Abstract

We show that it is feasible to design and manufacture a refractive logarithmic axicon that generates a quasi- diffraction-free/Bessel beam with nearly constant beam size and intensity over a predetermined range. The novel optical element was characterized with both coherent and incoherent light, and good correspondence with the predicted behavior of the intensity distribution and spot size was found. The energy flow was also found to be nearly constant over most of the designed range. Logarithmic axicons may find applications in situations where large depth of field and uniform axial intensity/energy distributions are important.

© 2010 Optical Society of America

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2009 (2)

2008 (1)

2007 (1)

2006 (1)

2005 (3)

P. Fischer, C. T. A. Brown, J. E. Morris, C. Lopez-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, Opt. Express 13, 6657 (2005).
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[CrossRef]

2003 (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, J. Opt. A 5, S164 (2003).
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1998 (1)

M. Honkanen and J. Turunen, Opt. Commun. 154, 368 (1998).
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1993 (1)

1992 (3)

1990 (1)

1987 (1)

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1954 (1)

Bara, S.

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Booth, M. J.

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[CrossRef]

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[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Fischer, P.

Friberg, T.

Z. Jaroszewicz, A. Burvall, and T. Friberg, Opt. Photonics News 16, 34 (2005).
[CrossRef]

George, N.

Golub, I.

Honkanen, M.

M. Honkanen and J. Turunen, Opt. Commun. 154, 368 (1998).
[CrossRef]

Jaroszewicz, Z.

Juskaitis, R.

Kolodziejczyk, A.

Konforti, N.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, J. Opt. A 5, S164 (2003).
[CrossRef]

Lopez-Mariscal, C.

Makowski, M.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Marom, E.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, J. Opt. A 5, S164 (2003).
[CrossRef]

McLeod, J. H.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Mikula, G.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Mirtchev, T.

Morris, J. E.

Nelson, J. S.

Prokopowicz, C.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Ren, H.

Sibbett, W.

Sochacki, J.

Staronski, L. R.

Sypek, M.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Tremblay, R.

Turunen, J.

M. Honkanen and J. Turunen, Opt. Commun. 154, 368 (1998).
[CrossRef]

Wilson, T.

Wright, E. M.

Zalevsky, Z.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, J. Opt. A 5, S164 (2003).
[CrossRef]

Zhao, Y.

Appl. Opt. (2)

J. Opt. A (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, J. Opt. A 5, S164 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Opt. Commun. (1)

M. Honkanen and J. Turunen, Opt. Commun. 154, 368 (1998).
[CrossRef]

Opt. Eng. (1)

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (8)

Opt. Photonics News (1)

Z. Jaroszewicz, A. Burvall, and T. Friberg, Opt. Photonics News 16, 34 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Other (1)

Z. Jaroszewicz, in Research and Development Treatises (SPIE Polish Chapter, 1997), Vol. 5.

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Figures (4)

Fig. 1
Fig. 1

Sag (thickness) versus radius of a forward logarithmic axicon (solid line) and lenses with f = 50 mm (dashed curve) and f = 150 mm (dotted curve).

Fig. 2
Fig. 2

(a) Measured on-axis intensity distributions of beams produced by a forward logarithmic axicon with a sag shown in Fig. 1 for a white-light source (solid curve) and for a laser (dotted curve). (b) Calculated on-axis intensity distributions of a forward logarithmic axicon with the same parameters as in Fig. 1. (c) Measured on-axis intensity distribution for a classical, 5 ° base angle, axicon.

Fig. 3
Fig. 3

Transverse intensity distributions of beams produced by (a) classical axicon and (b) logarithmic axicon with a calibration scale.

Fig. 4
Fig. 4

Quasi-Bessel beam spot size of a forward logarithmic axicon as a function of distance from the axicon.

Equations (2)

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φ ( r ) = 1 2 a ln ( f 1 + a r 2 ) + const,
N = Int ( 1.67 ω / Δ F W H M 1 / 2 2 ) ,

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