Abstract

A new concept based on the theory of Dammann gratings is proposed for the generation of circular optical beams. This grating shows that it can achieve equal intensity and equal spacing with acceptable efficiency that is controlled by set of transition points. A numerical solution is also presented together with the fabrication of 4-order circular Dammann grating by e-beam lithography. Experimental results agree well with the scalar diffraction theory. This grating has the potential to be further developed into practical applications.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  5. M. Toda, "Single mode behavior of a circular grating for potential disk-shaped DFB lasers," IEEE J. Quantum Electron. 26, 473-481 (1990).
    [CrossRef]
  6. C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
    [CrossRef]
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  8. C. B. Burckhardt, "Diffraction of a plane wave at a sinusoidally stratified dielectric grating," J. Opt. Soc. Am. 56, 1502-1509 (1966).
    [CrossRef]
  9. J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. 28, 1267-1275 (1989).
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    [CrossRef]
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    [CrossRef] [PubMed]

2006 (1)

2003 (1)

2001 (1)

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, "The use of circular optical grating for measuring angular toation of mirrors," Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

1999 (1)

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

1995 (1)

1992 (1)

1990 (2)

X. H. Zheung and S. Lacroix, "Mode coupling in circular-cylindrical system and its application to fingerprint resonators," J. Vac. Sci. Technol. B 8, 1509-1516 (1990).

M. Toda, "Single mode behavior of a circular grating for potential disk-shaped DFB lasers," IEEE J. Quantum Electron. 26, 473-481 (1990).
[CrossRef]

1989 (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. 28, 1267-1275 (1989).

1971 (1)

H. Dammann and K. Gortler, "High efficiency in-line multiple imaging by means of multiple phase holograms," Opt. Commun. 3, 312-315 (1971).
[CrossRef]

1966 (1)

Abraham, M. C.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Burckhardt, C. B.

Chung, P. S.

Dammann, H.

H. Dammann and K. Gortler, "High efficiency in-line multiple imaging by means of multiple phase holograms," Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Downs, M. M.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. 28, 1267-1275 (1989).

Farhoud, M.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Fu, Y.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, "The use of circular optical grating for measuring angular toation of mirrors," Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Gortler, K.

H. Dammann and K. Gortler, "High efficiency in-line multiple imaging by means of multiple phase holograms," Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Hwang, M.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Jahns, J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. 28, 1267-1275 (1989).

Jia, J.

Lacroix, S.

X. H. Zheung and S. Lacroix, "Mode coupling in circular-cylindrical system and its application to fingerprint resonators," J. Vac. Sci. Technol. B 8, 1509-1516 (1990).

Liu, L.

Morrison, R. L.

Prise, M. E.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. 28, 1267-1275 (1989).

Quan, C.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, "The use of circular optical grating for measuring angular toation of mirrors," Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Ram, R. J.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Ross, C. A.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Savas, T.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Schattenburg, M.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Shang, H. M.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, "The use of circular optical grating for measuring angular toation of mirrors," Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Smith, H. I.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Streibl, N.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. 28, 1267-1275 (1989).

Tay, C. J.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, "The use of circular optical grating for measuring angular toation of mirrors," Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Toda, M.

M. Toda, "Single mode behavior of a circular grating for potential disk-shaped DFB lasers," IEEE J. Quantum Electron. 26, 473-481 (1990).
[CrossRef]

Toh, S. L.

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, "The use of circular optical grating for measuring angular toation of mirrors," Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Walker, S. J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. 28, 1267-1275 (1989).

Walsh, M.

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

Zhao, S.

Zheung, X. H.

X. H. Zheung and S. Lacroix, "Mode coupling in circular-cylindrical system and its application to fingerprint resonators," J. Vac. Sci. Technol. B 8, 1509-1516 (1990).

Zhou, C.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. Toda, "Single mode behavior of a circular grating for potential disk-shaped DFB lasers," IEEE J. Quantum Electron. 26, 473-481 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Vac. Sci. Technol. B (2)

C. A. Ross, H. I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M. C. Abraham, and R. J. Ram, "Fabrication of patterned media for high density magnetic storage," J. Vac. Sci. Technol. B 17, 3168-3176 (1999).
[CrossRef]

X. H. Zheung and S. Lacroix, "Mode coupling in circular-cylindrical system and its application to fingerprint resonators," J. Vac. Sci. Technol. B 8, 1509-1516 (1990).

Opt. Commun. (1)

H. Dammann and K. Gortler, "High efficiency in-line multiple imaging by means of multiple phase holograms," Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Opt. Eng. (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, "Dammann gratings for laser beam shaping," Opt. Eng. 28, 1267-1275 (1989).

Opt. Lasers Eng. (1)

H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, "The use of circular optical grating for measuring angular toation of mirrors," Opt. Lasers Eng. 36, 487-500 (2001).
[CrossRef]

Opt. Lett. (2)

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Figures (6)

Fig. 1
Fig. 1

(Color online) Concept of CDG.

Fig. 2
Fig. 2

CDG Profile Design.

Fig. 3
Fig. 3

a. Transition Points in cross-section of Circular Dammann Grating. b. Circular Profile of Circular Dammann Grating with ϕ = π and θ = 0 .

Fig. 4
Fig. 4

(Color online) Fabricated 4-order CDG with 200× magnification.

Fig. 5
Fig. 5

(Color online) Output image of 4-order CDG.

Fig. 6
Fig. 6

4-order circle intensities distribution along different diffraction order.

Tables (1)

Tables Icon

Table 1 Some Numerical Solutions of CDG

Equations (10)

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

A ( x ) = n = 0 N 1 exp ( j θ n ) r e c t [ x ( x n + 1 + x n ) / 2 x n + 1 x n ] ,
M ( n ) = | k = 0 N 1 ( 1 ) k j x k x k + 1 exp ( j 2 π n x ) d x | .
n t h o r d e r :
P n = n × | M ( n ) | 2 = 1 n π 2 { [ k = 1 N ( 1 ) k cos ( 2 π n x k ) ] 2 + [ k = 1 N ( 1 ) k sin ( 2 π n x k ) ] 2 } ,
0 t h o r d e r :
P 0 = [ 2 k = 1 N ( 1 ) k x k + 1 ] 2 .
x k = x k N / 2 + 0.5 ,
η = i = n n P 2 i 1 .
Δ = min | x k +1 x k | .
u n i = max ( P n ) min ( P n ) max ( P n ) + min ( P n ) .

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