Abstract

This work both numerically and experimentally investigates the reflectance from the smooth side of a semi-transparent 508-µm-thick window with metallic gratings attached on the other side. The incident light is oblique and linearly polarized, and its wavelength ranges from 2.5 to 25 µm. Three gratings with various levels of profile complexity and periods are investigated. Influences from the intrinsic material absorption, light refraction, total internal reflection, interference, and diffraction on both the specular and hemispherical reflectance are studied. Moreover, the applicability of effective medium theory to our samples is verified.

© 2015 Optical Society of America

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References

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2014 (5)

2013 (3)

2011 (4)

2010 (2)

2009 (2)

2008 (3)

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W. Prather, “Thin film solar cell design based on photonic crystal and diffractive grating structures,” Opt. Express 16(19), 15238–15248 (2008).
[PubMed]

Y. B. Chen, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of submicron metallic slit arrays,” J. Heat Transfer 130(8), 082404 (2008).
[Crossref]

2007 (1)

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129(1), 79–90 (2007).
[Crossref]

2005 (1)

B. J. Lee, V. P. Khuu, and Z. M. Zhang, “Partially coherent spectral transmittance of dielectric thin films with rough surfaces,” J. Thermophys. Heat Transf. 19(3), 360–366 (2005).

2003 (1)

2000 (1)

C. E. Chryssou, “Gain-equalizing filters for wavelength division multiplexing optical communication systems: a comparison of notch and long-period grating filters for integrated optoelectronics,” Opt. Commun. 184(5–6), 375–384 (2000).
[Crossref]

1995 (1)

1965 (1)

Alamariu, B. A.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Alonso-Ramos, C.

Aristov, A. K.

Bai, P.

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Bai, W.

Balram, K.

Baños, R.

Barnett, A.

Bartoli, F.

Bermel, P.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Bolten, J.

Broderick, K. A.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Brongersma, M.

Cai, L.

Cheben, P.

Chen, C.

Chen, J.

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Chen, L.

Chen, Y.

Chen, Y. B.

Y. B. Chen and F. C. Chiu, “Trapping mid-infrared rays in a lossy film with the Berreman mode, epsilon near zero mode, and magnetic polaritons,” Opt. Express 21(18), 20771–20785 (2013).
[Crossref] [PubMed]

Y. B. Chen and M. J. Huang, “Infrared reflectance from a compound grating and its alternative componential gratings,” J. Opt. Soc. Am. B 27(10), 2078–2086 (2010).
[Crossref]

Y. B. Chen, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of submicron metallic slit arrays,” J. Heat Transfer 130(8), 082404 (2008).
[Crossref]

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129(1), 79–90 (2007).
[Crossref]

Cheng, S. L.

Chiu, F. C.

Chryssou, C. E.

C. E. Chryssou, “Gain-equalizing filters for wavelength division multiplexing optical communication systems: a comparison of notch and long-period grating filters for integrated optoelectronics,” Opt. Commun. 184(5–6), 375–384 (2000).
[Crossref]

Creazzo, T.

Dewan, R.

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[Crossref]

Du, W. M.

L. M. Zhang, F. Xue, W. M. Du, C. B. Han, C. Zhang, and Z. L. Wang, “Transparent paper-based triboelectric nanogenerator as a page mark and anti-theft sensor,” Nano Res. 7(8), 1215–1223 (2014).
[Crossref]

Duan, L.

Duan, X.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Fu, S.

Gan, Q.

Gao, F.

Gargallo, B.

Gaylord, T. K.

Giesecke, A. L.

Gonzalo Wangüemert-Pérez, J.

Grann, E. B.

Halir, R.

Han, C. B.

L. M. Zhang, F. Xue, W. M. Du, C. B. Han, C. Zhang, and Z. L. Wang, “Transparent paper-based triboelectric nanogenerator as a page mark and anti-theft sensor,” Nano Res. 7(8), 1215–1223 (2014).
[Crossref]

Hessel, A.

Hong, C.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Honsberg, C.

Huang, K. C. Y.

Huang, M. J.

Huang, Y.

Jing, Q.

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Joannopoulos, J.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Jun, Y. K.

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A neutron dark-field imaging experiment with a neutron grating interferometer at a thermal neutron beam line at HANARO,” J. Korean Phys. Soc. 58(4), 730–734 (2011).
[Crossref]

Kafafi, Z.

Khuu, V. P.

B. J. Lee, V. P. Khuu, and Z. M. Zhang, “Partially coherent spectral transmittance of dielectric thin films with rough surfaces,” J. Thermophys. Heat Transf. 19(3), 360–366 (2005).

Kimerling, L. C.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Kleinjans, H.

Knipp, D.

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[Crossref]

Kohl, J.

Kurioz, Y.

Kwon, O. Y.

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A neutron dark-field imaging experiment with a neutron grating interferometer at a thermal neutron beam line at HANARO,” J. Korean Phys. Soc. 58(4), 730–734 (2011).
[Crossref]

Lee, B. J.

Y. B. Chen, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of submicron metallic slit arrays,” J. Heat Transfer 130(8), 082404 (2008).
[Crossref]

B. J. Lee, V. P. Khuu, and Z. M. Zhang, “Partially coherent spectral transmittance of dielectric thin films with rough surfaces,” J. Thermophys. Heat Transf. 19(3), 360–366 (2005).

Lee, S. W.

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A neutron dark-field imaging experiment with a neutron grating interferometer at a thermal neutron beam line at HANARO,” J. Korean Phys. Soc. 58(4), 730–734 (2011).
[Crossref]

Li, J.

Liu, D.

Liu, J.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Liu, Y.

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Lu, Y. H.

Miller, D.

Ming, H.

Moharam, M. G.

Molina-Fernández, I.

Muñoz, P.

Mutitu, J. G.

Nam, D.

Nishi, Y.

Novoselskii, V. V.

O’Carroll, D. M.

Oliner, A. A.

Ortega-Moñux, A.

Ouyang, J.

Pan, C.

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Pantina, J. A.

Pérez-Galacho, D.

Pommet, D. A.

Prather, D. W.

Reznikov, Y.

Roy, A.

Saraswat, K.

Schmid, J. H.

Semenov, G. B.

Shchedrunova, T. V.

Sheremet, N.

Shi, S.

Shum, P. P.

Slyusarenko, K.

Sohn, H. K.

Song, G.

Sukhdeo, D.

Tang, M.

Timans, P. J.

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129(1), 79–90 (2007).
[Crossref]

Trunov, M.

Wahlbrink, T.

Wang, L. P.

Wang, P.

Wang, Z. L.

L. M. Zhang, F. Xue, W. M. Du, C. B. Han, C. Zhang, and Z. L. Wang, “Transparent paper-based triboelectric nanogenerator as a page mark and anti-theft sensor,” Nano Res. 7(8), 1215–1223 (2014).
[Crossref]

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Wei, H.

Xu, D. X.

Xue, F.

L. M. Zhang, F. Xue, W. M. Du, C. B. Han, C. Zhang, and Z. L. Wang, “Transparent paper-based triboelectric nanogenerator as a page mark and anti-theft sensor,” Nano Res. 7(8), 1215–1223 (2014).
[Crossref]

Yi, Y.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Yu, M. B.

Yuan, Z.

Zeng, L.

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Zhang, C.

L. M. Zhang, F. Xue, W. M. Du, C. B. Han, C. Zhang, and Z. L. Wang, “Transparent paper-based triboelectric nanogenerator as a page mark and anti-theft sensor,” Nano Res. 7(8), 1215–1223 (2014).
[Crossref]

Zhang, J.

Zhang, L. M.

L. M. Zhang, F. Xue, W. M. Du, C. B. Han, C. Zhang, and Z. L. Wang, “Transparent paper-based triboelectric nanogenerator as a page mark and anti-theft sensor,” Nano Res. 7(8), 1215–1223 (2014).
[Crossref]

Zhang, P.

Zhang, Z. M.

L. P. Wang and Z. M. Zhang, “Phonon-mediated magnetic polaritons in the infrared region,” Opt. Express 19(S2), A126–A135 (2011).
[Crossref] [PubMed]

Y. B. Chen, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of submicron metallic slit arrays,” J. Heat Transfer 130(8), 082404 (2008).
[Crossref]

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129(1), 79–90 (2007).
[Crossref]

B. J. Lee, V. P. Khuu, and Z. M. Zhang, “Partially coherent spectral transmittance of dielectric thin films with rough surfaces,” J. Thermophys. Heat Transf. 19(3), 360–366 (2005).

Zhao, Z.

Zheng, R. S.

Zhou, Y. S.

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Zhu, B.

Zhu, G.

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93(22), 221105 (2008).
[Crossref]

Chin. Opt. Lett. (1)

J. Appl. Phys. (1)

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009).
[Crossref]

J. Heat Transfer (2)

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129(1), 79–90 (2007).
[Crossref]

Y. B. Chen, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of submicron metallic slit arrays,” J. Heat Transfer 130(8), 082404 (2008).
[Crossref]

J. Korean Phys. Soc. (1)

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A neutron dark-field imaging experiment with a neutron grating interferometer at a thermal neutron beam line at HANARO,” J. Korean Phys. Soc. 58(4), 730–734 (2011).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Opt. Technol. (1)

J. Thermophys. Heat Transf. (1)

B. J. Lee, V. P. Khuu, and Z. M. Zhang, “Partially coherent spectral transmittance of dielectric thin films with rough surfaces,” J. Thermophys. Heat Transf. 19(3), 360–366 (2005).

Nano Lett. (1)

G. Zhu, J. Chen, Y. Liu, P. Bai, Y. S. Zhou, Q. Jing, C. Pan, and Z. L. Wang, “Linear-grating triboelectric generator based on sliding electrification,” Nano Lett. 13(5), 2282–2289 (2013).
[Crossref] [PubMed]

Nano Res. (1)

L. M. Zhang, F. Xue, W. M. Du, C. B. Han, C. Zhang, and Z. L. Wang, “Transparent paper-based triboelectric nanogenerator as a page mark and anti-theft sensor,” Nano Res. 7(8), 1215–1223 (2014).
[Crossref]

Opt. Commun. (1)

C. E. Chryssou, “Gain-equalizing filters for wavelength division multiplexing optical communication systems: a comparison of notch and long-period grating filters for integrated optoelectronics,” Opt. Commun. 184(5–6), 375–384 (2000).
[Crossref]

Opt. Express (8)

D. Nam, D. Sukhdeo, A. Roy, K. Balram, S. L. Cheng, K. C. Y. Huang, Z. Yuan, M. Brongersma, Y. Nishi, D. Miller, and K. Saraswat, “Strained germanium thin film membrane on silicon substrate for optoelectronics,” Opt. Express 19(27), 25866–25872 (2011).
[Crossref] [PubMed]

J. Kohl, J. A. Pantina, and D. M. O’Carroll, “Enhancing surface plasmon leakage at the metal/semiconductor interface: towards increased light outcoupling efficiency in organic optoelectronics,” Opt. Express 22(7), 7644–7656 (2014).
[Crossref] [PubMed]

L. P. Wang and Z. M. Zhang, “Phonon-mediated magnetic polaritons in the infrared region,” Opt. Express 19(S2), A126–A135 (2011).
[Crossref] [PubMed]

B. Gargallo, P. Muñoz, R. Baños, A. L. Giesecke, J. Bolten, T. Wahlbrink, and H. Kleinjans, “Reflective arrayed waveguide gratings based on Sagnac loop reflectors with custom spectral response,” Opt. Express 22(12), 14348–14362 (2014).
[Crossref] [PubMed]

Z. Zhao, M. Tang, F. Gao, P. Zhang, L. Duan, B. Zhu, S. Fu, J. Ouyang, H. Wei, J. Li, P. P. Shum, and D. Liu, “Temperature compensated magnetic field sensing using dual S-bend structured optical fiber modal interferometer cascaded with fiber Bragg grating,” Opt. Express 22(22), 27515–27523 (2014).
[Crossref] [PubMed]

J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W. Prather, “Thin film solar cell design based on photonic crystal and diffractive grating structures,” Opt. Express 16(19), 15238–15248 (2008).
[PubMed]

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[Crossref] [PubMed]

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Opt. Lett. (2)

Other (5)

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E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic Press, 1998).

P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry, 2nd ed. (Wiley-Interscience, 2007).

T. C. Choy, Effective Medium Theory: Principles and Applications (Oxford University, 1999).

K. K. Sharma, Optics: Principles and Applications (Academic Press, 2006).

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Figures (7)

Fig. 1
Fig. 1 Diffraction from gratings at backside of semi-transparent Si substrate at oblique (θ inc = 30°) incidence of (a) TM and (b) TE waves. Grating period to wavelength ratio (Λ/λ) is smaller in (a) than in (b). (R) and (T) are reflected and transmitted diffracted waves, respectively. (E) and (H) are electric and magnetic field vectors of a wave, respectively.
Fig. 2
Fig. 2 Fabrication process and SEM images of three samples (SG_I, SG_II, and CG). The fabrication process contains four steps: exposure, development, deposition, and lift-off. Lateral dimensions of each sample are marked on its image.
Fig. 3
Fig. 3 Optical constants (n, κ) of bulk Au, Si, Ti, and effective media using f = 0.42 (SG_I) and f = 0.75 (CG). (a) n and (b) κ of intrinsic materials and (c) n and (d) κ of effective media.
Fig. 4
Fig. 4 Specular reflectance (Rs ) and hemispherical reflectance (Rh ) from SG_I at incidence of (a) TM and (b) TE waves. Text inside parentheses specifies origin of spectrum (experiments (Exp), rigorous coupled-wave analysis (RCWA), and effective medium theory (EMT)).
Fig. 5
Fig. 5 Rs and Rh from SG_II at incidence of (a) TM and (b) TE waves.
Fig. 6
Fig. 6 Rs and Rh from CG at incidence of (a) TM and (b) TE waves.
Fig. 7
Fig. 7 Measured Rs from SG_I, SG_II, and CG. Predicted wavelengths of Rayleigh anomalies and their responsible diffracted waves are marked.

Tables (2)

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Table 1 Grating profiles and dimensions for SG_I, SG_II, and CG.

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Table 2 Occurrence wavelength λ (in µm) of Rayleigh anomalies and responsible diffracted wave for three samples. Transition marks are utilized in Figs. 4-7 .

Equations (3)

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n f sin θ i n c = n w sin θ R j + j λ Λ = n f sin θ T j + j λ Λ
ε EM = f ε m + ( 1 f ) ε f
1 ε EM = f ε m + 1 f ε f

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