Abstract

We propose two-dimensional gratings comprised of a large number of identical and similarly oriented hexagonal holes for the high order diffraction suppression. An analytical study of the diffraction property for such gratings, based on both square and triangle arrays, is described. The dependence of the high order diffraction property on the hole shape and size is investigated. Notably, theoretical calculation reveals that the 2nd, 3rd and 4th order diffractions adjacent to the 1st order diffraction can be completely suppressed, and the 5th order diffraction efficiency is as low as 0.01%, which will be submerged in the background noise for most practical applications. The 1st order diffraction intensity efficiency 6.93% can be achieved as the hexagonal holes along y-axis connect with each other. For the case of b=Py/3, the 1st order diffraction intensity efficiency is 3.08%. The experimental results are also presented, confirming the theoretical predictions. Especially, our two-dimensional gratings have the ability to form free-standing structures which are highly desired for the x-ray region. Comparing with the grating of the square array, the grating of the triangle array is easy to be fabricated by silicon planar process due to the large spacing between any two adjacent holes. Our results should be of great interest in a wide spectrum unscrambling from the infrared to the x-ray region.

© 2017 Optical Society of America

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2016 (1)

2015 (4)

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]

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[Crossref]

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)

H. P. Zang, 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]

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]

2011 (2)

2010 (3)

2008 (4)

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(9), 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]

2005 (1)

R. L. C. Filho, M. G. P. Homem, R. Landers, and A. N. de Brito, “Advances on the Brazilian toroidal grating monochromator (TGM) beamline,” J. Electron Spectrosc. Relat. Phenom. 144–147, 1125–1127 (2005).
[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)

1989 (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(9), 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]

Cambril, E.

Cao, L.

Cao, L. F.

H. P. Zang, 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(9), 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.

Collin, S.

Cui, M. Q.

H. P. Zang, 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]

de Brito, A. N.

R. L. C. Filho, M. G. P. Homem, R. Landers, and A. N. de Brito, “Advances on the Brazilian toroidal grating monochromator (TGM) beamline,” J. Electron Spectrosc. Relat. Phenom. 144–147, 1125–1127 (2005).
[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. Zang, 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.

Filho, R. L. C.

R. L. C. Filho, M. G. P. Homem, R. Landers, and A. N. de Brito, “Advances on the Brazilian toroidal grating monochromator (TGM) beamline,” J. Electron Spectrosc. Relat. Phenom. 144–147, 1125–1127 (2005).
[Crossref]

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]

Fu, S.

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. Zang, 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. Zang, 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]

Guérineau, N.

Gupta, S.

Haidar, R.

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]

He, S.

Homem, M. G. P.

R. L. C. Filho, M. G. P. Homem, R. Landers, and A. N. de Brito, “Advances on the Brazilian toroidal grating monochromator (TGM) beamline,” J. Electron Spectrosc. Relat. Phenom. 144–147, 1125–1127 (2005).
[Crossref]

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(9), 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]

Huo, T.

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. Zang, 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. Zang, 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.

Landers, R.

R. L. C. Filho, M. G. P. Homem, R. Landers, and A. N. de Brito, “Advances on the Brazilian toroidal grating monochromator (TGM) beamline,” J. Electron Spectrosc. Relat. Phenom. 144–147, 1125–1127 (2005).
[Crossref]

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]

Meekins, J. F.

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]

Pelouard, J.-L.

Primot, J.

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]

Qiu, K.

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.

Vincent, G.

Wang, C.

Wang, C. K.

H. P. Zang, 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.

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 keV using compound photon sieves,” Opt. Lett. 35(23), 4048–4050 (2010).
[Crossref] [PubMed]

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. Zang, 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. Zang, 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.

Zang, H. P.

H. P. Zang, 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, B. H.

H. P. Zang, 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, Q.

Zhang, W. H.

H. P. Zang, 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. Zang, 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. Zang, 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(9), 091119 (2007).
[Crossref]

Zheng, J.

Zhou, C.

Zhou, H.

Zhou, W.

Zhou, W. M.

H. P. Zang, 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. Zang, 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. Opt. (1)

Appl. Phys. Lett. (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(9), 091119 (2007).
[Crossref]

H. P. Zang, 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]

Chin. Opt. Lett. (1)

J. Electron Spectrosc. Relat. Phenom. (1)

R. L. C. Filho, M. G. P. Homem, R. Landers, and A. N. de Brito, “Advances on the Brazilian toroidal grating monochromator (TGM) beamline,” J. Electron Spectrosc. Relat. Phenom. 144–147, 1125–1127 (2005).
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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]

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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]

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[Crossref] [PubMed]

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 keV using compound photon sieves,” Opt. Lett. 35(23), 4048–4050 (2010).
[Crossref] [PubMed]

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Other (1)

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Figures (7)

Fig. 1
Fig. 1 The two-dimensional gratings comprised of hexagonal holes. The side of the hexagonal hole along the x axis is 2 a 1 , the diagonal along the x axis is 2 a and the height along the y axis is 2 b . (a) The square array with periods P x and P y . (b) The triangle array with periods 2 P x and P y . (c) The coordinate systems of the grating plane and the diffraction plane.
Fig. 2
Fig. 2 The dependence of the m-th order diffraction intensity on a , a 1 and P x . The white dash line denotes the m-th order diffraction intensity vanishes: the 2nd order diffraction (a), the 3rd order diffraction (b), and the 4th order diffraction (c).
Fig. 3
Fig. 3 (a) The far-field diffraction intensity pattern of the square array of hexagonal holes. (b) The same as (a) except for the triangle array. (c) The intensity distribution of the 0th and 1st order diffractions of the square array of hexagonal holes. (d) The same as (c) except for the triangle array. (e) Blue curve: the diffraction intensity along the ξ axis of the square array of hexagonal holes. Red curve: the diffraction patterns of 1:1 transmission gratings. (f) The same as (c) except for the triangle array.
Fig. 4
Fig. 4 The absolute diffraction efficiencies of the 2nd, 3rd, and 4th order diffractions versus the deviation D 1 .
Fig. 5
Fig. 5 (a) The fabricated hexagonal hole. (b) The simulated hexagonal hole. (c) The round corner 1 of hexagonal hole. (d) The round corner 2 of hexagonal hole. (e) The absolute diffraction efficiencies of the 2nd, 3rd, and 4th order diffractions versus the deviation D 2 .
Fig. 6
Fig. 6 (a) Microphotograph of the fabricated two-dimensional grating with the square array of hexagonal holes. (b) The same as (a) except for the triangle array. (c) Experimental setup for the optical measurement.
Fig. 7
Fig. 7 (a) The far-field diffraction intensity pattern of the square array of hexagonal holes. (b) The same as (a) except for the triangle array. (c) The intensity distribution of the 0th and 1st order diffractions of the square array of hexagonal holes. (d) The same as (c) except for the triangle array. (e) The diffraction intensity along the ξ axis for the square array. (f) The same as (c) except for the triangle array.

Equations (10)

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U ( p , q ) = C N e i k ( p x n + q y n ) Α e i k ( p x ' + q y ' ) d x ' d y ' .
I ( p , q ) = U ( p , q ) U * ( p , q ) = I 0 sin 2 ( N x k p P x / 2 ) N x 2 sin 2 ( k p P x / 2 ) sin 2 ( N y k q P y / 2 ) N y 2 sin 2 ( k q P y / 2 ) | cos ( k p a 1 k q b ) cos k p a k p ( a + a 1 ) ( k p ( a a 1 ) + k q b ) + cos k p a cos ( k p a 1 + k q b ) k p ( a + a 1 ) ( k p ( a a 1 ) + k q b ) | 2 .
I ( p , q ) = U ( p , q ) U * ( p , q ) = I 0 sin 2 ( N x / 2 k p 2 P x / 2 ) ( N x / 2 ) 2 sin 2 ( k p 2 P x / 2 ) sin 2 ( N y k q P y / 2 ) N y 2 sin 2 ( k q P y / 2 ) cos 2 ( k p P x 2 + k q P y 4 ) | cos ( k p a 1 k q b ) cos k p a k p ( a + a 1 ) ( k p ( a a 1 ) + k q b ) + cos k p a cos ( k p a 1 + k q b ) k p ( a + a 1 ) ( k p ( a a 1 ) + k q b ) | 2 .
I ( p ) = I 0 sin 2 ( N x k p P x / 2 ) N x 2 sin 2 ( k p P x / 2 ) ( sin ( k p ( a + a 1 ) / 2 ) sin ( k p ( a a 1 ) / 2 ) k p ( a + a 1 ) / 2 k p ( a a 1 ) / 2 ) 2 .
t ( x ) = { 2 b , | x | a 1 , 2 b ( a x ) a a 1 , a 1 < | x | a , 0 , a | x | P x / 2.
I ( p ) = | U ( P ) | 2 = 1 cos N x k p P x 1 cos k p P x | C a a t ( x ) e i k p x d x | 2 = C 2 ( N x 2 ( a + a 1 ) b ) 2 sin 2 ( N x k p P x / 2 ) N x 2 sin 2 ( k p P x / 2 ) ( sin ( k p ( a + a 1 ) / 2 ) k p ( a + a 1 ) / 2 sin ( k p ( a a 1 ) / 2 ) k p ( a a 1 ) / 2 ) 2 .
I ( m ) = I 0 ( sin ( m ( a + a 1 ) π / P x ) sin ( m ( a a 1 ) π / P x ) m ( a + a 1 ) π / P x m ( a a 1 ) π / P x ) 2 .
a + a 1 = n m P x or | a a 1 | = n m P x , n = 1 , 2 , 3 , ...
I ( n ) = I 0 ( 2 a 1 a + a 1 sin ( 2 n π b / P y ) 2 n π b / P y + a a 1 a + a 1 ( sin ( 2 n π b / 2 / P y ) 2 n π b / 2 / P y ) 2 ) 2 = I 0 ( 1 3 sin ( 2 n π b / P y ) 2 n π b / P y + 2 3 ( sin ( n π b / P y ) n π b / P y ) 2 ) 2 .
I ( 1 2 , n ) = I 0 cos 2 ( n π / 2 ) | cos ( π a 1 / P x 2 n π b / P y ) cos ( π a / P x ) π ( a + a 1 ) / P x ( π ( a a 1 ) / P x + 2 n π b / P y ) + cos ( π a / P x ) cos ( π a 1 / P x + 2 n π b / P y ) π ( a + a 1 ) / P x ( π ( a a 1 ) / P x + 2 n π b / P y ) | 2 .

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