Abstract

The conventional means of generating Bessel–Gauss beams by axicons in the laboratory results in the distinct disadvantage of an abrupt change in intensity at the boundary of the non–diffracting region. We outline theoretically and then demonstrate experimentally a concept for the creation of Bessel–like beams that have a z–dependent cone angle, thereby allowing for a far greater quasi non–diffracting propagation region.

©2010 Optical Society of America

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References

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    [Crossref]
  2. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
    [Crossref]
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    [Crossref]
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  5. I. A. Litvin and A. Forbes, “Bessel-Gauss resonator with internal amplitude filter,” Opt. Commun. 281(9), 2385–2392 (2008).
    [Crossref]
  6. N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel beams in uniaxial crystals,” Quantum Electron. 31(1), 85–89 (2001).
    [Crossref]
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    [Crossref]
  10. A. V. Goncharov, A. Burvall, and C. Dainty, “Systematic design of an anastigmatic lens axicon,” Appl. Opt. 46(24), 6076–6080 (2007).
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2009 (3)

2008 (2)

2007 (2)

M. Dong and J. Pu, “On-axis irradiance distribution of axicons illuminated by spherical wave,” Opt. Laser Technol. 39(6), 1258–1261 (2007).
[Crossref]

A. V. Goncharov, A. Burvall, and C. Dainty, “Systematic design of an anastigmatic lens axicon,” Appl. Opt. 46(24), 6076–6080 (2007).
[Crossref] [PubMed]

2001 (1)

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel beams in uniaxial crystals,” Quantum Electron. 31(1), 85–89 (2001).
[Crossref]

2000 (1)

T. Tanaka and S. Yamamoto, “Comparison of aberration between axicon and lens,” Opt. Commun. 184(1-4), 113–118 (2000).
[Crossref]

1999 (1)

1998 (2)

Z. Jaroszewicz and J. Morales, “Lens axicons: systems composed of a diverging aberrated lens and a perfect converging lens,” J. Opt. Soc. Am. A 15(9), 2383–2390 (1998).
[Crossref]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[Crossref]

1997 (2)

1991 (1)

1989 (1)

1987 (1)

J. Durnin, “Exact solution for nondiffracting beams: I. The scalar theory,” J. Opt. Soc. Am. B 4(4), 651–654 (1987).
[Crossref]

Aruga, T.

Biegert, J.

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[Crossref]

Bowlan, P.

Burvall, A.

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[Crossref]

Cižmár, T.

Clerici, M.

Dainty, C.

Dholakia, K.

Di Trapani, P.

Dong, M.

M. Dong and J. Pu, “On-axis irradiance distribution of axicons illuminated by spherical wave,” Opt. Laser Technol. 39(6), 1258–1261 (2007).
[Crossref]

Durnin, J.

J. Durnin, “Exact solution for nondiffracting beams: I. The scalar theory,” J. Opt. Soc. Am. B 4(4), 651–654 (1987).
[Crossref]

Faccio, D.

Forbes, A.

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

I. A. Litvin and A. Forbes, “Bessel-Gauss resonator with internal amplitude filter,” Opt. Commun. 281(9), 2385–2392 (2008).
[Crossref]

Friberg, A. T.

Goncharov, A. V.

Herman, R. M.

Jaroszewicz, Z.

Jedrkiewicz, O.

Khilo, N. A.

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel beams in uniaxial crystals,” Quantum Electron. 31(1), 85–89 (2001).
[Crossref]

Lewis, J. W. L.

Li, R.

Li, S. W.

Litvin, I. A.

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

I. A. Litvin and A. Forbes, “Bessel-Gauss resonator with internal amplitude filter,” Opt. Commun. 281(9), 2385–2392 (2008).
[Crossref]

Lõhmus, M.

Lotti, A.

McLaren, M. G.

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

Morales, J.

Parigger, C.

Petrova, E. S.

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel beams in uniaxial crystals,” Quantum Electron. 31(1), 85–89 (2001).
[Crossref]

Piksarv, P.

Plemmons, D. H.

Pu, J.

M. Dong and J. Pu, “On-axis irradiance distribution of axicons illuminated by spherical wave,” Opt. Laser Technol. 39(6), 1258–1261 (2007).
[Crossref]

Rubino, E.

Ryzhevich, A. A.

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel beams in uniaxial crystals,” Quantum Electron. 31(1), 85–89 (2001).
[Crossref]

Saari, P.

Takabe, M.

Tanaka, T.

T. Tanaka and S. Yamamoto, “Comparison of aberration between axicon and lens,” Opt. Commun. 184(1-4), 113–118 (2000).
[Crossref]

Tang, Y.

Trebino, R.

Turunen, J.

Valtna-Lukner, H.

Vasara, A.

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[Crossref]

Wiggins, T. A.

Yamamoto, S.

T. Tanaka and S. Yamamoto, “Comparison of aberration between axicon and lens,” Opt. Commun. 184(1-4), 113–118 (2000).
[Crossref]

Yoshikado, S. Y.

Appl. Opt. (4)

J. Opt. Soc. Am. A (3)

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

J. Durnin, “Exact solution for nondiffracting beams: I. The scalar theory,” J. Opt. Soc. Am. B 4(4), 651–654 (1987).
[Crossref]

Opt. Commun. (4)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4-6), 207–211 (1998).
[Crossref]

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[Crossref]

I. A. Litvin and A. Forbes, “Bessel-Gauss resonator with internal amplitude filter,” Opt. Commun. 281(9), 2385–2392 (2008).
[Crossref]

T. Tanaka and S. Yamamoto, “Comparison of aberration between axicon and lens,” Opt. Commun. 184(1-4), 113–118 (2000).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

M. Dong and J. Pu, “On-axis irradiance distribution of axicons illuminated by spherical wave,” Opt. Laser Technol. 39(6), 1258–1261 (2007).
[Crossref]

Quantum Electron. (1)

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel beams in uniaxial crystals,” Quantum Electron. 31(1), 85–89 (2001).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 The optical set–up for the formation of a Bessel–like beam with a cone angle that reduces with propagation distance z.
Fig. 2
Fig. 2 Intensity distribution (a) and angular spectrum (b) of the beam after the second axicon at z = 15 m and f = 0.18 m.
Fig. 3
Fig. 3 Far–field intensity distribution (a) and its central part (b) at z = 15 m and f = 0.28 m.
Fig. 4
Fig. 4 Dependence of the on–axis BLB intensity with propagation distance z (for short distances from the axicon): (a) standard parameters and f = 0.18 m, (b) γ 1 = 0.5°; γ 2 = 0.6° and f = 0.5 m.
Fig. 5
Fig. 5 Dependence of the on–axis BLB and equivalent Gaussian intensity with propagation distance z (for long distances from the axicon): (a) standard parameters and f = 0.18 m, (b) γ 1 = 0.5°; γ 2 = 0.6° and f = 0.5 m.
Fig. 6
Fig. 6 Experimentally measured transverse intensity distribution of the beam as a whole at different distances from the second axicon: (a) z = 0.9 m, (b) z = 6.4 m, (c) the central part of the beam at z = 6.4 m, and (d) the Fourier transform of the field. The outer diameter of the annular field is approximately 30 mm in (а) and 60 mm in (b).

Equations (7)

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a 1 ( ρ , z 1 ) = i λ z 1 exp ( i k 0 ρ 2 2 z 1 ) 0 2 π 0 exp ( ρ 1 2 ρ 0 2 i k 0 γ 1 ρ 1 i k 0 ρ ρ 1 z 1 cos ( ϕ ϕ 1 ) ) ρ 1 d ρ 1 d ϕ 1 ,
a 1 ( ρ , z 1 ) i f z 1 f 1 γ 1 z 1 ρ exp [ i k 0 2 z 1 ( ρ 2 + z 1 / f 1 + i z 1 / z 0 ( z 1 / f 1 ) 2 + ( z 1 / z 0 ) 2 ( ρ γ 1 z 1 ) 2 ) ] ,
a 2 ( ρ , z ) = i λ z 0 2 π 0 a 1 ( ρ 1 , z 1 ) exp ( i k 0 ( ρ 2 + ρ 1 2 2 ρ ρ 1 cos ( ϕ ϕ 1 ) ) 2 z i k 0 γ 2 ρ 1 ) ρ 1 d ρ 1 d ϕ 1 = exp ( i k 0 ρ 2 2 R ( z ) ) [ g + ( ρ , z ) exp ( i k 0 γ ( z ) ρ ) i g ( ρ , z ) exp ( i k 0 γ ( z ) ρ ) ]
g ± ( ρ , z ) = f 2 ( z + z 1 f ) [ γ 2 γ 1 ( 1 + z 1 z ) ] z ρ ± 1 ;
R ( z ) = z ( 1 + z z 1 f ) ;
γ ( z ) = γ 2 z 1 + ( γ 1 γ 2 ) f z 1 + z f .
a 2 ( ρ , z ) 1 2 π k 0 γ ( z ) ρ 2 ( g + ( ρ , z ) + g ( ρ , z ) ) × exp [ i k 0 2 ( ρ 2 z + ρ 2 R ( z ) γ 2 ( z ) R ( z ) ) ] J 0 [ k 0 γ ( z ) ρ ]

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