Abstract

Phase engineering of an axicon’s phase transmission function results in an exponential growth of an on-axis intensity of a diffraction-free or Bessel beam. We show that in a lossy medium obeying Beer’s absorption law/exponential intensity decrease, a beam focused by such an optical element propagates with nearly constant intensity while preserving the quasi-diffraction-free property. Absorption-free beams may find applications in illumination, atmospheric propagation, biomedicine/light diffusion in live tissues, and other situations where light absorption hinders beam propagation.

© 2009 Optical Society of America

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References

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2007 (5)

2006 (2)

2005 (1)

For a recent review on axicons and their applications, see Z. Jaroszewicz, A. Burvall, and A. T. Friberg, Opt. Photonics News 16(4), 34 (2005).
[CrossRef]

2004 (2)

1995 (1)

1993 (1)

1992 (2)

1987 (2)

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

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

1981 (1)

1977 (1)

1954 (1)

1952 (1)

G. T. di Francia, Nuovo Cimento, Suppl. 9, 426 (1952).
[CrossRef]

Agrawal, G. P.

Bara, S.

Bokor, N.

N. Davidson and N. Bokor, Opt. Lett. 29, 3540 (2004).
[CrossRef]

Burvall, A.

For a recent review on axicons and their applications, see Z. Jaroszewicz, A. Burvall, and A. T. Friberg, Opt. Photonics News 16(4), 34 (2005).
[CrossRef]

Chen, N.

Choudhury, A.

Christodoulides, D. N.

G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

Davidson, N.

N. Davidson and N. Bokor, Opt. Lett. 29, 3540 (2004).
[CrossRef]

di Francia, G. T.

G. T. di Francia, Nuovo Cimento, Suppl. 9, 426 (1952).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Durnin, J.

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

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

Eberly, J. H.

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

Friberg, A. T.

For a recent review on axicons and their applications, see Z. Jaroszewicz, A. Burvall, and A. T. Friberg, Opt. Photonics News 16(4), 34 (2005).
[CrossRef]

Golub, I.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Jaroszewicz, Z.

Kalosha, V. P.

Kolodziejczyk, A.

Lax, M.

McLeod, J. H.

Miceli, J. J.

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

Saleh, B. E. A.

B. E. A. Saleh and M. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Sheng, S. C.

S. C. Sheng, Ph.D. dissertation (Stanford University, 1980).

Sheppard, C. J. R.

Siegman, A. E.

Singh, J.

Siviloglou, G. A.

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Sochacki, J.

Teich, M.

B. E. A. Saleh and M. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Xu, Y.

Zamboni-Rached, M.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Nuovo Cimento, Suppl. (1)

G. T. di Francia, Nuovo Cimento, Suppl. 9, 426 (1952).
[CrossRef]

Opt. Express (2)

Opt. Lett. (10)

Opt. Photonics News (1)

For a recent review on axicons and their applications, see Z. Jaroszewicz, A. Burvall, and A. T. Friberg, Opt. Photonics News 16(4), 34 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

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

Other (3)

B. E. A. Saleh and M. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

S. C. Sheng, Ph.D. dissertation (Stanford University, 1980).

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Figures (4)

Fig. 1
Fig. 1

On-axis intensity distributions of beams produced by a logarithmic axicon with geometric parameters d 1 = 0.2 m , d 2 = 0.8 m , and R = 5 mm . The beams propagate in (a) a lossless medium and (b) a medium with power absorption coefficient α = 6 m 1 .

Fig. 2
Fig. 2

Phase retardation of an exponential intensity axicon. The geometric parameters are d 1 = 0.2 m , d 2 = 0.8 m , and R = 5 mm , and the exponential factor is β = 6 m 1 . The dashed and dotted curves correspond to the phases of perfect lenses of focal lengths d 1 and d 2 , respectively.

Fig. 3
Fig. 3

On-axis intensity distributions of beams produced by an exponential axicon with the same geometric parameters as in Fig. 2 and exponential factor β = 6 m 1 . The beams propagate in (a) a lossless medium and (b) an absorbing medium with α = 6 m 1 .

Fig. 4
Fig. 4

Spatial profiles of the quasi-Bessel beams described in Figs. 3b (solid curve) and 1b (dashed curve) at z = d 2 = 0.8 m in the absorbing medium with α = 6 m 1 .

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