to investigate the effect of the shape of holes in metallic films on the propagation constant or effective refractive index, several studies have focused on single rectangular holes [22–24]. Collin et al. introduced a simple analytic expression for the effective index, integrating the effect of the metal via the skin depth [24]. They found that for a rectangular hole, the propagation constant could be controlled by the length of the sides normal to the incident polarization direction. Since transmission through an SHA is characterized by the periodicity and shape of the holes, the use of rectangular holes with gradually changing shapes may represent a practical approach to achieve good phase control.
In the present study, the possibility of using a rectangular-hole SHA to achieve an inclined wavefront is experimentally investigated. Figure 1 depicts the unit cell and the hole-shape transition scheme. The SHA has alternating stacks of three silica (SiO2) and two aluminum (Al) layers on a SiO2 substrate perforated by rectangular nanoholes periodically arranged in a square lattice. The rectangular holes have sides of length wx and wy, where wy is equal to a/2, and a is the periodicity. The light is normal incident and has y-polarization. In the transition structure, the holes gradually change from narrow to wide rectangles for the purpose of creating an inclined wavefront. Hereafter, the structure with equally-sized rectangular holes will be referred to as uniform SHAs, whereas the structure with gradually changing rectangular holes will be referred to as the transition SHA. The remainder of this paper is organized as follows. Section 2 presents the transmission phase control mechanism for a uniform SHA. The resonant frequencies are extracted from the dispersion diagram of laterally propagating SPPs, and the transmission phase and amplitude are numerically calculated. In Sec. 3, the inclined wavefront generated by the transition SHA is computed based on these results. Sections 4 and 5 experimentally validate the uniform and transition SHAs, respectively. Finally, conclusions are presented in Sec. 6.
Fig. 1 (a) Unit cell structure of periodic SHA. (b) Geometric arrangement of transition SHA. The double-headed arrow represents the incident polarization direction. (c) Schematic of inclined wavefront produced by transition SHA.
2. Verification of transmission phase control by a uniform SHA
The resonances at which light can couple to SPPs are found from the dispersion diagram for IMIMI (insulator-metal-insulator-metal-insulator) layers. Since the target wavelength is 1.5 μm, the outer and gap SPPs can be calculated [6, 25] and are plotted in Fig. 2(a). The dispersion for outer and gap SPPs is indicated by the black solid and dashed lines, respectively. Normal incident y-polarized light couples to SPPs by creating a grating momentum from the periodic hole array at energies of 0.83 eV for an outer SPP and 0.65 eV for a gap SPP. For the numerical calculations, commercial finite-element-method software (Comsol Multiphysics) is used, and the frequency dependence of the permittivity of Al is assumed to follow the Lorentz-Drude model [26]. The refractive index of SiO2 is taken to be 1.45. The phase is expressed as a shift relative to that in a vacuum layer having the same thickness as the target structure.
Fig. 2 (a) Dispersion of an IMIMI structure for an outer SPP (black solid line) and a gap SPP (dashed line). The gray vertical line represents the reciprocal lattice vector for periodic holes with y-polarized normal incident light. (b) Numerically calculated transmittance. The double-headed arrows indicate the incident polarization direction. (c) Numerically calculated phase relative to that in a vacuum layer having the same thickness as the SHA. (d) Magnified plots of the transmitted phase near 0.83 eV for various side lengths wx.
From the calculated transmission spectra in Fig. 2(b) and phase in Fig. 2(c), several key features can be noted. First, a high transmittance and a significant phase shift occur near the resonance frequencies of 0.83 and 0.65 eV. Therefore, a rectangular-hole SHA is suitable for transmission phase control. Second, there is a clear effect of the hole shape on the transmitted phase. For a narrow SHA (wx = 0.4a), the phase exhibits a rapid shift compared to that for a wide SHA (wx = 0.6a). In other words, the dependence of the phase on frequency (the dispersion) is stronger for a narrow SHA. Hence, the dispersion can be tuned by varying the length of the sides of the rectangular holes that are normal to the polarization direction. Third, the outer and gap SPPs have a different effect on the dispersion. Based on the phase near the resonance frequencies in Fig. 2(c), the dispersion around 0.83 eV due to an outer SPP is stronger than that around 0.65 eV due to a gap SPP. Hereafter, phase control using a rectangular-hole SHA at around 0.83 eV will be considered.
3. Numerical study of transition SHA for inclined wavefront formation
In order to realize an inclined wavefront, a gradual linearly varying transmission phase is required. As described in Sec. 2, the phase produced by a uniform SHA can be controlled by changing the length of the sides normal to the polarization direction. Thus, as described in Ref. [27], the basic geometric unit for enhanced transmission is a linear chain of subwavelength holes along the polarization direction. Therefore, an SHA with periodicity along the polarization direction and gradually varying rectangular hole shapes normal to the polarization direction has the potential to enable 1-dimensional beam steering.
However, as seen in Fig. 2(d), linear scaling of wx from 0.4a to 0.6a does not give rise to a linear phase shift at certain frequencies. [Consider the width of the double-headed arrows in Fig. 2(d).] Therefore, nonlinear scaling of wx is required. To simulate the inclined wavefront produced by an SHA, a numerical calculation for an 11-hole array is performed for the structure depicted in Fig. 3(a). Normal incident y-polarized light and periodic boundary conditions along the y-axis are assumed. The structure has gradually varying hole shapes along the x-axis. Figure 3(b) represents the phase of Ey in the xz-plane. In the region outlined by the dashed line, 11 rectangular holes are aligned, which become increasingly wider from wx = 0.4a on the left to wx = 0.6a on the right. As can be seen in the Fig. 3(b), the outgoing wavefront can be tuned from being almost flat at 0.832 eV to oblique at 0.810 eV. Thus, the numerical simulation confirms the possibility of producing an inclined wavefront using a transition SHA.
Fig. 3 (a) Structure for achieving an inclined wavefront using a transition SHA. From the left side, the 11 holes in the transition SHA have wx values of 0.4a, 0.408a, 0.415a, 0.425a, 0.435a, 0.45a, 0.465a, 0.485a, 0.51a, 0.55a, and 0.6a. (b) Numerical results for the phase in the transition region.
4. Experimental evaluation of uniform SHA
In this section, experimental results for a uniform SHA will be discussed. The fabrication and measurement techniques are similar to those reported previously [17]. The SHA structure is fabricated using multilayer deposition, electron beam lithography, and layer-by-layer dry etching. Transmission spectra are measured using a microscope spectrometer with an incoherent light source. The transmitted phase is evaluated using a in-house-built interferometric microscope. This microscope produces an interferometric phase image consisting of bright and dark fringes superimposed on a normal microscopic image. The phase from the SHA is determined by comparing the interferometric fringe of the target structure to a known dispersion region.
Figure 4(a) depicts the fabricated structure. Since the fabricated structures have both uniform SHAs and a transition SHA, the transmittance and phase for the uniform SHAs is measured microscopically. Transmittance and phase normalization is carried out with respect to the through-hole region. Figures 4(b)–(d) represent scanning electron microscopy images of the rectangular-hole SHA.
Fig. 4 (a) Geometry of the fabricated structure. (b)–(d) Scanning electron micrographs of the fabricated SHA. (b) Transition region in which the rectangular holes are gradually varying in shape. (c) Top view of narrow SHA (wx=0.4a). (d) Top view of wide SHA (wx=0.6a).
Figure 5(a) plots the calculated and measured transmission spectra for rectangular-hole SHAs with wx of 0.4a and 0.6a. The horizontal axis represents the transmittance, and the vertical axis is the photon energy. The measured transmittance agrees with the numerical calculations. Figure 5(b) graphs the calculated and measured transmission phase. The horizontal axis is the phase relative to a vacuum layer having the same thickness as the SHA, and the vertical axis is the photon energy. Again, the calculated and measurement results agree. While the narrow and wide SHAs exhibit similar phases at 0.83 eV, the phase for the narrow SHA changes more rapidly and the phase difference between the two SHAs increases monotonically as the frequency decreases to around 0.80 eV. Thus, dispersion control of an SHA by varying the hole side length is experimentally confirmed.
Fig. 5 (a) Calculated (lines) and measured (symbols) transmission spectra for a narrow SHA (blue) and a wide SHA (orange). (b) Transmission phase for a narrow SHA and a wide SHA.
5. Experimental validation of inclined wavefront production by transition SHA
Using the structure in Fig. 4(a), an inclined wavefront is produced by the transition SHA. Figures 6(a) and (b) present typical interferometric images at frequencies of 0.827 eV and 0.810 eV, respectively. Figure 6(c) shows an enlarged portion of Fig. 6(b) and the corresponding region in the fabricated structure. Figure 6(d) plots the phase distribution for the beam-steering element at various frequencies. The phase differences are determined from the displacements of the interferometric fringes relative to that in the narrow SHA. Whereas the interferometric fringes for both uniform SHA regions are flat, the phase difference gradually changes in the transition region. The maximum phase difference observed in the frequency range from 0.80 to 0.83 eV is 0.6π, consistent with the results in Fig. 5. This value of 0.6π is five times larger than the previously reported value [17].
Fig. 6 (a) Interferometric images of the fabricated structure at a frequency of 0.827 eV. (b) Images at 0.810 eV. (c) Magnified portion of (b) and the corresponding region in the fabricated structure. (d) Phase distribution determined from analysis of the interferometric images at various frequencies. The horizontal axis represents the position from the center of the transition region.
For evaluation of directivity control in optics, a far field measurement is a major concern [2, 15, 28]. Here we present the result of the far field measurement of our phase control element. In order to obtain the far field image, or Fourier image, of the limited sample area, we adopted the in-house-built microscope with an aperture (Fig. 7(a)) [29]. This microscope consists of two optical systems, which share several optical components. One is a microscope to magnify the real space image (blue line in Fig. 7(a)), the other is to observe the Fourier image (orange line). Aperture A, which is placed at the conjugate point of the sample, behaves like a field stop of Köhler illumination; and it permits the observation of the limited sample area, that is, transition SHA in this case. Therefore, we can observe the Fourier image through the transition SHA itself. Figure 7 (b) represents the cut line plots of the Fourier image on various frequencies. The horizontal axis represents the transverse wave vector kx/k0, where k0 is a wave vector in vacuum. Although Fourier images are broadened due to the diffraction through small area, peak shift proportional to the amount of incident frequency shift can be observed. Shift-direction and quantities agree well with interferometric measurements. These, interferometric and far-field, measurements results imply that the planar rectangular-hole SHA whose hole shapes gradually vary have potential to control a wavefront.
Fig. 7 (a) Experimental setup based on a near-infrared microscope (Olympus, BX-51IR). L, laser illumination from wavelength tunable laser (λ =1470 – 1545 nm); S, Sample; OL, objective lens (Olympus LMPlanIR, 50X); FP, back focal plane of the OL (Fourier Plane); M, mirror; IL, imaging lens; A, variable aperture; L1, L2 lens; BS, beam splitter; CCD1, USB visible camera; CCD2, near-infrared camera; IM-1, schematic of the top viewed sample, color relations are same as Fig. 4(a); IM-2, schematic of the real space image created on CCD1; IM-3, schematic of the Fourier image created on CCD2. (b) Cut line plots of the Fourier images. Inset images are Fourier images corresponding to the energies of 0.821 eV, 0.816 eV, 0.810 eV and 0.805 eV from the top, respectively. White dashed line on the inset images represents kx/k0 = 0.
Two issues remain with regard to achieving a beam-steering element with an unlimited steering angle and for wide apertures. The first is the low transmittance of a narrow-hole SHA, and the other is that the phase difference range is still less than 0 to 2π. The first issue can be solved by covering the top surface of the SHA with an index-matching material. A three-times increase in transmittance has been measured for a narrow-hole SHA using a silicone elastomer as the matching material. The symmetric arrangement results in high transmittance, particularly for a narrow-hole SHA.
Regarding the second issue, there are several possible improvements on structural configurations that can be implemented within current fabrication restrictions. For instance, the current structure is composed with only simple hole shapes and single periodic layer composition. Simple hole shapes, such as circles, squares, or rectangles, are still inadequate to realize the largest in-plane phase difference, and there remains some room to be optimized. Increasing the number of metal-dielectric layer pairs also enlarges the phase range, because by increasing the number of layer pairs, the property of negative refractive index region [30] is stabilized which gap-SPPs are closely related with. Additionally, thickness of each layer should be explored to achieve large phase shift and high transmission. Since these improvements involve a large number of design variables which are correlated, therefore our next task is application of advanced numerical structural optimization methods using adjoint system analysis [31].
6. Conclusion
Transmission phase control and an inclined wavefront for beam steering have been achieved using a rectangular-hole SHA with a gradually changing hole shape. The resonance frequency, at which the phase drastically changes and high transmittance occurs, was determined from the dispersion diagram for the IMIMI layers. The dependence of the transmitted phase on frequency, i.e., the dispersion, could be tuned by adjusting the length of the sides of the rectangular holes that were normal to the polarization direction. An in-plane phase difference of 0.6π was achieved between narrow and wide rectangular holes using an SHA with a thickness of one-sixth of the wavelength. The advantages of a rectangular-hole SHA for phase control are its ease of design and the intuitive nature of its physical structure.
Our approach that comprises unit cell design with gradual varying hole dimension has an analogy with the work by D. Fattal et al. [32]. They utilized high-index-contrast grating as unit cell, and achieved 0–2π phase range and high transmittance. High-index-contrast grating is one of the best ways to realize passive optical elements. Nevertheless, our approach still has significance for a wavefront control and an application of metamaterial. Our target is to achieve a beam steering device at fixed wavelength using tunable index material [33], although wavefront was controlled by sweeping the frequency of the incident light in the present study. Applying a tunable index material to high-index-contrast grating decreases the phase range, while, applying tunable index material to SHA has potential to control the resonance point of the SHA without sacrificing the phase range. We believe that a practical transmission-phase-control element using an SHA can be realized based on continuous studies of SHAs, and this work contributes to the metamaterials’ community and its application.
Acknowledgment
The authors would like to thank M. Ochiai for technical support. This work was supported in part by the New Energy and Industrial Technology Development Organization (NEDO) and the Nanotechnology Innovation Station of the National Institute for Materials Science (NIMS) in Japan.
References and links
1. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007) [CrossRef] [PubMed] .
2. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008) [CrossRef] [PubMed] .
3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998) [CrossRef] .
4. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005) [CrossRef] [PubMed] .
5. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892–894 (2006) [CrossRef] [PubMed] .
6. R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009) [CrossRef] .
7. A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101, 103902 (2008) [CrossRef] [PubMed] .
8. S. Maier, Plasmonics: Fundamentals and Applications (Springer Verlag, 2007).
9. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006) [CrossRef] [PubMed] .
10. H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008) [CrossRef] [PubMed] .
11. J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett. 107, 043903 (2011) [CrossRef] [PubMed] .
12. D. Inoue, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, Y. Sugimoto, and Y. Koide, “Polarization independent visible color filter comprising an aluminum film with surface-plasmon enhanced transmission through a subwavelength array of holes,” Appl. Phys. Lett. 98, 093113 (2011) [CrossRef] .
13. S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for cmos image sensor applications,” Nano Lett. 12, 4349–4354 (2012) [CrossRef] [PubMed] .
14. A. Rottler, M. Harland, M. Bröll, S. Schwaiger, D. Stickler, A. Stemmann, C. Heyn, D. Heitmann, and S. Mendach, “Rolled-up nanotechnology for the fabrication of three-dimensional fishnet-type gaas-metal metamaterials with negative refractive index at near-infrared frequencies,” Appl. Phys. Lett. 100, 151104 (2012) [CrossRef] .
15. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011) [CrossRef] [PubMed] .
16. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultra-thin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012) [CrossRef] [PubMed] .
17. T. Matsui, H. T. Miyazaki, A. Miura, T. Nomura, H. Fujikawa, K. Sato, N. Ikeda, D. Tsuya, M. Ochiai, Y. Sugimoto, M. Ozaki, M. Hangyo, and K. Asakawa, “Transmission phase control by stacked metal-dielectric hole array with two-dimensional geometric design,” Opt. Express 20, 16092–16103 (2012) [CrossRef] [PubMed] .
18. A. Ourir, A. D. Lustrac, and J. M. Lourtioz, “All-metamaterial-based subwavelength cavities (λ/60) for ultrathin directive antennas,” Appl. Phys. Lett. 88, 084103 (2006) [CrossRef] .
19. S. Wang, F. Garet, K. Blary, C. Croënne, E. Lheurette, J.-L. Coutaz, and D. Lippens, “Composite left/right-handed stacked hole arrays at submillimeter wavelengths,” J. Appl. Phys. 107, 074510 (2010) [CrossRef] .
20. H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006) [CrossRef] .
21. A. Ourir, S. N. Burokur, and A. D. Lustrac, “Phase-varying metamaterial for compact steerable directive antenna,” Electron. Lett. 43, 493–494 (2007) [CrossRef] .
22. R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13, 1933–1938 (2005) [CrossRef] [PubMed] .
23. F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006) [CrossRef] .
24. S. Collin, F. Pardo, and J. L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310–4320 (2007) [CrossRef] [PubMed] .
25. D. Woolf, M. Loncar, and F. Capasso, “The forces from coupled surface plasmon polaritons in planar waveguides,” Opt. Express 17, 19996–20011 (2009) [CrossRef] [PubMed] .
26. A. D. Rakić, A. B. Djurišíc, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998) [CrossRef] .
27. J. Bravo-Abad, F. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93, 227401 (2004) [CrossRef] [PubMed] .
28. J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013) [CrossRef] [PubMed] .
29. H. T. Miyazaki, H. Miyazaki, Y. Jimba, Y. Kurokawa, N. Shinya, and K. Miyano, “Light diffraction from a bilayer lattice of microspheres enhanced by specular resonance,” J. Appl. Phys. 95, 793–805 (2004) [CrossRef] .
30. Z. Ku, J. Zhang, and S. Brueck, “Bi-anisotropy of multiple-layer fishnet negative-index metamaterials due to angled sidewalls,” Opt. Express 17, 6782–6789 (2009) [CrossRef] [PubMed] .
31. T. Nomura, K. Sato, K. Taguchi, T. Kashiwa, and S. Nishiwaki, “Structural topology optimization for the design of broadband dielectric resonator antennas using the finite difference time domain technique,” Int. J. for Numer. Meth. Eng. 71, 1261–1296 (2007) [CrossRef] .
32. D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nature Photonics 4, 466–470 (2010) [CrossRef] .
33. H. Yoshida, T. Matsui, A. Miura, N. Ikeda, M. Ochiai, Y. Sugimoto, H. Fujikawa, and M. Ozaki, “Uniform liquid crystal alignment on metallic nanohole arrays by vapor-phase deposition of silane coupling agent,” Opt. Mater. Express 2, 893–899 (2012) [CrossRef] .
