Abstract

Based on the refractive laser beam shaping system, the dark hollow femtosecond pulse beam shaping technique with a phase-only liquid crystal spatial light modulator (LC-SLM) is demonstrated. The phase distribution of the LC-SLM is derived by the energy conservation and constant optical path principle. The effects of the shaping system on the temporal properties, including spectral phase distribution and bandwidth of the femtosecond pulse, are analyzed in detail. Experimental results show that the hollow intensity distribution of the output pulsed beam can be maintained much at more than 1200mm. The spectral phase of the pulse is changed, and the pulse width is expanded from 199 to 230fs, which is caused by the spatial–temporal coupling effect. The coupling effect mainly depends on the phase-only LC-SLM itself, not on its loaded phase distribution. The experimental results indicate that the proposed shaping setup can generate a dark hollow femtosecond pulsed beam effectively, because the temporal Gaussian waveform is unchanged.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2011 (1)

H. T. Ma, Z. J. Liu, X. J. Xu, X. L. Wang, Y. X. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light modulators,” J. Opt. 13, 015707 (2011).
[CrossRef]

2010 (5)

2008 (2)

2007 (3)

2006 (2)

2005 (1)

2003 (3)

2000 (3)

1998 (2)

M. Arif, M. M. Hossain, A. A. S. Awwal, and M. N. Islam, “Two-element refracting system for annular Gaussian-to-Bessel beam transformation,” Appl. Opt. 37, 4206–4209 (1998).
[CrossRef]

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[CrossRef]

1997 (1)

V. E. Peet, and R. V. Tsubin, “Multiphoton ionization and optical breakdown of xenon in annular laser beams,” Opt. Commun. 134, 69–74 (1997).
[CrossRef]

1994 (1)

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49, 4922–4927 (1994).
[CrossRef] [PubMed]

1993 (2)

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

X. Wang and M. G. Littman, “Laser cavity for generation of variable-radius rings of light,” Opt. Lett. 18, 767–768(1993).
[CrossRef] [PubMed]

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Ahmad, M. A.

Altucci, C.

Arif, M.

Arpali, C.

Atewart, B. W.

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49, 4922–4927 (1994).
[CrossRef] [PubMed]

Awwal, A. A. S.

Bashkansky, M.

Baykal, Y.

Bruzzese, R.

Cai, Y. J.

Carbon, M.

M. Carbon, “Laser beam shaping in space using adaptive optics,” Proc. SPIE 5087, 83–86 (2003).
[CrossRef]

Choi, K.

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49, 4922–4927 (1994).
[CrossRef] [PubMed]

D’Antuoni, D.

Dai, J. M.

Dholakia, K.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Dutton, Z.

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Elsaesser, T.

Eyyuboglu, H. T.

Fatemi, F. K.

Fenichel, H.

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49, 4922–4927 (1994).
[CrossRef] [PubMed]

Gerber, G.

Glushko, B.

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

Griebner, U.

Grunwald, R.

Hattori, T.

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[CrossRef]

Hnatovsky, C.

Hoffnagle, J. A.

Hossain, M. M.

Islam, M. N.

Jefferson, C. M.

Kemmer, R.

Koehl, R. M.

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[CrossRef]

Kreuzer, J. L.

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equi-phase surface,” U.S. patent 3,476,463 (4 November 1969).

Krolikowski, W.

Kryzhanovsky, B.

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

Lee, H. S.

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49, 4922–4927 (1994).
[CrossRef] [PubMed]

Lin, J.

Ling, Q.

Lisio, C. D.

Littman, M. G.

Liu, C. H.

Liu, J. L.

Liu, S. T.

Liu, X. H.

Liu, Z. J.

H. T. Ma, Z. J. Liu, X. J. Xu, X. L. Wang, Y. X. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light modulators,” J. Opt. 13, 015707 (2011).
[CrossRef]

H. T. Ma, Z. J. Liu, X. J. Xu, S. H. Wang, and C. H. Liu, “Near-diffraction-limited flattop laser beam adaptively generated by stochastic parallel gradient descent algorithm,” Opt. Lett. 35, 2973–2975 (2010).
[CrossRef] [PubMed]

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18, 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, H. C. Zhang, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Adaptive conversion of multimode beam to near diffraction-limited flattop beam based on dual phase-only liquid-crystal spatial light modulators,” Opt. Express 18, 27723–27730 (2010).
[CrossRef]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12, 045704(2010).
[CrossRef]

Z. J. Liu, J. M. Dai, X. G. Sun, and S. T. Liu, “Generation of hollow Gaussian beam by phase-only filtering,” Opt. Express 16, 19926–19933 (2008).
[CrossRef] [PubMed]

Z. J. Liu, H. F. Zhao, J. L. Liu, J. Lin, M. A. Ahmad, and S. T. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32, 2076–2078 (2007).
[CrossRef] [PubMed]

Lu, X. H.

Ma, H. T.

Ma, Y. X.

H. T. Ma, Z. J. Liu, X. J. Xu, X. L. Wang, Y. X. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light modulators,” J. Opt. 13, 015707 (2011).
[CrossRef]

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18, 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, H. C. Zhang, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Adaptive conversion of multimode beam to near diffraction-limited flattop beam based on dual phase-only liquid-crystal spatial light modulators,” Opt. Express 18, 27723–27730 (2010).
[CrossRef]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12, 045704(2010).
[CrossRef]

McGloin, D.

Melville, H.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Nelson, K. A.

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[CrossRef]

Nibbering, E. T. J.

Peet, V. E.

V. E. Peet, and R. V. Tsubin, “Multiphoton ionization and optical breakdown of xenon in annular laser beams,” Opt. Commun. 134, 69–74 (1997).
[CrossRef]

Pfeifer, T.

Rode1, A. V.

Sarkisyan, D.

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

Shvedov, V. G.

Sibbett, W.

Solimeno, S.

Spalding, G.

Spielmann, C.

Spitzenpfeil, R.

Sun, X. G.

Tschirschwitz, F.

Tsubin, R. V.

V. E. Peet, and R. V. Tsubin, “Multiphoton ionization and optical breakdown of xenon in annular laser beams,” Opt. Commun. 134, 69–74 (1997).
[CrossRef]

Walter, D.

Wang, F.

Wang, S. H.

Wang, X.

Wang, X. L.

H. T. Ma, Z. J. Liu, X. J. Xu, X. L. Wang, Y. X. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light modulators,” J. Opt. 13, 015707 (2011).
[CrossRef]

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18, 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, H. C. Zhang, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Adaptive conversion of multimode beam to near diffraction-limited flattop beam based on dual phase-only liquid-crystal spatial light modulators,” Opt. Express 18, 27723–27730 (2010).
[CrossRef]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12, 045704(2010).
[CrossRef]

Wang, Y. Z.

Winterfeldt, C.

Xi, F. J.

Xu, X. J.

Zhang, H. C.

Zhao, C. L.

Zhao, H. F.

Zhou, P.

H. T. Ma, Z. J. Liu, X. J. Xu, X. L. Wang, Y. X. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light modulators,” J. Opt. 13, 015707 (2011).
[CrossRef]

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18, 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, H. C. Zhang, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Adaptive conversion of multimode beam to near diffraction-limited flattop beam based on dual phase-only liquid-crystal spatial light modulators,” Opt. Express 18, 27723–27730 (2010).
[CrossRef]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12, 045704(2010).
[CrossRef]

Appl. Opt. (2)

J. Opt. (2)

H. T. Ma, Z. J. Liu, X. J. Xu, X. L. Wang, Y. X. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light modulators,” J. Opt. 13, 015707 (2011).
[CrossRef]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12, 045704(2010).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Opt. Commun. (2)

V. E. Peet, and R. V. Tsubin, “Multiphoton ionization and optical breakdown of xenon in annular laser beams,” Opt. Commun. 134, 69–74 (1997).
[CrossRef]

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[CrossRef]

Opt. Express (7)

D. Walter, T. Pfeifer, C. Winterfeldt, R. Kemmer, R. Spitzenpfeil, G. Gerber, and C. Spielmann, “Adaptive spatial control of fiber modes and their excitation for high-harmonic generation,” Opt. Express 14, 3433–3442 (2006).
[CrossRef] [PubMed]

H. T. Eyyuboglu, C. Arpali, and Y. Baykal, “Flat topped beams and their characteristics in turbulent media,” Opt. Express 14, 4196–4207 (2006).
[CrossRef] [PubMed]

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

F. K. Fatemi, M. Bashkansky, and Z. Dutton, “Dynamic high-speed spatial manipulation of cold atoms using acousto-optic and spatial light modulation,” Opt. Express 15, 3589–3596(2007).
[CrossRef] [PubMed]

Z. J. Liu, J. M. Dai, X. G. Sun, and S. T. Liu, “Generation of hollow Gaussian beam by phase-only filtering,” Opt. Express 16, 19926–19933 (2008).
[CrossRef] [PubMed]

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18, 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, H. C. Zhang, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Adaptive conversion of multimode beam to near diffraction-limited flattop beam based on dual phase-only liquid-crystal spatial light modulators,” Opt. Express 18, 27723–27730 (2010).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. A (1)

H. S. Lee, B. W. Atewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49, 4922–4927 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

B. Glushko, B. Kryzhanovsky, and D. Sarkisyan, “Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry,” Phys. Rev. Lett. 71, 243–246 (1993).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. Carbon, “Laser beam shaping in space using adaptive optics,” Proc. SPIE 5087, 83–86 (2003).
[CrossRef]

Other (1)

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equi-phase surface,” U.S. patent 3,476,463 (4 November 1969).

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Figures (5)

Fig. 1
Fig. 1

Configuration of the Keplerian beam shaping system.

Fig. 2
Fig. 2

(a) Surface distribution of the refractive component. (b) Phase distribution of the phase-only LC-SLM.

Fig. 3
Fig. 3

Experimental setup for the generation of HGB. Lenses 1 and 2 constitute a beam expander: HWP, half-wavelength plate; PBS, polarization beam splitter; NPBS, nonpolarization beam splitter.

Fig. 4
Fig. 4

(a) Cross section of the input quasi-Gaussian pulsed beam and its gray-scale image (inset). (b)–(f) Experimental results of the cross-section intensity distribution of the shaped beam with different propagation distance and their gray-scale images (insets).

Fig. 5
Fig. 5

Experimental results of the spectral phase distribution and temporal width of the shaped pulsed beam.

Equations (5)

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

P t ( R ) = ( R 2 / w 2 ) m exp ( R 2 / w 2 ) ,
0 r P i ( x ) x d x = 0 R P t ( ξ ) ξ d ζ .
R = h ( r ) .
z ( r ) = 0 r { ( n 2 1 ) + [ ( n 1 ) d h ( x ) + x ] 2 } 1 / 2 d x Z ( R ) = 0 R { ( n 2 1 ) + [ ( n 1 ) d h 1 ( x ) + x ] 2 } 1 / 2 d x ,
f p ( r ) = 2 π ( z e z ( r ) + n z ( r ) ) λ ,

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