Broadband Omnidirectional Diffuse Mirrors with Hierarchically

Letter Cite This: ACS Photonics XXXX, XXX, XXX−XXX

Broadband Omnidirectional Diffuse Mirrors with Hierarchically Designed All-Dielectric Surfaces Yoon-Jong Moon,† Jin-Young Na,† Yong Hyun Park,‡ Soo Bin Kim,‡ Sang Woon Lee,*,‡ and Sun-Kyung Kim*,† †

Department of Applied Physics, Kyung Hee University, Gyeonggi-do 17104, Republic of Korea Department of Energy Systems Research and Department of Physics, Ajou University, Gyeonggi-do 16499, Republic of Korea

‡

S Supporting Information *

ABSTRACT: An electromagnetic wave with a single wave vector can be converted into multiple partial ones, with discrete or continuum wave vectors, by means of diffraction or scattering elements; this phenomenon is called optical diffusion. Optical diffusion is a crucial light−matter interaction problem, particularly for lighting applications that require uniform illumination. However, omnidirectional diffuse mirrors with minimal absorption loss have not been reported thus far. Here, we demonstrate the high-diffusivity, lowabsorption reflecting surfaces, on which hexagonally arranged Al2O3 cones, with a pitch of 3 μm, are conformally covered with HfO2/Al2O3 multilayers. Spectrally resolved far-field measurements reveal that the hierarchically patterned surface diffuses reflected light uniformly over the entire range of azimuthal and polar angles at broadband wavelengths (λ = 400−800 nm), distinct to two-dimensional Al2O3 or Al patterned surfaces. Such omnidirectional optical diffusion is clearly identified by means of the momentum space representation; the hierarchical pattern allows all of the available diffraction modes to possess nearly equal amplitudes, which is strongly supported by near-to-far-field Fourier analysis. The degree of diffusivity is quantitatively evaluated with respect to different angular ranges (Δθ = 3°, 12°, and 24°) around a specular reflection angle. Under all of the considered metrics, the hierarchical pattern yields a relatively large diffusivity compared to the reference two-dimensional patterns. Measurements of reflectance spectra, together with full-vectorial electromagnetic simulations, suggest that the hierarchically patterned surface with a backside reflector serves as a high-reflectance diffuse mirror, contrasting with a patterned Al mirror that inevitably suffers from plasmonic absorption loss. These experimental and numerical findings studied herein will provide a fundamental platform for achieving omnidirectional optical diffusers. KEYWORDS: optical diffusers, hierarchical patterns, diffraction gratings, far-field measurements, near-to-far-field transform

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In photonics, hierarchical structures imply heterogeneous patterns that are composed of different scales or dimensions, which are exploited for tailoring transmission, reflection, and absorption of light over a broad range of incident wavelengths and angles.12−20 Hierarchical patterns are generally represented by nanoscale corrugations superimposed on micron pitch arrays or two-dimensional (2D) surface reliefs conformally covered with one-dimensional (1D) multilayers. For example, the Shin group realized an angle-insensitive reflector for blue wavelengths by using a 2D submicron-pitch surface covered with TiO2/SiO2 multilayers.15 The Glover group demonstrated a 1D long-pitch (∼30 μm) undulation surface overlaid with wavelength-scale periodic stripes that display a gradually red-shifted reflected color by increasing the viewing angles.16 Previous studies on hierarchical patterns have been focused mainly on creating a narrow-band reflecting color that holds for specific or broad viewing angles.

wing to the point-like source nature of semiconductor light-emitting diodes and lasers, the development of optical diffusers is central to diverse lighting applications such as backlights in liquid crystal displays,1 laser-pumped car headlights,2 and other general illumination applications.3 Highdiffusivity optical diffusers lead to uniform illumination, thereby minimizing the number of light sources in use. To uniformly spread out incident light with a narrow divergent angle, various types of optical diffusers, including prism sheets,4,5 nanoparticle embedded substrates,6 micron powders,7 and periodic8 or rough surfaces,9 have been proposed and demonstrated. Although these elements, which are based on scattering or diffraction, exhibit a decent diffusivity, they fail to obtain omnidirectional optical diffusion over a full range of solid angles; previously reported optical diffusers exhibit localized light distribution within a specific range of angles. Furthermore, metal-based diffuse mirrors typically suffer from unwanted plasmonic absorption loss due to their undulated surface features.10,11 Here, we report hierarchically designed alldielectric patterns that function as an omnidirectional reflecting surface over the whole visible spectrum. © XXXX American Chemical Society

Received: November 10, 2017 Published: January 3, 2018 A

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Figure 1. (a) Schematic illustration showing the diffraction of light by a periodically patterned surface. Inset: schematic illustration showing the scattering of light by a single optical element. (b) Schematic of a home-built wavelength-resolved far-field scanner. (c) SEM image of a fabricated submicron-pitch hierarchical pattern by using polystyrene spheres (left) and its spectrally integrated (λ = 400−800 nm) far-field profile for θi = 12° (right). Inset of the left panel: SEM image of an array of polystyrene spheres before deposition of the dielectric multilayers. (d) Cross-sectional SEM image of a fabricated 3 μm pitch hierarchical pattern showing Al2O3 cones covered with HfO2/Al2O3 multilayers. Inset: top-view SEM image of the same hierarchical pattern. (e) Schematics illustrating Al2O3 (left) and Al cones (middle) and the hierarchically patterned Al2O3 cones (right).

patterned structure (Methods). In preliminary experiments, we fabricated subwavelength-scale hierarchical patterns on a 100 μm-thick sapphire (Al2O3) substrate, in which densely packed polystyrene spheres with an average diameter of 400 nm were initially coated and covered with HfO2/Al2O3 multilayers, by performing an atomic layer deposition (ALD) process (Figure 1c and Methods). For the incident angle (θi) of 12°, the intensity of the reflected light was recorded at discrete θ and ϕ values with a step of 1° and mapped onto the (θ, ϕ) diagram, on which the origin corresponds to θ = 0°. The measured far-field data exhibits a pronounced single spot that is identified as a strong specular reflection, indicating that such a subwavelength-scale pattern is inappropriate for an optical diffuser.23 Therefore, we designed and fabricated micron-scale structured hierarchical patterns, in which hexagonally arranged Al2O3 cones with a pitch of 3 μm were covered with 3.5 pairs of HfO2/Al2O3 multilayers. The thicknesses (80, 84, 88, 88, 158, 89, and 117 nm) of the HfO2 and Al2O3 layers were set to different values to allow for broadband optical properties.19 The cross-sectional (Figure 1d) and top-view (inset, Figure 1d) scanning electron microscopy (SEM) images clearly show hexagonally arranged Al2O3 cones covered with the welldefined conformal dielectric stacks. For comparison, we prepared two types of patterned surfaces on the same sapphire substrates: an Al2O3 pattern with a backside Al mirror and a 100 nm-thick Al coated Al2O3 pattern, as schematically shown in Figure 1e. For various incident angles (θi = 12°, 30°, 45°, and 60°), the integrated (λ = 400−800 nm) far-field distribution of the three fabricated structures were obtained and mapped onto the (θ, ϕ) diagram, as shown in Figure 2. In each diagram, a relatively bright spot observed at θ = 12° corresponds to specular

In this study, we propose hexagonally arranged Al2O3 patterns, with a pitch of a few microns, covered with conformal Al2O3/HfO2 multilayers. We then characterize their ability to uniformly diffuse reflected light. The wavelength- and angledependent diffuse performances of the fabricated patterns were evaluated from the measurement of their spectrally resolved farfield distributions. For comparison, we prepared 2D Al2O3 and Al patterned surfaces as references. The omnidirectional nature of the hierarchical pattern was demonstrated by plotting its energy-momentum dispersion. The diffusivity of each patterned surface was quantified for which specular reflection was defined with various angular deviations. Measurements of reflectance spectra and full-vectorial electromagnetic simulations were carried out to analyze the absorption loss of each patterned surface.

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RESULTS AND DISCUSSION Far-Field Distribution of Reflected Light. According to the near-to-far-field transformation theorem, the far-field distribution of periodic objects is determined by the diffraction effect given by their periodicity in conjunction with the scattering effect given by the morphology of individual objects,21,22 as schematically shown in Figure 1a. Therefore, the far-field distribution can be dramatically tuned by tailoring the morphology of the constituent scattering objects. To accurately quantify the diffusivity of a given patterned surface, a home-built far-field scanner was used (Figure 1b). In this setup, light subject to both specular and diffuse reflection was collected by a programmed spectrometer rotating along the polar (θ) and azimuthal (ϕ) directions while a broadband (λ = 400−800 nm) colliminated light source impinged on a B

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Figure 2. Measured spectrally integrated (λ = 400−800 nm) far-field distributions for the Al2O3 pattern (a), the Al pattern (b), and the hierarchical pattern (c). The inner white dashed lines indicate the incidence of angles.

(Supporting Information, Figure S1).24 For each plot, the amplitudes of the high-order (m > 1) diffraction modes at a certain wavelength were normalized by that of the fundamental (m = 1) diffraction mode at the same wavelength. The calculated result shows that the hierarchical pattern maintains a high amplitude for second- to fifth-order diffraction modes, consistent with its measured far-field distribution, as shown in Figure 2c. Taken together, 2D patterned surfaces covered with 1D dielectric stacks, with a pitch of a few wavelengths, intensify the high-order diffraction modes, thereby giving rise to the omnidirectional diffuse reflection. Wavelength-Resolved Optical Diffusivity. To investigate the wavelength dependence of the observed optical diffusion, wavelength-revolved far-field distributions were acquired for the hierarchical pattern at eight sampled wavelengths (λ = 400, 440, 475, 485, 515, 640, 700, 740 nm), as shown in Figure 3a. The diagrams, numbered 1 through 8, present the data obtained at the short to long wavelengths in sequence. In each diagram, a dark region

reflection. In contrast with the previous submicron-pitch pattern (Figure 1c), 2D discrete fringes appear around each specular spot, assigned to diffraction modes with different orders, as will be discussed later. Notably, the hierarchical pattern yields much more uniform far-field fringes on the (θ, ϕ) diagram for all of the incident angles considered; even the fringes far distant from the specular spot, which are identified as high-order diffraction modes, possess a strong intensity. On the other hand, the far-field distributions of the dielectric and the metal cone patterns are relatively localized around each specular spot. It is worthwhile to mention that all of the measured far-field distributions are a consequence resulting from a single interaction between the incident light and patterned surfaces. Thus, the far-field distributions generally become more homogeneous if an optical system permits multiple reflections. To elucidate the superior optical diffusivity of the hierarchical pattern to the reference ones, we calculated the wavelength-resolved diffraction strength for the three structures considered, by using the reciprocity theorem C

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Figure 3. (a) Wavelength-resolved far-field distributions of the hierarchical pattern for an incident angle of 12°. The numbers, labeled 1 to 8, correspond to the wavelengths of 400, 440, 475, 485, 515, 640, 700, and 740 nm, respectively. (b) Momentum-energy dispersions of the Al2O3 pattern (left), the Al pattern (middle), and the hierarchical pattern (right) for the incident angle of 12°.

target applications. For Δθ = ± 12°, the hierarchical pattern yields a diffusivity as large as 0.8 for all of the wavelengths considered, outperforming the Al2O3 and the Al patterns (Figure 4a). The same trend is observed for different angular ranges (Δθ = ±3° and ±24°), although the level of their diffusivity is somewhat reduced or augmented (Supporting Information, Figure S3a,b). To highlight the broadband diffusivity of the hierarchically patterned surface, we plotted the spectrally averaged (λ = 400−800 nm) far-field intensity as a function of the angular range (Δθ; Figure 4b). Note that, for this plot, the angular spread was defined with respect to the normal direction (see the inset of Figure 4b). The result shows that the hierarchical pattern substantially outperforms the two reference patterns until Δθ reaches ∼60°, confirming its enhanced optical diffusion. Absorption Loss of Diffuse Mirrors. All-dielectric photonic elements experience minimal light absorption compared to their metallic counterparts, which inherently suffer from Ohmic loss at optical frequencies. If corrugated surfaces are introduced into metallic elements, additional absorption loss is usually accompanied by surface plasmon resonances.10,11 To reveal the resulting superiority of the alldielectric hierarchically patterned surface, we compared its reflectance spectrum with that of the Al patterned surface (Figure 5a). Integrating sphere reflectance measurements display that the hierarchical pattern with an Al backside reflector (as schematically shown in the inset of Figure 5a) yields a reflectance of approximately 0.8 over the visible to nearinfrared wavelengths, which is improved by a factor of 2

indicates the angular position (θi = 12° for these measurements) of an incident light source. For the wavelengths considered, the hierarchical pattern results in nearly equal amplitudes for all of the diffraction spots. For longer wavelengths, the angular spacing between two adjacent spots increases, resulting in a reduced number of spots. To identify the diffraction modes coupled to the incident light, the momentum-energy (θ, λ) dispersions were plotted for the three structures considered, as shown in Figure 3b. In the dispersion plots, the amplitude at a certain (θ, λ) was acquired by averaging all of the same (θ, λ) data sets with different ϕ values, ranging from 0 to 2π. In accordance with the far-field distribution data in Figure 2, the hierarchical pattern excites all of the available diffraction modes with a nearly constant amplitude, whereas the reference dielectric and metal patterns predominantly excite low-order diffraction modes. This dispersion feature is valid for other incident angles of θi = 30°, 45°, and 60° (Supporting Information, Figure S2), suggesting that the hierarchically patterned surface serves as an omnidirectional optical diffuser for a broad range of incident wavelengths and angles. Quantification of Optical Diffusivity. For quantitative analysis, we obtained the diffusivity of the three patterned surfaces, with a variation of the angular ranges (Δθs = ±3°, ±12°, and ±24°) defining specular reflection (see the schematics in Figure 4a, Supporting Information, Figure S3a,b). Note that the degree of diffusivity is a relative quantity that can differ across the angular range of a specular zone and thus, one needs to define an angular range appropriate for D

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Figure 5. (a) Measured reflectance spectra for a planar Al mirror, a patterned Al mirror, and a hierarchical pattern with a backside Al mirror. For comparison, a simulated reflectance is plotted for the same patterned Al mirror. Inset: schematic of a hierarchical pattern with a backside Al mirror. (b) Simulated absorption profiles for the patterned Al mirror acquired at the three different wavelengths (λ = 400, 600, and 800 nm).

Figure 4. (a) Measured optical diffusivity as a function of wavelength for the three patterns considered. Inset: schematic illustrating the definition of optical diffusivity. (b) Spectrally averaged (λ = 400−800 nm) optical diffusivity with a variation of specific angular range (Δθ) for the three patterns considered. Inset: schematic showing the definition of the angular range (Δθ).

compared with the patterned Al mirror. The reduced reflectance of the patterned Al is accurately reproduced by a finite-difference time-domain (FDTD) simulation (dashed blue, Figure 5a). To understand the reflectance degradation of the patterned Al mirror, we obtained the absorption profiles at λ = 400, 600, and 800 nm for a normally incident plane wave (Figure 5b). For all of the three profiles, a standing-wave nature, which is strongly localized at the Al−air interface, appears along the side surface of the Al cones. This aspect indicates a general feature of surface plasmon polaritons, accounting for the degraded reflectance of the patterned Al mirror.10,11 On the other hand, all-dielectric hierarchical patterns on a planar mirror experience minimal absorption loss while exhibiting a large diffusivity. In conclusion, we have demonstrated that hexagonally arranged Al2O3 micron cones, conformally covered with HfO2/Al2O3 multilayers that are designed as a hierarchically patterned surface, can dramatically increase the optical diffusivity over the entire visible spectrum by enhancing the strength of high-order diffraction modes. Measured far-field distributions and their corresponding momentum-energy dispersions clearly revealed the exceptional broadband omnidirectional optical diffusivity of the fabricated hierarchical pattern. For a specular reflection set with an angular range of ±12°, the degree of the optical diffusivity was as large as 0.8 at λ = 400−800 nm, outperforming the reference Al2O3 and Al patterns. Furthermore, the all-dielectric composition led to minimal light absorption, thereby yielding a reflectance of approximately 0.8 in the visible to near-infrared wavelengths, which is enhanced by a factor of 2 compared with a patterned

Al surface. We believe that the broadband, omnidirectional, and low-absorption diffuse reflection surfaces developed herein represent a substantial contribution to the development of illumination applications. Moreover, hierarchically patterned surfaces tailored with different dielectric materials and morphologies can serve as strong-diffraction dielectric gratings for other photonic applications including light emission and absorption devices.

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METHODS Deposition of Dielectric Multilayers. The Al2O3 film was grown using a traveling-wave type ALD system with a 150 mmscale wafer reactor (CN-1 Co., Atomic Class ALD system) at a typical ALD pressure of ∼1.5 Torr at 200 °C. Trimethylaluminum [TMA, Al(CH3)3] and ozone (O3) were used as the Al precursor and oxygen source, respectively. TMA was injected into the chamber from a canister (5 °C), and the O3 was introduced with N2 gas (O3 concentration of 200 g/m3). The ALD sequence consisted of TMA injection pulse/purge/O3 pulse/purge steps (0.6/10/2.2/11 s) with a growth rate of 1 Å/ cycle. Subsequently, an HfO2 film was grown on the pregrown Al2O3 film in the same ALD reactor under the same growth conditions (without vacuum break). Tetrakis (ethylmethylamino) Hafnium [TEMAHf, Hf[N(CH3)C2H5]4] and O3 were used as the Hf precursor and oxygen source. The Hf precursor was introduced from a bubbler at 55 °C, with an N2 carrier gas of 200 standard cubic centimeters per min (sccm). The ALD sequence of HfO2 consisted of TEMAHf pulse/purge/O3 pulse/purge steps (2.5/30/2.2/30 s) with a growth rate of E

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(2) Wierer, J. J.; Tsao, J. Y.; Sizov, D. S. Comparison between blue lasers and light-emitting diodes for future solid-state lighting. Laser Photon. Rev. 2013, 7, 963−993. (3) Mendez, E. R.; Garcia-Guerrero, E. E.; Escamilla, H. M.; Maradudin, A. A.; Leskova, T. A.; Shchegrov, A. V. Photofabrication of random achromatic optical diffusers for uniform illumination. Appl. Opt. 2001, 40, 1098−1107. (4) Hamilton, A. C.; Courtial, J. Optical properties of a Dove-prism sheet. J. Opt. A: Pure Appl. Opt. 2008, 10, 125302. (5) Yoon, H.; Oh, S.; Kang, D. S.; Park, J. M.; Choi, S. J.; Suh, K. Y.; Char, K.; Lee, H. H. Arrays of Lucius microprisms for directional allocation of light and autostereoscopic three-dimensional displays. Nat. Commun. 2011, 2, 455. (6) Kim, E.; Cho, H.; Kim, K.; Koh, T.; Chung, J.; Lee, J.; Park, Y.; Yoo, S. A Facile Route to Efficient, Low-Cost Flexible Organic LightEmitting Diodes: Utilizing the High Refractive Index and Built-In Scattering Properties of Industrial-Grade PEN Substrates. Adv. Mater. 2015, 27, 1624−1631. (7) Grum, F.; Luckey, G. W. Optical Sphere Paint and a Working Standard of Reflectance. Appl. Opt. 1968, 7, 2289−2294. (8) Ohzono, T.; Suzuki, K.; Yamaguchi, T.; Fukuda, N. Tunable Optical Diffuser Based on Deformable Wrinkles. Adv. Opt. Mater. 2013, 1, 374−380. (9) Garcia-Guerrero, E. E.; Mendez, E. R.; Escamilla, H. M. Design and fabrication of random phase diffusers for extending the depth of focus. Opt. Express 2007, 15, 910−923. (10) Kim, S.; Ee, H.; Choi, W.; Kwon, S.; Kang, J.; Kim, Y.; Kwon, H.; Park, H. Surface-plasmon-induced light absorption on a rough silver surface. Appl. Phys. Lett. 2011, 98, 011109. (11) Nagpal, P.; Lindquist, N. C.; Oh, S.; Norris, D. J. Ultrasmooth Patterned Metals for Plasmonics and Metamaterials. Science 2009, 325, 594−597. (12) Kim, J.; Lee, J.; Yang, S.; Kim, H. G.; Kweon, H.; Yoo, S.; Jeong, K. Biologically Inspired Organic Light-Emitting Diodes. Nano Lett. 2016, 16, 2994−3000. (13) Kwon, Y. W.; Park, J.; Kim, T.; Kang, S. H.; Kim, H.; Shin, J.; Jeon, S.; Hong, S. W. Flexible Near-Field Nanopatterning with Ultrathin, Conformal Phase Masks on Nonplanar Substrates for Biomimetic Hierarchical Photonic Structures. ACS Nano 2016, 10, 4609−4617. (14) Vukusic, P.; Sambles, J. R.; Lawrence, C. R.; Wootton, R. J. Quantified interference and diffraction in single Morpho butterfly scales. Proc. R. Soc. London, Ser. B 1999, 266, 1403−1411. (15) Chung, K.; et al. Flexible, Angle-Independent, Structural Color Reflectors Inspired by Morpho Butterfly Wings. Adv. Mater. 2012, 24, 2375−2379. (16) Whitney, H. M.; Kolle, M.; Andrew, P.; Chittka, L.; Steiner, U.; Glover, B. J. Floral Iridescence, Produced by Diffractive Optics, Acts As a Cue for Animal Pollinators. Science 2009, 323, 130−133. (17) Vogel, N.; Utech, S.; England, G. T.; Shirman, T.; Phillips, K. R.; Koay, N.; Burgess, I. B.; Kolle, M.; Weitz, D. A.; Aizenberg, J. Color from hierarchy: Diverse optical properties of micron-sized spherical colloidal assemblies. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 10845− 10850. (18) Biro, L. P.; Vigneron, J. Photonic nanoarchitectures in butterflies and beetles: valuable sources for bioinspiration. Laser Photon. Rev. 2011, 5, 27−51. (19) Kinoshita, S.; Yoshioka, S. Structural Colors in Nature: The Role of Regularity and Irregularity in the Structure. ChemPhysChem 2005, 6, 1442−1459. (20) Ahmed, R.; Yetisen, A. K.; Butt, H. High Numerical Aperture Hexagonal Stacked Ring-Based Bidirectional Flexible Polymer Microlens Array. ACS Nano 2017, 11, 3155−3165. (21) Zayed, A. I. A Convolution and Product Theorem for the Fractional Fourier Transform. IEEE Signal Processing Lett. 1998, 5, 101−103. (22) Vukusic, P.; Sambles, J. R.; Lawrence, C. R.; Wootton, R. J. Quantified interference and diffraction in single Morpho butterfly scales. Proc. R. Soc. London, Ser. B 1999, 266, 1403−1411.

1.2 Å/cycle. By repeating these ALD processes, the HfO2/ Al2O3 stack was coated along the surface of the microstructured Al2O3 cones. Optical Measurements. The far-field distributions were measured by a home-built far-field scanner equipped with a spectrometer (USB4000, Ocean Optics) and a Xe lamp source (450 W, Newport). The detector was programmed to rotate along the polar (ϕ) and azimuthal (θ) directions with a step size of 1°. The Xe light was transported by an optical fiber and two identical circular metal apertures with a diameter of 2.0 mm were used to collimate the incident beam. The optical diffusivity is defined as (It − Is)/It, where It is total sum of the intensity at all (θ, ϕ) and Is is the sum of the intensity within a specific angular range (Δθ = ±3°, ±12°, and ±24°) around a specular reflection angle. The reflectance spectra were measured by a spectrometer (USB4000, Ocean Optics) where a specimen was mounted at the center of an integrating sphere (CSRM-RTC-060-SL, Labsphere) to collect all of the diffuse light.25 The incident angle was set to 45° for all of the reflectance measurements. Full-Vectorial Numerical Simulations. Homebuilt FDTD code was used for all of the optical simulations. To calculate the wavelength-resolved diffraction strength, we first simulated the scattered power of a single object by using the total-field scattered-field method.26 The simulated scattered power was transformed into a far-field distribution for a 3 μm pitch hexagonal lattice condition by means of the reciprocity theorem.24 For the reflectance simulations, a plane wave with an incident angle of 45°, which is identical to the experimental condition, was used and the periodic boundary conditions were adopted along the in-plane directions. A spatial resolution of 10 nm was used for all of the x-, y-, and z-coordinates in all of the simulation models.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.7b01364. Additional figures (PDF).

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Sang Woon Lee: 0000-0002-6448-5444 Sun-Kyung Kim: 0000-0002-0715-0066 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT, and Future Planning (NRF-2017R1A2B4005480) and the Ministry of Education (NRF-2017R1D1A1B03031729).

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REFERENCES

(1) Kim, G. H. A PMMA composite as an optical diffuser in a liquid crystal display backlighting unit (BLU). Eur. Polym. J. 2005, 41, 1729− 1737. F

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ACS Photonics (23) Hecht, E. Hecht Optics; Addison-Wesley: United States, 1998. (24) Moon, Y.; et al. Microstructured Air Cavities as High-Index Contrast Substrates with Strong Diffraction for Light-Emitting Diodes. Nano Lett. 2016, 16, 3301−3308. (25) Storm, S. L.; Springsteen, A.; Ricker, T. M. The Use of Center Mount Sample Holders in Reflectance Spectroscopy. Labsphere Application Note No. 02 1998, 1−8. (26) Taflove, A.; Hagness, S. C. Computational Electrodynamics: The Finite-Difference Time-Domain Method; Artech House: Boston, 2005.

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