Abstract

We investigate the focusing properties of a double-ring-shaped azimuthally polarized beam by a high numerical aperture (NA) lens axicon based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal hole of 0.5λ having large uniform focal depth of 48λ without any annular aperture. We also observed that the distribution of the total intensity near the focus has little variation with the degree of truncation β of the incident beam by the pupil. The authors expect such a super-long dark channel may find applications in optical, biological, and atmospheric sciences.

© 2012 Optical Society of America

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References

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K. B. Rajesh, N. Veera Bagu Suresh, P. M. Anbarasan, and K. Gokulakrishnan, Opt. Laser Technol. 43, 1037 (2011).
[Crossref]

K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, T. V. S. Pillai, and N. Veera Bagu Suresh, Optik 122, 1619 (2011).
[Crossref]

B. Tian and J. Pu, Opt. Lett 36, 2014 (2011).
[Crossref]

2010 (3)

2009 (1)

2008 (2)

2005 (1)

J. X. Pu, X. Y. Liu, and S. Nemoto, Opt. Commun. 252, 7 (2005).
[Crossref]

2004 (2)

2001 (1)

2000 (2)

1998 (1)

1959 (1)

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

Ahluwalia, B.

Anbarasan, P. M.

K. B. Rajesh, N. Veera Bagu Suresh, P. M. Anbarasan, and K. Gokulakrishnan, Opt. Laser Technol. 43, 1037 (2011).
[Crossref]

K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, T. V. S. Pillai, and N. Veera Bagu Suresh, Optik 122, 1619 (2011).
[Crossref]

K. B. Rajesh, Z. Jaroszewicz, and P. M. Anbarasan, Opt. Express 18, 26799 (2010).
[Crossref]

K. B. Rajesh and P. M. Anbarasan, Chin. Opt. Lett. 6, 785 (2008).
[Crossref]

K. B. Rajesh and P. M. Anbarasan, Chin. Opt. Lett. 6, 785 (2008).
[Crossref]

Arlt, J.

Bigelow, N. P.

Bouma, B. E.

Brown, T.

Dally, A.

Desyatnikov, A. S.

Ejnisman, R.

Gokulakrishnan, K.

K. B. Rajesh, N. Veera Bagu Suresh, P. M. Anbarasan, and K. Gokulakrishnan, Opt. Laser Technol. 43, 1037 (2011).
[Crossref]

He, X.

Isenhower, L.

Izdebskaya, Y. V.

Jaroszewicz, Z.

Kivshar, Y. S.

Krolikowski, W.

Lee, S.

Liu, X. Y.

J. X. Pu, X. Y. Liu, and S. Nemoto, Opt. Commun. 252, 7 (2005).
[Crossref]

Morales, J.

Nemoto, S.

J. X. Pu, X. Y. Liu, and S. Nemoto, Opt. Commun. 252, 7 (2005).
[Crossref]

Padgett, M.

Pillai, T. V. S.

K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, T. V. S. Pillai, and N. Veera Bagu Suresh, Optik 122, 1619 (2011).
[Crossref]

Pu, J.

B. Tian and J. Pu, Opt. Lett 36, 2014 (2011).
[Crossref]

Pu, J. X.

J. X. Pu, X. Y. Liu, and S. Nemoto, Opt. Commun. 252, 7 (2005).
[Crossref]

Rahman, A.

Rajesh, K. B.

K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, T. V. S. Pillai, and N. Veera Bagu Suresh, Optik 122, 1619 (2011).
[Crossref]

K. B. Rajesh, N. Veera Bagu Suresh, P. M. Anbarasan, and K. Gokulakrishnan, Opt. Laser Technol. 43, 1037 (2011).
[Crossref]

K. B. Rajesh, Z. Jaroszewicz, and P. M. Anbarasan, Opt. Express 18, 26799 (2010).
[Crossref]

K. B. Rajesh and P. M. Anbarasan, Chin. Opt. Lett. 6, 785 (2008).
[Crossref]

K. B. Rajesh and P. M. Anbarasan, Chin. Opt. Lett. 6, 785 (2008).
[Crossref]

Richards, B.

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

Rode, A. V.

Rudy, P.

Saffman, M.

Shvedov, V. G.

Tao, S.

Tearney, G. J.

Tian, B.

B. Tian and J. Pu, Opt. Lett 36, 2014 (2011).
[Crossref]

Veera Bagu Suresh, N.

K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, T. V. S. Pillai, and N. Veera Bagu Suresh, Optik 122, 1619 (2011).
[Crossref]

K. B. Rajesh, N. Veera Bagu Suresh, P. M. Anbarasan, and K. Gokulakrishnan, Opt. Laser Technol. 43, 1037 (2011).
[Crossref]

Wang, J.

Williams, W.

Wolf, E.

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

Xu, P.

Yelin, D.

Youngworth, K.

Yuan, X.

Zhan, M.

Chin. Opt. Lett. (2)

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

Opt. Commun. (1)

J. X. Pu, X. Y. Liu, and S. Nemoto, Opt. Commun. 252, 7 (2005).
[Crossref]

Opt. Express (5)

Opt. Laser Technol. (1)

K. B. Rajesh, N. Veera Bagu Suresh, P. M. Anbarasan, and K. Gokulakrishnan, Opt. Laser Technol. 43, 1037 (2011).
[Crossref]

Opt. Lett (1)

B. Tian and J. Pu, Opt. Lett 36, 2014 (2011).
[Crossref]

Opt. Lett. (4)

Optik (1)

K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, T. V. S. Pillai, and N. Veera Bagu Suresh, Optik 122, 1619 (2011).
[Crossref]

Proc. R. Soc. A (1)

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

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Figures (5)

Fig. 1.
Fig. 1.

Scheme for a double-ring-shaped azimuthally polarized beam focused by high NA objective lens axicon.

Fig. 2.
Fig. 2.

Intensity distribution of the focused field near focus for the double-ring-shaped azimuthally polarized beam focused with (a)  δ = 0 (full aperture lens), (b)  δ = 0.7575 (annular lens), and (c) high NA lens axicon. The other parameters are β = 1.2 and NA = 0.6 .

Fig. 3.
Fig. 3.

Intensity distribution of the focused field near focus for the double-ring-shaped azimuthally polarized beam focused by a high NA lens with (a)  δ = 0 (full aperture lens), (b)  δ = 0.7575 (annular lens), and (c) high NA lens axicon. The other parameters are β = 1.2 and NA = 0.9 .

Fig. 4.
Fig. 4.

(a) FWHM of the focal hole generated by the annular lens ( δ = 0.75 ) (black line) and the proposed high NA lens axicon ( δ = 0 ) (red line). (b) shows the DOF of the high NA lens axicon (red line) is much larger when compared to the annular aperture lens (black line).

Fig. 5.
Fig. 5.

Intensity distribution of the focused field near focus for the double-ring-shaped azimuthally polarized beam focused by a high NA lens axicon ( NA = 0.9 ) for (a)  β = 1.3 and (b)  β = 1.5 .

Equations (3)

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E ( r , φ , z ) = [ E r E φ E z ] = [ 0 2 A δ · α α cos 1 2 ( θ ) sin ( θ ) A ( θ ) J 1 ( k r sin θ ) e i k z cos θ d θ 0 ] ,
A ( θ ) = β 2 sin θ sin 2 θ exp [ ( β sin θ sin α ) 2 ] L p 1 [ 2 ( β sin θ sin α ) 2 ] ,
T ( θ ) = exp ( I k ( ψ ( sin ( θ ) sin α ) ) 4 + ( 1 2 f ( sin ( θ ) sin α ) 2 ) ) .

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