Abstract

We propose quasi-periodic two-dimensional gratings comprised of a large number of circular holes for the high order diffraction suppression. By using Kirchhoff’s diffraction theory, we analytically investigate the diffraction property of the grating and optimize the structure parameters to suppress the high order diffractions. We analyze the dependence of the high order diffractions on the hole location and size. Notably, theoretical analysis reveals that the 3rd and even order diffractions can be completely suppressed, and the 5th order diffraction is as low as 0.02% of the 1st order diffraction, thereby allowing to submerge in the background noise for most practical applications. The desired diffraction pattern containing the 0th and ± 1st order diffractions results from the constructive interference of lights from different holes, which locate according to some statistical law distribution. The experimental results are also presented, confirming the theoretical predictions. Especially, our gratings have two advantages: the ability to form free-standing structures and large tolerance up to ± 10% deviation of the hole size. The former is highly desired for the x-ray and extreme ultraviolet regions, while the latter ease the fabrication difficulties of the current planar silicon technology. Our results should possess broad potential applications in a wide spectrum unscrambling from the infrared to the x-ray region.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Two-dimensional gratings of hexagonal holes for high order diffraction suppression

Ziwei Liu, Lina Shi, Tanchao Pu, Hailiang Li, Jiebin Niu, Guanya Wang, and Changqing Xie
Opt. Express 25(2) 1339-1349 (2017)

Blazed high-efficiency x-ray diffraction via transmission through arrays of nanometer-scale mirrors

Ralf K. Heilmann, Minseung Ahn, Eric M. Gullikson, and Mark L. Schattenburg
Opt. Express 16(12) 8658-8669 (2008)

Diffraction efficiency of 200-nm-period critical-angle transmission gratings in the soft x-ray and extreme ultraviolet wavelength bands

Ralf K. Heilmann, Minseung Ahn, Alex Bruccoleri, Chih-Hao Chang, Eric M. Gullikson, Pran Mukherjee, and Mark L. Schattenburg
Appl. Opt. 50(10) 1364-1373 (2011)

References

  • View by:
  • |
  • |
  • |

  1. C. Palmer, Diffraction Grating Handbook (Richardson Grating Laboratory, 2005).
  2. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
  3. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).
  4. M. Born and E. Wolf, Principle of Optics (Pergamon, 1980).
  5. P. Jin, Y. Gao, T. Liu, X. Li, and J. Tan, “Resist shaping for replication of micro-optical elements with continuous relief in fused silica,” Opt. Lett. 35(8), 1169–1171 (2010).
    [Crossref] [PubMed]
  6. D. Attwood, Soft X-ray and Extreme Ultraviolet Radiation, Principles and Applications (Cambridge University Press, 1999), p. 55.
  7. S. Gupta, “Single-Order Transmission Diffraction Gratings based on Dispersion Engineered All-dielectric Metasurfaces,” J. Opt. Soc. Am. A 33(8), 1641–1647 (2016).
    [Crossref] [PubMed]
  8. L. Zhu, J. Kapraun, J. Ferrara, and C. J. Chang-Hasnain, “Flexible photonic metastructures for tunable coloration,” Optica 2(3), 255–258 (2015).
    [Crossref]
  9. Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15(3), 1615–1621 (2015).
    [Crossref] [PubMed]
  10. 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(8), 5577–5584 (2008).
    [Crossref] [PubMed]
  11. C. Zhou, T. Seki, T. Kitamura, Y. Kuramoto, T. Sukegawa, N. Ishii, T. Kanai, J. Itatani, Y. Kobayashi, and S. Watanabe, “Wavefront analysis of high-efficiency, large-scale, thin transmission gratings,” Opt. Express 22(5), 5995–6008 (2014).
    [Crossref] [PubMed]
  12. H. Zhang, J. Zhu, Z. Zhu, Y. Jin, Q. Li, and G. Jin, “Surface-plasmon-enhanced GaN-LED based on a multilayered M-shaped nano-grating,” Opt. Express 21(11), 13492–13501 (2013).
    [Crossref] [PubMed]
  13. M. E. Warren, R. E. Smith, G. A. Vawter, and J. R. Wendt, “High-efficiency subwavelength diffractive optical element in GaAs for 975 nm,” Opt. Lett. 20(12), 1441–1443 (1995).
    [Crossref] [PubMed]
  14. L. F. Pease, P. Deshpande, Y. Wang, W. B. Russel, and S. Y. Chou, “Self-formation of sub-60-nm half-pitch gratings with large areas through fracturing,” Nat. Nanotechnol. 2(9), 545–548 (2007).
    [Crossref] [PubMed]
  15. F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Diffraction of gratings with rough edges,” Opt. Express 16(24), 19757–19769 (2008).
    [Crossref] [PubMed]
  16. L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
    [Crossref]
  17. H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
    [Crossref]
  18. N. Gao and C. Xie, “High-order diffraction suppression using modulated groove position gratings,” Opt. Lett. 36(21), 4251–4253 (2011).
    [Crossref] [PubMed]
  19. L. Kuang, L. Cao, X. Zhu, S. Wu, Z. Wang, C. Wang, S. Liu, S. Jiang, J. Yang, Y. Ding, C. Xie, and J. Zheng, “Quasi-sinusoidal single-order diffraction transmission grating used in x-ray spectroscopy,” Opt. Lett. 36(20), 3954–3956 (2011).
    [Crossref] [PubMed]
  20. Q. Fan, Y. Liu, C. Wang, Z. Yang, L. Wei, X. Zhu, C. Xie, Q. Zhang, F. Qian, Z. Yan, Y. Gu, W. Zhou, G. Jiang, and L. Cao, “Single-order diffraction grating designed by trapezoidal transmission function,” Opt. Lett. 40(11), 2657–2660 (2015).
    [Crossref] [PubMed]
  21. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
    [Crossref] [PubMed]
  22. K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
    [Crossref] [PubMed]
  23. C. Xie, X. Zhu, H. Li, L. Shi, Y. Hua, and M. Liu, “Toward two-dimensional nanometer resolution hard X-ray differential-interference-contrast imaging using modified photon sieves,” Opt. Lett. 37(4), 749–751 (2012).
    [Crossref] [PubMed]
  24. F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole Array as a Lens,” Nano Lett. 8(8), 2469–2472 (2008).
    [Crossref] [PubMed]
  25. F. M. Huang, N. I. Zheludev, Y. Chen, and F. J. G. Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(21), 091119 (2007).
    [Crossref]

2016 (1)

2015 (4)

L. Zhu, J. Kapraun, J. Ferrara, and C. J. Chang-Hasnain, “Flexible photonic metastructures for tunable coloration,” Optica 2(3), 255–258 (2015).
[Crossref]

Q. Fan, Y. Liu, C. Wang, Z. Yang, L. Wei, X. Zhu, C. Xie, Q. Zhang, F. Qian, Z. Yan, Y. Gu, W. Zhou, G. Jiang, and L. Cao, “Single-order diffraction grating designed by trapezoidal transmission function,” Opt. Lett. 40(11), 2657–2660 (2015).
[Crossref] [PubMed]

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15(3), 1615–1621 (2015).
[Crossref] [PubMed]

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (1)

2012 (2)

C. Xie, X. Zhu, H. Li, L. Shi, Y. Hua, and M. Liu, “Toward two-dimensional nanometer resolution hard X-ray differential-interference-contrast imaging using modified photon sieves,” Opt. Lett. 37(4), 749–751 (2012).
[Crossref] [PubMed]

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

2011 (2)

2010 (1)

2008 (3)

2007 (3)

F. M. Huang, N. I. Zheludev, Y. Chen, and F. J. G. Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(21), 091119 (2007).
[Crossref]

L. F. Pease, P. Deshpande, Y. Wang, W. B. Russel, and S. Y. Chou, “Self-formation of sub-60-nm half-pitch gratings with large areas through fracturing,” Nat. Nanotechnol. 2(9), 545–548 (2007).
[Crossref] [PubMed]

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

2001 (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

1995 (1)

Abajo, F. J. G.

F. M. Huang, N. I. Zheludev, Y. Chen, and F. J. G. Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(21), 091119 (2007).
[Crossref]

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Aydin, K.

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15(3), 1615–1621 (2015).
[Crossref] [PubMed]

Bernabeu, E.

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Butun, S.

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15(3), 1615–1621 (2015).
[Crossref] [PubMed]

Cao, L.

Cao, L. F.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

Chang-Hasnain, C. J.

Chen, Y.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole Array as a Lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

F. M. Huang, N. I. Zheludev, Y. Chen, and F. J. G. Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(21), 091119 (2007).
[Crossref]

Chou, S. Y.

L. F. Pease, P. Deshpande, Y. Wang, W. B. Russel, and S. Y. Chou, “Self-formation of sub-60-nm half-pitch gratings with large areas through fracturing,” Nat. Nanotechnol. 2(9), 545–548 (2007).
[Crossref] [PubMed]

Clausnitzer, T.

Cui, M. Q.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Deshpande, P.

L. F. Pease, P. Deshpande, Y. Wang, W. B. Russel, and S. Y. Chou, “Self-formation of sub-60-nm half-pitch gratings with large areas through fracturing,” Nat. Nanotechnol. 2(9), 545–548 (2007).
[Crossref] [PubMed]

Ding, Y.

Ding, Y. K.

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

Fan, Q.

Fan, W.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Fedotov, V. A.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole Array as a Lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

Ferrara, J.

Förster, E.

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

Fuhrmann, A.

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

Gao, N.

Gao, Y.

Gao, Y. L.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Garcia-Vidal, F. J.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

Gu, Y.

Gu, Y. Q.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Gupta, S.

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Hong, M.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

Hua, Y.

Huang, F. M.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole Array as a Lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

F. M. Huang, N. I. Zheludev, Y. Chen, and F. J. G. Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(21), 091119 (2007).
[Crossref]

Huang, K.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

Ishii, N.

Itatani, J.

Jiang, G.

Q. Fan, Y. Liu, C. Wang, Z. Yang, L. Wei, X. Zhu, C. Xie, Q. Zhang, F. Qian, Z. Yan, Y. Gu, W. Zhou, G. Jiang, and L. Cao, “Single-order diffraction grating designed by trapezoidal transmission function,” Opt. Lett. 40(11), 2657–2660 (2015).
[Crossref] [PubMed]

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Jiang, S.

Jin, G.

Jin, P.

Jin, Y.

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Kämpfe, T.

Kanai, T.

Kao, T. S.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole Array as a Lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

Kapraun, J.

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Kitamura, T.

Kley, E.-B.

Kobayashi, Y.

Kuang, L.

Kuang, L. Y.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

Kuramoto, Y.

Li, H.

Li, Q.

Li, X.

Li, Z.

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15(3), 1615–1621 (2015).
[Crossref] [PubMed]

Liu, H.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

Liu, M.

Liu, S.

Liu, S. Y.

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

Liu, T.

Liu, Y.

Luk’yanchuk, B.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

Palacios, E.

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15(3), 1615–1621 (2015).
[Crossref] [PubMed]

Parriaux, O.

Pease, L. F.

L. F. Pease, P. Deshpande, Y. Wang, W. B. Russel, and S. Y. Chou, “Self-formation of sub-60-nm half-pitch gratings with large areas through fracturing,” Nat. Nanotechnol. 2(9), 545–548 (2007).
[Crossref] [PubMed]

Qian, F.

Qiu, C.-W.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

Russel, W. B.

L. F. Pease, P. Deshpande, Y. Wang, W. B. Russel, and S. Y. Chou, “Self-formation of sub-60-nm half-pitch gratings with large areas through fracturing,” Nat. Nanotechnol. 2(9), 545–548 (2007).
[Crossref] [PubMed]

Sanchez-Brea, L. M.

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Seki, T.

Shi, L.

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Smith, R. E.

Sukegawa, T.

Tan, J.

Teng, J.

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

Tishchenko, A. V.

Torcal-Milla, F. J.

Tünnermann, A.

Vawter, G. A.

Wang, C.

Wang, C. K.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

Wang, Y.

L. F. Pease, P. Deshpande, Y. Wang, W. B. Russel, and S. Y. Chou, “Self-formation of sub-60-nm half-pitch gratings with large areas through fracturing,” Nat. Nanotechnol. 2(9), 545–548 (2007).
[Crossref] [PubMed]

Wang, Z.

Warren, M. E.

Watanabe, S.

Wei, L.

Q. Fan, Y. Liu, C. Wang, Z. Yang, L. Wei, X. Zhu, C. Xie, Q. Zhang, F. Qian, Z. Yan, Y. Gu, W. Zhou, G. Jiang, and L. Cao, “Single-order diffraction grating designed by trapezoidal transmission function,” Opt. Lett. 40(11), 2657–2660 (2015).
[Crossref] [PubMed]

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Wendt, J. R.

Wu, S.

Xie, C.

Xie, C. Q.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Yan, Z.

Yang, J.

Yang, Z.

Zhang, B. H.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Zhang, H.

Zhang, H. P.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Zhang, Q.

Zhang, W. H.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Zhao, Y. D.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Zhao, Z. Q.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Zheludev, N. I.

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole Array as a Lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

F. M. Huang, N. I. Zheludev, Y. Chen, and F. J. G. Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(21), 091119 (2007).
[Crossref]

Zheng, J.

Zhou, C.

Zhou, W.

Zhou, W. M.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Zhu, J.

Zhu, L.

Zhu, X.

Zhu, X. L.

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

Zhu, Z.

Appl. Phys. Lett. (3)

L. F. Cao, E. Förster, A. Fuhrmann, C. K. Wang, L. Y. Kuang, S. Y. Liu, and Y. K. Ding, “Single order x-ray diffraction with binary sinusoidal transmission grating,” Appl. Phys. Lett. 90(5), 053501 (2007).
[Crossref]

H. P. Zhang, C. K. Wang, Y. L. Gao, W. M. Zhou, L. Y. Kuang, L. Wei, W. Fan, W. H. Zhang, Z. Q. Zhao, L. F. Cao, Y. Q. Gu, B. H. Zhang, G. Jiang, X. L. Zhu, C. Q. Xie, Y. D. Zhao, and M. Q. Cui, “Elimination of higher-order diffraction using zigzag transmission grating in soft x-ray region,” Appl. Phys. Lett. 100(11), 111904 (2012).
[Crossref]

F. M. Huang, N. I. Zheludev, Y. Chen, and F. J. G. Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(21), 091119 (2007).
[Crossref]

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

Nano Lett. (2)

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15(3), 1615–1621 (2015).
[Crossref] [PubMed]

F. M. Huang, T. S. Kao, V. A. Fedotov, Y. Chen, and N. I. Zheludev, “Nanohole Array as a Lens,” Nano Lett. 8(8), 2469–2472 (2008).
[Crossref] [PubMed]

Nat. Commun. (1)

K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6, 7059 (2015).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

L. F. Pease, P. Deshpande, Y. Wang, W. B. Russel, and S. Y. Chou, “Self-formation of sub-60-nm half-pitch gratings with large areas through fracturing,” Nat. Nanotechnol. 2(9), 545–548 (2007).
[Crossref] [PubMed]

Nature (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (6)

Optica (1)

Other (5)

D. Attwood, Soft X-ray and Extreme Ultraviolet Radiation, Principles and Applications (Cambridge University Press, 1999), p. 55.

C. Palmer, Diffraction Grating Handbook (Richardson Grating Laboratory, 2005).

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

M. Born and E. Wolf, Principle of Optics (Pergamon, 1980).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a) The quasi-triangle array of circular holes: each hole shifts sfrom the lattice points along the ξ axis according to the probability distribution ρ(s) . (b) The coordinate systems of the grating plane and the diffraction plane.

Fig. 2
Fig. 2

(a) The dependence of the 2nd order diffraction intensity on r/ P ξ and a/ P ξ . The dash lines denote the 2nd order diffraction disappears. (b) Same as (a), except for the 3rd order diffraction.

Fig. 3
Fig. 3

(a) The far-field diffraction intensity pattern of the quasi-triangle array of circular holes. (b) The diffraction intensity along the x axis. Insets: the 0th and 1st order diffractions.

Fig. 4
Fig. 4

(a) The far-field diffraction intensity pattern of the quasi-triangle array of 90601 circular holes. (b) The diffraction intensity along the x axis. Insets: the 0th and 1st order diffractions.

Fig. 5
Fig. 5

Experimental setup for the optical measurement. Inset: Microphotograph of the fabricated quasi-triangle array of circular holes.

Fig. 6
Fig. 6

(a) The far-field diffraction intensity pattern of the quasi-triangle array of circular holes. (b) The diffraction intensity along the ξ.

Fig. 7
Fig. 7

The 2nd, 3rd, 4th and 5th order diffraction intensities versus the hole diameter.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I(p,q)= I 0 [ 2 J 1 (kr p 2 + q 2 ) kr p 2 + q 2 ] 2 | m=1 N ξ n=1 N η e ik(p ξ m,n +q η m,n ) | 2 = I 0 [ 2 J 1 (kr p 2 + q 2 ) kr p 2 + q 2 ] 2 | a a ( 1 2a ) 2 m=1 N ξ n=1 N η e ik(pm P ξ +ps+qnPη) ds | 2 = I 0 [ 2 J 1 (kr p 2 + q 2 ) kr p 2 + q 2 ] 2 sin c 2 (kpa/π) [ sin( N ξ /2kp P ξ /2) N ξ /2sin(kp P ξ /2) ] 2 [ sin( N η kq P η /2) N η sin(kp P η /2) ] 2 cos 2 (kp P ξ /4+kq P η /4).
I(p)= I 0 [ sin(kp P ξ N ξ /4) N ξ sin(kp P ξ /4) ] 2 [ 2 J 1 (kpr) kpr ] 2 sinc 2 (kpa/π).
I(m)= I 0 [ 2 J 1 (2πmr/ P ξ ) 2πmr/ P ξ ] 2 sin c 2 (2ma/ P ξ ).
I αβ (m)={ I(m)(1+ (S1) 2 α 2 +2(S1)αcosβ), for m=0, I(m)(1+ α 2 2αcosβ), for m0.

Metrics