Abstract

The three-dimensional distribution of light intensity that is modulated by a pure phase-shifting apodizer is studied. Results show that the Strehl ratio can be altered by the proposed apodizer and by the waist width of incident Gaussian beams. By changing geometrical parameters of the proposed apodizer, we can increase the focal depth to several times that of the original system. The proposed apodizer can also be used to realize focal splitting and local minimum of intensity, which may be advantageous for constructing an optical trap. Furthermore, the local minimum of intensity number is tunable by changing the parameters of the apodizer.

© 2005 Optical Society of America

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References

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2003 (1)

2002 (3)

2001 (1)

2000 (2)

1988 (1)

1986 (1)

1985 (1)

1984 (1)

1983 (1)

1971 (1)

1960 (1)

W. T. Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
[CrossRef]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[CrossRef] [PubMed]

J. Arlt, M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25, 191–193 (2000).
[CrossRef]

Ashkin, A.

Bai, H.

Berriel, L. R.

Bjorkholm, J. E.

Chu, S.

Dholakia, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[CrossRef] [PubMed]

Diaz, A.

Dziedzic, J. M.

Gan, F.

Gan, X.

Ganic, D.

Gbur, G.

Ghosh, A.

Gu, M.

Hain, M.

Indebetouw, G.

Korpel, A.

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[CrossRef] [PubMed]

McCrikerd, J. T.

Montes, E.

Ojeda-Castaneda, J.

Padgett, M. J.

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[CrossRef] [PubMed]

Pieper, R. J.

Sanyal, S.

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[CrossRef] [PubMed]

Somalingam, S.

Stankovic, S.

Tschudi, T.

Visser, T. D.

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[CrossRef] [PubMed]

Wang, H.

Welford, W. T.

W. T. Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
[CrossRef]

Appl. Opt. (7)

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

W. T. Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
[CrossRef]

Opt. Lett. (5)

Science (1)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

System setup. The incident Gaussian beams are modulated by a three-portion phase-shifting apodizer with phase shifts of 0, π, and 0 for its inner, middle, and outer concentric portions, respectively.

Fig. 2
Fig. 2

Three-dimensional distributions of the Strehl ratio for (a) a = 0.1, (b) a = 0.5, and (c) a = 0.9.

Fig. 3
Fig. 3

Three-dimensional distribution of intensity for w = 0.3: (a) three-dimensional intensity distribution for w = 0.3 and a = b; (b) three-dimensional intensity distribution of the apodized system for w = 0.3, b = 0.4, and a = 0.54.

Fig. 4
Fig. 4

Three-dimensional distribution of the intensity of the apodized system for w = 0.8 and a = 0.7: (a) a = b = 0.7, (b) b = 0.6, (c) b = 0.4, and (d) b = 0.1.

Equations (2)

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G ( ρ , u ) = 2 j = 1 3 exp ( i ϕ j ) r j - 1 r j r J 0 ( ρ r ) × exp [ - ( 1 w 2 + i u 2 ) r 2 ] d r ,
S = [ G a b ( 0 , 0 ) / G a = b = 0 ( 0 , 0 ) ] 2 = { 4 exp ( - 2 w 2 b 2 ) + 1 + 4 exp ( - 2 w 2 a 2 ) + exp ( - 2 w 2 ) - 4 exp ( - 1 w 2 b 2 ) + 4 exp ( - 1 w 2 a 2 ) - 2 exp ( - 1 w 2 ) - 8 exp ( - a 2 + b 2 w 2 ) + 4 exp ( - b 2 + 1 w 2 ) - 4 exp ( - a 2 + 1 w 2 ) } 2 × [ 1 - exp ( - 1 w 2 ) ] - 4 .

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