Abstract

We demonstrate the annular flattop beam shaping technique with dual phase only liquid crystal spatial light modulators (LC-SLM) based on the refractive laser beam shaping systems. One LC-SLM redistributes the intensity distribution, and the other restores the initial underlying wave front. Differing from the conventional annular beam shaping technique, the wave front of the output beam can be maintained. The influences of deviations of beam waist and beam shape on the output beam profile are discussed in detail. Experimental results show that approximate 71% of the power is enclosed in a region with less than 7% rms intensity variation. The 4.1mm diameter near-diffraction-limited beam retains an annular flattop intensity distribution without significant diffraction peaks for a working distance of more than 24cm in the near field.

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2009 (2)

2008 (4)

2007 (2)

H. T. Eyyuboglu and Y. Baykal, “Scintillations of cos-Gaussian and annular beams,” J. Opt. Soc. Am. A 24(1), 56–162 (2007).

X. Chu and G. Zhou, “Power coupling of a two-Cassegrain-telescopes system in turbulent atmosphere in a slant path,” Opt. Express 15(12), 7697–7707 (2007).
[Crossref] [PubMed]

2006 (4)

2005 (2)

2003 (1)

2001 (1)

2000 (1)

1998 (1)

1995 (1)

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75(18), 3253–3256 (1995).
[Crossref] [PubMed]

1994 (1)

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: Quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).
[Crossref] [PubMed]

1992 (1)

Anderson, D. Z.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75(18), 3253–3256 (1995).
[Crossref] [PubMed]

Arif, M.

Awwal, A. A. S.

Baykal, Y.

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

Y. Chen, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation properties of dark hollow beams in a weak turbulent atmosphere,” Appl. Phys. B 90(1), 87–92 (2008).
[Crossref]

H. T. Eyyuboglu and Y. Baykal, “Scintillations of cos-Gaussian and annular beams,” J. Opt. Soc. Am. A 24(1), 56–162 (2007).

Y. Baykal, “Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium,” J. Opt. Soc. Am. A 22(4), 672–679 (2005).
[Crossref]

Becker, M. F.

Burke, G. J.

Cai, Y.

Cai, Y. J.

Chai, L.

Chan, Y. C.

Chen, Y.

Y. Chen, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation properties of dark hollow beams in a weak turbulent atmosphere,” Appl. Phys. B 90(1), 87–92 (2008).
[Crossref]

Chu, X.

Cornell, E. A.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75(18), 3253–3256 (1995).
[Crossref] [PubMed]

Dholakia, K.

D. P. Rhodes, D. M. Gherardi, J. Livesey, D. Mcgloin, H. Melville, T. Freegarde, and K. Dholakia, “Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation,” J. Mod. Opt. 53(4), 547–556 (2006).
[Crossref]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11(2), 158–166 (2003).
[Crossref] [PubMed]

Dowd, P.

Eyyuboglu, H. T.

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref] [PubMed]

Y. Chen, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation properties of dark hollow beams in a weak turbulent atmosphere,” Appl. Phys. B 90(1), 87–92 (2008).
[Crossref]

H. T. Eyyuboglu and Y. Baykal, “Scintillations of cos-Gaussian and annular beams,” J. Opt. Soc. Am. A 24(1), 56–162 (2007).

Freegarde, T.

D. P. Rhodes, D. M. Gherardi, J. Livesey, D. Mcgloin, H. Melville, T. Freegarde, and K. Dholakia, “Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation,” J. Mod. Opt. 53(4), 547–556 (2006).
[Crossref]

Gherardi, D. M.

D. P. Rhodes, D. M. Gherardi, J. Livesey, D. Mcgloin, H. Melville, T. Freegarde, and K. Dholakia, “Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation,” J. Mod. Opt. 53(4), 547–556 (2006).
[Crossref]

Hannan, P. G.

He, S. L.

Heinzen, D. J.

Hoffnagle, J. A.

Hossain, M. M.

Hu, M. L.

Islam, M. N.

Izdebskaya, Ya.

Jefferson, C. M.

Kohn, R. N.

Korotkova, O.

Lam, Y. L.

Li, J. H.

Li, Y. F.

Liang, J.

Lin, Q.

Liu, C.

Livesey, J.

D. P. Rhodes, D. M. Gherardi, J. Livesey, D. Mcgloin, H. Melville, T. Freegarde, and K. Dholakia, “Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation,” J. Mod. Opt. 53(4), 547–556 (2006).
[Crossref]

Lu, X.

Marksteiner, S.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: Quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).
[Crossref] [PubMed]

Mcgloin, D.

D. P. Rhodes, D. M. Gherardi, J. Livesey, D. Mcgloin, H. Melville, T. Freegarde, and K. Dholakia, “Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation,” J. Mod. Opt. 53(4), 547–556 (2006).
[Crossref]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11(2), 158–166 (2003).
[Crossref] [PubMed]

Melville, H.

D. P. Rhodes, D. M. Gherardi, J. Livesey, D. Mcgloin, H. Melville, T. Freegarde, and K. Dholakia, “Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation,” J. Mod. Opt. 53(4), 547–556 (2006).
[Crossref]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11(2), 158–166 (2003).
[Crossref] [PubMed]

Montgomery, D.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75(18), 3253–3256 (1995).
[Crossref] [PubMed]

Qu, J.

Renn, M. J.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75(18), 3253–3256 (1995).
[Crossref] [PubMed]

Rhodes, D. P.

D. P. Rhodes, D. M. Gherardi, J. Livesey, D. Mcgloin, H. Melville, T. Freegarde, and K. Dholakia, “Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation,” J. Mod. Opt. 53(4), 547–556 (2006).
[Crossref]

Rolston, S. L.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: Quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).
[Crossref] [PubMed]

Savage, C. M.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: Quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).
[Crossref] [PubMed]

Serebryannikov, E. E.

Shvedov, V.

Sibbett, W.

Song, Y. J.

Spalding, G. C.

Thompson, C. A.

Vdovin, O.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75(18), 3253–3256 (1995).
[Crossref] [PubMed]

Volyar, A.

Wang, C. Y.

Wang, F.

Wang, Y.

Wang, Z.

Webb, K. J.

White, D. A.

Wieman, C. E.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75(18), 3253–3256 (1995).
[Crossref] [PubMed]

Yuan, X.

Yuan, Y.

Zhang, S.

Zhao, C.

Zheltikov, A. M.

Zhou, G.

Zoller, P.

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: Quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).
[Crossref] [PubMed]

Appl. Opt. (4)

Appl. Phys. B (1)

Y. Chen, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation properties of dark hollow beams in a weak turbulent atmosphere,” Appl. Phys. B 90(1), 87–92 (2008).
[Crossref]

J. Mod. Opt. (1)

D. P. Rhodes, D. M. Gherardi, J. Livesey, D. Mcgloin, H. Melville, T. Freegarde, and K. Dholakia, “Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation,” J. Mod. Opt. 53(4), 547–556 (2006).
[Crossref]

J. Opt. Soc. Am. A (3)

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. A (1)

S. Marksteiner, C. M. Savage, P. Zoller, and S. L. Rolston, “Coherent atomic waveguides from hollow optical fibers: Quantized atomic motion,” Phys. Rev. A 50(3), 2680–2690 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75(18), 3253–3256 (1995).
[Crossref] [PubMed]

Other (1)

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U.S. patent 3,476,463, 1969.

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Figures (11)

Fig. 1
Fig. 1

Optical configurations of the refractive beam shaping system. (a) Galilean type; (b) Keplerian type.

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Fig. 2
Fig. 2

Intensity and phase distributions: (a) output beam after passing through the shaping system and its gray scale image (inset); (b) corresponding phase distribution and its gray scale image (inset); (c) corresponding far field intensity distribution and its gray scale image (inset).

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Fig. 3
Fig. 3

Intensity and phase distributions of the output beam for the incident beam with beam waist 2.7mm, 3mm, 3.3mm: (a) Intensity distributions; (b) corresponding phase distributions.

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Fig. 4
Fig. 4

Intensity and phase distributions of the output beam for the input beam with combination of Gaussian profiles from Eq. (5), e1= 0.9, e2= 0.1: (a) Intensity distributions; (b) corresponding phase distributions.

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Fig. 5
Fig. 5

Intensity and phase distributions of the output beam by changing the distance between two aspheric lenses. (a) Intensity distributions; (b) corresponding phase distributions.

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Fig. 6
Fig. 6

Experimental setup for generation of annular flattop laser beam.

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Fig. 7
Fig. 7

Cross section of the input quasi-Gaussian beam and its gray-scale image (inset). The solid line shows the intensity distribution of the input beam and the dashed line shows the fitting result with Gaussian profile expansion from Eq. (5).

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Fig. 8
Fig. 8

Surface and phase distributions of the Galilean shaping system: (a) Surface distributions; (b) phase distributions.

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Fig. 9
Fig. 9

Cross section of the output annular flattop beam and its gray-scale image (inset).

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Fig. 10
Fig. 10

Relative rms variation and power-in-the-bucket curves: (a) Measured dependence of the relative rms variation of the output intensity on efficiency compared with the theoretical value; (b) power-in-the-bucket curves before and after re-collimating and their gray-scale images (inset).

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Fig. 11
Fig. 11

Intensity distribution of the output beam after propagation in the near field: (a) at 12cm from the LC-SLM 2; (b) at 18cm from the LC-SLM 2; (c) at 24cm from the LC-SLM 2.

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Equations (7)

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f p h a s e 1 ( r ) = 2 π [ z e d g e − z ( r ) + n z ( r ) ] λ
f p h a s e 2 ( R ) = 2 π [ n Z e d g e − n Z ( R ) + Z ( R ) ] λ ,
P ( r ) = exp ( − 2 r 2 / w 2 ) ,
P a n n u l a r ( r ) = { 1 + exp [ β 1 ( r R 1 − 1 ) ] } − 1 − { 1 + exp [ β 2 ( r R 2 − 1 ) ] } − 1 ,
P i n p u t ( r ) = ∑ i e i exp ( − 2 r 2 w i 2 ) ,
S E = { 2 r 2 2 − r 1 2 ∫ r 1 r 2 [ P a n n u l a r ( x ) − 2 r 2 2 − r 1 2 ∫ r 1 r 2 P a n n u l a r ( x ) x d x ] 2 x d x } 1 2 2 r 2 2 − r 1 2 ∫ r 1 r 2 P a n n u l a r ( x ) x d x
η = 2 π ∫ r 1 r 2 P a n n u l a r ( x ) x d x W t o t a l ,

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