Abstract

We proposed a method of polarization shaping in the focal region with the polarization modulation of incident light. By using an iterative optimization based on a vectorial diffraction calculation with the help of the fast Fourier transform, we can tailor the polarization structure in the focal plane. This provides a novel way to control the vectorial feature of the focal volume with the help of polarization tailoring, which is different from the method using wavefront shaping. The capability of polarization-only modulation on the incident light is demonstrated by optical experiments.

© 2010 Optical Society of America

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References

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2010 (3)

2009 (5)

2008 (4)

H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef] [PubMed]

H. Wand, L. Shi, B. Lukyanchu, C. Sheppard, and C. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

T. G. Jabbour and S. M. Kuebler, Opt. Express 16, 7203 (2008).
[CrossRef] [PubMed]

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, Nat. Photon. 2, 311 (2008).
[CrossRef]

2007 (4)

2006 (3)

2003 (2)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

2002 (2)

2001 (1)

N. Huse, A. Schonle, and S. W. Hell, J Biomed. Opt. 6, 480 (2001).
[CrossRef]

2000 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
[CrossRef]

Abouraddy, A. F.

A. F. Abouraddy and K. C. Toussaint, Jr., Phys. Rev. Lett. 96, 153901 (2006).
[CrossRef] [PubMed]

Bartels, R. A.

Beversluis, M. R.

Boruah, B. R.

B. R. Boruah, Appl. Opt. 49, 701 (2010).
[CrossRef] [PubMed]

B. R. Boruah and M. A. A. Neil, Opt. Commun. 282, 4660 (2009).
[CrossRef]

Brown, T. G.

Chen, J.

X. Wang, Y. Li, J. Chen, C. Guo, J. Ding, and H. Wang, Opt. Express 18, 10786 (2010).
[CrossRef] [PubMed]

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, Opt. Commun. 282, 3421 (2009).
[CrossRef]

Chen, W.

W. Chen and Q. Zhan, J. Opt. 12, 045707 (2010).
[CrossRef]

Chong, C.

H. Wand, L. Shi, B. Lukyanchu, C. Sheppard, and C. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Dickey, F. M.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis Group, 2006).

Ding, J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Fan, Y.

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, Opt. Commun. 282, 3421 (2009).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Guo, C.

Hell, S. W.

N. Huse, A. Schonle, and S. W. Hell, J Biomed. Opt. 6, 480 (2001).
[CrossRef]

Helseth, L. E.

L. E. Helseth, Opt. Commun. 212, 343 (2002).
[CrossRef]

Holswade, S. C.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis Group, 2006).

Huse, N.

N. Huse, A. Schonle, and S. W. Hell, J Biomed. Opt. 6, 480 (2001).
[CrossRef]

Iglesias, I.

I. Iglesias and B. Vohnsena, Opt. Commun. 271, 40 (2007).
[CrossRef]

Jabbour, T. G.

Kozawa, Y.

Kuebler, S. M.

Lasser, T.

Leger, J.

Leitgeb, R. A.

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Leutenegger, M.

Levy, U.

Li, Y.

Lukyanchu, B.

H. Wand, L. Shi, B. Lukyanchu, C. Sheppard, and C. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Masihzadeh, O.

Neil, M. A. A.

B. R. Boruah and M. A. A. Neil, Opt. Commun. 282, 4660 (2009).
[CrossRef]

Ni, W.

Novotny, L.

Pereira, S. F.

H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef] [PubMed]

Qin, J.

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, Opt. Commun. 282, 3421 (2009).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Ramsay, E.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, Nat. Photon. 2, 311 (2008).
[CrossRef]

Rao, R.

Reid, D. T.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, Nat. Photon. 2, 311 (2008).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
[CrossRef]

Sato, S.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).

Schlup, P.

Schonle, A.

N. Huse, A. Schonle, and S. W. Hell, J Biomed. Opt. 6, 480 (2001).
[CrossRef]

Serrels, K. A.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, Nat. Photon. 2, 311 (2008).
[CrossRef]

Shealy, D. L.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis Group, 2006).

Sheppard, C.

H. Wand, L. Shi, B. Lukyanchu, C. Sheppard, and C. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Sheppard, C. J. R.

Shi, L.

H. Wand, L. Shi, B. Lukyanchu, C. Sheppard, and C. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Taylor & Francis Group, 2006).

Stranick, S. J.

Tang, W. T.

Toussaint, K. C.

A. F. Abouraddy and K. C. Toussaint, Jr., Phys. Rev. Lett. 96, 153901 (2006).
[CrossRef] [PubMed]

Urbach, H. P.

H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef] [PubMed]

Vohnsena, B.

I. Iglesias and B. Vohnsena, Opt. Commun. 271, 40 (2007).
[CrossRef]

Wand, H.

H. Wand, L. Shi, B. Lukyanchu, C. Sheppard, and C. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Wang, H.

Wang, X.

Warburton, R. J.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, Nat. Photon. 2, 311 (2008).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
[CrossRef]

Yew, E. Y. S.

Youngworth, K. S.

Zhan, Q.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

J Biomed. Opt. (1)

N. Huse, A. Schonle, and S. W. Hell, J Biomed. Opt. 6, 480 (2001).
[CrossRef]

J. Opt. (1)

W. Chen and Q. Zhan, J. Opt. 12, 045707 (2010).
[CrossRef]

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

Nat. Photon. (2)

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, Nat. Photon. 2, 311 (2008).
[CrossRef]

H. Wand, L. Shi, B. Lukyanchu, C. Sheppard, and C. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Nature (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Opt. Commun. (4)

I. Iglesias and B. Vohnsena, Opt. Commun. 271, 40 (2007).
[CrossRef]

B. R. Boruah and M. A. A. Neil, Opt. Commun. 282, 4660 (2009).
[CrossRef]

L. E. Helseth, Opt. Commun. 212, 343 (2002).
[CrossRef]

X. Wang, J. Ding, J. Qin, J. Chen, Y. Fan, and H. Wang, Opt. Commun. 282, 3421 (2009).
[CrossRef]

Opt. Express (6)

Opt. Lett. (4)

Optik (Jena) (1)

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).

Phys. Rev. Lett. (3)

H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef] [PubMed]

A. F. Abouraddy and K. C. Toussaint, Jr., Phys. Rev. Lett. 96, 153901 (2006).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. A (1)

B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
[CrossRef]

Other (3)

J. J. Stamnes, Waves in Focal Regions (Taylor & Francis Group, 2006).

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor & Francis Group, 2006).

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

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Figures (4)

Fig. 1
Fig. 1

Flow chart for iteratively searching for the optimal polarization-only modulation. The initial polarization angle φ 0 ( x , y ) is a uniform random number in [ 0 , 2 π ] and is renewed after each iteration step. Ω s denotes the support region wherein the field is nonzero.

Fig. 2
Fig. 2

Quadruple-ring-shaped polarization distribution in the focal plane. Polarization-only modulated vector beam with the wavelength λ = 532 nm is focused by a 0.12 NA lens. The width of each ring stripe is 100 λ . The simulation (first row) and experimental results (second row) are presented for comparison. The arrows in the inset give the polarization direction of the analyzer.

Fig. 3
Fig. 3

Polarization structure in the focal plane depicted by Archimedean spiral pattern. Each region is filled by turns with only one of x- and y-polarized components.

Fig. 4
Fig. 4

Four polarization patterns in the focal plane, located on the x and y axes, respectively. Each pattern consists of two concentric circular regions filled by one of x- and y-polarized components. Polarization structure pattern in the left-most column is depicted on a larger size scale for clear viewing.

Equations (4)

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E i ( x , y , z ) = E 0 cos ( φ 0 ( x , y ) ) i + E 0 ( sin φ 0 ( x , y ) ) j ,
E ( x , y , z ) = F { E t ( θ , φ ) e i k z z / cos θ } ,
E t ( θ , φ ) = l 0 ( θ ) cos θ ( [ cos θ cos 2 ϕ + sin 2 ϕ ( cos θ 1 ) sin ϕ cos ϕ cos ϕ sin θ ] cos φ 0 + [ ( cos θ 1 ) sin ϕ cos ϕ cos θ sin 2 ϕ + cos 2 ϕ sin ϕ sin θ ] sin φ 0 ) ,
l 0 ( θ ) = { 1 if 0 θ arcsin ( NA ) 0 otherwise ,

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