We propose and demonstrate the adaptive conversion of a multimode beam into a near-diffraction-limited flattop beam in the near field based on a combination of dual-phase-only liquid-crystal spatial light modulators (LC-SLMs) and the stochastic parallel gradient descent (SPGD) algorithm. One phase-only LC-SLM redistributes the intensity of the multimode beam, and the other compensates the wavefront of the output beam. The SPGD algorithm adaptively optimizes the phase distributions of dual-phase-only LC-SLMs to reduce the variance between the actual beam shape and the target beam shape. The experimental results on a fiber multimode beam show that the system is capable of adaptively creating square and rectangle flattop beams with desired parameters. Beam quality can be greatly improved by this system. The power in the main lobe of the far-field spot is about 4 times larger than that of the input multimode beam.

©2010 Optical Society of America

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  1. J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008).
    [Crossref] [PubMed]
  2. V. Eckhouse, M. Fridman, N. Davidson, and A. A. Friesem, “Phase locking and coherent combining of high-order-mode fiber lasers,” Opt. Lett. 33(18), 2134–2136 (2008).
    [Crossref] [PubMed]
  3. J. R. Marciante, R. G. Roides, V. V. Shkunov, and D. A. Rockwell, “Near-diffraction-limited operation of step-index large-mode-area fiber lasers via gain filtering,” Opt. Lett. 35(11), 1828–1830 (2010).
    [Crossref] [PubMed]
  4. F. D. Teodoro, J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “Diffraction-limited, 300-kW peak-power pulses from a coiled multimode fiber amplifier,” Opt. Lett. 27(7), 518–520 (2002).
  5. J. Liang, R. N. Kohn, M. F. Becker, and D. J. Heinzen, “1.5% root-mean-square flat-intensity laser beam formed using a binary-amplitude spatial light modulator,” Appl. Opt. 48(10), 1955–1962 (2009).
    [Crossref] [PubMed]
  6. J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39(30), 5488–5499 (2000).
  7. A. A. Ishaaya, V. Eckhouse, L. Shimshi, N. Davidson, and A. A. Friesem, “Intracavity coherent addition of single high-order modes,” Opt. Lett. 30(14), 1770–1772 (2005).
    [Crossref] [PubMed]
  8. A. A. Ishaaya, G. Machavariani, N. Davidson, A. A. Friesem, and E. Hasman, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28(7), 504–506 (2003).
    [Crossref] [PubMed]
  9. R. El-Agmy, H. Bulte, A. H. Greenaway, and D. Reid, “Adaptive beam profile control using a simulated annealing algorithm,” Opt. Express 13(16), 6085–6091 (2005).
    [Crossref] [PubMed]
  10. H. Ma, P. Zhou, X. Wang, Y. Ma, F. Xi, X. Xu, and Z. Liu, “Near-diffraction-limited annular flattop beam shaping with dual-phase-only liquid crystal spatial light modulators,” Opt. Express 18(8), 8251–8260 (2010).
    [Crossref] [PubMed]
  11. M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A 15(10), 2745–2758 (1998).
  12. P. Zhou, Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, “Coherent beam combination of three two-tone fiber amplifiers using stochastic parallel gradient descent algorithm,” Opt. Lett. 34(19), 2939–2941 (2009).
    [Crossref] [PubMed]

2010 (2)

2009 (2)

2008 (2)

2005 (2)

2003 (1)

2002 (1)

2000 (1)

1998 (1)

Barty, C. P. J.

Beach, R. J.

Becker, M. F.

Bulte, H.

Davidson, N.

Dawson, J. W.

Eckhouse, V.

El-Agmy, R.

Fridman, M.

Friesem, A. A.

Greenaway, A. H.

Hasman, E.

Heebner, J. E.

Heinzen, D. J.

Hoffnagle, J. A.

Ishaaya, A. A.

Jefferson, C. M.

Kliner, D. A. V.

Kohn, R. N.

Koplow, J. P.

Liang, J.

Liu, Z.

Ma, H.

Ma, Y.

Machavariani, G.

Marciante, J. R.

Messerly, M. J.

Moore, S. W.

Pax, P. H.

Reid, D.

Rockwell, D. A.

Roides, R. G.

Shimshi, L.

Shkunov, V. V.

Shverdin, M. Y.

Siders, C. W.

Sivokon, V. P.

Sridharan, A. K.

Stappaerts, E. A.

Teodoro, F. D.

Vorontsov, M. A.

Wang, X.

Xi, F.

Xu, X.

Zhou, P.

Appl. Opt. (2)

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

Opt. Express (3)

Opt. Lett. (6)

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Figures (7)

Fig. 1
Fig. 1 Experimental setup for conversion of multimode fiber laser beam into near-diffraction-limited flattop laser beam in the near field.
Fig. 2
Fig. 2 Near-field and far-field intensity distributions of the input multimode beam. (a) Near- field intensity distribution recorded by CCD1. (b) Far-field intensity distribution recorded by CCD2.
Fig. 3
Fig. 3 Intensity distribution of the output beam and evolution of the fit error as the algorithm proceeds. (a) Intensity distribution. (b) Evolution of the fit error.
Fig. 4
Fig. 4 Far-field intensity distribution of the output beam without being compensated by LC-SLM2.
Fig. 5
Fig. 5 Far-field intensity distribution of the output beam being compensated by LC-SLM2 and evolution of the relative phase error metric during the SPGD algorithm execution. (a) Far-field intensity distribution (solid line corresponds to experimental result and dashed line corresponds to ideal result).(b) Evolution of the relative phase error metric.
Fig. 6
Fig. 6 PIB curves of the far-field intensity distribution of the input multimode beam, output beam without being compensated by LC-SLM2, and output beam compensated by LC-SLM2.
Fig. 7
Fig. 7 Adaptive conversion of multimode beam into rectangle flattop beam with desired parameters: (a) target beam profiles (top row corresponding to flattop beam with parameters a = 0.0035, b = 0.0055, p = 6, q = 6; bottom row corresponding to flattop beam with parameters a = 0.0055, b = 0.0035, p = 6, q = 6). (b) Experimental results of the rectangle flattop beam. (c). Corresponding evolutions of the fit error as the algorithm proceeded.

Equations (4)

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ϕ j = i = 2 n a i Z i ( r , θ ) ,
J f i t e r r o r = x y [ I t arg e t ( x , y ) I c a m e r a ( x , y ) ] 2 ,
I t arg e t ( x , y ) = exp { [ a ( x x o ) ] 2 p [ b ( y y o ) ] 2 q } ,
J c o m p e n s a t i o n = I f a r f i e l d ( x , y ) 2 d x d y ,