High order diffraction suppression by quasi-periodic two-dimensional gratings

Jiebin Niu; Lina Shi; Ziwei Liu; Tanchao Pu; Hailiang Li; Guanya Wang; Changqing Xie

doi:10.1364/OME.7.000366

High order diffraction suppression by quasi-periodic two-dimensional gratings

Jiebin Niu, Lina Shi, Ziwei Liu, Tanchao Pu, Hailiang Li, Guanya Wang, and Changqing Xie

Optical Materials Express
Vol. 7,
Issue 2,
pp. 366-375
(2017)
•https://doi.org/10.1364/OME.7.000366

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Jiebin Niu, Lina Shi, Ziwei Liu, Tanchao Pu, Hailiang Li, Guanya Wang, and Changqing Xie, "High order diffraction suppression by quasi-periodic two-dimensional gratings," Opt. Mater. Express 7, 366-375 (2017)

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Related Topics
Table of Contents Category
- Diffraction and Gratings
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Binary optics (050.1380)
- Diffraction gratings (050.1950)
- Optical design and fabrication (220.0220)
- Spectroscopy, high-resolution (300.6320)

About this Article
History
- Original Manuscript: November 30, 2016
- Revised Manuscript: January 1, 2017
- Manuscript Accepted: January 4, 2017
- Published: January 6, 2017

Accessible

Open Access

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.

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References

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Year
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[Crossref] [PubMed]
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[Crossref]

2016 (1)

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]

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]

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)

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]

N. Gao and C. Xie, “High-order diffraction suppression using modulated groove position gratings,” Opt. Lett. 36(21), 4251–4253 (2011).
[Crossref] [PubMed]

2010 (1)

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]

2008 (3)

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]

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]

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]

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)

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]

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.

Aydin, K.

Bernabeu, E.

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]

Berndt, R.

Butun, S.

Cao, L.

Cao, L. F.

Chang-Hasnain, C. J.

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

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.

Clausnitzer, T.

Cui, M. Q.

Deshpande, P.

Ding, Y.

Ding, Y. K.

Fan, Q.

Fan, W.

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.

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

Förster, E.

Fuhrmann, A.

Gao, N.

N. Gao and C. Xie, “High-order diffraction suppression using modulated groove position gratings,” Opt. Lett. 36(21), 4251–4253 (2011).
[Crossref] [PubMed]

Gao, Y.

Gao, Y. L.

Garcia-Vidal, F. J.

Gu, Y.

Gu, Y. Q.

Gupta, S.

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]

Harm, S.

Hong, M.

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.

Ishii, N.

Itatani, J.

Jiang, G.

Jiang, S.

Jin, G.

Jin, P.

Jin, Y.

Johnson, R. L.

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.

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

Kipp, L.

Kitamura, T.

Kley, E.-B.

Kobayashi, Y.

Kuang, L.

Kuang, L. Y.

Kuramoto, Y.

Li, H.

Li, Q.

Li, X.

Li, Z.

Liu, H.

Liu, M.

Liu, S.

Liu, S. Y.

Liu, T.

Liu, Y.

Luk’yanchuk, B.

Palacios, E.

Parriaux, O.

Pease, L. F.

Qian, F.

Qiu, C.-W.

Russel, W. B.

Sanchez-Brea, L. M.

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]

Seemann, R.

Seki, T.

Shi, L.

Skibowski, M.

Smith, R. E.

Sukegawa, T.

Tan, J.

Teng, J.

Tishchenko, A. V.

Torcal-Milla, F. J.

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]

Tünnermann, A.

Vawter, G. A.

Wang, C.

Wang, C. K.

Wang, Y.

Wang, Z.

Warren, M. E.

Watanabe, S.

Wei, L.

Wendt, J. R.

Wu, S.

Xie, C.

N. Gao and C. Xie, “High-order diffraction suppression using modulated groove position gratings,” Opt. Lett. 36(21), 4251–4253 (2011).
[Crossref] [PubMed]

Xie, C. Q.

Yan, Z.

Yang, J.

Yang, Z.

Zhang, B. H.

Zhang, H.

Zhang, H. P.

Zhang, Q.

Zhang, W. H.

Zhao, Y. D.

Zhao, Z. Q.

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.

Zhu, J.

Zhu, L.

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

Zhu, X.

Zhu, X. L.

Zhu, Z.

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(21), 091119 (2007).
[Crossref]

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

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]

Nano Lett. (2)

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)

Nat. Nanotechnol. (1)

Nature (1)

Opt. Express (4)

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]

Opt. Lett. (6)

N. Gao and C. Xie, “High-order diffraction suppression using modulated groove position gratings,” Opt. Lett. 36(21), 4251–4253 (2011).
[Crossref] [PubMed]

Optica (1)

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

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).

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Fig. 1 (a) The quasi-triangle array of circular holes: each hole shifts

s

from 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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

Fig. 5 Experimental setup for the optical measurement. Inset: Microphotograph of the fabricated quasi-triangle array of circular holes.

Download Full Size | PPT Slide | PDF

Fig. 6 (a) The far-field diffraction intensity pattern of the quasi-triangle array of circular holes. (b) The diffraction intensity along the

ξ

Download Full Size | PPT Slide | PDF

Fig. 7 The 2nd, 3rd, 4th and 5th order diffraction intensities versus the hole diameter.

Download Full Size | PPT Slide | PDF

Equations (4)

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

\begin{array}{l} I (p, q) = I_{0} \cdot {[\frac{2 J_{1} (k r \sqrt{p^{2} + q^{2}})}{k r \sqrt{p^{2} + q^{2}}}]}^{2} \cdot {| \sum_{m = 1}^{N_{ξ}} \sum_{n = 1}^{N_{η}} e^{- i k (p ξ_{m, n} + q η_{m, n})} |}^{2} \\ = I_{0} \cdot {[\frac{2 J_{1} (k r \sqrt{p^{2} + q^{2}})}{k r \sqrt{p^{2} + q^{2}}}]}^{2} \cdot {| \int_{- a}^{a} {(\frac{1}{2 a})}^{2} \sum_{m = 1}^{N_{ξ}} \sum_{n = 1}^{N_{η}} e^{- i k (p m P_{ξ} + p s + q n P η)} d s |}^{2} \\ = I_{0} \cdot {[\frac{2 J_{1} (k r \sqrt{p^{2} + q^{2}})}{k r \sqrt{p^{2} + q^{2}}}]}^{2} \cdot \sin c^{2} (k p a / π) \\ \begin{matrix}  \end{matrix} \cdot {[\frac{\sin (N_{ξ} / 2 \cdot k p P_{ξ} / 2)}{N_{ξ} / 2 \cdot \sin (k p P_{ξ} / 2)}]}^{2} \cdot {[\frac{\sin (N_{η} \cdot k q P_{η} / 2)}{N_{η} \cdot \sin (k p P_{η} / 2)}]}^{2} \cdot \cos^{2} (k p P_{ξ} / 4 + k q P_{η} / 4) . \end{array}

I (p) = I_{0} \cdot {[\frac{\sin (k p P_{ξ} N_{ξ} / 4)}{N_{ξ} \cdot \sin (k p P_{ξ} / 4)}]}^{2} \cdot {[\frac{2 J_{1} (k p r)}{k p r}]}^{2} \cdot {sinc}^{2} (k p a / π) .

I (m) = I_{0} \cdot {[\frac{2 J_{1} (2 π m r / P_{ξ})}{2 π m r / P_{ξ}}]}^{2} \cdot \sin c^{2} (2 m a / P_{ξ}) .

I_{α β} (m) = {\begin{matrix} \begin{matrix} I (m) \cdot (1 + {(S - 1)}^{2} \cdot α^{2} + 2 (S - 1) \cdot α \cdot \cos β), & f o r & m = 0, \end{matrix} \\ \begin{matrix} I (m) \cdot (1 + α^{2} - 2 \cdot α \cdot \cos β), & f o r & m \neq 0. \end{matrix} \end{matrix}

Abstract

References

2016 (1)

2015 (4)

2014 (1)

2013 (1)

2012 (2)

2011 (2)

2010 (1)

2008 (3)

2007 (3)

2001 (1)

1995 (1)

Abajo, F. J. G.

Adelung, R.

Aydin, K.

Bernabeu, E.

Berndt, R.

Butun, S.

Cao, L.

Cao, L. F.

Chang-Hasnain, C. J.

Chen, Y.

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