Abstract

The design of highly efficient fused silica transmission gratings with deep-etched triangular-shaped grooves in the 1st order diffraction is realized by the rigorous coupled wave analysis (RCWA). The antireflective effect of a subwavelength triangular-groove grating with gradient effective refractive index results in the higher diffraction efficiency (>99.9%). The performance of the presented gratings is clearly better than traditional rectangular and blazed ones. The gratings are designed under Littrow mounting at a wavelength of 1064 nm to be used in high-power laser systems. A detailed fabrication tolerance, covering not only the errors in height but also the errors in the lateral dimension, is demonstrated. The physical process of the diffraction characteristics for such a triangular-groove grating can be well explained by the simplified modal method based on two-beam interference of the first two propagating modes excited by the incident wave. Based on the fact that the transmittance derived from the modal method is in good agreement with that calculated by the RCWA, the simplified modal method can be effectively utilized as an easily designed tool of the triangular-shaped gratings.

© 2012 Optical Society of America

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  1. H. T. Nguyen, B. W. Shore, S. J. Bryan, J. A. Britten, R. D. Boyd, and M. D. Perry, “High-efficiency fused-silica transmission gratings,” Opt. Lett. 22, 142–144 (1997).
    [CrossRef]
  2. R. D. Boyd, J. A. Britten, D. E. Decker, B. W. Shore, B. C. Stuart, M. D. Perry, and L. Li, “High-efficiency metallic diffraction gratings for laser applications,” Appl. Opt. 34, 1697–1706 (1995).
    [CrossRef]
  3. B. W. Shore, M. D. Perry, J. A. Britten, R. D. Boyd, M. D. Feit, H. T. Nguyen, R. Chow, and G. E. Loomis, “Design of high efficiency dielectric reflection gratings,” J. Opt. Soc. Am. A 14, 1124–1136 (1997).
    [CrossRef]
  4. K. Hehl, J. Bischoff, U. Mohaupt, M. Palme, B. Schnabel, L. Wenke, R. Bodefeld, W. Theobald, E. Welsch, R. Sauerbrey, and H. Heyer, “High-efficiency dielectric reflection gratings: design, fabrication, and analysis,” Appl. Opt. 38, 6257–6271 (1999).
    [CrossRef]
  5. M. D. Perry, R. D. Boyd, J. A. Britten, D. Decker, B. W. Shore, C. Shannon, and E. Shults, “High-efficiency multilayer dielectric diffraction gratings,” Opt. Lett. 20, 940–942 (1995).
    [CrossRef]
  6. J. Néauport, E. Journot, G. Gaborit, and P. Bouchut, “Design, optical characterization, and operation of large transmission gratings for the laser integration line and laser megajoule facilities,” Appl. Opt. 44, 3143–3152 (2005).
    [CrossRef]
  7. S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm,” Appl. Opt. 45, 2567–2571 (2006).
    [CrossRef]
  8. T. Clausnitzer, J. Limpert, K. Zollner, H. Zellmer, H. J. Fuchs, E. B. Kley, A. Tunnermann, M. Jupe, and D. Ristau, “Highly efficient transmission gratings in fused silica for chirped pulse amplification systems,” Appl. Opt. 42, 6934–6938 (2003).
    [CrossRef]
  9. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, A. V. Tishchenko, and O. Parriaux, “Highly-dispersive dielectric transmission gratings with 100% diffraction efficiency,” Opt. Express 16, 5577–5584 (2008).
    [CrossRef]
  10. M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1391 (1982).
    [CrossRef]
  11. X. Jing, J. Ma, S. Liu, Y. Jin, H. He, J. Shao, and Z. Fan, “Analysis and design of transmittance for an antireflective surface microstructure,” Opt. Express 17, 16119–16134 (2009).
    [CrossRef]
  12. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  13. J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281, 3295–3300 (2008).
    [CrossRef]
  14. L. F. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  15. P. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998).
    [CrossRef]
  16. P. Lu, C. Zhou, J. Feng, and H. Cao, “Unified design of wavelength-independent deep-etched fused-silica gratings,” Opt. Commun. 283, 4135–4140 (2010).
    [CrossRef]
  17. Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
    [CrossRef]
  18. S. Fahr, T. Clausnitzer, E.-B. Kley, and A. Tünnermann, “Reflective diffractive beam splitter for laser interferometers,” Appl. Opt. 46, 6092–6095 (2007).
    [CrossRef]
  19. B. Wang, C. Zhou, J. Feng, H. Ru, and J. Zheng, “Wideband two-port beam splitter of a binary fused silica phase grating,” Appl. Opt. 47, 4004–4008 (2008).
    [CrossRef]
  20. M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of ultrahigh aspect ratio freestanding gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 25, 2593–2597 (2007).
    [CrossRef]
  21. J. Feng, C. Zhou, H. Cao, and P. Lv, “Deep etched sinusoidal polarizing beam splitter grating,” Appl. Opt. 49, 1739–1743 (2010).
    [CrossRef]
  22. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997).
    [CrossRef]
  23. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
    [CrossRef]
  24. J. Zheng, C. Zhou, B. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
    [CrossRef]
  25. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko, and O. Parriaux, “An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings,” Opt. Express 13, 10448–10456 (2005).
    [CrossRef]
  26. R. E. Collin, “Reflection and transmission at a slotted dielectric interface,” Can. J. Phys. 34, 398–411 (1956).
    [CrossRef]
  27. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  28. A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309–330 (2005).
    [CrossRef]
  29. J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Dual-function beam splitter of a subwavelength fused silica grating,” Appl. Opt. 48, 2697–2701 (2009).
    [CrossRef]
  30. H. Zhao and D. Yuan, “Design of fused silica rectangular transmission gratings for polarizing beam splitter based on modal method,” Appl. Opt. 49, 759–763 (2010).
    [CrossRef]
  31. J. Feng, C. Zhou, B. Wang, J. Zheng, W. Jia, H. Cao, and P. Lv, “Three-port beam splitter of a binary fused silica grating,” Appl. Opt. 47, 6638–6643 (2008).
    [CrossRef]
  32. E. Garnet, A. V. Tishchenko, and O. Parriaux, “Cancellation of the zeroth order in a phase mask by mode interplay in a high index contrast binary grating,” Appl. Opt. 46, 6719–6726 (2007).
    [CrossRef]
  33. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, A. Tishchenko, and O. Parriaux, “Investigation of the polarization-dependent diffraction of deep dielectric rectangular transmission gratings illuminated in Littrow mounting,” Appl. Opt. 46, 819–826 (2007).
    [CrossRef]
  34. J. Zheng, C. Zhou, J. Feng, and B. Wang, “Polarizing beam splitter of deep-etched triangular groove fused silica gratings,” Opt. Lett. 33, 1554–1556 (2008).
    [CrossRef]
  35. Y. Ono, Y. Kimura, Y. Ohta, and N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
    [CrossRef]
  36. R. C. Enger and S. K. Case, “Optical elements with ultrahigh spatial frequency surface corrugation,” Appl. Opt. 22, 3220–3228 (1983).
    [CrossRef]
  37. F. Xu, R. Tyan, P. Sun, Y. Fainman, C. Cheng, and A. Scherer, “Fabrication, modeling, and characterization of form-birefringent nanostructures,” Opt. Lett. 20, 2457–2459 (1995).
    [CrossRef]
  38. B. Wang, C. Zhou, S. Wang, and J. Feng, “Polarizing beam splitter of a deep-etched fused silica grating,” Opt. Lett. 32, 1299–1301 (2007).
    [CrossRef]
  39. W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
    [CrossRef]

2010

2009

2008

2007

2006

2005

2003

1999

1998

P. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998).
[CrossRef]

1997

1996

1995

1987

1983

1982

1981

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

1956

R. E. Collin, “Reflection and transmission at a slotted dielectric interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Ahn, M.

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of ultrahigh aspect ratio freestanding gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 25, 2593–2597 (2007).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Bischoff, J.

Bodefeld, R.

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Bouchut, P.

Boyd, R. D.

Britten, J. A.

Bryan, S. J.

Cao, H.

Case, S. K.

Chang, Y. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Chattopadhyay, S.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Chen, K. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Chen, L. C.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Cheng, C.

Chow, R.

Clausnitzer, T.

Collin, R. E.

R. E. Collin, “Reflection and transmission at a slotted dielectric interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Decker, D.

Decker, D. E.

Enger, R. C.

Fahr, S.

Fainman, Y.

Fan, Z.

Fan, Z. X.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281, 3295–3300 (2008).
[CrossRef]

Feit, M. D.

Feng, J.

Fuchs, H. J.

Gaborit, G.

Garnet, E.

Gaylord, T. K.

Grann, E. B.

He, H.

Hehl, K.

Heilmann, R. K.

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of ultrahigh aspect ratio freestanding gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 25, 2593–2597 (2007).
[CrossRef]

Heyer, H.

Hsu, C. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Hsu, Y. K.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Huang, Y. F.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Jen, Y. J.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Jia, W.

Jin, Y.

Jin, Y. X.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281, 3295–3300 (2008).
[CrossRef]

Jing, X.

Journot, E.

Jupe, M.

Kämpfe, T.

Kimura, Y.

Kley, E. B.

Kley, E.-B.

Lalanne, P.

P. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998).
[CrossRef]

Lee, C. S.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Li, L.

Li, L. F.

Limpert, J.

Liu, S.

Liu, S. J.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281, 3295–3300 (2008).
[CrossRef]

Liu, T. A.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Lo, H. C.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Loomis, G. E.

Lu, P.

P. Lu, C. Zhou, J. Feng, and H. Cao, “Unified design of wavelength-independent deep-etched fused-silica gratings,” Opt. Commun. 283, 4135–4140 (2010).
[CrossRef]

Lv, P.

Ma, J.

Ma, J. Y.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281, 3295–3300 (2008).
[CrossRef]

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Moharam, M. G.

Mohaupt, U.

Néauport, J.

Nguyen, H. T.

Nishida, N.

Ohta, Y.

Ono, Y.

Palme, M.

Pan, C. L.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Parriaux, O.

Peng, C. Y.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Perry, M. D.

Peschel, U.

Pommet, D. A.

Ristau, D.

Ru, H.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sauerbrey, R.

Schattenburg, M. L.

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of ultrahigh aspect ratio freestanding gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 25, 2593–2597 (2007).
[CrossRef]

Scherer, A.

Schnabel, B.

Shannon, C.

Shao, J.

Shao, J. D.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281, 3295–3300 (2008).
[CrossRef]

Shore, B. W.

Shults, E.

Stuart, B. C.

Sun, P.

Theobald, W.

Tishchenko, A.

Tishchenko, A. V.

Tunnermann, A.

Tünnermann, A.

Tyan, R.

Wang, B.

Wang, S.

Wang, W.

Welsch, E.

Wenke, L.

Xu, C.

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281, 3295–3300 (2008).
[CrossRef]

Xu, F.

Yuan, D.

Zellmer, H.

Zhang, Y.

Zhao, H.

Zheng, J.

Zhou, C.

P. Lu, C. Zhou, J. Feng, and H. Cao, “Unified design of wavelength-independent deep-etched fused-silica gratings,” Opt. Commun. 283, 4135–4140 (2010).
[CrossRef]

J. Feng, C. Zhou, H. Cao, and P. Lv, “Deep etched sinusoidal polarizing beam splitter grating,” Appl. Opt. 49, 1739–1743 (2010).
[CrossRef]

J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Dual-function beam splitter of a subwavelength fused silica grating,” Appl. Opt. 48, 2697–2701 (2009).
[CrossRef]

J. Feng, C. Zhou, B. Wang, J. Zheng, W. Jia, H. Cao, and P. Lv, “Three-port beam splitter of a binary fused silica grating,” Appl. Opt. 47, 6638–6643 (2008).
[CrossRef]

J. Zheng, C. Zhou, B. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
[CrossRef]

B. Wang, C. Zhou, J. Feng, H. Ru, and J. Zheng, “Wideband two-port beam splitter of a binary fused silica phase grating,” Appl. Opt. 47, 4004–4008 (2008).
[CrossRef]

J. Zheng, C. Zhou, J. Feng, and B. Wang, “Polarizing beam splitter of deep-etched triangular groove fused silica gratings,” Opt. Lett. 33, 1554–1556 (2008).
[CrossRef]

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

B. Wang, C. Zhou, S. Wang, and J. Feng, “Polarizing beam splitter of a deep-etched fused silica grating,” Opt. Lett. 32, 1299–1301 (2007).
[CrossRef]

S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm,” Appl. Opt. 45, 2567–2571 (2006).
[CrossRef]

Zollner, K.

Appl. Opt.

R. D. Boyd, J. A. Britten, D. E. Decker, B. W. Shore, B. C. Stuart, M. D. Perry, and L. Li, “High-efficiency metallic diffraction gratings for laser applications,” Appl. Opt. 34, 1697–1706 (1995).
[CrossRef]

K. Hehl, J. Bischoff, U. Mohaupt, M. Palme, B. Schnabel, L. Wenke, R. Bodefeld, W. Theobald, E. Welsch, R. Sauerbrey, and H. Heyer, “High-efficiency dielectric reflection gratings: design, fabrication, and analysis,” Appl. Opt. 38, 6257–6271 (1999).
[CrossRef]

J. Néauport, E. Journot, G. Gaborit, and P. Bouchut, “Design, optical characterization, and operation of large transmission gratings for the laser integration line and laser megajoule facilities,” Appl. Opt. 44, 3143–3152 (2005).
[CrossRef]

S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm,” Appl. Opt. 45, 2567–2571 (2006).
[CrossRef]

T. Clausnitzer, J. Limpert, K. Zollner, H. Zellmer, H. J. Fuchs, E. B. Kley, A. Tunnermann, M. Jupe, and D. Ristau, “Highly efficient transmission gratings in fused silica for chirped pulse amplification systems,” Appl. Opt. 42, 6934–6938 (2003).
[CrossRef]

S. Fahr, T. Clausnitzer, E.-B. Kley, and A. Tünnermann, “Reflective diffractive beam splitter for laser interferometers,” Appl. Opt. 46, 6092–6095 (2007).
[CrossRef]

B. Wang, C. Zhou, J. Feng, H. Ru, and J. Zheng, “Wideband two-port beam splitter of a binary fused silica phase grating,” Appl. Opt. 47, 4004–4008 (2008).
[CrossRef]

J. Feng, C. Zhou, H. Cao, and P. Lv, “Deep etched sinusoidal polarizing beam splitter grating,” Appl. Opt. 49, 1739–1743 (2010).
[CrossRef]

J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Dual-function beam splitter of a subwavelength fused silica grating,” Appl. Opt. 48, 2697–2701 (2009).
[CrossRef]

H. Zhao and D. Yuan, “Design of fused silica rectangular transmission gratings for polarizing beam splitter based on modal method,” Appl. Opt. 49, 759–763 (2010).
[CrossRef]

J. Feng, C. Zhou, B. Wang, J. Zheng, W. Jia, H. Cao, and P. Lv, “Three-port beam splitter of a binary fused silica grating,” Appl. Opt. 47, 6638–6643 (2008).
[CrossRef]

E. Garnet, A. V. Tishchenko, and O. Parriaux, “Cancellation of the zeroth order in a phase mask by mode interplay in a high index contrast binary grating,” Appl. Opt. 46, 6719–6726 (2007).
[CrossRef]

T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, A. Tishchenko, and O. Parriaux, “Investigation of the polarization-dependent diffraction of deep dielectric rectangular transmission gratings illuminated in Littrow mounting,” Appl. Opt. 46, 819–826 (2007).
[CrossRef]

Y. Ono, Y. Kimura, Y. Ohta, and N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
[CrossRef]

R. C. Enger and S. K. Case, “Optical elements with ultrahigh spatial frequency surface corrugation,” Appl. Opt. 22, 3220–3228 (1983).
[CrossRef]

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

Can. J. Phys.

R. E. Collin, “Reflection and transmission at a slotted dielectric interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of ultrahigh aspect ratio freestanding gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 25, 2593–2597 (2007).
[CrossRef]

Nat. Nanotechnol.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
[CrossRef]

Opt. Acta.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Opt. Commun.

P. Lu, C. Zhou, J. Feng, and H. Cao, “Unified design of wavelength-independent deep-etched fused-silica gratings,” Opt. Commun. 283, 4135–4140 (2010).
[CrossRef]

J. Y. Ma, S. J. Liu, Y. X. Jin, C. Xu, J. D. Shao, and Z. X. Fan, “Novel method for design of surface relief guided-mode resonant gratings at normal incidence,” Opt. Commun. 281, 3295–3300 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309–330 (2005).
[CrossRef]

Phys. Rev. B

P. Lalanne, “Effective properties and band structures of lamellar subwavelength crystals: plane-wave method revisited,” Phys. Rev. B 58, 9801–9807 (1998).
[CrossRef]

Sov. Phys. JETP

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

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Figures (20)

Fig. 1.
Fig. 1.

Schematic illustration of a deep-etched triangular groove grating. n0 and ng, refractive indices of air and fused silica substrate, respectively; ns, refractive index of grating, ng=ns; Λ, grating period; h, groove depth; K, grating vector; θi, incident angle of Littrow mounting; θ0 and θ1, the diffraction angle of the zeroth and the 1st diffractive orders, respectively.

Fig. 2.
Fig. 2.

Diffraction efficiencies of the transmitted 1st order as a function of the number of divided layers for different grating parameters.

Fig. 3.
Fig. 3.

Transmittance as a function of the grating period and groove depth in the 1st diffraction order under the Littrow mounting for TE polarization: (a) parameter scan of transmittance and (b) enlarged quantitative transmittance region.

Fig. 4.
Fig. 4.

(a) Diffraction efficiency versus the grating depth h with the grating period of 1000 and 1380 nm at the Littrow angles of 32.14° and 22.68°, respectively. (b) Transmittance characteristics with respect to the incident wavelength under corresponding Littrow angles.

Fig. 5.
Fig. 5.

Diffraction efficiency versus incident angle. (a) For the period 1000 nm and depth 2700 nm and (b) for the period 1380 nm and depth 3100 nm.

Fig. 6.
Fig. 6.

Transmittance as a function of the grating period and groove depth in the 1st diffraction order under the Littrow mounting for TM polarization.

Fig. 7.
Fig. 7.

(a) Diffraction efficiency versus the grating depth h with the grating period of 1100 nm at the Littrow angles of 28.92°. (b) Transmittance characteristics with respect to the incident wavelength under corresponding Littrow angles.

Fig. 8.
Fig. 8.

Diffraction efficiency versus incident angle for the period 1100 nm and depth 3800 nm.

Fig. 9.
Fig. 9.

Diffraction efficiency of the 1st order as a function of the grating period and the groove depth under the Littrow mounting for (a), (c) TE polarization and (b), (d) TM polarization. The dotted lines indicate the optimized values.

Fig. 10.
Fig. 10.

(a) Diffraction efficiency of the designed grating as a function of incident wavelength under Littrow mounting. (b) Diffraction efficiency as a function of incident angle.

Fig. 11.
Fig. 11.

Near field distribution of triangular gratings. (a) For TE polarization at the period 1000 nm and depth 2700 nm with the Littrow mounting angle of 32.14°. (b) For TM polarization at the period 1100 nm and depth 3800 nm with the Littrow mounting angle of 28.92°.

Fig. 12.
Fig. 12.

F(neff2) for a fused silica rectangular grating with a period of 1000 nm. (a) TE polarization for different fill factors and (b) TM polarization for different fill factors.

Fig. 13.
Fig. 13.

(a) Two modes diffraction model. (b) Effective rectangular grating stack of an approximated N-level for a period of triangular grating.

Fig. 14.
Fig. 14.

(a) Effective mode indices as a function of duty cycle f for different layers of a triangular grooves grating with the period of 745 nm. (b) Average difference of mode indices as a function of the grating period.

Fig. 15.
Fig. 15.

Diffraction efficiencies of the 0th and 1st diffractive orders versus groove depth calculated by RCWA and the simplified modal method, respectively. (a) For TE polarization at the grating period of 1000 nm, (b) for TM polarization at the period of 1100 nm, (c) for TE polarization at the period of 745 nm and (d) for TM polarization at the period of 745 nm.

Fig. 16.
Fig. 16.

Three propagating grating modes derived by F(neff2) for the grating period of 1.38 μm with the fill factor 0.5: (a) for TE polarization and (b) for TM polarization.

Fig. 17.
Fig. 17.

Contour of the diffraction efficiency versus the grating period and groove depth under the corresponding Littrow mounting. (a) Region of the period of 1000 nm and depth of 2700 nm and (b) region of the period of 1380 nm and depth of 3100 nm.

Fig. 18.
Fig. 18.

Contour of the diffraction efficiency versus grating period and groove depth under the corresponding Littrow mounting.

Fig. 19.
Fig. 19.

Diffraction efficiencies of the transmitted 1st order with two types of lateral fabrication errors for the designed gratings.

Fig. 20.
Fig. 20.

Comparison of the transmitted 1st order efficiencies between the optimized blazed gratings and the triangular gratings as a function of the normalized depth.

Tables (1)

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Table 1. Optimized Numerical Results Using RCWA and Their Physical Explanation Based on the Simplified Modal Method

Equations (10)

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cosαΛ=F(neff2),
F(neff2)=cos(βfΛ)cos[γ(1f)Λ]β2+γ22βγsin(βfΛ)sin[γ(1f)Λ],
F(neff2)=cos(βfΛ)cos[γ(1f)Λ]n04β2+ng4γ22n02ng2βγsin(βfΛ)sin[γ(1f)Λ].
η0=cos2(Δφ/2),
η1=sin2(Δφ/2),
Δφ=Δn¯effk0h,
Δn¯eff=1h0h(n0th(z)n1st(z))dz,
Δn¯eff=01(ni,0thni,1st)df,
Δφ=2πλΔn¯effhm=(2l+1)π,l=0,1,2,.
hm=(2l+1)λ2Δn¯eff,l=0,1,2.

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