Abstract

In the paper, the geometrical parameters and energetics of the extremely narrow pseudo-nondiffracting beams with the spot size of several micrometers are examined. The main attention is focused on design, realization and testing of the set-up enabling conversion of the laser diode beam or the fiber mode to the narrow Bessel-Gauss beam whose spot can be continuously relocated across the plane perpendicular to the beam propagation direction. Application of the laser convertor to the optical manipulation is demonstrated on experiments enabling transport of microparticles along a desired trajectory.

© 2009 Optical Society of America

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  1. C. J. R. Sheppard and T. Wilson, "Gaussian-beam theory of lenses with annular aperture," Microwaves Opt. Acoustics 2, 105 (1978).
    [CrossRef]
  2. J. Durnin, J. J. Micely, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
    [CrossRef] [PubMed]
  3. W. C. Soares, D. P. Caetano, and J. M. Hickmann, "Hermite-Bessel beams and the geometrical representation of nondiffracting beams with orbital angular momentum," Opt. Express 14, 4577-4582 (2006).
    [CrossRef] [PubMed]
  4. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, "Alternative formulation for invariant optical fields: Mathieu beams," Opt. Lett. 25, 1493-1495 (2000).
    [CrossRef]
  5. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, "Parabolic nondiffracting optical wavefields," Opt. Lett. 29, 44-46 (2004).
    [CrossRef] [PubMed]
  6. Z. Bouchal, "Controlled spatial shaping of nondiffracting patterns and arrays," Opt. Lett. 27, 1376-1378 (2002).
    [CrossRef]
  7. Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537 (2003).
    [CrossRef]
  8. M. R. Lapointe, "Review of non-diffracting Bessel beam experiments," Opt. Laser Technol. 24, 315-321 (1992).
    [CrossRef]
  9. Z. Bouchal, "Physical principle of experiments with pseudo-nondiffracting fields," Czech. J. Phys. 55, 1223-1236 (2005).
    [CrossRef]
  10. V. Bagini, F. Frezza, M. Santarsierro, G. Schettini, and G. S. Spagnolo, "Generalized Bessel-Gauss beams", J. Mod. Opt. 43, 1155 (1996).
  11. D. McGloin, and K. Dholakia, "Bessel beams: diffraction in a new light," Contemporary Physics 46, 15-28 (2005).
    [CrossRef]
  12. J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289 (2005).
    [CrossRef]
  13. Z. Bouchal, R. Čelechovský, and G. Swartzlander, Jr., "Spatially localized vortex structures," Monograph Localized waves, edited by H. E. Hernndez-Figueroa, M. Zamboni - Rached and E. Recami, J. Wiley & Sons., 2008 (ISBN 978-0-470-10885-7).
    [CrossRef]
  14. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
    [CrossRef] [PubMed]
  15. T. Čizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101-1-3 (2005).
    [CrossRef]
  16. J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
    [CrossRef]
  17. J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
    [CrossRef]
  18. T. Čizmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, "Generation of multiple Bessel beams for a biophotonics workstation," Opt. Express 16, 14024-14035 (2008).
    [CrossRef] [PubMed]
  19. Ch. Yu, M. R.Wang, A. J. Varela, and B. Cheng, "High-density non-diffracting beam for optical interconection," Opt. Commun. 177, 369-376 (2000).
    [CrossRef]

2008 (1)

2006 (1)

2005 (4)

T. Čizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101-1-3 (2005).
[CrossRef]

Z. Bouchal, "Physical principle of experiments with pseudo-nondiffracting fields," Czech. J. Phys. 55, 1223-1236 (2005).
[CrossRef]

D. McGloin, and K. Dholakia, "Bessel beams: diffraction in a new light," Contemporary Physics 46, 15-28 (2005).
[CrossRef]

J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289 (2005).
[CrossRef]

2004 (1)

2003 (1)

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537 (2003).
[CrossRef]

2002 (3)

Z. Bouchal, "Controlled spatial shaping of nondiffracting patterns and arrays," Opt. Lett. 27, 1376-1378 (2002).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

2001 (1)

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

2000 (2)

Ch. Yu, M. R.Wang, A. J. Varela, and B. Cheng, "High-density non-diffracting beam for optical interconection," Opt. Commun. 177, 369-376 (2000).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, "Alternative formulation for invariant optical fields: Mathieu beams," Opt. Lett. 25, 1493-1495 (2000).
[CrossRef]

1996 (1)

V. Bagini, F. Frezza, M. Santarsierro, G. Schettini, and G. S. Spagnolo, "Generalized Bessel-Gauss beams", J. Mod. Opt. 43, 1155 (1996).

1992 (1)

M. R. Lapointe, "Review of non-diffracting Bessel beam experiments," Opt. Laser Technol. 24, 315-321 (1992).
[CrossRef]

1987 (1)

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

1978 (1)

C. J. R. Sheppard and T. Wilson, "Gaussian-beam theory of lenses with annular aperture," Microwaves Opt. Acoustics 2, 105 (1978).
[CrossRef]

Arlt, J.

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Bagini, V.

V. Bagini, F. Frezza, M. Santarsierro, G. Schettini, and G. S. Spagnolo, "Generalized Bessel-Gauss beams", J. Mod. Opt. 43, 1155 (1996).

Bandres, M. A.

Bouchal, Z.

T. Čizmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, "Generation of multiple Bessel beams for a biophotonics workstation," Opt. Express 16, 14024-14035 (2008).
[CrossRef] [PubMed]

Z. Bouchal, "Physical principle of experiments with pseudo-nondiffracting fields," Czech. J. Phys. 55, 1223-1236 (2005).
[CrossRef]

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537 (2003).
[CrossRef]

Z. Bouchal, "Controlled spatial shaping of nondiffracting patterns and arrays," Opt. Lett. 27, 1376-1378 (2002).
[CrossRef]

Caetano, D. P.

Chávez-Cerda, S.

Cizmár, T.

T. Čizmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, "Generation of multiple Bessel beams for a biophotonics workstation," Opt. Express 16, 14024-14035 (2008).
[CrossRef] [PubMed]

T. Čizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101-1-3 (2005).
[CrossRef]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Dholakia, K.

T. Čizmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, "Generation of multiple Bessel beams for a biophotonics workstation," Opt. Express 16, 14024-14035 (2008).
[CrossRef] [PubMed]

T. Čizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101-1-3 (2005).
[CrossRef]

D. McGloin, and K. Dholakia, "Bessel beams: diffraction in a new light," Contemporary Physics 46, 15-28 (2005).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Frezza, F.

V. Bagini, F. Frezza, M. Santarsierro, G. Schettini, and G. S. Spagnolo, "Generalized Bessel-Gauss beams", J. Mod. Opt. 43, 1155 (1996).

Garcés-Chávez, V.

T. Čizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101-1-3 (2005).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Gunn-Moore, F.

Gutiérrez-Vega, J. C.

Hickmann, J. M.

Iturbe-Castillo, M. D.

Kollárová, V.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Lapointe, M. R.

M. R. Lapointe, "Review of non-diffracting Bessel beam experiments," Opt. Laser Technol. 24, 315-321 (1992).
[CrossRef]

McGloin, D.

D. McGloin, and K. Dholakia, "Bessel beams: diffraction in a new light," Contemporary Physics 46, 15-28 (2005).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

Micely, J. J.

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

Santarsierro, M.

V. Bagini, F. Frezza, M. Santarsierro, G. Schettini, and G. S. Spagnolo, "Generalized Bessel-Gauss beams", J. Mod. Opt. 43, 1155 (1996).

Schettini, G.

V. Bagini, F. Frezza, M. Santarsierro, G. Schettini, and G. S. Spagnolo, "Generalized Bessel-Gauss beams", J. Mod. Opt. 43, 1155 (1996).

Sheppard, C. J. R.

C. J. R. Sheppard and T. Wilson, "Gaussian-beam theory of lenses with annular aperture," Microwaves Opt. Acoustics 2, 105 (1978).
[CrossRef]

Sibbett, W.

T. Čizmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, "Generation of multiple Bessel beams for a biophotonics workstation," Opt. Express 16, 14024-14035 (2008).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Soares, W. C.

Spagnolo, G. S.

V. Bagini, F. Frezza, M. Santarsierro, G. Schettini, and G. S. Spagnolo, "Generalized Bessel-Gauss beams", J. Mod. Opt. 43, 1155 (1996).

Tsampoula, X.

Wilson, T.

C. J. R. Sheppard and T. Wilson, "Gaussian-beam theory of lenses with annular aperture," Microwaves Opt. Acoustics 2, 105 (1978).
[CrossRef]

Zemánek, P.

T. Čizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101-1-3 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

T. Čizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett. 86, 174101-1-3 (2005).
[CrossRef]

Contemporary Physics (1)

D. McGloin, and K. Dholakia, "Bessel beams: diffraction in a new light," Contemporary Physics 46, 15-28 (2005).
[CrossRef]

Czech. J. Phys. (2)

Z. Bouchal, "Physical principle of experiments with pseudo-nondiffracting fields," Czech. J. Phys. 55, 1223-1236 (2005).
[CrossRef]

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537 (2003).
[CrossRef]

J. Mod. Opt. (1)

V. Bagini, F. Frezza, M. Santarsierro, G. Schettini, and G. S. Spagnolo, "Generalized Bessel-Gauss beams", J. Mod. Opt. 43, 1155 (1996).

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

Microwaves Opt. Acoustics (1)

C. J. R. Sheppard and T. Wilson, "Gaussian-beam theory of lenses with annular aperture," Microwaves Opt. Acoustics 2, 105 (1978).
[CrossRef]

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

Opt. Commun. (3)

Ch. Yu, M. R.Wang, A. J. Varela, and B. Cheng, "High-density non-diffracting beam for optical interconection," Opt. Commun. 177, 369-376 (2000).
[CrossRef]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

M. R. Lapointe, "Review of non-diffracting Bessel beam experiments," Opt. Laser Technol. 24, 315-321 (1992).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

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

Other (1)

Z. Bouchal, R. Čelechovský, and G. Swartzlander, Jr., "Spatially localized vortex structures," Monograph Localized waves, edited by H. E. Hernndez-Figueroa, M. Zamboni - Rached and E. Recami, J. Wiley & Sons., 2008 (ISBN 978-0-470-10885-7).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Comparison of (a) the focused Gaussian beam and (b) the PND beam of the B-G type.

Fig. 2.
Fig. 2.

The B-G beam with the central spot radius 8 μm generated by the set-up in Fig. 1(b). Intensity spots at distances (a) 15 mm, (b) 125 mm and (c) 250 mm behind the lens.

Fig. 3.
Fig. 3.

The intensity spot of the B-G beam at (a) on-axis and (b) off-axis positions.

Fig. 4.
Fig. 4.

Illustration of the phase modulation of the spatial spectrum of the B-G beam resulting in the transverse relocation of the beam spot.

Fig. 5.
Fig. 5.

(a) Laser convertor C used in the set-up for conveying and transfer of microparticles along desired trajectory (F-fiber, LC -collimating lens, A-axicon, D-diasporometer, L 1, L 2, L 3-lenses, M-mirror, LM -microscope objective, S-sample). (b) Photo of the laser convertor with fiber optics illumination.

Fig. 6.
Fig. 6.

Efficiency of the power capture inside the propagation region of the B-G and the Gauss beams.

Fig. 7.
Fig. 7.

Catching and movement of the polystyrene bead along a required trajectory by means of the set-up with the laser convertor.

Equations (43)

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UN(r)=uN(x,y;kt)exp(ikzz) .
UN(r)=exp(ikzz)02πA(ψ)exp[iktρcos(ϑψ)]dψ,
ΦLΔxΔy=exp[ikt(Δxcosψ+Δysinψ)].
UPNρϑz=02πA(ψ)Gρϑzψdψ.
UPNρϑz=exp(ikt2z22kq)UGρzU(ρQ,ϑ,z),
U(ρQ,ϑ,z)=exp(ikzpz)02πA(ψ)exp[ikiρQcos(ϑψ)]dψ.
kzp=k(1kt22k2),
Q=1+zq.
UN(ρ,ϑ,z)=(1)mim2πJm(ktρ)exp(iikzz),
U(Qρ,ϑ,z)=(1)mim2πJm(ktQρ)exp(iikzpz).
IN(ρ)UN(ρ)2UN(0)2= J02 (ktρ) .
IBG(ρ,z)UBG(ρ,z)2UBG(0,0)2.
IBG(ρ,z)=w02w2 exp [2ρ2w2kt2z2q0k(z2+q02)] J0 (ktQρ)J0(ktQ*ρ) .
IBG(ρ,0)=J02(ktρ) exp (2ρ2w02) .
IBG(0,z)=w02w2 exp [kt2z2q0k(z2+q02)] .
IBG(0,z)=exp(2z2sin2θw02) .
zBG=w0sinθw0θ.
w0F=2kNA,
zG=kw0F2 .
θG=2kw0F .
θ2kρ0 .
zBG=kw0w0F2 .
KzBGzG=w02w0F .
w0F=ρ0=2kNA ,
zG=4kNA2 ,
zBG=f,
K=kfNA24 .
η(z)=Pz(z)P0 ,
ηG(z)=1exp(2RD2/w2)1exp(2RD2/w0F2) ,
w2=w0F2+z2λ2π2w0F2.
PZ=IBG(0,z)P0,
ηBG(z)=IBG (0,z) .
z=zG2 12RD2w0F2lnV,
V=1ηG[1exp(2RD2w0F2)] .
z=zBG lnηBG2.
A(ψ)=exp[ikt(Δxcosψ+Δysinψ)],
UNexp(ikzz) J0 [kt(xΔx)2+(yΔy)2] .
t(ψ)=exp[ikt(n1)αfcosψ] ,
Δx=(n1)αf.
ρ10.4λ(n1)(π2τ2)
ρ2=ρ1Γ1 1(0.4λr1)2(1Γ12) .
z2=z1/Γ12 .
h=(n1) α f2 .

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