Abstract

A novel circular Dammann grating is proposed to generate uniform-intensity impulse rings corresponding to different diffraction orders in the far field. The intensities of the rings are determined by the coefficients of the circular sine series decomposition of the grating function. The definition of diffraction efficiency and uniformity for this novel device are described. Numerical solutions of binary phase circular Dammann gratings are presented. A binary phase three-order circular Dammann grating of π phase depth is fabricated by an e-beam direct writing technique and is experimentally demonstrated.

© 2006 Optical Society of America

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References

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  1. T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
    [CrossRef]
  2. C. Colautti, L. M. Zerbino, E. E. Sicre, and M. Garavaglia, Appl. Opt. 26, 2061 (1987).
    [CrossRef] [PubMed]
  3. J. Sung, H. Hockel, J. Brown, and E. G. Johnson, J. Microlithogr. Microfabr. Microsyst. 4, 041603 (2005).
    [CrossRef]
  4. H. Dammann and K. Gortler, Opt. Commun. 3, 312 (1971).
    [CrossRef]
  5. C. Zhou, J. Jia, and L. Liu, Opt. Lett. 28, 2174 (2003).
    [CrossRef] [PubMed]
  6. I. Amidror, J. Opt. Soc. Am. A 14, 816 (1997).
    [CrossRef]
  7. I. Amidror, J. Opt. A 1, 621 (1999).
    [CrossRef]

2005 (1)

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, J. Microlithogr. Microfabr. Microsyst. 4, 041603 (2005).
[CrossRef]

2003 (1)

1999 (1)

I. Amidror, J. Opt. A 1, 621 (1999).
[CrossRef]

1997 (1)

1992 (1)

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

1987 (1)

1971 (1)

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

Amidror, I.

Anderson, E. H.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Brown, J.

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, J. Microlithogr. Microfabr. Microsyst. 4, 041603 (2005).
[CrossRef]

Colautti, C.

Dammann, H.

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

Erdogan, T.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Garavaglia, M.

Gortler, K.

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

Hall, D. G.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Hockel, H.

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, J. Microlithogr. Microfabr. Microsyst. 4, 041603 (2005).
[CrossRef]

Jia, J.

Johnson, E. G.

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, J. Microlithogr. Microfabr. Microsyst. 4, 041603 (2005).
[CrossRef]

King, O.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Liu, L.

Rooks, M. J.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Sicre, E. E.

Sung, J.

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, J. Microlithogr. Microfabr. Microsyst. 4, 041603 (2005).
[CrossRef]

Wicks, G. W.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Zerbino, L. M.

Zhou, C.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

J. Microlithogr. Microfabr. Microsyst. (1)

J. Sung, H. Hockel, J. Brown, and E. G. Johnson, J. Microlithogr. Microfabr. Microsyst. 4, 041603 (2005).
[CrossRef]

J. Opt. A (1)

I. Amidror, J. Opt. A 1, 621 (1999).
[CrossRef]

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

Opt. Commun. (1)

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

Opt. Lett. (1)

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Figures (5)

Fig. 1
Fig. 1

Illustration of a binary phase CDG in one period.

Fig. 2
Fig. 2

Theoretical normalized intensity of a three-order CDG.

Fig. 3
Fig. 3

Surface profile of the fabricated three-order CDG through the center.

Fig. 4
Fig. 4

(a) Experimental image of the fabricated three-order CDG and (b) cross section of intensities through the center.

Fig. 5
Fig. 5

First maximum of the normalized intensity of two-order (a) binary CDG and (b) four-phase-level CDG.

Tables (1)

Tables Icon

Table 1 Numerical Results of Binary Phase ( 0 , π ) CDGs

Equations (15)

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sin ( 2 π f r ) H f π 1 ( f + q ) 3 2 δ ( 1 2 ) ( q f ) .
g ( r ) = n = 1 c n sin ( 2 π n T r ) ,
c n = 2 T T g ( r ) sin ( 2 π n T r ) d r ,
G ( q ) = 1 π n = 1 c n n T ( n T + q ) 3 2 δ ( 1 2 ) ( q n T ) ,
c n = 2 n π [ 2 k = 1 N 2 1 ( 1 ) k cos ( 2 π n x k ) + ( 1 ) n + N 2 + 1 ] .
I n = 1 π c n n T ( n T + q ) 3 2 2 .
c n + 1 2 c n 2 = ( n + 1 ) n ,
Φ = i = 1 N ( I i I av ) 2 i = 1 N I i ,
η = 1 2 n = 1 N c n 2 ,
uni = max ( I n ) min ( I n ) max ( I n ) + min ( I n ) .
c n = 2 T T g ( r ) cos ( 2 π n T r ) d r ,
G ( q ) = c 0 2 1 π q δ ( q ) + 1 π n = 1 c n n T ( n T + q ) 3 2 δ ( 1 2 ) ( n T q ) .
c 0 = 2 [ ( 1 ) N 2 4 k = 1 N 2 ( ( 1 ) k x k ) ] ,
c n = 4 i n π k = 1 N 2 1 ( 1 ) k sin ( 2 π n x k ) .
exp ( j 2 π n f r ) = cos ( 2 π n f r ) + j sin ( 2 π n f r ) ,

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