Abstract

A new method of generating nondiffracting beams is presented. It consists of focusing a Gaussian beam in the vicinity of an opaque disk. A beam is generated whose central peak is surrounded by a wide number of bright rings (250). After collimation, the beam propagates without changing the rings’ radii, similar to a diffraction-free beam. The central peak can conserve its dimension over more than 5m. The diameter of the central peak is adjusted by choosing the focal length of the collimating lens. Experimental results are well predicted by our theoretical developments that simulate exactly the paraxial diffraction.

© 2007 Optical Society of America

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References

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2005 (1)

2004 (2)

K. A. Higginson, M. A. Costolo, and E. A. Rietman, "Adaptive geometric optics derived from nonlinear acoustic effects," Appl. Phys. Lett. 84, 843-845 (2004).
[CrossRef]

S. Khonina, V. Kotlyar, R. Skidanov, V. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, "Rotation of microparticles with Bessel beams generated by diffractive elements," J. Mol. Spectrosc. 51, 2167-2184 (2004).

2003 (1)

K. Wang, L. Zeng, and C. Yin, "Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement," Opt. Commun. 216, 99-103 (2003).
[CrossRef]

2000 (2)

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297-301 (2000).
[CrossRef]

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre Gaussian beams by axicon," Opt. Commun. 184, 105-112 (2000).
[CrossRef]

1999 (2)

T. Aruga, S. W. Li, S. Yoshikado, M. Takabe, and R. Li, "Nondiffracting narrow light beam with small atmospheric turbulence-influenced propagation," Appl. Opt. 38, 3152-3156 (1999).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Efficiency of second-harmonic generation with Bessel beams," Phys. Rev. A 60, 2438-2441 (1999).
[CrossRef]

1997 (1)

1996 (2)

S. P. Tewari, H. Huang, and R. W. Boyd, "Theory of third-harmonic generation using Bessel beams, and self-phase-matching," Phys. Rev. A 54, 2314-2325 (1996).
[CrossRef] [PubMed]

N. E. Andreev, S. S. Bychkov, V. V. Kotlyar, L. Ya. Margolin, L. N. Pyatnitskii, and P. G. Serafimovich, "Formation of high-power hollow Bessel light beams," Quantum Electron. 26, 126-130 (1996).
[CrossRef]

1993 (2)

1992 (1)

V. Kotlyar, S. Khonina, V. Soifer, M. Shinkaryev, and G. Uspleniev, "Trochoson," Opt. Commun. 91, 158-162 (1992).
[CrossRef]

1989 (2)

1987 (1)

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

K. A. Higginson, M. A. Costolo, and E. A. Rietman, "Adaptive geometric optics derived from nonlinear acoustic effects," Appl. Phys. Lett. 84, 843-845 (2004).
[CrossRef]

J. Mol. Spectrosc. (1)

S. Khonina, V. Kotlyar, R. Skidanov, V. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, "Rotation of microparticles with Bessel beams generated by diffractive elements," J. Mol. Spectrosc. 51, 2167-2184 (2004).

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

Opt. Commun. (4)

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre Gaussian beams by axicon," Opt. Commun. 184, 105-112 (2000).
[CrossRef]

V. Kotlyar, S. Khonina, V. Soifer, M. Shinkaryev, and G. Uspleniev, "Trochoson," Opt. Commun. 91, 158-162 (1992).
[CrossRef]

K. Wang, L. Zeng, and C. Yin, "Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement," Opt. Commun. 216, 99-103 (2003).
[CrossRef]

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297-301 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Efficiency of second-harmonic generation with Bessel beams," Phys. Rev. A 60, 2438-2441 (1999).
[CrossRef]

S. P. Tewari, H. Huang, and R. W. Boyd, "Theory of third-harmonic generation using Bessel beams, and self-phase-matching," Phys. Rev. A 54, 2314-2325 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

T. Wulle and S. Herminghaus, "Nonlinear optics of Bessel beams," Phys. Rev. Lett. 70, 1401-1404 (1993).
[CrossRef] [PubMed]

Quantum Electron. (1)

N. E. Andreev, S. S. Bychkov, V. V. Kotlyar, L. Ya. Margolin, L. N. Pyatnitskii, and P. G. Serafimovich, "Formation of high-power hollow Bessel light beams," Quantum Electron. 26, 126-130 (1996).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Diffracted beam 3.3 ± 0.2 cm after the disk.

Fig. 3
Fig. 3

Out-of-axis rings numbered 100 to 150.

Fig. 4
Fig. 4

Diffracted beam 11.5 ± 0.2 cm after the disk.

Fig. 5
Fig. 5

Divergence of the diffracted beam.

Fig. 6
Fig. 6

Diffracted beam pattern after a 25 cm focal length collimating lens at a distance of (a) 5 cm , (b) 1.3 m , and (c) 5.2 m after this lens.

Fig. 7
Fig. 7

Transverse intensity profiles calculated with truncated developments.

Fig. 8
Fig. 8

Theoretical simulation of Fig. 2.

Fig. 9
Fig. 9

Transverse beam intensity profile and theoretical fit.

Fig. 10
Fig. 10

Propagation through the lens L 2 : pattern calculated (a) just in front of the lens, (b) 5 cm after the lens, and (c) 1.3 m after the lens.

Fig. 11
Fig. 11

Normalized transverse intensity profiles just in front of the lens, 5     cm after the lens, and 1.3 m after the lens. The three curves are superposed.

Equations (19)

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E ( ξ , η , z ) = E 0 ( z ) exp ( ξ 2 + η 2 ω ( z ) 2 ) exp ( i π λ ξ 2 + η 2 R ( z ) ) ,
ω ( z ) = ω 0 2 [ 1 + ( z z 0 ) 2 ] ,
R ( z ) = z [ 1 + ( z 0 z ) 2 ] ,
E ( x , y , z c z q ) = exp ( i 2 π z c λ ) i λ z c + + E ( ξ , η , z q ) [ 1 T ( ξ , η ) ] exp { i π λ z c [ ( ξ x ) 2 + ( η y ) 2 ] } d ξ d η ,
T ( ξ , η ) = { 1 if ξ 2 + η 2 < D 2 , 0 otherwise . } .
I ( x , y , z c z q ) = E ( x , y , z c z q ) . E ( x , y , z c z q ) * ,
A 1 = K 2 exp [ β r 2 ( i M N ) ] ,
A 2 = π D 2 2 exp ( i β r 2 ) T 0 ( r ) .
T 0 ( r ) = exp ( i u 4 ) ( 2 π u ) 1 2 s = 0 K s ( 1 ) s J 2 s + 1 ( β D r ) β D r
K s = ( i ) s ( 2 s + 1 ) J s + 1 2 ( u 4 ) .
β = π λ z c ,
u = β D 2 2 ( 1 + λ z c b 1 ) i a 1 ( D 2 2 ) ,
K = [ π ω q 2 1 + i β ω q 2 ( z c R q 1 ) ] 1 2 ,
N = β ω q 2 1 + π 2 ω q 4 λ 2 ( 1 R q 1 z c ) 2 ,
M = 1 + N π ω q 2 λ ( 1 R q 1 z c ) ,
a 1 = 1 ω q 2 ,
b 1 = 1 λ R q .
t ( x , y ) = exp ( i π ( x 2 + y 2 ) λ f L 2 ) ,
E ( x , y , z ) = exp ( i 2 π z λ ) i λ z L 2 E ( ξ , η , z c z q ) exp [ i π λ f L 2 ( ξ 2 + η 2 ) ] exp { i π λ z [ ( ξ x ) 2 + ( η y ) 2 ] } d ξ d η .

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