Abstract

We experimentally demonstrate the generation of a flat-top intensity distribution using a radially polarized vector beam. Our approach uses higher numerical aperture focusing than what has been previously reported for a single, fixed, vector beam. In addition, the flat-top focus generated in our scheme exhibits a polarization gradient along the radial coordinate in the focal volume, with an on-axis longitudinal field component that persists over 2λ, which is a stark difference from conventional flat-top fields, which exhibit intensity profiles that are uniformly polarized. Our experimental results are found to be in good agreement with the theoretical prediction.

© 2014 Optical Society of America

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V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
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2001

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[CrossRef]

1993

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

1991

1981

1979

1959

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

Agresti, J.

Arpali, C.

Baykal, Y. K.

Belanger, P. A.

Bhardwaj, V. R.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
[CrossRef]

Borghi, R.

Brown, T. G.

Burch, J.

Burnham, R. L.

Cheng, W.

Cherezova, T. Y.

Chesnokov, S. S.

Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Corkum, P. B.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
[CrossRef]

D’Ambrosio, E.

Davis, J. A.

Defrutos, A. M.

DeSalvo, R.

Dickey, F. M.

F. M. Dickey and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, 2000).

Du, S. J.

Evans, G. H.

Eyyuboglu, H. T.

Forbes, A.

Forest, D.

Gan, X. S.

Gu, M.

B. H. Jia, X. S. Gan, and M. Gu, Opt. Express 13, 6821 (2005).
[CrossRef]

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

Han, W.

Hao, B.

Haskal, H. M.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2012).

Hnatovsky, C.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
[CrossRef]

Hoffnagle, J. A.

Holswade, S. C.

F. M. Dickey and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, 2000).

Jabbour, T. G.

Jefferson, C. M.

Jia, B. H.

Jiang, P. Z.

Kaptsov, L. N.

Kasinski, J. J.

Kudryashov, A. V.

Kuebler, S. M.

Lagrange, B.

Leger, J.

Leger, J. R.

Li, Y. J.

Litvin, I. A.

Liu, Z. J.

H. T. Ma, Z. J. Liu, P. Z. Jiang, X. J. Xu, and S. J. Du, Opt. Express 19, 13105 (2011).
[CrossRef]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Ma, H. T.

H. T. Ma, Z. J. Liu, P. Z. Jiang, X. J. Xu, and S. J. Du, Opt. Express 19, 13105 (2011).
[CrossRef]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Ma, Y. X.

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Mackowsky, J. M.

Michel, C.

Miller, J.

Montorio, J. L.

Moreno, I.

Morgado, N.

Murokh, A.

J. Rosenzweig, A. Murokh, and C. Pellegrini, Phys. Rev. Lett. 74, 2467 (1995).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2012).

Pare, C.

Pellegrini, C.

J. Rosenzweig, A. Murokh, and C. Pellegrini, Phys. Rev. Lett. 74, 2467 (1995).
[CrossRef]

Pinard, L.

Quintanilla, M.

Rajeev, P. P.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
[CrossRef]

Rayner, D. M.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
[CrossRef]

Remilleux, A.

Richards, B.

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

Rosenzweig, J.

J. Rosenzweig, A. Murokh, and C. Pellegrini, Phys. Rev. Lett. 74, 2467 (1995).
[CrossRef]

Roxworthy, B. J.

B. J. Roxworthy and K. C. Toussaint, New J. Phys. 12, 073012 (2010).
[CrossRef]

Samarkin, V. V.

Santarsiero, M.

Schadt, M.

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Sheppard, C. J. R.

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Simoni, B.

Simova, E.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
[CrossRef]

Stalder, M.

Tarallo, M. G.

Taylor, R. S.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
[CrossRef]

Toussaint, K. C.

S. Tripathi and K. C. Toussaint, Opt. Express 20, 10788 (2012).
[CrossRef]

B. J. Roxworthy and K. C. Toussaint, New J. Phys. 12, 073012 (2010).
[CrossRef]

Tripathi, S.

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Wang, X. L.

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Willems, P.

Wolf, E.

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

Xu, X. J.

H. T. Ma, Z. J. Liu, P. Z. Jiang, X. J. Xu, and S. J. Du, Opt. Express 19, 13105 (2011).
[CrossRef]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Yew, E. Y. S.

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

Youngworth, K. S.

Zhan, Q.

Zhan, Q. W.

Zhou, P.

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Adv. Opt. Photon.

Appl. Opt.

J. Mod. Opt.

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

J. Opt.

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

New J. Phys.

B. J. Roxworthy and K. C. Toussaint, New J. Phys. 12, 073012 (2010).
[CrossRef]

Opt. Commun.

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, Phys. Rev. Lett. 96, 057404 (2006).
[CrossRef]

J. Rosenzweig, A. Murokh, and C. Pellegrini, Phys. Rev. Lett. 74, 2467 (1995).
[CrossRef]

Proc. R. Soc. A

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

Other

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2012).

F. M. Dickey and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, 2000).

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Figures (6)

Fig. 1.
Fig. 1.

Intensities of Gaussian profile, 5th- and 20th-order SG profiles.

Fig. 2.
Fig. 2.

(a) Simulated intensity distribution in the focal plane for an input radial beam focused by a lens of NA=0.6 (red), 0.7 (green), 0.8 (purple), and 0.9 (blue). Calculated intensity and polarization (green arrows) distribution in the vicinity of focus for flat-top focusing for (b) the xy plane, and (c) the xz plane.

Fig. 3.
Fig. 3.

(a) Schematic of the experimental setup. (b) Fluorescence image of an isolated particle captured by the CCD camera and (c) the experimentally measured PSF of the system.

Fig. 4.
Fig. 4.

Intensity distribution in the focal plane recorded by the PMT for the (a) flat-top focus generated by a radially polarized beam, and for the (b) azimuthally polarized beam.

Fig. 5.
Fig. 5.

Simulated time-averaged distributions of intensity (|E|2) and the Poynting vector (Sz) in yz plane, calculated at NA=0.745 for (a), (b) a radially polarized beam, (c), (d) a linearly polarized Gaussian beam, and (e), (f) an azimuthally polarized beam.

Fig. 6.
Fig. 6.

Simulated time-averaged intensity distribution of the longitudinal component of the flat-top focus.

Equations (2)

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E(ρ,φ,z)=ikf22ω0n1n2E0eikf[i(I1I2)cosφi(I1I2)sinφ4I0],
I0=0θ0fωcosθsin3θJ0(kρsinθ)eikzcosθdθ,I1=0θ0fωcosθsin2θ(1+3cosθ)J1(kρsinθ)eikzcosθdθ,I2=0θ0fωcosθsin2θ(1cosθ)J1(kρsinθ)eikzcosθdθ,

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