Abstract

We propose using blazed gratings in the resonance domain with period larger than the wavelength for antireflection and polarization selection. The inherent problem in this region is wavelength dispersion, which is solved by analyzing the total reflectivity and electric field distribution. The positional relationship between the area of strong electric field, and the side and tip of the grating is crucial to the wavelength dispersion of total reflectivity.

© 2007 Optical Society of America

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2007 (3)

2006 (9)

X. Deng, J. J. Wang, and F. Liu, "Wideband antireflective polarizers based on integrated diffractive multilayer microstructures," Opt. Lett. 31, 344-346 (2006).
[PubMed]

H. Kikuta, S. Hino, A. Maruyama, and A. Mizutani, "Estimation method for the light extraction efficiency of light-emitting elements with a rigorous grating diffraction theory," J. Opt. Soc. Am. A 23, 1207-1213 (2006).

H. K. Cho, J. Jang, J.-H. Choi, J. Choi, J. Kim, J. S. Lee, B. Lee, Y. H. Choe, K.-D. Lee, S. H. Kim, K. Lee, S.-K. Kim, and Y.-H. Lee, "Light extraction enhancement from nano-imprinted photonic crystal GaN-based blue light-emitting diodes," Opt. Express 14, 8654-8660 (2006).
[PubMed]

M. Piwinski, D. Dziczek, L. Klosowski, R. Srivastava, and S. Chwirot, "Coincidence study of excitation of cadmium atoms by electron impact," J. Phys. B 39, 1945-1953 (2006).

Y.-G. Ju, G. Almuneau, T.-H. Kim, and B.-W. Lee, "Numerical analysis of high-index nano-composite encapsulant for light-emitting diodes," Jpn. J. Appl. Phys., Part 1 45, 2546-2549 (2006).

A. Adawi, R. Kullock, J. Turner, C. Vasilev, D. Lidzey, A. Tahraoui, P. Fry, D. Gibson, E. Smith, C. Foden, M. Roberts, F. Qureshi, and N. Athanassopoulou, "Improving the light extraction efficiency of polymeric light emitting diodes using two-dimensional photonic crystals," Org. Electron. 7, 222-228 (2006).

Y.-C. Kim, S.-H. Cho, and Y.-W. Song, "Planarized SiNx/spin-on-glass photonic crystal organic light-emitting diodes," Appl. Phys. Lett. 89, 173502 (2006).

B. C. Krummacher, M. K. Mathai, V. Choong, S. A. Choulis, F. So, and A. Winnacker, "General method to evaluate substrate surface modification techniques for light extraction enhancement of organic light emitting diodes," J. Appl. Phys. 100, 054702 (2006).

H. W. Choia and S. J. Chua, "Honeycomb GaN micro-light-emitting diodes," J. Vac. Sci. Technol. B 24, 1071-1023 (2006).

2005 (10)

M. Khizar, Z. Y. Fan, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Nitride deep-ultraviolet light-emitting diodes with microlens array," Appl. Phys. Lett. 86, 173504 (2005).

T. Nakamura, N. Tsutsumi, N. Juni, and H. Fujii, "Thin-film waveguiding mode light extraction in organic electroluminescent," J. Appl. Phys. 97, 054505 (2005).

A. Kitamura, S. Naka, H. Okada, and H. Onnagawa, "Improved light outcoupling in organic electroluminescent devices with random dots," Jpn. J. Appl. Phys. , Part 1 45, 613-616 (2005).

M. Fujita, K. Ishihara, T. Ueno, T. Asano, S. Noda, H. Ohata, T. Tsuji, H. Nakada, and N. Shimoji, "Optical and electrical characteristics of organic light-emitting diodes with two-dimensional photonic crystals in organic/electrode layers," Jpn. J. Appl. Phys. , Part 1 44, 3669-3677 (2005).

H. Kasugai, Y. Miyake, A. Honshio, S. Mishima, T. Kawashima, K. Iida, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, H. Kinoshita, and H. Shiomi, "High-efficiency nitride-based light-emitting diodes with moth-eye structure," Jpn. J. Appl. Phys. , Part 1 44, 7414-7417 (2005).

S. Kiyohara, M. Fujiwara, F. Matsubayashi, and K. Mori, "Organic light-emitting microdevices fabricated by nanoimprinting technology using diamond molds," Jpn. J. Appl. Phys. , Part 1 44, 3686-3690 (2005).

S. Banerjee, J. B. Cole, and T. Yatagai, "Calculation of dffraction characteristics of subwavelength conducting gratings using a high accuracy nonstandard finite-difference time-domain method," Opt. Rev. 12, 274-280 (2005).

T.-X. Lee, C.-Y. Lin, S.-H. Ma, and C.-C. Sun, "Analysis of position-dependent light extraction of GaN-based LEDs," Opt. Express 13, 4175-4179 (2005).
[PubMed]

L. Zhou and W. Liu, "Broadband polarizing beam splitter with an embedded metal-wire nanograting," Opt. Lett. 30, 1434-1436 (2005).
[PubMed]

X. Yang, Y. Yan, and G. Jin, "Polarized light-guide plate for liquid crystal display," Opt. Express 13, 8349-8356 (2005).
[PubMed]

2004 (5)

K.-W. Chien and H.-P. D. Shieh, "Design and fabrication of an integrated polarized light guide for liquid-crystal-display illumination," Appl. Opt. 43, 1830-1834 (2004).
[PubMed]

D. Yi, Y. Yan, H. Liu, S. Lu, and G. Jin, "Broadband polarizing beam splitter based on the form birefringence of a subwavelength grating in the quasi-static domain," Opt. Lett. 29, 754-756 (2004).
[PubMed]

D. Delbeke, R. Baets, and P. Muys, "Polarization-selective beam splitter based on a highly efficient simple binary diffraction grating," Appl. Opt. 43, 6157-6165 (2004).
[PubMed]

Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emitting diodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).

J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).

2003 (8)

Y. Do, Y. Kim, Y.-W. Song, C.-O. Cho, H. Jeon, Y.-J. Lee, S.-H. Kim, and Y.-H. Lee, "Enhanced light extraction from organic light-emitting diodes with 2D SiO2/SiNx photonic crystals," Adv. Mater. 15, 1214-1218 (2003).

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, "Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings," Appl. Phys. Lett. 83, 1918-1920 (2003).

H. Ichikawa and T. Baba, "Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal," Appl. Phys. Lett. 84, 457-459 (2003).

Y. Kanamori, K. Kobayashi, H. Yugami, and K. Hane, "Subwavelength antireflection gratings for GaSb in visible and near-infrared," J. Appl. Phys. 42, 4020-4023 (2003).

X. J. Yu and H. S. Kwok, "Optical wire-grid polarizers at oblique angles of incidence," J. Appl. Phys. 93, 4407-4412 (2003).

F. Yamada, H. Numata, and Y. Taira, "Multi-layered flat-surface micro-optical components directly moled on an LCD panel," J. Soc. Inf. Disp. 11, 525-531 (2003).

C. Huh, K.-S. Lee, E.-J. Kang, and S.-J. Park, "Improved light-output and electrical performance of InGaN-based light-emitting diode by microroughening of the p-GaN surface," J. Appl. Phys. 93, 9383-9385 (2003).

J. B. Cole and S. Banerjee, "Applications of nonstandard finite difference models to computational electromagnetics," J. Diff. Eqns. 9, 1099-1112 (2003).

2002 (3)

A. Tagaya, S. Ishii, K. Yokoyama, E. Higuchi, and Y. Koike, "The advanced highly scattering optical transmission polymer backlight for liquid crystal displays," Jpn. J. Appl. Phys. , Part 1 41, 2241-2248 (2002).

J. B. Cole, "High-accuracy Yee algorithm based on nonstandard finite differences: new developments and verfications," IEEE Trans. Antennas Propag. 50, 1185-1191 (2002).

K. Asakawa and T. Hiraoka, "Nanopatterning with microdomains of block copolymers using reactive-ion etching selectivity," Jpn. J. Appl. Phys. , Part 1 41, 6112-6118 (2002).

2001 (3)

H.-Y. Ryu, J.-K. Hwang, D.-S. Song, I.-Y. Han, Y.-H. Lee, and D.-H. Jang, "Effect of nonradiative recombination on light emitting of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).

N. Stutzmann, H. Jagt, T. A. Tervoort, C. W. M. Bastiaansen, and P. Smith, "Novel polarized-light emitting polymer systems: II. use of form birefringent polarization-selective mirrors," Jpn. J. Appl. Phys. , Part 1 40, 5972-5975 (2001).

S. Omori, "Polarization and color separator using binary phase grating with subwavelength period," Opt. Rev. 8, 254-259 (2001).

2000 (4)

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
[PubMed]

R. E. Benenson, "Light polarization by transmission: a laboratory experiment," Eur. J. Phys. 21, 571-578 (2000).

S. Hava and M. Auslender, "Design and analysis of low-reflection grating microstructures for a solar energy absorber," Sol. Energy Mater. Sol. Cells 61, 143-151 (2000).

Y. Kanamori, H. Kikuta, and K. Hane, "Broadband antireflection gratings for glass substrates fabricated fast atom beam etching," Jpn. J. Appl. Phys. , Part 2 39, L735-L737 (2000).

1999 (2)

A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. M. J. Zhao, and A. Wang, "Angle-dependent reflectance measurements on photovoltaic materials and solar cells," Opt. Commun. 172, 139-151 (1999).

Y. Kanamori, M. Sasaki, and K. Hane, "Broadband antireflection gratings fabricated upon silicon substrates," Opt. Lett. 24, 1422-1424 (1999).

1997 (1)

S. Fan, P. R. Villeneuve, J. Joannopoulos, and E. Shubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).

1994 (1)

Adv. Mater. (1)

Y. Do, Y. Kim, Y.-W. Song, C.-O. Cho, H. Jeon, Y.-J. Lee, S.-H. Kim, and Y.-H. Lee, "Enhanced light extraction from organic light-emitting diodes with 2D SiO2/SiNx photonic crystals," Adv. Mater. 15, 1214-1218 (2003).

Appl. Opt. (4)

Appl. Phys. Lett. (7)

M. Khizar, Z. Y. Fan, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Nitride deep-ultraviolet light-emitting diodes with microlens array," Appl. Phys. Lett. 86, 173504 (2005).

N. C. Dasa, "Increase in midwave infrared light emitting diode light output due to substrate thinning and texturing," Appl. Phys. Lett. 90, 011111 (2007).

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, "Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings," Appl. Phys. Lett. 83, 1918-1920 (2003).

H. Ichikawa and T. Baba, "Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal," Appl. Phys. Lett. 84, 457-459 (2003).

J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).

H.-Y. Ryu, J.-K. Hwang, D.-S. Song, I.-Y. Han, Y.-H. Lee, and D.-H. Jang, "Effect of nonradiative recombination on light emitting of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).

Y.-C. Kim, S.-H. Cho, and Y.-W. Song, "Planarized SiNx/spin-on-glass photonic crystal organic light-emitting diodes," Appl. Phys. Lett. 89, 173502 (2006).

Eur. J. Phys. (1)

R. E. Benenson, "Light polarization by transmission: a laboratory experiment," Eur. J. Phys. 21, 571-578 (2000).

IEEE Trans. Antennas Propag. (1)

J. B. Cole, "High-accuracy Yee algorithm based on nonstandard finite differences: new developments and verfications," IEEE Trans. Antennas Propag. 50, 1185-1191 (2002).

J. Appl. Phys. (6)

X. J. Yu and H. S. Kwok, "Optical wire-grid polarizers at oblique angles of incidence," J. Appl. Phys. 93, 4407-4412 (2003).

C. Huh, K.-S. Lee, E.-J. Kang, and S.-J. Park, "Improved light-output and electrical performance of InGaN-based light-emitting diode by microroughening of the p-GaN surface," J. Appl. Phys. 93, 9383-9385 (2003).

T. Nakamura, N. Tsutsumi, N. Juni, and H. Fujii, "Thin-film waveguiding mode light extraction in organic electroluminescent," J. Appl. Phys. 97, 054505 (2005).

B. C. Krummacher, M. K. Mathai, V. Choong, S. A. Choulis, F. So, and A. Winnacker, "General method to evaluate substrate surface modification techniques for light extraction enhancement of organic light emitting diodes," J. Appl. Phys. 100, 054702 (2006).

Y. R. Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emitting diodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).

Y. Kanamori, K. Kobayashi, H. Yugami, and K. Hane, "Subwavelength antireflection gratings for GaSb in visible and near-infrared," J. Appl. Phys. 42, 4020-4023 (2003).

J. Diff. Eqns. (1)

J. B. Cole and S. Banerjee, "Applications of nonstandard finite difference models to computational electromagnetics," J. Diff. Eqns. 9, 1099-1112 (2003).

J. Opt. Soc. Am. A (2)

J. Phys. B (1)

M. Piwinski, D. Dziczek, L. Klosowski, R. Srivastava, and S. Chwirot, "Coincidence study of excitation of cadmium atoms by electron impact," J. Phys. B 39, 1945-1953 (2006).

J. Soc. Inf. Disp. (1)

F. Yamada, H. Numata, and Y. Taira, "Multi-layered flat-surface micro-optical components directly moled on an LCD panel," J. Soc. Inf. Disp. 11, 525-531 (2003).

J. Vac. Sci. Technol. B (1)

H. W. Choia and S. J. Chua, "Honeycomb GaN micro-light-emitting diodes," J. Vac. Sci. Technol. B 24, 1071-1023 (2006).

Jpn. J. Appl. Phys. (8)

A. Kitamura, S. Naka, H. Okada, and H. Onnagawa, "Improved light outcoupling in organic electroluminescent devices with random dots," Jpn. J. Appl. Phys. , Part 1 45, 613-616 (2005).

Y. Kanamori, H. Kikuta, and K. Hane, "Broadband antireflection gratings for glass substrates fabricated fast atom beam etching," Jpn. J. Appl. Phys. , Part 2 39, L735-L737 (2000).

H. Kasugai, Y. Miyake, A. Honshio, S. Mishima, T. Kawashima, K. Iida, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, H. Kinoshita, and H. Shiomi, "High-efficiency nitride-based light-emitting diodes with moth-eye structure," Jpn. J. Appl. Phys. , Part 1 44, 7414-7417 (2005).

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Figures (22)

Fig. 1
Fig. 1

(Color online) Top view and side view of the grating illustrating the method of measuring reflectivity. The dove prism is placed on the back surface of the grating like the tail of a pigeon. Some of the incident light is reflected and detected, and the remainder is transmitted through the grating and is scattered in the dove prism. Λ is the period, d is the depth and ds is the substrate thickness of the grating.

Fig. 2
Fig. 2

Arrangement of gratings on the mold. The period of the gratings is 1.08, 1.8, 3, and 5 μ m from left to right. The stripes of the gratings are in the longitudinal direction.

Fig. 3
Fig. 3

(Color online) Wavelength dependence of reflectivity on the surface relief in case A. The aspect ratio is varied from 0.5 to 2. ds in Fig. 1 is set to infinity. Regarding the polarization mode, (a) is TE and (b) is TM.

Fig. 4
Fig. 4

Grating and incident light. The definition of incidence angle θ is shown. The side of the grating and its normal line form the angle of incidence.

Fig. 5
Fig. 5

(Color online) Total reflectivity of the grating for different aspect ratios and refractive indexes in case A. The incidence angle θ is defined in Fig. 4. ds in Fig. 1 is set to infinity. Regarding the polarization mode, (a) is TE and (b) is TM.

Fig. 6
Fig. 6

(Color online) Total reflectivity of the grating for different aspect ratios and refractive indexes in case A. The incidence angle θ is defined in Fig. 4. ds in Fig. 1 is set to infinity. Regarding the polarization mode, (a) is TE and (b) is TM. Λ∕λ is 9.1 or 18.2. The refractive index is 1.5 or 3.

Fig. 7
Fig. 7

(Color online) Total reflectivity of the grating for different aspect ratios and refractive indexes in case B. The incidence angle θ is defined in Fig. 4. ds in Fig. 1 is set to infinity. Regarding the polarization mode, (a) is TE and (b) is TM.

Fig. 8
Fig. 8

(Color online) Total reflectivity of the grating for different aspect ratios and refractive indexes in case B. The incidence angle θ is defined in Fig. 4. ds in Fig. 1 is set to infinity. Regarding the polarization mode, (a) is TE and (b) is TM. Λ / λ is 9.1 or 18.2. The refractive index is 1.5 or 3.

Fig. 9
Fig. 9

(a) Path of reflected light and the relationship of α 1 , α 2 , and θ a . (b) Path of reflected light of two times reflection. (c) Path of reflected light of four times reflection.

Fig. 10
Fig. 10

(Color online) (a) Axis of electric field. (b) The grating and the field for FDTD calculation. (c) The phase distribution of both the incident light and scattered light in TM mode and case A. The electric field along the Y axis is shown. The period is 4λ and the aspect ratio is 1. ds is set to zero and a dove prism is removed in Fig. 1. Phase value is relative.

Fig. 11
Fig. 11

(Color online) Phase distribution of the scattered light in TE mode and case A. The period is 2λ and the aspect ratio is 1. ds is set to zero and the dove prism in Fig. 1 is removed.

Fig. 12
Fig. 12

(Color online) Phase distribution of the scattered light in TE mode and case A. The electric field along the Y axis is shown. The period is 3λ. Aspect ratios are (a) 0.5 and (b) 1.

Fig. 13
Fig. 13

(Color online) Phase distribution of the scattered light in TE mode and case A. The period is 4λ and the aspect ratios of (a)–(d) are 0.5, 1, 1.5, and 3, respectively.

Fig. 14
Fig. 14

(Color online) Phase distribution of the scattered light in TE mode for the rectangular grating. The period is 4λ and the aspect ratio is 1. ds is set to zero.

Fig. 15
Fig. 15

(Color online) Phase distribution of the scattered light in TM mode and case A. The electric field along the Y axis is shown. The aspect ratio is 1. (a) The period is 2λ. (b) The period is 4λ.

Fig. 16
Fig. 16

(Color online) Phase distribution of the scattered light in TE mode and case B. The aspect ratio is 1. The periods are (a) 2λ and (b) 4λ.

Fig. 17
Fig. 17

(Color online) Phase distribution of the scattered light in TE mode and case A. The wavelength is changed and the aspect ratio is 1. (a)–(c) have periods 3.03λ, 3.5λ, and 4.13λ, respectively. The reflectivities of (a) and (c) are low and that of (b) is high.

Fig. 18
Fig. 18

(Color online) Phase distribution of the scattered light in TE mode and case B. The wavelength is changed and aspect ratio is 1. (a)–(c) have periods 2.84λ, 3.03λ, and 3.8λ, respectively. The reflectivities of (a) and (c) are high and that of (b) is low.

Fig. 19
Fig. 19

(Color online) Total reflectivity of the grating against substrate thickness. The polarizations are TE and TM and aspect ratio is 0.5 or 1.

Fig. 20
Fig. 20

(Color online) Electric field intensity for the gratings with different substrate thickness. ds is (a) 0.55λ, (b) 0.65λ, and (c) 0.85λ, respectively. The reflectivities of (a) and (c) are high and that of (b) is low.

Fig. 21
Fig. 21

(Color online) Total reflectivity against Λ / λ for polarization TE or TM. λ was changed. Horizontal axis is log scale. (a) The aspect ratio is 1, and the refractive index is 1.5. When Λ / λ is 9.1, d s / λ is 0.55 or 0.65. (b) The grating, substrate 1, and substrate 2 sandwiched by air. (c) The aspect ratio of the grating is 0.5. The refractive index of substrate 1 and the grating is 1.52 and that of substrate 2 is 1.575 in (b). When Λ / λ is 9.1, d 1 / λ is 3.64 and d 2 / λ is 181.2.

Fig. 22
Fig. 22

(Color online) Total reflectivity of the grating with a base against incidence angle θ b . Λ / λ is 9.1, d s / λ is 0.55 or 0.64. The polarizations are TE and TM. The transverse axis is the incidence angle θ b . The angle is derived from Snell's law as illustrated in the left figure. Refractive index n is (a) 1.5 and (b) 1.9.

Tables (5)

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Table 1 Comparison of Total Reflectivities of Rectangular Grating and Triangular Grating a

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Table 2 Total Reflectivities of Experiment and Calculation for the Surface Relief of the Grating in Case A a

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Table 3 ds of Experiment and Calculation for the Grating in Case A a

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Table 4 Polarization Ratio of TE to TM About Total Reflectivities of Experiment and Calculation for the Grating With the Base and the Surface Relief in Case A a

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Table 5 Angle of the Local Minimum of Total Reflectivity in Fig. 22 and θBr

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