Abstract

In this paper, we propose a compact seven-port beam splitter which is constructed using only a single-layer high-density grating with a dual duty cycle structure. The properties of this grating are investigated by a simplified modal method. The diffraction efficiency can be achieved around 10% more than conventional Dammann gratings while the uniformity can still be maintained at less than 1%. The effect of deviations from the design parameters on the performance of the grating is also presented.

© 2011 Optical Society of America

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  1. H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
    [CrossRef]
  2. U. Killat, G. Rabe, and W. Rave, “Binary phase grating for star couples with a high splitting ratio,” Fiber Integrat. Opt. 4, 159–167 (1982).
    [CrossRef]
  3. M. G. MoharamT. K. Gaylord, “Diffraction analysis of dielectric surface relief gratings,” J. Opt. Soc. Am. 72, 1385–1392(1982).
    [CrossRef]
  4. J. Turunen, A. Vasara, J. Westerholm, and A. Salin, “Stripegeometry two dimensional Dammann gratings,” Opt. Commun. 74, 245–252 (1989).
    [CrossRef]
  5. R. L. Morrison, “Symmetries that simplify the design of spot-array phase gratings,” J. Opt. Soc. Am. A 9, 464–471 (1992).
    [CrossRef]
  6. A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, and S. Kuisma, “Binary surface-relief gratings for array illuminators in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
    [CrossRef] [PubMed]
  7. G. Li, C. Zhou, and E. Dai, “Splitting of femtosecond laser pulses by using a Dammann grating and compensation gratings,” J. Opt. Soc. Am. A 22, 767–772 (2005).
    [CrossRef]
  8. F. J. Wen and P. S. Chung, “Two-dimensional optical splitters with polymer optical fibre arrays,” J. Opt. A: Pure Appl. Opt. 9, 723–727 (2007).
    [CrossRef]
  9. M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4453–4458 (1992).
    [CrossRef] [PubMed]
  10. D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Subwavelength transmission grating retarders for use at 10.6 μm,” Appl. Opt. 35, 6195–6202 (1996).
    [CrossRef] [PubMed]
  11. F. Nikolajeff, B. Löfving, M. Johansson, J. Bengtsson, S. Hård, and C. Heine, “Fabrication and simulation of diffractive optical elements with superimposed antireflection subwavelength gratings,” Appl. Opt. 39, 4842–4846 (2000).
    [CrossRef]
  12. J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt. 42, 3234–3240 (2003).
    [CrossRef] [PubMed]
  13. T. Oonishi, T. Konishi, and K. Itoh, “Deterministic design of binary phase-only blazed grating with subwavelength features under limitation on spatial resolution of fabrication technique,” Appl. Opt. 46, 5019–5026 (2007).
    [CrossRef] [PubMed]
  14. 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] [PubMed]
  15. H. K. Khanfar and R. M. A. Azzam, “Broadband IR polarizing beam splitter using a subwavelength-structured one-dimensional photonic-crystal layer embedded in a high-index prism,” Appl. Opt. 48, 5121–5126 (2009).
    [CrossRef] [PubMed]
  16. L. 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]
  17. 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).
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    [CrossRef]
  19. 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]
  20. 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] [PubMed]
  21. Q. Bi, J. Zheng, M. Sun, F. Zhang, X. Xie, and Z. Lin, “Design of rectangular-groove fused-silica gratings as polarizing beam splitters,” Opt. Express 18, 11969–11978 (2010).
    [CrossRef] [PubMed]
  22. H. Cao, C. Zhou, J. Feng, P. Lu, and J. Ma, “Design and fabrication of a polarization-independent wideband transmission fused-silica grating,” Appl. Opt. 49, 4108–4112(2010).
    [CrossRef] [PubMed]
  23. J. Feng, C. Zhou, H. Cao, and P. Lv, “Deep-etched sinusoidal polarizing beam splitter grating,” Appl. Opt. 49, 1739–1743(2010).
    [CrossRef] [PubMed]
  24. J. F. Wen and P. S. Chung, “Design of high density diffraction grating,” 2010 15th Optolectronics and Communications Conference (IEEE, 2010), pp. 400–401.
  25. C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
    [CrossRef] [PubMed]

2010 (3)

2009 (3)

2008 (1)

2007 (3)

2005 (2)

2003 (1)

2000 (1)

1996 (1)

1995 (1)

1992 (3)

1989 (1)

J. Turunen, A. Vasara, J. Westerholm, and A. Salin, “Stripegeometry two dimensional Dammann gratings,” Opt. Commun. 74, 245–252 (1989).
[CrossRef]

1982 (2)

U. Killat, G. Rabe, and W. Rave, “Binary phase grating for star couples with a high splitting ratio,” Fiber Integrat. Opt. 4, 159–167 (1982).
[CrossRef]

M. G. MoharamT. K. Gaylord, “Diffraction analysis of dielectric surface relief gratings,” J. Opt. Soc. Am. 72, 1385–1392(1982).
[CrossRef]

1981 (1)

L. 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]

1977 (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Adams, J. L.

L. 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]

Andrewartha, J. R.

L. 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]

Azzam, R. M. A.

Bengtsson, J.

Bi, Q.

Botten, L. C.

L. 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]

Brundrett, D. L.

Cao, H.

Chung, P. S.

F. J. Wen and P. S. Chung, “Two-dimensional optical splitters with polymer optical fibre arrays,” J. Opt. A: Pure Appl. Opt. 9, 723–727 (2007).
[CrossRef]

J. F. Wen and P. S. Chung, “Design of high density diffraction grating,” 2010 15th Optolectronics and Communications Conference (IEEE, 2010), pp. 400–401.

Clausnitzer, T.

Craig, M. S.

L. 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]

Dai, E.

Dammann, H.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Evans, M. S.

Farmiga, N. O.

Farn, M. W.

Feng, J.

Forsberg, E.

Gaylord, T. K.

Glytsis, E. N.

Han, Z.

Hård, S.

He, S.

Heine, C.

Hirsh, J. I.

Ichikawa, H.

Itoh, K.

Jaakkola, T.

Johansson, M.

Kämpfe, T.

Khanfar, H. K.

Killat, U.

U. Killat, G. Rabe, and W. Rave, “Binary phase grating for star couples with a high splitting ratio,” Fiber Integrat. Opt. 4, 159–167 (1982).
[CrossRef]

Kley, E.-B.

Klotz, E.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Konishi, T.

Kuisma, S.

Li, G.

Lin, Z.

Liu, L.

Löfving, B.

Lu, P.

Lv, P.

Ma, J.

Marciante, J. R.

McPhedran, R. C.

L. 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]

Miller, J. M.

Moharam, M. G.

Morrison, R. L.

Nikolajeff, F.

Noponen, E.

Oonishi, T.

Parriaux, O.

Peschel, U.

Rabe, G.

U. Killat, G. Rabe, and W. Rave, “Binary phase grating for star couples with a high splitting ratio,” Fiber Integrat. Opt. 4, 159–167 (1982).
[CrossRef]

Rave, W.

U. Killat, G. Rabe, and W. Rave, “Binary phase grating for star couples with a high splitting ratio,” Fiber Integrat. Opt. 4, 159–167 (1982).
[CrossRef]

Salin, A.

J. Turunen, A. Vasara, J. Westerholm, and A. Salin, “Stripegeometry two dimensional Dammann gratings,” Opt. Commun. 74, 245–252 (1989).
[CrossRef]

Shen, S.

Sun, M.

Ta, H. T.

Taghizadeh, M. R.

Tishchenko, A. V.

Tünnermann, A.

Turunen, J.

Vasara, A.

Wang, B.

Wen, F. J.

F. J. Wen and P. S. Chung, “Two-dimensional optical splitters with polymer optical fibre arrays,” J. Opt. A: Pure Appl. Opt. 9, 723–727 (2007).
[CrossRef]

Wen, J. F.

J. F. Wen and P. S. Chung, “Design of high density diffraction grating,” 2010 15th Optolectronics and Communications Conference (IEEE, 2010), pp. 400–401.

Westerholm, J.

Xie, X.

Zhang, F.

Zheng, J.

Zhou, C.

Appl. Opt. (12)

M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31, 4453–4458 (1992).
[CrossRef] [PubMed]

D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Subwavelength transmission grating retarders for use at 10.6 μm,” Appl. Opt. 35, 6195–6202 (1996).
[CrossRef] [PubMed]

F. Nikolajeff, B. Löfving, M. Johansson, J. Bengtsson, S. Hård, and C. Heine, “Fabrication and simulation of diffractive optical elements with superimposed antireflection subwavelength gratings,” Appl. Opt. 39, 4842–4846 (2000).
[CrossRef]

J. R. Marciante, N. O. Farmiga, J. I. Hirsh, M. S. Evans, and H. T. Ta, “Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features,” Appl. Opt. 42, 3234–3240 (2003).
[CrossRef] [PubMed]

T. Oonishi, T. Konishi, and K. Itoh, “Deterministic design of binary phase-only blazed grating with subwavelength features under limitation on spatial resolution of fabrication technique,” Appl. Opt. 46, 5019–5026 (2007).
[CrossRef] [PubMed]

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] [PubMed]

H. K. Khanfar and R. M. A. Azzam, “Broadband IR polarizing beam splitter using a subwavelength-structured one-dimensional photonic-crystal layer embedded in a high-index prism,” Appl. Opt. 48, 5121–5126 (2009).
[CrossRef] [PubMed]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, and S. Kuisma, “Binary surface-relief gratings for array illuminators in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[CrossRef] [PubMed]

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] [PubMed]

H. Cao, C. Zhou, J. Feng, P. Lu, and J. Ma, “Design and fabrication of a polarization-independent wideband transmission fused-silica grating,” Appl. Opt. 49, 4108–4112(2010).
[CrossRef] [PubMed]

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

C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
[CrossRef] [PubMed]

Fiber Integrat. Opt. (1)

U. Killat, G. Rabe, and W. Rave, “Binary phase grating for star couples with a high splitting ratio,” Fiber Integrat. Opt. 4, 159–167 (1982).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

F. J. Wen and P. S. Chung, “Two-dimensional optical splitters with polymer optical fibre arrays,” J. Opt. A: Pure Appl. Opt. 9, 723–727 (2007).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Acta (2)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

L. 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. (1)

J. Turunen, A. Vasara, J. Westerholm, and A. Salin, “Stripegeometry two dimensional Dammann gratings,” Opt. Commun. 74, 245–252 (1989).
[CrossRef]

Opt. Express (2)

Other (1)

J. F. Wen and P. S. Chung, “Design of high density diffraction grating,” 2010 15th Optolectronics and Communications Conference (IEEE, 2010), pp. 400–401.

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Figures (4)

Fig. 1
Fig. 1

Schematic of a low-contrast grating.

Fig. 2
Fig. 2

Diffraction efficiency of the seven-port beam splitter.

Fig. 3
Fig. 3

(a) Actual profile and (b) output diffracted spots.

Fig. 4
Fig. 4

Comparisons between theoretical and practical results.

Equations (6)

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2 E x 2 + 2 E z 2 + k i 2 E y ( x , z ) = 0.
θ ( x ) = { cos β x 0 < x a 1 θ ( a 1 ) cos [ γ ( x a 1 ) ] β 2 γ φ ( a 1 ) sin [ γ ( x a 1 ) ] a 1 < x a 2 θ ( a 2 ) cos [ β ( x a 2 ) ] ( γ β θ ( a 1 ) sin [ γ ( a 2 a 1 ) ] + β φ ( a 1 ) cos [ γ ( a 2 a 1 ) ] ) sin [ β ( x a 2 ) ] a 2 < x a 3 θ ( a 3 ) cos [ γ ( x a 3 ) ] ( β γ θ ( a 2 ) sin [ β ( a 3 a 2 ) ] + θ ( a 1 ) sin [ γ ( a 2 a 1 ) ] cos [ β ( a 3 a 2 ) ] + β 2 γ φ ( a 1 ) cos [ γ ( a 2 a 1 ) ] cos [ β ( a 3 a 2 ) ] ) sin [ γ ( x a 3 ) ] a 3 < x d ,
φ ( x ) = { 1 β sin β x 0 < x a 1 φ ( a 1 ) cos [ γ ( x a 1 ) ] + 1 γ θ ( a 1 ) sin [ γ ( x a 1 ) ] a 1 < x a 2 φ ( a 2 ) cos [ β ( x a 2 ) ] ( γ β φ ( a 1 ) sin [ γ ( a 2 a 1 ) ] 1 β θ ( a 1 ) cos [ γ ( a 2 a 1 ) ] ) sin [ β ( x a 2 ) ] a 2 < x a 3 φ ( a 3 ) cos [ γ ( x a 3 ) ] ( β γ φ ( a 2 ) sin [ β ( a 3 a 2 ) ] + φ ( a 1 ) sin [ γ ( a 2 a 1 ) ] cos [ β ( a 3 a 2 ) ] 1 γ θ ( a 1 ) cos [ γ ( a 2 a 1 ) ] cos [ β ( a 3 a 2 ) ] ) sin [ γ ( x a 3 ) ] a 3 < x d .
τ A = A θ ( d ) + B ψ ( d ) τ B = A θ ( d ) + B ψ ( d ) [ θ ( d ) τ ] [ ψ ( d ) τ ] θ ( d ) ψ ( d ) = 0 τ [ θ ( d ) + ψ ( d ) ] = 1 + τ 2 ( θ ( d ) ψ ( d ) θ ( d ) ψ ( d ) = 1 ) θ ( d ) + ψ ( d ) = | 1 + τ 2 τ | = 2 cos ( α 0 d )
| E n ( x ) | = | 1 d 0 d A n d x | 2 = | 1 d 0 d exp ( j n k x x ) i = 1 N t i n i U i ( x ) exp ( j k n i eff h ) d x | 2 .
U n ( x ) U n 1 ( x ) = 0 d U n ( x ) U n 1 ( x ) d x 0 d | U n ( x ) | 2 d x 0 d | U n 1 ( x ) | 2 d x ,

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