Abstract

We present a new method for efficiently transforming a high-order mode beam into a nearly Gaussian beam with much higher beam quality. The method is based on modulation of phases of different lobes by stochastic parallel gradient descent algorithm and coherent addition after phase flattening. We demonstrate the method by transforming an LP11 mode into a nearly Gaussian beam. The experimental results reveal that the power in the diffraction-limited bucket in the far field is increased by more than a factor of 1.5.

© 2011 Optical Society of America

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2011

W. P. Grice and R. S. Bennink, “Spatial entanglement and optimal single-mode coupling,” Phys. Rev. A 83, 023810(2011).
[CrossRef]

2009

2007

2005

E. Daly, C. Dainty, G. O’Connor, and T. Glynn, “Wave-front correction of a femtosecond laser using a deformable mirror,” Proc. SPIE 5708, 71–82 (2005).
[CrossRef]

2004

2003

2002

2000

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182, 205–208 (2000).
[CrossRef]

R. Oron, N. Davidson, and A. A. Friesem, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
[CrossRef]

1999

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

1998

1997

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, and M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” Proc. SPIE 3126, 221–227(1997).
[CrossRef]

1996

T. Graf and J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[CrossRef]

1993

G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems 5 (Morgan Kaufmann, 1993), pp. 244–251.

1992

N. Davidson, A. A. Friesem, and E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

1989

Bahk, S. W.

Balmer, J. E.

T. Graf and J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[CrossRef]

Bennink, R. S.

W. P. Grice and R. S. Bennink, “Spatial entanglement and optimal single-mode coupling,” Phys. Rev. A 83, 023810(2011).
[CrossRef]

Blit, S.

Carhart, G. W.

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, and M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” Proc. SPIE 3126, 221–227(1997).
[CrossRef]

Cauwenberghs, G.

G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems 5 (Morgan Kaufmann, 1993), pp. 244–251.

Cederquist, J. N.

Chen, X.

Chvykov, V.

Dainty, C.

E. Daly, C. Dainty, G. O’Connor, and T. Glynn, “Wave-front correction of a femtosecond laser using a deformable mirror,” Proc. SPIE 5708, 71–82 (2005).
[CrossRef]

Daly, E.

E. Daly, C. Dainty, G. O’Connor, and T. Glynn, “Wave-front correction of a femtosecond laser using a deformable mirror,” Proc. SPIE 5708, 71–82 (2005).
[CrossRef]

Danziger, Y.

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

Davidson, N.

G. Machavariani, A. A. Ishaaya, L. Shimshi, N. Davidson, and A. A. Friesem, “Efficient mode transformations of degenerate Laguerre-Gaussian beams,” Appl. Opt. 43, 2561–2567 (2004).
[CrossRef] [PubMed]

A. A. Ishaaya, G. Machavariani, N. Davidson, and A. A. Friesem, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef] [PubMed]

G. Machavariani, N. Davidson, A. A. Ishaaya, A. A. Friesem, and E. Hasman, “Efficient formation of a high-quality beam from a pure high-order Hermite-Gaussian mode,” Opt. Lett. 27, 1501–1503 (2002).
[CrossRef]

R. Oron, L. Shimshi, S. Blit, N. Davidson, A. A. Friesem, and E. Hasman, “Laser operation with orthogonally polarized transverse modes,” Appl. Opt. 41, 3634–3637(2002).
[CrossRef] [PubMed]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182, 205–208 (2000).
[CrossRef]

R. Oron, N. Davidson, and A. A. Friesem, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

Eismann, M. T.

Friesem, A. A.

G. Machavariani, A. A. Ishaaya, L. Shimshi, N. Davidson, and A. A. Friesem, “Efficient mode transformations of degenerate Laguerre-Gaussian beams,” Appl. Opt. 43, 2561–2567 (2004).
[CrossRef] [PubMed]

A. A. Ishaaya, G. Machavariani, N. Davidson, and A. A. Friesem, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef] [PubMed]

R. Oron, L. Shimshi, S. Blit, N. Davidson, A. A. Friesem, and E. Hasman, “Laser operation with orthogonally polarized transverse modes,” Appl. Opt. 41, 3634–3637(2002).
[CrossRef] [PubMed]

G. Machavariani, N. Davidson, A. A. Ishaaya, A. A. Friesem, and E. Hasman, “Efficient formation of a high-quality beam from a pure high-order Hermite-Gaussian mode,” Opt. Lett. 27, 1501–1503 (2002).
[CrossRef]

R. Oron, N. Davidson, and A. A. Friesem, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182, 205–208 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

Glynn, T.

E. Daly, C. Dainty, G. O’Connor, and T. Glynn, “Wave-front correction of a femtosecond laser using a deformable mirror,” Proc. SPIE 5708, 71–82 (2005).
[CrossRef]

Graf, T.

T. Graf and J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[CrossRef]

Gray, S.

Grice, W. P.

W. P. Grice and R. S. Bennink, “Spatial entanglement and optimal single-mode coupling,” Phys. Rev. A 83, 023810(2011).
[CrossRef]

Hasman, E.

G. Machavariani, N. Davidson, A. A. Ishaaya, A. A. Friesem, and E. Hasman, “Efficient formation of a high-quality beam from a pure high-order Hermite-Gaussian mode,” Opt. Lett. 27, 1501–1503 (2002).
[CrossRef]

R. Oron, L. Shimshi, S. Blit, N. Davidson, A. A. Friesem, and E. Hasman, “Laser operation with orthogonally polarized transverse modes,” Appl. Opt. 41, 3634–3637(2002).
[CrossRef] [PubMed]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182, 205–208 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

Ishaaya, A. A.

Jackel, S.

Kalintchenko, G.

Li, M.

Liu, A.

Liu, Z.

Lumer, Y.

Ma, H.

Ma, Y.

Machavariani, G.

Maksimchuk, A.

Meir, A.

Moshe, I.

Mourou, G. A.

O’Connor, G.

E. Daly, C. Dainty, G. O’Connor, and T. Glynn, “Wave-front correction of a femtosecond laser using a deformable mirror,” Proc. SPIE 5708, 71–82 (2005).
[CrossRef]

Oron, R.

R. Oron, L. Shimshi, S. Blit, N. Davidson, A. A. Friesem, and E. Hasman, “Laser operation with orthogonally polarized transverse modes,” Appl. Opt. 41, 3634–3637(2002).
[CrossRef] [PubMed]

R. Oron, N. Davidson, and A. A. Friesem, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182, 205–208 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

Planchon, T. A.

Ricklin, J. C.

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, and M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” Proc. SPIE 3126, 221–227(1997).
[CrossRef]

Rousseau, P.

Shimshi, L.

Sivokon, V. P.

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, 2745–2758(1998).
[CrossRef]

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, and M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” Proc. SPIE 3126, 221–227(1997).
[CrossRef]

Tai, A. M.

Vorontsov, M. A.

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, 2745–2758(1998).
[CrossRef]

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, and M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” Proc. SPIE 3126, 221–227(1997).
[CrossRef]

Walton, D. T.

Wang, J.

Wang, X.

Xu, X.

Yanovsky, V.

Zenteno, L. A.

Zhou, P.

Appl. Opt.

Appl. Phys. Lett.

N. Davidson, A. A. Friesem, and E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Opt. Commun.

T. Graf and J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182, 205–208 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. A

W. P. Grice and R. S. Bennink, “Spatial entanglement and optimal single-mode coupling,” Phys. Rev. A 83, 023810(2011).
[CrossRef]

Proc. SPIE

E. Daly, C. Dainty, G. O’Connor, and T. Glynn, “Wave-front correction of a femtosecond laser using a deformable mirror,” Proc. SPIE 5708, 71–82 (2005).
[CrossRef]

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, and M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” Proc. SPIE 3126, 221–227(1997).
[CrossRef]

Other

G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems 5 (Morgan Kaufmann, 1993), pp. 244–251.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the mode conversion system.

Fig. 2
Fig. 2

Intensity distribution of LP 11 mode. (a) The near-field intensity distribution, (b) the far-field intensity distribution.

Fig. 3
Fig. 3

Experimental result of LP 11 mode conversion. (a) Captured image of far-field intensity distribution before conversion, (b) captured image of far-field intensity distribution after conversion, (c) the quality evaluation function curve.

Fig. 4
Fig. 4

Ideal and experimental intensity distributions of the Gaussian beam.

Equations (4)

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

J = I 2 ( x , y ) d x d y ,
E = cos φ · J 1 ( 3.8317 · r a ) ,
PIB = | x | < r , | y | < r I far - field 2 d x d y I far - field 2 d x d y ,
k = PIB experiment / PIB ideal ,

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