Abstract

We studied the conditions for generating passive Bessel–Gauss beams by using an axicon. We designed an appropriate Gaussian resonator and extracted a quasi-fundamental Gaussian mode from a pulsed Nd:YAG laser pumped by a Xenon flash lamp and measured its parameters, such as propagation factor, divergence angle, and Rayleigh range. Then we generated passive Bessel–Gauss beams using an axicon and investigated their propagation properties, theoretically and experimentally. For example, for the axicon of 1°, the output energy and the Rayleigh range of the generated Bessel–Gauss beams were measured to be 58 mJ and 229.3 mm, respectively. We compared these properties with our results of the Gaussian mode. Finally, by using axicons with different apex angles, and also by changing the beam spot size on the axicon, we generated Bessel–Gauss beams and studied their properties theoretically and experimentally.

© 2012 Optical Society of America

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References

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  1. M. Fortin, M. Piche, and E. F. Borra, “Optical test with Bessel beam interferometry,” Opt. Express 12, 5887–5895 (2004).
    [CrossRef]
  2. J. Arlt, V. G. Chavez, W. Sibbet, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
    [CrossRef]
  3. Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–578 (2003).
    [CrossRef]
  4. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef]
  5. D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. J. Phys. 46, 15–28 (2005).
    [CrossRef]
  6. F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
    [CrossRef]
  7. M. Lie and B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
    [CrossRef]
  8. W. X. Cong, N. X. Chen, and B. Y. Gu, “Generation of non-diffracting beams by diffractive phase elements,” J. Opt. Soc. Am. A 15, 2362–2364 (1998).
    [CrossRef]
  9. 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]
  10. Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
    [CrossRef]
  11. Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
    [CrossRef]
  12. Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
    [CrossRef]
  13. H. Weber and N. Hodgson, Laser Resonator and Beam Propagation (Springer, 2005).
  14. W. Koechner, Solid-State Laser Engineering (Springer, 2006).

2012 (1)

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
[CrossRef]

2011 (1)

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
[CrossRef]

2010 (1)

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[CrossRef]

2005 (1)

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

2004 (2)

M. Lie and B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[CrossRef]

M. Fortin, M. Piche, and E. F. Borra, “Optical test with Bessel beam interferometry,” Opt. Express 12, 5887–5895 (2004).
[CrossRef]

2003 (1)

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

2001 (2)

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

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]

1998 (1)

1987 (2)

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

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

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, “Nondiffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–578 (2003).
[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]

Chen, N. X.

Cong, W. X.

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]

Duelk, M.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
[CrossRef]

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[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.

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Gu, B. Y.

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Hamamo, K.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[CrossRef]

Hamamoto, K.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
[CrossRef]

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
[CrossRef]

Hinokuma, Y.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[CrossRef]

Hodgson, N.

H. Weber and N. Hodgson, Laser Resonator and Beam Propagation (Springer, 2005).

Katranji, E. G.

Khilo, A. N.

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer, 2006).

Lie, M.

M. Lie and B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[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]

Minato, T.

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[CrossRef]

Mukai, K.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
[CrossRef]

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
[CrossRef]

Navaretti, P.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
[CrossRef]

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Piche, M.

Ryzhevich, A. A.

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]

Velez, C.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
[CrossRef]

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[CrossRef]

Weber, H.

H. Weber and N. Hodgson, Laser Resonator and Beam Propagation (Springer, 2005).

Yao, B.

M. Lie and B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[CrossRef]

Zang, Z.

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
[CrossRef]

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
[CrossRef]

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “Thermal resistance reduction in high power superluminescent diodes by using active multi-mode interferometer,” Appl. Phys. Lett. 100, 031108 (2012).
[CrossRef]

Contemp. J. Phys. (1)

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

Czech. J. Phys. (1)

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

IEEE Photon. Technol. Lett. (1)

Z. Zang, T. Minato, P. Navaretti, Y. Hinokuma, M. Duelk, C. Velez, and K. Hamamo, “High power (>110  mW) superluminescent diodes using active multi-mode interferometer,” IEEE Photon. Technol. Lett. 22, 721–723 (2010).
[CrossRef]

IEICE Trans. Electron. (1)

Z. Zang, K. Mukai, P. Navaretti, M. Duelk, C. Velez, and K. Hamamoto, “High power and stable high coupling efficiency (66%) superluminescent light emitting diodes by using active multi-mode interferometer,” IEICE Trans. Electron. E94-C, 862–864 (2011).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

M. Lie and B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[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. Express (1)

Phys. Rev. Lett. (1)

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

Other (2)

H. Weber and N. Hodgson, Laser Resonator and Beam Propagation (Springer, 2005).

W. Koechner, Solid-State Laser Engineering (Springer, 2006).

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Figures (11)

Fig. 1.
Fig. 1.

Passive generation of Bessel–Gauss beam. Bessel–Gauss beam is generated in the interference region.

Fig. 2.
Fig. 2.

Propagation of Bessel–Gauss beam (intensity versus radial distance) (γ=1°, n=1.5, w0=2mm, zmax=229.2mm). (a) z=70mm, (b) z=150mm, and (c) z=350mm.

Fig. 3.
Fig. 3.

Theoretical investigations to determine resonator length. (a) Mode volume versus radius of the rear mirror. (b) Divergence angle versus g factor.

Fig. 4.
Fig. 4.

Theoretical investigations to determine the location of laser rod. (a), (b) Beam spot size on the out coupler and rear mirror versus location of laser rod from out coupler (mm), respectively.

Fig. 5.
Fig. 5.

Designed Gaussian resonator.

Fig. 6.
Fig. 6.

Transverse intensity profile of the quasi-fundamental Gaussian mode at z=200mm from output coupler.

Fig. 7.
Fig. 7.

Experimental setup for generating Bessel–Gauss beams.

Fig. 8.
Fig. 8.

Transverse intensity profile of pulsed Bessel–Gauss beam at (a) z=70mm, (b) z=150mm, and (c) z=350mm.

Fig. 9.
Fig. 9.

Transverse intensity profile of generated Bessel–Gauss beam from an He–Ne laser by using an axicon (γ=1°, w0=2mm, zmax=229.29mm). (a) z=70mm, (b) z=150mm, and (c) z=350mm.

Fig. 10.
Fig. 10.

(a) γ=1°, w0=1, 2 mm, z=200mm, the greater the beam spot size on the axicon, the longer the Rayleigh range. (b) γ=1°, 5°, w0=1mm, z=80mm, the smaller the axicon opening angle, the longer the Rayleigh range.

Fig. 11.
Fig. 11.

(a) Radial intensity of generated Bessel–Gauss beam from an Nd:YAG laser and (b) He–Ne laser by using an axicon at z=350mm).

Equations (8)

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E(r,z)=AJ0(βr)exp[iαz],
E(r,0)=AJ0(βr)exp[(r/w0)2],
Zmax=w0(n1)γ,
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)](r+2β2z2k2)},
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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