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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 15574–15583
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Highly transparent sapphire micro-grating structures with large diffuse light scattering

Yeong Hwan Ko and Jae Su Yu  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 15574-15583 (2011)
http://dx.doi.org/10.1364/OE.19.015574


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Abstract

The highly transparent micro-grating structures (MGSs) of sapphire substrate with large diffuse light scattering were theoretically and experimentally studied. From the finite difference time domain simulation, it was found that the degree of diffuse light scattering is strongly dependent on the size of grating structures. For a highly transparent property, the sapphire MGSs were optimally designed by the theoretical calculations using the rigorous coupled wave analysis method. The order of taper, geometry (i.e., width and height), and pitch length of MGSs were optimized to maximize their average total transmittance over a wide wavelength range of 300-1800 nm. Additionally, the influence of the deposition of low-refractive index material such as SiO2 onto sapphire MGSs on the transmittance characteristics was investigated. To verify experimentally the feasibility, the sapphire MGSs were fabricated by the conventional lithography and dry etching processes. The SiO2 deposited sapphire MGS exhibited a further increase in the total transmittance due to its relatively more graded refractive index profile while maintaining a significantly enhanced diffuse light scattering. The experimental data were in a reasonable agreement with the theoretical results.

© 2011 OSA

1. Introduction

Over the past decades, the patterned surface structures such as the grating structures [1

1. N. F. Hartman and T. K. Gaylord, “Antireflection gold surface-relief gratings: experimental characteristics,” Appl. Opt. 27(17), 3738–3743 (1988). [CrossRef] [PubMed]

4

4. S. J. Choi and S. Y. Huh, “Direct structuring of a biomimetic anti-reflective, self-cleaning surface for light harvesting in organic solar cells,” Macromol. Rapid Commun. 31(6), 539–544 (2010). [CrossRef] [PubMed]

], corrugated surface structures [5

5. M. I. Elhaj and M. Schadt, “Optical polymer thin films with isotropic and anisotropic nano-corrugated surface topologies,” Nature 410(6830), 796–799 (2001). [CrossRef] [PubMed]

7

7. Y. Wang, N. Lu, H. Xu, G. Shi, M. Xu, X. Lin, H. Li, W. Wang, D. Qi, Y. Lu, and L. Chi, “Biomimetic corrugated silicon nanocone arrays for self-cleaning antireflection coatings,” Nano Res. 3(7), 520–527 (2010). [CrossRef]

] and photonic crystals [8

8. W. Śmigaj, B. Gralak, R. Pierre, and G. Tayeb, “Antireflection gratings for a photonic-crystal flat lens,” Opt. Lett. 34(22), 3532–3534 (2009). [CrossRef] [PubMed]

, 9

9. J. M. Park, S. G. Lee, H. R. Park, and M. H. Lee, “Self-collimating photonic crystal antireflection structure for both TE and TM polarizations,” Opt. Express 18(12), 13083–13093 (2010). [CrossRef] [PubMed]

] have allowed a modification in the property of light to travel between air and the substrate material. Particularly, subwavelength surface relief structures, i.e., a period smaller than wavelength of incident light, such as the parabola subwavelength grating structures (SGSs) or hemi-urchin shaped nanostructures, exhibited superior antireflective properties in the broadband and wide acceptance angle [10

10. Y. M. Song, S. J. Jang, J. S. Yu, and Y. T. Lee, “Bioinspired parabola subwavelength structures for improved broadband antireflection,” Small 6(9), 984–987 (2010). [CrossRef] [PubMed]

, 11

11. Y. H. Ko and J. S. Yu, “Design of hemi-urchin shaped ZnO nanostructures for broadband and wide-angle antireflection coatings,” Opt. Express 19(1), 297–305 (2011). [CrossRef] [PubMed]

]. These structures are promising alternatives to overcome some problems in the conventional multilayer antireflection coatings including the material selection, thickness mismatch, and thermal instability [12

12. S. Walheim, E. Schaffer, J. Mlynek, and U. Steiner, “Nanophase-separated polymer films as high-performance antireflection coatings,” Science 283(5401), 520–522 (1999). [CrossRef] [PubMed]

]. Generally, the SGS could suppress efficiently the Fresnel reflection at the interface between two different optical media (i.e., air and the substrate material) over a wide range of wavelengths because the incident light at the surface allows only the zeroth order diffraction [13

13. K. Crabtree and R. A. Chipman, “Subwavelength-grating-induced wavefront aberrations: a case study,” Appl. Opt. 46(21), 4549–4554 (2007). [CrossRef] [PubMed]

,14

14. Y. M. Song, H. J. Choi, J. S. Yu, and Y. T. Lee, “Design of highly transparent glasses with broadband antireflective subwavelength structures,” Opt. Express 18(12), 13063–13071 (2010). [CrossRef] [PubMed]

]. Thus, the SGSs have been beneficently used to enhance the light coupling/absorption in many applications including optoelectronic devices, photovoltaic devices, and glass components [15

15. Y. M. Song, E. S. Choi, G. C. Park, C. Y. Park, S. J. Jang, and Y. T. Lee, “Disordered antireflective nanostructures on GaN-based light-emitting diodes using Ag nanoparticles for improved light extraction efficiency,” Appl. Phys. Lett. 97(9), 093110 (2010). [CrossRef]

18

18. J. Jonsson and F. Nikolaje, “Investigation of optical properties of injection molded subwavelength gratings,” Proc. SPIE 4779, 23–30 (2002). [CrossRef]

]. The various fabrication methods such as photolithography, e-beam lithography, nanoimprint lithography, laser interference lithography and hybrid nano-pattering lithography have been also employed [14

14. Y. M. Song, H. J. Choi, J. S. Yu, and Y. T. Lee, “Design of highly transparent glasses with broadband antireflective subwavelength structures,” Opt. Express 18(12), 13063–13071 (2010). [CrossRef] [PubMed]

, 19

19. D. L. Brundrett, T. K. Gaylord, and E. N. Glytsis, “Polarizing mirror/absorber for visible wavelengths based on a silicon subwavelength grating: design and fabrication,” Appl. Opt. 37(13), 2534–2541 (1998). [CrossRef] [PubMed]

22

22. P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997). [CrossRef]

].

2. Modeling and simulation of sapphire MGSs

Before designing and optimizing the geometry of sapphire MGSs for broadband and high total transmittance, the behaviors of light in the sapphire SGS and MGS need to be theoretically explored by FDTD simulations. In this work, the sapphire MGS with a size of 2 μm was chosen because the explored wavelength range of the incident is 300-1800 nm. Figure 1
Fig. 1 Calculated electric fields of light propagating from air to the (a) sapphire SGS (width: 300 nm, height: 300 nm) and (b) sapphire MGS (width: 2 μm, height: 2 μm) with parabolic shapes.
shows the contour plots of the calculated electric field distributions for light propagating from air to the (a) sapphire SGS (width: 300 nm, height: 300 nm) and (b) sapphire MGS (width: 2 μm, height: 2 μm) with parabolic shapes. In FDTD simulations, the Ey, i.e., amplitude of y-polarized electric field, was calculated when the plane wave was launched from the air and then propagated in the z direction. Here, the incident plane wave with a Gaussian beam profile was normalized at λ = 600 nm. The refractive index of sapphire was used as ~1.76. For the sapphire SGS, the light was transmitted straightly in the z direction though there is a weak interference pattern at its surface, as shown in Fig. 1(a). This means that the zeroth order diffracted light dominantly passes through the sapphire SGS. When the light was propagated into the sapphire MGS, in contrast, it created such strong light interference patterns with a wide angular spread, which can be expected to get more chances to experience the multiple diffuse scattering. This also may increase the probability to generate higher order diffractions outside the escape cone for increasing the optical path length in device applications. It is noticeable that the grating structure with a period (Λ) larger than the wavelength (λ) of incident light provides higher order diffracted transmissions, resulting in the efficient diffuse light scattering. The transmitted light with higher order diffraction modes in periodic grating structures can be explained by satisfying the boundary condition of continuity of the tangential electric field at the surface of the periodic grating structure followed as [28

28. S. L. Chuang, Physics of optoelectronic devices, (John Wiley & Sons. Inc. 1995).

, 29

29. S. L. Chuang and J. A. Kong, “Wave scattering and guidance by dielectric waveguides with periodic surfaces,” J. Opt. Soc. Am. 73(5), 669–679 (1983). [CrossRef]

]
kx,msapphire=kxair+m2πΛ,
(1)
where kxair is the incident horizontal wave number in air, m is the particular integer, and kx,msapphire is the transmitted m th order horizontal wave number in the sapphire substrate. By using the relationship of kxair=2πsinθi/λ and kx,msapphire=2πnsapphiresinθt,m/λ, the Eq. (1) can be expressed as a function of wavelength-to-period ratio (λ/Λ) given by
sinθi+m(λΛ)=nsapphiresinθt,m,
(2)
where nsapphire is the refractive index of sapphire substrate, θi is the incident angle and θt,m is the m th order angle of transmission. The geometry of sapphire MGSs should be optimized for efficient light scattering while keeping still high total transmittance because the wavelength-to-period ratio should be minimized to allow higher order diffraction modes in Eq. (2). Therefore, we designed and optimized the grating structure of sapphire substrate by maximizing the total transmittance, keeping its period larger than the wavelength of the incident light. For this, the geometry of sapphire MGSs was optimized by subsequently determining the shape, width, height, and pitch length of sapphire MGSs as the geometric parameters. To determine the shape of sapphire MGSs, at first, the order of taper (OT) can be defined as a parameter in the equation of the tapered cone as follows [11

11. Y. H. Ko and J. S. Yu, “Design of hemi-urchin shaped ZnO nanostructures for broadband and wide-angle antireflection coatings,” Opt. Express 19(1), 297–305 (2011). [CrossRef] [PubMed]

]:
z=(rWMGS2)OT+HMGSandx2+y2=r2(0zHMGS),
(3)
where r is the radius of circle in the xy plane of a Cartesian coordinate system, and HMGS and WMGS are the height and width of sapphire MGSs, respectively. By changing the OT, for various shapes of sapphire MGSs with a periodic hexagonal array, the total transmittance was calculated over a wide range of wavelength (λ = 300-1800 nm) by the RCWA simulations. Herein, the initial geometry of sapphire MGSs was considered as WMGS = 2 μm, HMGS = 2 μm, and P = 0.5 μm, where P is the distance between MGSs (i.e., pitch length).

3. Results and discussion

3.1. Design optimization of sapphire MGSs

Figure 2
Fig. 2 (a) Contour plot of the calculated total transmittance spectra as a function of OT for the sapphire MGS with WMGS = 2 μm, HMGS = 2 μm, and P = 0.5 μm and (b) calculated average total transmittance as a function of OT. The insets of (b) show the corresponding computational geometries of the sapphire MGSs for OT = 1 and 2.3.
shows (a) the contour plot of the calculated total transmittance spectra as a function of OT for the sapphire MGS with WMGS = 2 μm, HMGS = 2 μm, and P = 0.5 μm and (b) the calculated average total transmittance as a function of OT at wavelengths of 300-1800 nm. The insets of Fig. 2(b) show the corresponding computational geometries of the sapphire MGSs with periodic hexagonal array for OT = 1 and 2.3. As shown in Fig. 2(a), the total transmittance was increased with increasing the OT from 0.5 to 2.5, but it was slightly decreased above 2.5 of OT. Particularly, for OT > 1.5, the high total transmittance region with values of > 92% extended into the wavelength ranges of 700-800 nm and 1650-1800 nm. It is clear that the total transmittance can be improved by enhancing the light coupling efficiency between air and the modified surface of sapphire MGSs because the shape of grating structure affects significantly the change of refractive index profile and provides an antireflective surface [14

14. Y. M. Song, H. J. Choi, J. S. Yu, and Y. T. Lee, “Design of highly transparent glasses with broadband antireflective subwavelength structures,” Opt. Express 18(12), 13063–13071 (2010). [CrossRef] [PubMed]

, 30

30. R. Bouffaron, L. Escoubas, V. Brissonneau, J. J. Simon, G. Berginc, P. Torchio, F. Flory, and P. Masclet, “Spherically shaped micro-structured antireflective surfaces,” Opt. Express 17(24), 21590–21597 (2009). [CrossRef] [PubMed]

, 31

31. W. Zhou, M. Tao, L. Chen, and H. Yang, “Microstructured surface design for omnidirectional antireflection coatings on solar cells,” J. Appl. Phys. 102(10), 103105 (2007). [CrossRef]

]. To determine the optimum value of OT, the calculated total transmittance was averaged over a wide wavelength range of 300-1800 nm. As shown in Fig. 2(b), the maximum average total transmittance of 89.36% was obtained at OT = 2.3. In comparison of the computational geometries at OT = 1 and 2.3, it is evident that the parabolic shape of sapphire MGSs provides the more efficient light coupling than the conical shape.

After determining the optimal shape of sapphire MGSs, the total transmittance as a function of WMGS was investigated. Figure 3
Fig. 3 (a) Contour plot of the calculated total transmittance spectra as a function of WMGS for the sapphire MGS with HMGS = 2 μm, OT = 2.3, and P = 0.5 μm and (b) calculated average total transmittance as a function of WMGS.
shows (a) the contour plot of the calculated total transmittance spectra as a function of WMGS for the sapphire MGS with HMGS = 2 μm, OT = 2.3, and P = 0.5 μm and (b) the calculated average total transmittance as a function of WMGS. The total transmittance was slightly increased at long wavelengths of 1600-1800 nm with the increase of WMGS, but it was not largely influenced by the change of WMGS. As shown in Fig. 3(b), the average total transmittance was increased only by 0.86% as the width was increased from 1.8 μm to 3 μm. This indicates that the width of micro-scale grating structures is not the dominant factor in affecting their total transmittance characteristics. Therefore, we determined the 2.5 μm of WMGS as a normal value.

The contour plot of the calculated total transmittance spectra as a function of HMGS with WMGS = 2.5 μm, OT = 2.3, and P = 0.5 μm is shown in Fig. 4(a)
Fig. 4 (a) Contour plot of the calculated total transmittance spectra as a function of HMGS for the sapphire MGS with WMGS = 2.5 μm, HMGS = 2 μm, and P = 0.5 μm and (b) calculated average total transmittance as a function of HMGS. The insets of (b) show the corresponding computational geometries of the sapphire MGSs for HMGS = 2 μm, 5 μm, and 10 μm.
. Figure 4(b) shows the calculated average total transmittance as a function of HMGS. The insets of Fig. 4(b) show the corresponding computational geometries of the sapphire MGSs with periodic hexagonal array for HMGS = 2 μm, 5 μm, and 10 μm. In contrast with WMGS, the total transmittance was significantly modified by changing the HMGS. As the HMGS became higher, the low total transmittance region with values of < 88% could be efficiently reduced in the wide range of wavelengths. This is because the incident light experiences a long relaxation length by the change of refractive index due to the higher height which leads to the higher total transmittance characteristics. As can be seen in Fig. 4(b), the average total transmittance was rapidly increased with increasing the HMGS from 1 μm to 5 μm, and it was slowly increased at HMGS > 5 μm. However, the relatively higher height has technical problems including the patterning and deep dry etching processes in actual device applications. Therefore, the optimal HMGS value was determined as 5 μm (i.e., aspect ratio of 2).

Figure 5
Fig. 5 (a) Contour plot of the calculated total transmittance spectra as a function of P for the sapphire MGS with OT = 2.3, WMGS = 2.5 μm, and HMGS = 5 μm and (b) calculated average total transmittance as a function of P.
shows (a) the contour plot of the calculated total transmittance spectra as a function of P for the sapphire MGS with OT = 2.3, WMGS = 2.5 μm, HMGS = 5 μm and (b) the calculated average total transmittance as a function of P. The P is defined by a schematic drawing in the inset of Fig. 5(a). When the sapphire MGS was arranged and packed more closely (i.e., shorter P), the total transmittance was increased. Especially, the total transmittance was significantly decreased with increasing the P from 1 μm to 2 μm, as shown in Fig. 5(a). It is noted that a somewhat loosely packed array exhibits the better light coupling between air and the micro patterned surface of substrate than that of the closely packed array [31

31. W. Zhou, M. Tao, L. Chen, and H. Yang, “Microstructured surface design for omnidirectional antireflection coatings on solar cells,” J. Appl. Phys. 102(10), 103105 (2007). [CrossRef]

]. The high total transmittance region with values of > 92% was distributed over a wide range of wavelengths for P < 0.5 μm. In comparison to the closely packed sapphire MGS (P = 0), the low total transmittance region with values of < 88% was reduced at long wavelengths of 1100-1500 nm. By considering the average total transmittance in Fig. 5(b), the optimal sapphire MGS with OT = 2.3, WMGS = 2.5 μm, HMGS = 5 μm, and P = 0.5 μm was determined, exhibiting a maximum average total transmittance of 90.8%.

3.2. SiO2 layer on the sapphire MGS

In order to design the sapphire MGS for higher total transmittance, we used the geometries of SiO2 layer on the sapphire MGS. The enhanced light coupling efficiency can be expected because the SiO2/Sapphire MGS by the use of SiO2 layer provides a relatively more graded refractive index profile. Furthermore, the SiO2 film on the sapphire MGS provides better surface protection. There may be also an improvement in the light scattering property due to the rough surface of deposited SiO2 films on the sapphire MGS. For this reason, we investigated the influence of the SiO2 layer onto the sapphire MGS on the total transmittance characteristics. Figure 6
Fig. 6 (a) Contour plot of the calculated total transmittance spectra as a function of HSiO2 for the SiO2/sapphire MGS with OT = 2.3, WMGS = 2.5 μm, HMGS = 5 μm, and P = 0.5 μm and (b) calculated average total transmittance as a function of HSiO2. The inset of (b) shows the refractive index profile of a cross-sectional view in the computational geometry.
shows (a) the contour plot of the calculated total transmittance as a function of wavelength for different heights of SiO2 layer (HSiO2) in the SiO2/sapphire MGS with OT = 2.3, WMGS = 2.5 μm, HMGS = 5 μm, and P = 0.5 μm and (b) the calculated average total transmittance as a function ofHSiO2. The inset of Fig. 6(b) shows the refractive index profile of a cross-sectional view in the computational geometry. In the theoretical modeling of the geometries of SiO2 layer on the sapphire MGS, we assumed that the SiO2 are deposited uniformly along the vertical and lateral directions. As shown in Fig. 6(a), the total transmittance could be considerably increased with increasing the HSiO2. The high total transmittance region with values of > 94% extended into the wavelength ranges of 700-1100 nm and 1500-1800 nm, and the low total transmittance region with values of < 89% was partially reduced at wavelengths of 1100-1500 nm. As shown in Fig. 6(b), the average total transmittance was increased efficiently with slight fluctuations. This can be explained by the fact that the SiO2 layer acts as the interference layer which reduces Fresnel reflections. The total transmittance of SiO2/sapphire MGS was enhanced by the more graded refractive index profile. The refractive index difference between air and the surface of sapphire MGSs could be relaxed by an intermediate refractive index of SiO2 layer, thus leading to the improved total transmittance characteristics.

4. Fabrication and characterization

To test simply the experimental feasibility of the predicted concept by the theoretical calculation, we fabricated the sapphire MGSs and SiO2/sapphire MGSs. For fabricating the sapphire MGS, the double-side polished sapphire substrate of ~200 μm was used to pattern the arrays of microstructures by a conventional lithography process including the photoresist patterning followed by dry etching. By using the inductively coupled plasma (ICP) etching with BCl3/He mixture gases, the hexagonally arrayed sapphire MGS with 1.5 μm of height, 2.5 μm of width, and 0.55 μm of pitch length was prepared. For SiO2/sapphire MGSs, the SiO2 layer was deposited on the sapphire MGS by plasma enhanced chemical vapor deposition process with SiH4/N2O as precursors. In order to experimentally characterize the transmission properties, the total transmittance of the samples was measured by using UV-VIS-NIR spectrophotometer (Cary 5000, Varian, USA) with an integrating sphere to collect all scattered light in the wavelength range of 300-1800 nm. The specular transmittance (i.e., zeroth order transmittance) was measured by the light falling directly to the detector. In this system, the photomultiplier tube (PMT) for 300-800 nm and an InGaAs dectector for 800-1800 nm were used. The diffuse transmittance was obtained from the difference between the total transmittance and the specular transmittance [32

32. D. W. Kang, S. H. Kuk, K. S. Ji, S. W. Ahn, and M. K. Han, “Highly transparent and high haze bilayer Al-doped ZnO thin film employing oxygen-controlled seed layer,” Jpn. J. Appl. Phys. 49(3), 031101 (2010). [CrossRef]

].

Figure 7
Fig. 7 Measured (solid lines) and calculated (dash lines) total transmittance spectra for sapphire, sapphire MGS, and 500 nm SiO2/sapphire MGS. The insets show the cross-sectional SEM images of the sapphire MGS and 500 nm SiO2/sapphire MGS.
shows the measured (solid lines) and calculated (dash lines) total transmittance spectra for sapphire, sapphire MGS, and 500 nm SiO2/sapphire MGS at normal incidence of 8° (i.e., near-normal incidence). The cross-sectional field emission scanning electron microscopy (FE-SEM) images of the sapphire MGS and 500 nm SiO2/sapphire MGS are shown in the inset. For calculating the total transmittance of the fabricated sapphire MGS, the computational geometry of OT = 1.7, WMGS = 2.5 μm, HMGS = 1.5 μm, and P = 0.55 μm, which was estimated from the SEM images, was used. For bare sapphire substrate, the poor total transmittance of < ~86% was observed over a wide wavelength range. However, the total transmittance was efficiently increased by modifying the surface of sapphire through the MGS. At the wavelength regions of 300-1100 nm and 1600-1800 nm, the increased total transmittance was clearly observed, indicating an average total transmittance of 90.1% in the visible wavelength range. For 500 nm SiO2/sapphire MGS, the total transmittance was further increased up to an average value of ~93% with slightly increased oscillations. This is caused by the use of SiO2 layer with the intermediate refractive index as mentioned above. In measured total transmittance spectra, slight fluctuations in the wavelength range of ~800-900 nm occurred while switching between the PMT and the InGaAs detector. The calculated transmittance data reasonably agreed with the experimental results.

To estimate the portion of light that is scattered or diffused (i.e., diffuse transmittance) in the total transmittance, the diffuse transmittance was measured. Figure 8
Fig. 8 Measured diffuse transmittance spectra of the sapphire, sapphire MGS, and 500 nm SiO2/sapphire MGS at normal incidence. The inset shows the photographic images of the sapphire and SiO2 sapphire MGS and the top-view SEM image of the SiO2/sapphire MGS.
shows the measured diffuse transmittance spectra of the sapphire MGS, and 500 nm SiO2/sapphire MGS at normal incidence. For comparison, the diffuse transmittance spectra of the sapphire substrate are also shown. The inset shows the photographic images of the sapphire and SiO2/sapphire MGS and the top-view SEM image of the SiO2/sapphire MGS. The bare sapphire substrate exhibited very low diffuse transmittance of < 7.5% in the wide range of wavelengths. Instead, for sapphire MGS, a significant increase in the diffuse transmittance was observed, indicating an average diffuse transmittance of 85.2% in the visible wavelength range. This can be reasonably confirmed by the results of FDTD simulation in Fig. 1. The 500 nm SiO2/sapphire MGS yielded a further increase in the diffuse transmittance, resulting from the more enhanced total transmittance as well as the rough surface of deposited SiO2 layer as can be seen in SEM image of SiO2/sapphire MGS. In comparison of the photographic image of SiO2/sapphire MGS with that of bare sapphire substrate as shown in the insets of Fig. 8, the considerable light scattering property can be also observed with the naked eye. The experimental results indicate that the sapphire MGSs provide the strong light scattering property as well as the highly transparent sapphire substrate.

5. Conclusion

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0025071).

References and links

1.

N. F. Hartman and T. K. Gaylord, “Antireflection gold surface-relief gratings: experimental characteristics,” Appl. Opt. 27(17), 3738–3743 (1988). [CrossRef] [PubMed]

2.

K. Kintaka, J. Nishii, A. Mizutani, H. Kikuta, and H. Nakano, “Antireflection microstructures fabricated upon fluorine-doped SiO2 films,” Opt. Lett. 26(21), 1642–1644 (2001). [CrossRef] [PubMed]

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L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226(1-6), 81–88 (2003). [CrossRef]

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S. J. Choi and S. Y. Huh, “Direct structuring of a biomimetic anti-reflective, self-cleaning surface for light harvesting in organic solar cells,” Macromol. Rapid Commun. 31(6), 539–544 (2010). [CrossRef] [PubMed]

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M. I. Elhaj and M. Schadt, “Optical polymer thin films with isotropic and anisotropic nano-corrugated surface topologies,” Nature 410(6830), 796–799 (2001). [CrossRef] [PubMed]

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O. Deparis, N. Khuzayim, A. Parker, and J. P. Vigneron, “Assessment of the antireflection property of moth wings by three-dimensional transfer-matrix optical simulations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4 Pt 1), 041910 (2009). [CrossRef] [PubMed]

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Y. Wang, N. Lu, H. Xu, G. Shi, M. Xu, X. Lin, H. Li, W. Wang, D. Qi, Y. Lu, and L. Chi, “Biomimetic corrugated silicon nanocone arrays for self-cleaning antireflection coatings,” Nano Res. 3(7), 520–527 (2010). [CrossRef]

8.

W. Śmigaj, B. Gralak, R. Pierre, and G. Tayeb, “Antireflection gratings for a photonic-crystal flat lens,” Opt. Lett. 34(22), 3532–3534 (2009). [CrossRef] [PubMed]

9.

J. M. Park, S. G. Lee, H. R. Park, and M. H. Lee, “Self-collimating photonic crystal antireflection structure for both TE and TM polarizations,” Opt. Express 18(12), 13083–13093 (2010). [CrossRef] [PubMed]

10.

Y. M. Song, S. J. Jang, J. S. Yu, and Y. T. Lee, “Bioinspired parabola subwavelength structures for improved broadband antireflection,” Small 6(9), 984–987 (2010). [CrossRef] [PubMed]

11.

Y. H. Ko and J. S. Yu, “Design of hemi-urchin shaped ZnO nanostructures for broadband and wide-angle antireflection coatings,” Opt. Express 19(1), 297–305 (2011). [CrossRef] [PubMed]

12.

S. Walheim, E. Schaffer, J. Mlynek, and U. Steiner, “Nanophase-separated polymer films as high-performance antireflection coatings,” Science 283(5401), 520–522 (1999). [CrossRef] [PubMed]

13.

K. Crabtree and R. A. Chipman, “Subwavelength-grating-induced wavefront aberrations: a case study,” Appl. Opt. 46(21), 4549–4554 (2007). [CrossRef] [PubMed]

14.

Y. M. Song, H. J. Choi, J. S. Yu, and Y. T. Lee, “Design of highly transparent glasses with broadband antireflective subwavelength structures,” Opt. Express 18(12), 13063–13071 (2010). [CrossRef] [PubMed]

15.

Y. M. Song, E. S. Choi, G. C. Park, C. Y. Park, S. J. Jang, and Y. T. Lee, “Disordered antireflective nanostructures on GaN-based light-emitting diodes using Ag nanoparticles for improved light extraction efficiency,” Appl. Phys. Lett. 97(9), 093110 (2010). [CrossRef]

16.

Y. M. Song, G. C. Park, S. J. Jang, J. H. Ha, J. S. Yu, and Y. T. Lee, “Multifunctional light escaping architecture inspired by compound eye surface structures: From understanding to experimental demonstration,” Opt. Express 19(S2), A157–A165 (2011). [CrossRef] [PubMed]

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J. Jonsson and F. Nikolaje, “Investigation of optical properties of injection molded subwavelength gratings,” Proc. SPIE 4779, 23–30 (2002). [CrossRef]

19.

D. L. Brundrett, T. K. Gaylord, and E. N. Glytsis, “Polarizing mirror/absorber for visible wavelengths based on a silicon subwavelength grating: design and fabrication,” Appl. Opt. 37(13), 2534–2541 (1998). [CrossRef] [PubMed]

20.

W. Ge, C. Wang, Y. Xue, B. Cao, B. Zhang, and K. Xu, “Tunable ultra-deep subwavelength photolithography using a surface plasmon resonant cavity,” Opt. Express 19(7), 6714–6723 (2011). [CrossRef] [PubMed]

21.

C. C. Yu, Y. T. Chen, D. H. Wan, H. L. Chen, S. L. Ku, and Y. F. Chou, “Using one-step, dual-side nanoimprint lithography to fabricate low-cost, highly flexible wave plates exhibiting broadband antireflection,” J. Electrochem. Soc. 158(6), J195–J199 (2011). [CrossRef]

22.

P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997). [CrossRef]

23.

Z. Jehl, J. Rousset, F. Donsanti, G. Renou, N. Naghavi, and D. Lincot, “Electrodeposition of ZnO nanorod arrays on ZnO substrate with tunable orientation and optical properties,” Nanotechnology 21(39), 395603 (2010). [CrossRef] [PubMed]

24.

S. S. Lo, D. Haung, and D. J. Jan, “Haze ratio enhancement using a closely packed ZnO monolayer structure,” Opt. Express 18(2), 662–669 (2010). [CrossRef] [PubMed]

25.

C. Haase and H. Stiebig, “Thin-flm silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. 91(6), 061116 (2007). [CrossRef]

26.

S. Mokkapati, F. J. Beck, A. Polman, and K. R. Catchpole, “Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells,” Appl. Phys. Lett. 95(5), 053115 (2009). [CrossRef]

27.

R. Bouffaron, L. Escoubas, J. J. Simon, Ph. Torchio, F. Flory, G. Berginc, Ph. Masclet, C. Perret, and P. Schiavone, “Design and fabrication of infrared antireflecting bi-periodic micro-structured surfaces,” Proc. SPIE 6992, 69920H (2008). [CrossRef]

28.

S. L. Chuang, Physics of optoelectronic devices, (John Wiley & Sons. Inc. 1995).

29.

S. L. Chuang and J. A. Kong, “Wave scattering and guidance by dielectric waveguides with periodic surfaces,” J. Opt. Soc. Am. 73(5), 669–679 (1983). [CrossRef]

30.

R. Bouffaron, L. Escoubas, V. Brissonneau, J. J. Simon, G. Berginc, P. Torchio, F. Flory, and P. Masclet, “Spherically shaped micro-structured antireflective surfaces,” Opt. Express 17(24), 21590–21597 (2009). [CrossRef] [PubMed]

31.

W. Zhou, M. Tao, L. Chen, and H. Yang, “Microstructured surface design for omnidirectional antireflection coatings on solar cells,” J. Appl. Phys. 102(10), 103105 (2007). [CrossRef]

32.

D. W. Kang, S. H. Kuk, K. S. Ji, S. W. Ahn, and M. K. Han, “Highly transparent and high haze bilayer Al-doped ZnO thin film employing oxygen-controlled seed layer,” Jpn. J. Appl. Phys. 49(3), 031101 (2010). [CrossRef]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(220.2740) Optical design and fabrication : Geometric optical design
(310.1210) Thin films : Antireflection coatings

ToC Category:
Diffraction and Gratings

History
Original Manuscript: June 7, 2011
Revised Manuscript: July 14, 2011
Manuscript Accepted: July 19, 2011
Published: July 28, 2011

Citation
Yeong Hwan Ko and Jae Su Yu, "Highly transparent sapphire micro-grating structures with large diffuse light scattering," Opt. Express 19, 15574-15583 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15574


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References

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  13. K. Crabtree and R. A. Chipman, “Subwavelength-grating-induced wavefront aberrations: a case study,” Appl. Opt. 46(21), 4549–4554 (2007). [CrossRef] [PubMed]
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  15. Y. M. Song, E. S. Choi, G. C. Park, C. Y. Park, S. J. Jang, and Y. T. Lee, “Disordered antireflective nanostructures on GaN-based light-emitting diodes using Ag nanoparticles for improved light extraction efficiency,” Appl. Phys. Lett. 97(9), 093110 (2010). [CrossRef]
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  18. J. Jonsson and F. Nikolaje, “Investigation of optical properties of injection molded subwavelength gratings,” Proc. SPIE 4779, 23–30 (2002). [CrossRef]
  19. D. L. Brundrett, T. K. Gaylord, and E. N. Glytsis, “Polarizing mirror/absorber for visible wavelengths based on a silicon subwavelength grating: design and fabrication,” Appl. Opt. 37(13), 2534–2541 (1998). [CrossRef] [PubMed]
  20. W. Ge, C. Wang, Y. Xue, B. Cao, B. Zhang, and K. Xu, “Tunable ultra-deep subwavelength photolithography using a surface plasmon resonant cavity,” Opt. Express 19(7), 6714–6723 (2011). [CrossRef] [PubMed]
  21. C. C. Yu, Y. T. Chen, D. H. Wan, H. L. Chen, S. L. Ku, and Y. F. Chou, “Using one-step, dual-side nanoimprint lithography to fabricate low-cost, highly flexible wave plates exhibiting broadband antireflection,” J. Electrochem. Soc. 158(6), J195–J199 (2011). [CrossRef]
  22. P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997). [CrossRef]
  23. Z. Jehl, J. Rousset, F. Donsanti, G. Renou, N. Naghavi, and D. Lincot, “Electrodeposition of ZnO nanorod arrays on ZnO substrate with tunable orientation and optical properties,” Nanotechnology 21(39), 395603 (2010). [CrossRef] [PubMed]
  24. S. S. Lo, D. Haung, and D. J. Jan, “Haze ratio enhancement using a closely packed ZnO monolayer structure,” Opt. Express 18(2), 662–669 (2010). [CrossRef] [PubMed]
  25. C. Haase and H. Stiebig, “Thin-flm silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett. 91(6), 061116 (2007). [CrossRef]
  26. S. Mokkapati, F. J. Beck, A. Polman, and K. R. Catchpole, “Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells,” Appl. Phys. Lett. 95(5), 053115 (2009). [CrossRef]
  27. R. Bouffaron, L. Escoubas, J. J. Simon, Ph. Torchio, F. Flory, G. Berginc, Ph. Masclet, C. Perret, and P. Schiavone, “Design and fabrication of infrared antireflecting bi-periodic micro-structured surfaces,” Proc. SPIE 6992, 69920H (2008). [CrossRef]
  28. S. L. Chuang, Physics of optoelectronic devices, (John Wiley & Sons. Inc. 1995).
  29. S. L. Chuang and J. A. Kong, “Wave scattering and guidance by dielectric waveguides with periodic surfaces,” J. Opt. Soc. Am. 73(5), 669–679 (1983). [CrossRef]
  30. R. Bouffaron, L. Escoubas, V. Brissonneau, J. J. Simon, G. Berginc, P. Torchio, F. Flory, and P. Masclet, “Spherically shaped micro-structured antireflective surfaces,” Opt. Express 17(24), 21590–21597 (2009). [CrossRef] [PubMed]
  31. W. Zhou, M. Tao, L. Chen, and H. Yang, “Microstructured surface design for omnidirectional antireflection coatings on solar cells,” J. Appl. Phys. 102(10), 103105 (2007). [CrossRef]
  32. D. W. Kang, S. H. Kuk, K. S. Ji, S. W. Ahn, and M. K. Han, “Highly transparent and high haze bilayer Al-doped ZnO thin film employing oxygen-controlled seed layer,” Jpn. J. Appl. Phys. 49(3), 031101 (2010). [CrossRef]

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