Abstract

The intensity distributions of a tightly focused radially polarized beam that has a double-ring-shaped transverse mode pattern were calculated based on vector diffraction theory. The distribution of the longitudinal component near the focus varied drastically with the degree of truncation of the incident beam by a pupil. When the ratio of the pupil radius to the beam radius was 1.3, the longitudinal component disappeared at the focal point, owing to destructive interference. This dark area surrounded by an intense light field was of the order of the wavelength, with excellent intensity symmetry.

© 2006 Optical Society of America

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References

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2005 (3)

2004 (2)

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, Appl. Phys. Lett. 84, 3855 (2004).
[CrossRef]

Q. Zhan, Opt. Express 12, 3377 (2004).
[CrossRef] [PubMed]

2002 (1)

T. Freegarde and K. Dholakia, Phys. Rev. A 66, 013413 (2002).
[CrossRef]

2001 (1)

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

2000 (4)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

J. Arlt and M. J. Padgett, Opt. Lett. 25, 191 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
[CrossRef] [PubMed]

1999 (2)

V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999).
[CrossRef]

A. V. Nesterov and V. G. Niziev, Appl. Phys. B 33, 1817 (1999).

1998 (1)

1997 (1)

1993 (1)

1990 (1)

1972 (2)

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

1965 (1)

A. Boivin and E. Wolf, Phys. Rev. 138, 1561 (1965).
[CrossRef]

1959 (1)

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

Ahmed, M. A.

T. Moser, H. Glur, V. Romano, F. Pigeon, O. Parriaux, M. A. Ahmed, and T. Graf, Appl. Phys. B 80, 707 (2005).
[CrossRef]

Arlt, J.

Beversluis, M.

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Boivin, A.

A. Boivin and E. Wolf, Phys. Rev. 138, 1561 (1965).
[CrossRef]

Bomzon, Z.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Brown, T.

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Brown, T. G.

Clark, G. H.

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Dholakia, K.

T. Freegarde and K. Dholakia, Phys. Rev. A 66, 013413 (2002).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Ford, D. H.

Freegarde, T.

T. Freegarde and K. Dholakia, Phys. Rev. A 66, 013413 (2002).
[CrossRef]

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Glur, H.

T. Moser, H. Glur, V. Romano, F. Pigeon, O. Parriaux, M. A. Ahmed, and T. Graf, Appl. Phys. B 80, 707 (2005).
[CrossRef]

Graf, T.

T. Moser, H. Glur, V. Romano, F. Pigeon, O. Parriaux, M. A. Ahmed, and T. Graf, Appl. Phys. B 80, 707 (2005).
[CrossRef]

Hasman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Kim, G. H.

Kimura, W. D.

Kozawa, Y.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Li, Y.

Matsumura, K.

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Miyaji, G.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, Appl. Phys. Lett. 84, 3855 (2004).
[CrossRef]

Miyanaga, N.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, Appl. Phys. Lett. 84, 3855 (2004).
[CrossRef]

Moser, T.

T. Moser, H. Glur, V. Romano, F. Pigeon, O. Parriaux, M. A. Ahmed, and T. Graf, Appl. Phys. B 80, 707 (2005).
[CrossRef]

Mushiake, Y.

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Nakajima, N.

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999).
[CrossRef]

A. V. Nesterov and V. G. Niziev, Appl. Phys. B 33, 1817 (1999).

Niziev, V. G.

A. V. Nesterov and V. G. Niziev, Appl. Phys. B 33, 1817 (1999).

V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999).
[CrossRef]

Novotny, L.

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Ohbayashi, K.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, Appl. Phys. Lett. 84, 3855 (2004).
[CrossRef]

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Padgett, M. J.

Parriaux, O.

T. Moser, H. Glur, V. Romano, F. Pigeon, O. Parriaux, M. A. Ahmed, and T. Graf, Appl. Phys. B 80, 707 (2005).
[CrossRef]

Pigeon, F.

T. Moser, H. Glur, V. Romano, F. Pigeon, O. Parriaux, M. A. Ahmed, and T. Graf, Appl. Phys. B 80, 707 (2005).
[CrossRef]

Pohl, D.

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Richards, B.

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

Romano, V.

T. Moser, H. Glur, V. Romano, F. Pigeon, O. Parriaux, M. A. Ahmed, and T. Graf, Appl. Phys. B 80, 707 (2005).
[CrossRef]

Sato, S.

Sueda, K.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, Appl. Phys. Lett. 84, 3855 (2004).
[CrossRef]

Tidwell, S. C.

Tovar, A. A.

Tsubakimoto, K.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, Appl. Phys. Lett. 84, 3855 (2004).
[CrossRef]

Wolf, E.

A. Boivin and E. Wolf, Phys. Rev. 138, 1561 (1965).
[CrossRef]

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

Youngworth, K.

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Youngworth, K. S.

Zhan, Q.

Zhang, Y.

Zhao, Y.

Appl. Opt. (2)

Appl. Phys. B (2)

T. Moser, H. Glur, V. Romano, F. Pigeon, O. Parriaux, M. A. Ahmed, and T. Graf, Appl. Phys. B 80, 707 (2005).
[CrossRef]

A. V. Nesterov and V. G. Niziev, Appl. Phys. B 33, 1817 (1999).

Appl. Phys. Lett. (3)

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, Appl. Phys. Lett. 84, 3855 (2004).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. D (1)

V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999).
[CrossRef]

Opt. Commun. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. (1)

A. Boivin and E. Wolf, Phys. Rev. 138, 1561 (1965).
[CrossRef]

Phys. Rev. A (1)

T. Freegarde and K. Dholakia, Phys. Rev. A 66, 013413 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Proc. IEEE (1)

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

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

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Figures (4)

Fig. 1
Fig. 1

(a) Theoretical intensity distribution of radially polarized TEM 11 * modes and (b) instantaneous polarization state.

Fig. 2
Fig. 2

Calculated intensity profiles at the focal point ( z = 0 ) for β 0 = ( a ) 2.5, (b) 2.0, (c) 1.5, (d) 1.3, with a NA of 1.2 and n = 1.33 . The total intensity (solid curve), the longitudinal component (dashed curve), and the radial component (dotted curve) are represented in each figure. Every intensity profile is normalized to the maximum of the total intensity in (b). The horizontal axis is in units of wavelength.

Fig. 3
Fig. 3

Calculated intensity distributions of (a) the radial component and (b) the longitudinal component in the focal area for β 0 = 1.3 with a NA of 1.2 and n = 1.33 . Both axes are in units of wavelength.

Fig. 4
Fig. 4

Total intensity distribution in the focal area obtained by summation of the results of Fig. 3. Inset, intensity profiles in (a) the beam propagation direction, (b) the radial direction, and (c) the direction of minimal intensity. Both axes are in units of wavelength.

Equations (4)

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E ( r , ϕ , z ) = E r e ̂ r + E r e ̂ z ,
E r ( r , ϕ , z ) = A 0 θ max cos 1 2 ( θ ) sin ( 2 θ ) l 0 ( θ ) J 1 ( k r sin θ ) exp ( i k z cos θ ) d θ ,
E z ( r , ϕ , z ) = 2 i A 0 θ max cos 1 2 ( θ ) sin 2 ( θ ) l 0 ( θ ) J 0 ( k r sin θ ) exp ( i k z cos θ ) d θ ,
l 0 ( θ ) = β 0 2 sin θ sin 2 θ max exp [ ( β 0 sin θ sin θ max ) 2 ] L p 1 [ 2 ( β 0 sin θ sin θ max ) 2 ] .

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