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Focusing of doughnut laser beams by a high numerical-aperture objective in free space

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Abstract

We report on, in this letter, a phenomenon that the central zero-intensity point of a doughnut beam, caused by phase singularity, disappears in the focus, when such a beam is focused by a high numerical-aperture objective in free space. In addition, the focal shape of the doughnut beam of a given topological charge exhibits the increased ring intensity in the direction orthogonal to the incident polarization state and an elongation in the polarization direction. These phenomena are caused by the effect of depolarization, associated with a high numerical-aperture objective, and become pronounced by the use of a central obstruction in the objective aperture.

©2003 Optical Society of America

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Figures (5)

Fig. 1.
Fig. 1. Calculated intensity distribution in the focal region of a doughnut beam focused by an objective with NA=1 ((a)–(c)) and NA=0.2 ((d)–(f)): (a) and (d) Topological charge 1; (b) and (e) Topological charge 2; (c) and (f) Topological charge 3.
Fig. 2.
Fig. 2. Contour plots of the intensity distribution in the focal region of an objective with NA=1, illuminated by a doughnut beam of topological charge 1. (a) |Ex |2; (b) |Ey |2; (c)|Ez |2; (d) |E| 2.
Fig. 3.
Fig. 3. Contour plots of the intensity distribution in the focal region of an objective with NA=1, illuminated by a doughnut beam of topological charge 2. (a) |Ex |2; (b) |Ey |2; (c) |Ez |2; (d) |E| 2.
Fig. 4.
Fig. 4. Contour plots of the intensity distribution in the focal region of an objective with NA=1, illuminated by a doughnut beam of topological charge 3. (a) |Ex |2; (b) |Ey |2; (c) |Ez |2; (d) |E| 2.
Fig. 5.
Fig. 5. Dependence of the peak ratio of |Ez |2/ |Ex |2 on the numerical aperture (a) and on the obstruction radius ε (b).

Equations (3)

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E ( r 2 , ψ , z 2 ) = i λ Ω cos θ exp ( in φ ) exp [ i k r 2 sin θ cos ( φ ψ ) ] exp ( i k z 2 cos θ )
{ [ cos θ + sin 2 φ ( 1 cos θ ) ] i + cos φ sin φ ( cos θ 1 ) j + cos φ sin θ k }
sin θd θd φ
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