Abstract

Nondiffracting Bessel–Gauss beams are assumed as the superposition of infinite numbers of Gaussian beams whose wave vectors lie on a cone. Based on such a description, different methods are suggested to generate these fields. In this paper, we followed an active scheme to generate these beams. By introducing an axicon-based resonator, we designed the appropriate resonator, studied its resonance modes, and analyzed the beam propagation outside the resonator. Experimentally, we succeeded to obtain Bessel–Gauss beams of the first kind and zero order. We also investigated the changes in effective parameters on the output beam, both theoretically and experimentally.

© 2012 Optical Society of America

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References

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    [CrossRef]
  2. D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. J. Phys. 46, 15–28 (2005).
    [CrossRef]
  3. G. Scott and N. McArdle, “Efficient generation of a nearly diffraction-free beam using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
    [CrossRef]
  4. A. N. Khilo, E. G. Katranji, and A. A. Ryzhevich, “Axicon-based resonator: analytical description and experiment,” J. Opt. Soc. Am. A 18, 1986–1992 (2001).
    [CrossRef]
  5. M. Fortin, M. Piche, and E. F. Borra, “Optical test with Bessel beam interferometry,” Opt. Express 12, 5887–5895 (2004).
    [CrossRef]
  6. J. Arlt, V. G. Chavez, W. Sibbet, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
    [CrossRef]
  7. Z. Bouchal, “Non-diffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–578 (2003).
    [CrossRef]
  8. Z. Buchal, J. Wanger, and M. Chlup, “Self-reconstruction of a distorted non-diffracting beam,” Opt. Commun. 151, 207–211 (1998).
    [CrossRef]
  9. W. Koechner, Solid-State Laser Engineering (Springer Science & Business Media, 2006).
  10. H. Weber and N. Hodgson, Laser Resonator and Beam Propagation (Springer Science & Business Media, 2005).
  11. P. Muys and E. Vandamme, “Direct generation of Bessel beams,” Appl. Opt. 41, 6375–6379 (2002).
    [CrossRef]
  12. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970).
    [CrossRef]

2005

D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. J. Phys. 46, 15–28 (2005).
[CrossRef]

2004

2003

Z. Bouchal, “Non-diffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–578 (2003).
[CrossRef]

2002

2001

A. N. Khilo, E. G. Katranji, and A. A. Ryzhevich, “Axicon-based resonator: analytical description and experiment,” J. Opt. Soc. Am. A 18, 1986–1992 (2001).
[CrossRef]

J. Arlt, V. G. Chavez, W. Sibbet, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

1998

Z. Buchal, J. Wanger, and M. Chlup, “Self-reconstruction of a distorted non-diffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

1992

G. Scott and N. McArdle, “Efficient generation of a nearly diffraction-free beam using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[CrossRef]

1987

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

1970

Arlt, J.

J. Arlt, V. G. Chavez, W. Sibbet, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Borra, E. F.

Bouchal, Z.

Z. Bouchal, “Non-diffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–578 (2003).
[CrossRef]

Buchal, Z.

Z. Buchal, J. Wanger, and M. Chlup, “Self-reconstruction of a distorted non-diffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Chavez, V. G.

J. Arlt, V. G. Chavez, W. Sibbet, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Chlup, M.

Z. Buchal, J. Wanger, and M. Chlup, “Self-reconstruction of a distorted non-diffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Collins, S. A.

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. J. Phys. 46, 15–28 (2005).
[CrossRef]

J. Arlt, V. G. Chavez, W. Sibbet, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Fortin, M.

Hodgson, N.

H. Weber and N. Hodgson, Laser Resonator and Beam Propagation (Springer Science & Business Media, 2005).

Katranji, E. G.

Khilo, A. N.

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer Science & Business Media, 2006).

McArdle, N.

G. Scott and N. McArdle, “Efficient generation of a nearly diffraction-free beam using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[CrossRef]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. J. Phys. 46, 15–28 (2005).
[CrossRef]

Miceli, J. J.

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

Muys, P.

Piche, M.

Ryzhevich, A. A.

Scott, G.

G. Scott and N. McArdle, “Efficient generation of a nearly diffraction-free beam using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[CrossRef]

Sibbet, W.

J. Arlt, V. G. Chavez, W. Sibbet, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Vandamme, E.

Wanger, J.

Z. Buchal, J. Wanger, and M. Chlup, “Self-reconstruction of a distorted non-diffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Weber, H.

H. Weber and N. Hodgson, Laser Resonator and Beam Propagation (Springer Science & Business Media, 2005).

Appl. Opt.

Contemp. J. Phys.

D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. J. Phys. 46, 15–28 (2005).
[CrossRef]

Czech. J. Phys.

Z. Bouchal, “Non-diffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–578 (2003).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

Z. Buchal, J. Wanger, and M. Chlup, “Self-reconstruction of a distorted non-diffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

J. Arlt, V. G. Chavez, W. Sibbet, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Opt. Eng.

G. Scott and N. McArdle, “Efficient generation of a nearly diffraction-free beam using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

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

Other

W. Koechner, Solid-State Laser Engineering (Springer Science & Business Media, 2006).

H. Weber and N. Hodgson, Laser Resonator and Beam Propagation (Springer Science & Business Media, 2005).

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Figures (9)

Fig. 1.
Fig. 1.

Gaussian beams superpose in a conical region to create Bessel–Gauss beams.

Fig. 2.
Fig. 2.

The length of the axicon-based resonator as a function of beam spot size on the axicon.

Fig. 3.
Fig. 3.

Normalized mode volume as a function of location of the rod from output mirror. The closer the laser rod to the output mirror is, the larger the mode volume of the resonator is.

Fig. 4.
Fig. 4.

Beam spot size on the output mirror as a function of the location of the rod from this mirror. The closer the rod to the plane mirror, the larger the beam size on this mirror, and so the longer the Rayleigh range.

Fig. 5.
Fig. 5.

Designed resonator.

Fig. 6.
Fig. 6.

Generated Bessel–Gauss field on the output mirror; the first three modes: (a) J1, (b) J2, and (c) J3.

Fig. 7.
Fig. 7.

Propagation of Bessel–Gauss beam (intensity versus radial distance) (δ=0.5°, n=1.5, w0=2mm, zmax=400mm). (a) z=0, (b) z=200mm, (c) z=300mm, d) z=800mm.

Fig. 8.
Fig. 8.

Transverse and radial intensity of pulsed Bessel–Gauss beam, generated from resonator with 400 mm length, at (a) z=200mm, (b) z=400mm, (c) z=600mm.

Fig. 9.
Fig. 9.

Transverse and radial intensity of pulsed Bessel–Gauss beam, generated from resonator with 448 mm length, at (a) z=200mm, (b) z=430mm, (c) z=600mm.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E(ρ,0)=E0J0(βρ)exp[(ρw02)].
L=a2(n1)δ,
Nf=a2λL,
γE(x)=K(x,x)E(x)dx,
E(ρ,0)=AJ0(βρ)exp[(ρw0)2],
Zmax=w0(n1)δ,
E(r,z)=(ikz)exp[i(kz+kr22z)]×0E(ρ,0)exp[ikρ22z]J0(kρrz)ρdρ,
E(r,z)=(Aw0w(z))exp{i[(kβ22k)zϕ(z)]}×J0[βr(1+izL)]exp{[1w2(z)+ik2R(z)](r2+β2z2k2)},
L=kw022
w(z)=w0[1+(zL)2]12,φ(z)=arctan(zL),R(z)=z+L2z.
E(r,z)=(iAw04πβrzk)×exp[i(kz+kr22z)]×exp[((rβzk)w2)].

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