Abstract

Diffraction optical devices of modest degrees of freedom (DOF), such as deformable mirrors, have not been exploited as general-purpose transformers of optical fields. Described in this Letter is a method that guides deformable mirrors to optimal surfaces allowed by the DOF for various desirable outcomes. The method is based on a modal optimization procedure with the help of Walsh functions in controlling the variables of the mirrors, i.e. the actuators. It is shown that a deformable mirror of modest DOF can provide field transformations for arbitrary beam-splitting, formation of ring-shaped beams, and coherent beam combining.

© 2011 Optical Society of America

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References

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    [CrossRef]

2011 (1)

T. G. Bifano, Nat. Photon. 5, 21 (2011).
[CrossRef]

2010 (1)

2005 (2)

2003 (1)

1999 (1)

1998 (1)

1997 (1)

T. Haist, M. Schonleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Beauchamp, K. G.

K. G. Beauchamp, Walsh Functions and Their Applications (Academic Press, 1975).

Bifano, T. G.

T. G. Bifano, Nat. Photon. 5, 21 (2011).
[CrossRef]

Fan, T. Y.

T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
[CrossRef]

Grier, D. G.

Haist, T.

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
[CrossRef]

T. Haist, M. Schonleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Ladavac, K.

Lee, S.-H.

Polin, M.

Reicherter, M.

Roichman, Y.

Schonleber, M.

T. Haist, M. Schonleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Sivokon, V. P.

Spivey, C.

F. Wang and C. Spivey, 2010, in Frontiers in Optics, OSA Technical Digest (CD), paper FTuO1.

Tiziani, H. J.

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
[CrossRef]

T. Haist, M. Schonleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 3rd ed. (CRC Press, 2011).

Vorontsov, M. A.

Wagemann, E. U.

Wang, F.

F. Wang, Appl. Opt. 49, G60 (2010).
[CrossRef]

F. Wang and C. Spivey, 2010, in Frontiers in Optics, OSA Technical Digest (CD), paper FTuO1.

Wolfram, S.

S. Wolfram, A New Kind of Science (Wolfram Media, Champaign, IL, 2002).

Yuan, X.-C.

Zhang, D. W.

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005).
[CrossRef]

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

Nat. Photon. (1)

T. G. Bifano, Nat. Photon. 5, 21 (2011).
[CrossRef]

Opt. Commun. (1)

T. Haist, M. Schonleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (5)

K. G. Beauchamp, Walsh Functions and Their Applications (Academic Press, 1975).

F. Wang and C. Spivey, 2010, in Frontiers in Optics, OSA Technical Digest (CD), paper FTuO1.

S. Wolfram, A New Kind of Science (Wolfram Media, Champaign, IL, 2002).

Adaptive Optics for Vision Science, J.Porter, H.Queener, J.Lin, K.Thorn, and A.Awwal eds. (Wiley-Interscience, Hoboken, N.J., USA, 2006).
[CrossRef]

R. K. Tyson, Principles of Adaptive Optics, 3rd ed. (CRC Press, 2011).

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Figures (4)

Fig. 1
Fig. 1

Row A: formation of seven beams in a hexagon pattern; row B: formation of nine beams arranged in a spiral. From left to right: deformable-mirror phase maps, focal-plane light distributions in logarithm display, and focal-plane light distributions in linear display. The angle spans of the intensity displays are 120 λ / D edge to edge, D being the diameter of the incident beam.

Fig. 2
Fig. 2

Focal-plane light intensity distributions (bottom row) shown with the corresponding phase maps of the deformable mirror (top row). The angle spans of the intensity displays are the same as Fig. 1.

Fig. 3
Fig. 3

Combination of coherent beams. Row A: combination of five beams in a linear array; row B: five beams with a pentagon arrangement.

Fig. 4
Fig. 4

Focal-plane beam profiles for the first source arrangement, in linear (left) and logarithm (right) displays. The dashed lines are for flat mirror; the solid lines are for optimized mirror.

Equations (5)

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

U = h · exp ( j k a k W k ) = h · ( cos a k j sin a k · W k ) exp ( j k k a k W k ) = A · cos a k j B · sin a k ,
E = A ͡ · cos a k j B ͡ · sin a k ,
I = | E | 2 = C 0 + C 1 [ cos ( a k + φ ) ] 2 ,
cost function = m 1 I m ,
cost function = p 1 I p + g · c I c ,

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