Abstract

We report the reduction of sidelobes in tight focusing patterns of radially higher-order Laguerre–Gaussian (LG) beams with nonhelical phase structures. Numerical calculations based on the vectorial Debye theory reveal that a class of annular masks reduces sidelobes in the tight focusing patterns only for radially even-order LG beams. The present scheme produces small focal spots beyond the diffraction limit suitable for application to scanning microscopy, laser fine processing, etc.

© 2008 Optical Society of America

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References

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2007

2006

2005

2004

M. Martínez-Corral, R. Martínez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

S. S. Sherif and P. Török, J. Mod. Opt. 51, 2007 (2004).

C. J. R. Sheppard and A. Choudhury, Appl. Opt. 43, 4322 (2004).
[CrossRef] [PubMed]

2003

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

2002

2000

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

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

1965

A. Boivin and E. Wolf, Phys. Rev. 138, B1561 (1965).
[CrossRef]

1959

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A A253, 358 (1959).

Appl. Opt.

Appl. Phys. Lett.

M. Martínez-Corral, R. Martínez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

J. Mod. Opt.

S. S. Sherif and P. Török, J. Mod. Opt. 51, 2007 (2004).

J. Opt. Soc. Am. A

Opt. Commun.

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

Opt. Express

Opt. Lett.

Phys. Rev.

A. Boivin and E. Wolf, Phys. Rev. 138, B1561 (1965).
[CrossRef]

Phys. Rev. Lett.

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

Proc. R. Soc. London Ser. A

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A A253, 358 (1959).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of focusing of the LG p = 2 l = 0 beam. (b) Geometrical configuration of coordinates. S and I denote points on the wavefront and in the image space, respectively. O indicates the geometrical focus.

Fig. 2
Fig. 2

(a) Half-maximum areas of the central spots for the LG 2 0 beam focused through the mask as functions of β. (b) Power concentrations (η’s) to the central spots as functions of β. Open symbols are those with mask while corresponding closed symbols are those without mask.

Fig. 3
Fig. 3

(a),(b) Focusing patterns of the LG 2 0 beam with and without mask, respectively. (c),(d) E 2 distributions in the y z plane corresponding to (a) and (b), respectively. The white bar in (b) indicates the wavelength. All figures are calculated for NA = 0.85 (air).

Fig. 4
Fig. 4

(a),(b) Focusing patterns of the masked LG 4 0 and LG 6 0 beams, respectively. (c),(d) E 2 distributions on the y z plane corresponding to (a) and (b), respectively. The white bar in (b) indicates the length scale. β is chosen as 3.3 (for the LG 4 0 beam) or 3.8 (for the LG 6 0 beam), whereas NA is commonly 0.85 (air).

Fig. 5
Fig. 5

(a) Focusing pattern of the masked LG 2 0 beam under the condition of NA = 1.2 (water) and β = 2.0 , and (b) the corresponding E 2 distribution on the y z plane ( x = 0 ) . A white bar in (a) shows the length scale.

Equations (3)

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u p l = 0 ( r ) exp ( r 2 w 0 2 ) L p 0 ( 2 r 2 w 0 2 ) .
E ( ρ , φ , z ) = i A π 0 α d θ 0 2 π d ϕ sin θ ( cos θ ) 1 2 e 0 ( θ , ϕ ) × u p ( θ ) e i [ z ̃ cos θ ρ ̃ sin θ cos ( ϕ φ ) ] ,
e 0 ( θ , ϕ ) = 1 2 ( ( 1 cos θ ) sin 2 ϕ ( 1 + cos θ ) + ( 1 cos θ ) cos 2 ϕ 2 sin θ cos ϕ ) .

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