Abstract

A quasi-Dammann grating is proposed to generate array spots with proportional-intensity orders in the far field. To describe the performance of the grating, the uniformities of the array spots are redefined. A two-dimensional even-sampling encode scheme is adopted to design the quasi-Dammann grating. Numerical solutions of the binary-phase quasi-Dammann grating with proportional-intensity orders are given. The experimental results with a third-order quasi-Dammann grating, which has an intensity proportion of 3:2:1 from zero order to second order, are presented.

© 2008 Optical Society of America

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References

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    [CrossRef]

2006 (1)

2005 (2)

Y. Chen, C. H. Gan, L. X. Wang, and G. Yu, Appl. Surf. Sci. 245, 316 (2005).
[CrossRef]

J. W. Sung, H. Hockel, and E. G. Johnson, Opt. Lett. 30, 150 (2005).
[CrossRef] [PubMed]

2003 (1)

1996 (1)

M. B. Stern, Microelectron. Eng. 32, 369 (1996).
[CrossRef]

1995 (1)

S. Teiwes, B. Schillinger, and T. Beth, Proc. SPIE 2404, 40 (1995).
[CrossRef]

1994 (1)

1992 (1)

1971 (1)

H. Dammann and K. Gőrter, Opt. Commun. 3, 312 (1971).
[CrossRef]

Beth, T.

S. Teiwes, B. Schillinger, and T. Beth, Proc. SPIE 2404, 40 (1995).
[CrossRef]

Chen, Y.

Y. Chen, C. H. Gan, L. X. Wang, and G. Yu, Appl. Surf. Sci. 245, 316 (2005).
[CrossRef]

Dammann, H.

H. Dammann and K. Gőrter, Opt. Commun. 3, 312 (1971).
[CrossRef]

Gan, C. H.

Y. Chen, C. H. Gan, L. X. Wang, and G. Yu, Appl. Surf. Sci. 245, 316 (2005).
[CrossRef]

Gorter, K.

H. Dammann and K. Gőrter, Opt. Commun. 3, 312 (1971).
[CrossRef]

Hockel, H.

Itoh, M.

Jia, J.

Johnson, E. G.

Liu, L. R.

Schillinger, B.

S. Teiwes, B. Schillinger, and T. Beth, Proc. SPIE 2404, 40 (1995).
[CrossRef]

Sheun Chung, P.

Stern, M. B.

M. B. Stern, Microelectron. Eng. 32, 369 (1996).
[CrossRef]

Sung, J. W.

Taghizadeh, M. R.

Teiwes, S.

S. Teiwes, B. Schillinger, and T. Beth, Proc. SPIE 2404, 40 (1995).
[CrossRef]

Turunen, J.

Vasara, A.

Wang, L. X.

Y. Chen, C. H. Gan, L. X. Wang, and G. Yu, Appl. Surf. Sci. 245, 316 (2005).
[CrossRef]

Westerholm, J.

Yatagai, T.

Yoshikawa, N.

Yu, G.

Y. Chen, C. H. Gan, L. X. Wang, and G. Yu, Appl. Surf. Sci. 245, 316 (2005).
[CrossRef]

Zhao, S.

Zhou, C. H.

Appl. Opt. (2)

Appl. Surf. Sci. (1)

Y. Chen, C. H. Gan, L. X. Wang, and G. Yu, Appl. Surf. Sci. 245, 316 (2005).
[CrossRef]

Microelectron. Eng. (1)

M. B. Stern, Microelectron. Eng. 32, 369 (1996).
[CrossRef]

Opt. Commun. (1)

H. Dammann and K. Gőrter, Opt. Commun. 3, 312 (1971).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (1)

S. Teiwes, B. Schillinger, and T. Beth, Proc. SPIE 2404, 40 (1995).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Experimental system for optical demonstration of a QDG. The He–Ne laser beam is expanded and collimated as a uniform laser beam to illuminate the grating, and the proportional-intensity array pattern is captured by a laser beam analyzer in the focal plane of the lens.

Fig. 2
Fig. 2

Illustration of the phase distribution of one period of the grating with white cells for zero-phase delay and black cells for π-phase delay.

Fig. 3
Fig. 3

Orders of the QDGs. The spots with the same color belong to the same order.

Fig. 4
Fig. 4

Designed result of the third-order QDG with proportional intensity 3:2:1 from zero order to second order: (a) phase distribution of one period and (b) output intensity profile.

Fig. 5
Fig. 5

Surface profile of the fabricated third-order QDG with proportional intensity.

Fig. 6
Fig. 6

Experimental images of the fabricated third-order QDG with proportional intensity: (a) two-dimensional laser beam distribution, (b) intensity distribution along the lines n = 0 and m = 2 , 1 , 0 , 1 , 2 in the pattern measured by a laser beam analyzer, (c) three-dimensional laser beam distribution.

Equations (5)

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I 0 , 0 = I ( 0 , 0 ) = ( A λ f ) 2 [ exp ( j ϕ 2 ) exp ( j ϕ 1 ) ] L + exp ( j ϕ 1 ) 2 ,
I + m , + n = I m , n = ( A λ f ) 2 exp ( j ϕ 2 ) exp ( j ϕ 1 ) 2 sin c 2 ( m d ) sin c 2 ( n d ) l = 1 L exp { j 2 π [ m d ( x l + 1 2 ) + n d ( y l + 1 2 ) ] } 2 ,
I m , + n = I + m , n = ( A λ f ) 2 exp ( j ϕ 2 ) exp ( j ϕ 1 ) 2 sin c 2 ( m d ) sin c 2 ( n d ) l = 1 L exp { j 2 π [ m d ( x l + 1 2 ) n d ( y l + 1 2 ) ] } 2 ,
E 2 = α [ m = M M n = N N ( I m , n η E I ̂ m , n ) 2 ] + ( 1 α ) ( 1 η E ) 2 ,
E 2 = α { [ β 1 ( I ( 0 ) η E I ̂ ( 0 ) ) ] 2 + [ β 2 ( I ( 1 ) η E I ̂ ( 1 ) ) ] 2 + + [ β M ( I ( M ) η E I ̂ ( M ) ) ] 2 } + ( 1 α ) ( 1 η E ) 2 ,

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