Abstract

This paper considers the transverse optical properties of an absorbing ring when it is lighted by a symmetrical Laguerre–Gauss beam TEMp0. It is demonstrated that the insertion of an opaque ring having adequate size inside a diaphragmed laser cavity is able to improve greatly (rate of about 100%) the discrimination between the TEM00 and the TEM10 modes, while keeping the diffraction losses unchanged or even decreased.

© 2010 Optical Society of America

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  1. A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
  2. H. Kogelnik and T. Li, “Laser beams and resonator,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  3. K. Ait-Ameur and G. Stephan, “Effective beam truncation of the fundamental mode in an apertured cavity,” Opt. Lett. 18, 938–940 (1993).
    [CrossRef] [PubMed]
  4. K. Ait-Ameur, “Influence of the longitudinal position of an aperture inside a cavity on the transverse mode discrimination,” Appl. Opt. 32, 7366–7372 (1993).
    [CrossRef] [PubMed]
  5. K. Ait-Ameur, M. Brunel, and F. Sanchez, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
    [CrossRef]
  6. N. Passilly, M. Fromager, and K. Ait-Ameur, “Improvement of the self-Q-switching behavior of a Cr:LiSAF laser using a binary diffractive optics,” Appl. Opt. 43, 5047–5059 (2004).
    [CrossRef] [PubMed]
  7. R. de Saint Denis, N. Passilly, and K. Ait-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
    [CrossRef]
  8. S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35, 1075–1085 (1999).
    [CrossRef]
  9. J. Bourderionnet, N. Huot, A. Brignon, and J. P. Huignard, “Spatial mode control of a diode-pumped Nd:YAG laser by use of an intracavity holographic phase plate,” Opt. Lett. 25, 1579–1581 (2000).
    [CrossRef]
  10. R. de Saint Denis, N. Passilly, M. Fromager, E. Cagniot, and K. Ait-Ameur, “Diffraction properties of opaque disks outside and inside a laser cavity,” Opt. Commun. 281, 4758–4761 (2008).
    [CrossRef]
  11. I. A. Litvin and A. Forbes, “Bessel-Gauss resonator with internal amplitude filter,” Opt. Commun. 281, 2385–2392(2008).
    [CrossRef]
  12. M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular filters,” Opt. Commun. 165, 267–278 (1999).
    [CrossRef]
  13. M. Martinez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10, 98–103 (2002).
    [PubMed]
  14. V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
    [CrossRef]
  15. K. Ait-Ameur, “Effects of a phase aperture on the fundamental mode of a hard-apertured cavity,” J. Mod. Opt. 49, 1157–1168(2002).
    [CrossRef]
  16. K. Ait-Ameur, F. Sanchez, and M. Brunel, “The transfer of TEM00 and TEM01 beams through a hard-aperture,” J. Mod. Opt. 47, 1203–1211 (2000).
  17. E. Cagniot, Z. Derrar-Kaddour, M. Fromager, and K. Aït-Ameur, “Improving both transverse mode discrimination and diffraction losses in a plano-concave cavity,” Opt. Commun. 281, 4449–4454 (2008).
    [CrossRef]
  18. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Elsevier, 2007), p. 106.
  19. D. R. Hall and P. E. Jackson, The Physics and Technology of Laser Resonators (Institute of Physics, 1992), p. 137.
  20. A. E. Siegman, Lasers (University Science, 1986), Chap. 17.
  21. U. D. Zeitner and F. Wyroski, “High modal discrimination for laser resonators with Gaussian output beam,” J. Mod. Opt. 46, 1309–1314 (1999).
  22. A. A. Napartovitch, N. N. Elkin, V. N. Troschieva, D. V. Vysotski, and J. R. Leger, “Simplified intracavity phase plates for increasing laser-mode discrimination,” Appl. Opt. 38, 3025–3029 (1999).
    [CrossRef]
  23. W. W. Rigrod, “Isolation of axi-symmetrical optical-resonator modes,” Appl. Phys. Lett. 2, 51–53 (1963).
    [CrossRef]
  24. K. M. Abramski, H. J. Baker, A. D. Colley, and R. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
    [CrossRef]
  25. D. Chen, Z. Wang, and J. R. Leger, “Measurement of the modal properties of a diffracted-optic graded-phase resonator,” Opt. Lett. 20, 663–665 (1995).
    [CrossRef] [PubMed]
  26. M. Ciofini, A. Labate, R. Meucci, and P. Y. Wang, “Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations,” Opt. Commun. 154, 307–312 (1998).
    [CrossRef]
  27. K. Aït-Ameur, H. Ladjouze, and G. Stéphan, “Diffraction effects in a resonant cavity with two non-equivalent apertures,” Appl. Opt. 31, 397–405 (1992).
    [CrossRef] [PubMed]
  28. R. de Saint Denis, N. Passilly, and K. Aït-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
    [CrossRef]
  29. Z. Derrar-Kaddour, A. Taleb, K. Aït-Ameur, G. Martel, and E. Cagniot, “Alternative model for computing intensity patterns through apertured ABCD systems,” Opt. Commun. 281, 1384–1395 (2008).
    [CrossRef]
  30. P.-A. Bélanger, Y. Champagne, and C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
    [CrossRef]
  31. R. Martinez-Herrero and P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18, 1669–1671 (1993).
    [CrossRef] [PubMed]
  32. Z. Mei and D. Zhao, “The generalized beam propagation factor of truncated standard and elegant Laguerre-Gaussian beams,” J. Opt. A Pure Appl. Opt. 6, 1005–1011.
    [CrossRef]
  33. S. Amano and T. Mochizuki, “Propagation characteristics of diffracted M2 beam,” Appl. Opt. 41, 6325–6331(2002).
    [CrossRef] [PubMed]
  34. S. Amarande, A. Giesen, and H. Hügel, “Propagation analysis of self-convergent beam width and characterization of hard-edge diffracted beams,” Appl. Opt. 39, 3914–3924(2000).
    [CrossRef]
  35. S. Vicalvi, R. Borghi, M. Santarsiero, and F. Gori, “Shape-invariance error for axially symmetric light beams,” IEEE J. Quantum Electron. 34, 2109–2116 (1998).
    [CrossRef]
  36. A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
    [CrossRef]
  37. N. Passilly, G. Martel, and K. Aït-Ameur, “Beam propagation factor of truncated Laguerre-Gauss beams,” J. Mod. Opt. 51, 2279–2286 (2004).

2008

R. de Saint Denis, N. Passilly, M. Fromager, E. Cagniot, and K. Ait-Ameur, “Diffraction properties of opaque disks outside and inside a laser cavity,” Opt. Commun. 281, 4758–4761 (2008).
[CrossRef]

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

E. Cagniot, Z. Derrar-Kaddour, M. Fromager, and K. Aït-Ameur, “Improving both transverse mode discrimination and diffraction losses in a plano-concave cavity,” Opt. Commun. 281, 4449–4454 (2008).
[CrossRef]

Z. Derrar-Kaddour, A. Taleb, K. Aït-Ameur, G. Martel, and E. Cagniot, “Alternative model for computing intensity patterns through apertured ABCD systems,” Opt. Commun. 281, 1384–1395 (2008).
[CrossRef]

2007

V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
[CrossRef]

2006

R. de Saint Denis, N. Passilly, and K. Aït-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Ait-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

2004

N. Passilly, M. Fromager, and K. Ait-Ameur, “Improvement of the self-Q-switching behavior of a Cr:LiSAF laser using a binary diffractive optics,” Appl. Opt. 43, 5047–5059 (2004).
[CrossRef] [PubMed]

N. Passilly, G. Martel, and K. Aït-Ameur, “Beam propagation factor of truncated Laguerre-Gauss beams,” J. Mod. Opt. 51, 2279–2286 (2004).

2002

2000

J. Bourderionnet, N. Huot, A. Brignon, and J. P. Huignard, “Spatial mode control of a diode-pumped Nd:YAG laser by use of an intracavity holographic phase plate,” Opt. Lett. 25, 1579–1581 (2000).
[CrossRef]

K. Ait-Ameur, M. Brunel, and F. Sanchez, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

K. Ait-Ameur, F. Sanchez, and M. Brunel, “The transfer of TEM00 and TEM01 beams through a hard-aperture,” J. Mod. Opt. 47, 1203–1211 (2000).

S. Amarande, A. Giesen, and H. Hügel, “Propagation analysis of self-convergent beam width and characterization of hard-edge diffracted beams,” Appl. Opt. 39, 3914–3924(2000).
[CrossRef]

1999

S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35, 1075–1085 (1999).
[CrossRef]

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

U. D. Zeitner and F. Wyroski, “High modal discrimination for laser resonators with Gaussian output beam,” J. Mod. Opt. 46, 1309–1314 (1999).

A. A. Napartovitch, N. N. Elkin, V. N. Troschieva, D. V. Vysotski, and J. R. Leger, “Simplified intracavity phase plates for increasing laser-mode discrimination,” Appl. Opt. 38, 3025–3029 (1999).
[CrossRef]

1998

S. Vicalvi, R. Borghi, M. Santarsiero, and F. Gori, “Shape-invariance error for axially symmetric light beams,” IEEE J. Quantum Electron. 34, 2109–2116 (1998).
[CrossRef]

M. Ciofini, A. Labate, R. Meucci, and P. Y. Wang, “Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations,” Opt. Commun. 154, 307–312 (1998).
[CrossRef]

1995

1994

P.-A. Bélanger, Y. Champagne, and C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

1993

1992

K. Aït-Ameur, H. Ladjouze, and G. Stéphan, “Diffraction effects in a resonant cavity with two non-equivalent apertures,” Appl. Opt. 31, 397–405 (1992).
[CrossRef] [PubMed]

K. M. Abramski, H. J. Baker, A. D. Colley, and R. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

1990

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[CrossRef]

1966

1963

W. W. Rigrod, “Isolation of axi-symmetrical optical-resonator modes,” Appl. Phys. Lett. 2, 51–53 (1963).
[CrossRef]

1961

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Abramski, K. M.

K. M. Abramski, H. J. Baker, A. D. Colley, and R. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

Ait-Ameur, K.

R. de Saint Denis, N. Passilly, M. Fromager, E. Cagniot, and K. Ait-Ameur, “Diffraction properties of opaque disks outside and inside a laser cavity,” Opt. Commun. 281, 4758–4761 (2008).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Ait-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

N. Passilly, M. Fromager, and K. Ait-Ameur, “Improvement of the self-Q-switching behavior of a Cr:LiSAF laser using a binary diffractive optics,” Appl. Opt. 43, 5047–5059 (2004).
[CrossRef] [PubMed]

K. Ait-Ameur, “Effects of a phase aperture on the fundamental mode of a hard-apertured cavity,” J. Mod. Opt. 49, 1157–1168(2002).
[CrossRef]

K. Ait-Ameur, F. Sanchez, and M. Brunel, “The transfer of TEM00 and TEM01 beams through a hard-aperture,” J. Mod. Opt. 47, 1203–1211 (2000).

K. Ait-Ameur, M. Brunel, and F. Sanchez, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

K. Ait-Ameur and G. Stephan, “Effective beam truncation of the fundamental mode in an apertured cavity,” Opt. Lett. 18, 938–940 (1993).
[CrossRef] [PubMed]

K. Ait-Ameur, “Influence of the longitudinal position of an aperture inside a cavity on the transverse mode discrimination,” Appl. Opt. 32, 7366–7372 (1993).
[CrossRef] [PubMed]

Aït-Ameur, K.

E. Cagniot, Z. Derrar-Kaddour, M. Fromager, and K. Aït-Ameur, “Improving both transverse mode discrimination and diffraction losses in a plano-concave cavity,” Opt. Commun. 281, 4449–4454 (2008).
[CrossRef]

Z. Derrar-Kaddour, A. Taleb, K. Aït-Ameur, G. Martel, and E. Cagniot, “Alternative model for computing intensity patterns through apertured ABCD systems,” Opt. Commun. 281, 1384–1395 (2008).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Aït-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

N. Passilly, G. Martel, and K. Aït-Ameur, “Beam propagation factor of truncated Laguerre-Gauss beams,” J. Mod. Opt. 51, 2279–2286 (2004).

K. Aït-Ameur, H. Ladjouze, and G. Stéphan, “Diffraction effects in a resonant cavity with two non-equivalent apertures,” Appl. Opt. 31, 397–405 (1992).
[CrossRef] [PubMed]

Amano, S.

Amarande, S.

Andrés, P.

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Baker, H. J.

K. M. Abramski, H. J. Baker, A. D. Colley, and R. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

Bélanger, P.-A.

P.-A. Bélanger, Y. Champagne, and C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

Borghi, R.

S. Vicalvi, R. Borghi, M. Santarsiero, and F. Gori, “Shape-invariance error for axially symmetric light beams,” IEEE J. Quantum Electron. 34, 2109–2116 (1998).
[CrossRef]

Bourderionnet, J.

Brignon, A.

Brunel, M.

K. Ait-Ameur, M. Brunel, and F. Sanchez, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

K. Ait-Ameur, F. Sanchez, and M. Brunel, “The transfer of TEM00 and TEM01 beams through a hard-aperture,” J. Mod. Opt. 47, 1203–1211 (2000).

Caballero, M. T.

Cagniot, E.

E. Cagniot, Z. Derrar-Kaddour, M. Fromager, and K. Aït-Ameur, “Improving both transverse mode discrimination and diffraction losses in a plano-concave cavity,” Opt. Commun. 281, 4449–4454 (2008).
[CrossRef]

R. de Saint Denis, N. Passilly, M. Fromager, E. Cagniot, and K. Ait-Ameur, “Diffraction properties of opaque disks outside and inside a laser cavity,” Opt. Commun. 281, 4758–4761 (2008).
[CrossRef]

Z. Derrar-Kaddour, A. Taleb, K. Aït-Ameur, G. Martel, and E. Cagniot, “Alternative model for computing intensity patterns through apertured ABCD systems,” Opt. Commun. 281, 1384–1395 (2008).
[CrossRef]

Champagne, Y.

P.-A. Bélanger, Y. Champagne, and C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

Chen, D.

Ciofini, M.

M. Ciofini, A. Labate, R. Meucci, and P. Y. Wang, “Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations,” Opt. Commun. 154, 307–312 (1998).
[CrossRef]

Colley, A. D.

K. M. Abramski, H. J. Baker, A. D. Colley, and R. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

de Saint Denis, R.

R. de Saint Denis, N. Passilly, M. Fromager, E. Cagniot, and K. Ait-Ameur, “Diffraction properties of opaque disks outside and inside a laser cavity,” Opt. Commun. 281, 4758–4761 (2008).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Ait-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Aït-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

Derrar-Kaddour, Z.

Z. Derrar-Kaddour, A. Taleb, K. Aït-Ameur, G. Martel, and E. Cagniot, “Alternative model for computing intensity patterns through apertured ABCD systems,” Opt. Commun. 281, 1384–1395 (2008).
[CrossRef]

E. Cagniot, Z. Derrar-Kaddour, M. Fromager, and K. Aït-Ameur, “Improving both transverse mode discrimination and diffraction losses in a plano-concave cavity,” Opt. Commun. 281, 4449–4454 (2008).
[CrossRef]

Elkin, N. N.

Forbes, A.

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

Fox, A. G.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Fromager, M.

R. de Saint Denis, N. Passilly, M. Fromager, E. Cagniot, and K. Ait-Ameur, “Diffraction properties of opaque disks outside and inside a laser cavity,” Opt. Commun. 281, 4758–4761 (2008).
[CrossRef]

E. Cagniot, Z. Derrar-Kaddour, M. Fromager, and K. Aït-Ameur, “Improving both transverse mode discrimination and diffraction losses in a plano-concave cavity,” Opt. Commun. 281, 4449–4454 (2008).
[CrossRef]

N. Passilly, M. Fromager, and K. Ait-Ameur, “Improvement of the self-Q-switching behavior of a Cr:LiSAF laser using a binary diffractive optics,” Appl. Opt. 43, 5047–5059 (2004).
[CrossRef] [PubMed]

Giesen, A.

Gori, F.

S. Vicalvi, R. Borghi, M. Santarsiero, and F. Gori, “Shape-invariance error for axially symmetric light beams,” IEEE J. Quantum Electron. 34, 2109–2116 (1998).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Elsevier, 2007), p. 106.

Hall, D. R.

D. R. Hall and P. E. Jackson, The Physics and Technology of Laser Resonators (Institute of Physics, 1992), p. 137.

Hall, R. R.

K. M. Abramski, H. J. Baker, A. D. Colley, and R. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

Herzig, H.-P.

V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
[CrossRef]

Hügel, H.

Huignard, J. P.

Huot, N.

Jackson, P. E.

D. R. Hall and P. E. Jackson, The Physics and Technology of Laser Resonators (Institute of Physics, 1992), p. 137.

Kogelnik, H.

Kowalczyk, M.

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Labate, A.

M. Ciofini, A. Labate, R. Meucci, and P. Y. Wang, “Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations,” Opt. Commun. 154, 307–312 (1998).
[CrossRef]

Ladjouze, H.

Leger, J.

S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35, 1075–1085 (1999).
[CrossRef]

Leger, J. R.

Li, T.

H. Kogelnik and T. Li, “Laser beams and resonator,” Appl. Opt. 5, 1550–1567 (1966).
[CrossRef] [PubMed]

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Litvin, I. A.

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

Makki, S.

S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35, 1075–1085 (1999).
[CrossRef]

Martel, G.

Z. Derrar-Kaddour, A. Taleb, K. Aït-Ameur, G. Martel, and E. Cagniot, “Alternative model for computing intensity patterns through apertured ABCD systems,” Opt. Commun. 281, 1384–1395 (2008).
[CrossRef]

N. Passilly, G. Martel, and K. Aït-Ameur, “Beam propagation factor of truncated Laguerre-Gauss beams,” J. Mod. Opt. 51, 2279–2286 (2004).

Martinez-Corral, M.

M. Martinez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10, 98–103 (2002).
[PubMed]

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Martinez-Herrero, R.

Mei, Z.

Z. Mei and D. Zhao, “The generalized beam propagation factor of truncated standard and elegant Laguerre-Gaussian beams,” J. Opt. A Pure Appl. Opt. 6, 1005–1011.
[CrossRef]

Mejias, P. M.

Meucci, R.

M. Ciofini, A. Labate, R. Meucci, and P. Y. Wang, “Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations,” Opt. Commun. 154, 307–312 (1998).
[CrossRef]

Mochizuki, T.

Napartovitch, A. A.

Paeder, V.

V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
[CrossRef]

Paré, C.

P.-A. Bélanger, Y. Champagne, and C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

Passilly, N.

R. de Saint Denis, N. Passilly, M. Fromager, E. Cagniot, and K. Ait-Ameur, “Diffraction properties of opaque disks outside and inside a laser cavity,” Opt. Commun. 281, 4758–4761 (2008).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Ait-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Aït-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

N. Passilly, G. Martel, and K. Aït-Ameur, “Beam propagation factor of truncated Laguerre-Gauss beams,” J. Mod. Opt. 51, 2279–2286 (2004).

N. Passilly, M. Fromager, and K. Ait-Ameur, “Improvement of the self-Q-switching behavior of a Cr:LiSAF laser using a binary diffractive optics,” Appl. Opt. 43, 5047–5059 (2004).
[CrossRef] [PubMed]

Rigrod, W. W.

W. W. Rigrod, “Isolation of axi-symmetrical optical-resonator modes,” Appl. Phys. Lett. 2, 51–53 (1963).
[CrossRef]

Ruffieux, P.

V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Elsevier, 2007), p. 106.

Sanchez, F.

K. Ait-Ameur, F. Sanchez, and M. Brunel, “The transfer of TEM00 and TEM01 beams through a hard-aperture,” J. Mod. Opt. 47, 1203–1211 (2000).

K. Ait-Ameur, M. Brunel, and F. Sanchez, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

Santarsiero, M.

S. Vicalvi, R. Borghi, M. Santarsiero, and F. Gori, “Shape-invariance error for axially symmetric light beams,” IEEE J. Quantum Electron. 34, 2109–2116 (1998).
[CrossRef]

Scharf, T.

V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[CrossRef]

A. E. Siegman, Lasers (University Science, 1986), Chap. 17.

Stelzer, E. H. K.

Stephan, G.

Stéphan, G.

Swoger, J.

Taleb, A.

Z. Derrar-Kaddour, A. Taleb, K. Aït-Ameur, G. Martel, and E. Cagniot, “Alternative model for computing intensity patterns through apertured ABCD systems,” Opt. Commun. 281, 1384–1395 (2008).
[CrossRef]

Troschieva, V. N.

Vicalvi, S.

S. Vicalvi, R. Borghi, M. Santarsiero, and F. Gori, “Shape-invariance error for axially symmetric light beams,” IEEE J. Quantum Electron. 34, 2109–2116 (1998).
[CrossRef]

Voelkel, R.

V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
[CrossRef]

Vysotski, D. V.

Wang, P. Y.

M. Ciofini, A. Labate, R. Meucci, and P. Y. Wang, “Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations,” Opt. Commun. 154, 307–312 (1998).
[CrossRef]

Wang, Z.

Weible, K. J.

V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
[CrossRef]

Wyroski, F.

U. D. Zeitner and F. Wyroski, “High modal discrimination for laser resonators with Gaussian output beam,” J. Mod. Opt. 46, 1309–1314 (1999).

Zapata-Rodriguez, C. J.

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Zeitner, U. D.

U. D. Zeitner and F. Wyroski, “High modal discrimination for laser resonators with Gaussian output beam,” J. Mod. Opt. 46, 1309–1314 (1999).

Zhao, D.

Z. Mei and D. Zhao, “The generalized beam propagation factor of truncated standard and elegant Laguerre-Gaussian beams,” J. Opt. A Pure Appl. Opt. 6, 1005–1011.
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

W. W. Rigrod, “Isolation of axi-symmetrical optical-resonator modes,” Appl. Phys. Lett. 2, 51–53 (1963).
[CrossRef]

K. M. Abramski, H. J. Baker, A. D. Colley, and R. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

Bell Syst. Tech. J.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

IEEE J. Quantum Electron.

S. Vicalvi, R. Borghi, M. Santarsiero, and F. Gori, “Shape-invariance error for axially symmetric light beams,” IEEE J. Quantum Electron. 34, 2109–2116 (1998).
[CrossRef]

S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35, 1075–1085 (1999).
[CrossRef]

J. Eur. Opt. Soc. Rapid Publ.

V. Paeder, T. Scharf, P. Ruffieux, H.-P. Herzig, R. Voelkel, and K. J. Weible, “Microlenses with annular amplitude and phase masks,” J. Eur. Opt. Soc. Rapid Publ. 2, 07005 (2007).
[CrossRef]

J. Mod. Opt.

K. Ait-Ameur, “Effects of a phase aperture on the fundamental mode of a hard-apertured cavity,” J. Mod. Opt. 49, 1157–1168(2002).
[CrossRef]

K. Ait-Ameur, F. Sanchez, and M. Brunel, “The transfer of TEM00 and TEM01 beams through a hard-aperture,” J. Mod. Opt. 47, 1203–1211 (2000).

U. D. Zeitner and F. Wyroski, “High modal discrimination for laser resonators with Gaussian output beam,” J. Mod. Opt. 46, 1309–1314 (1999).

N. Passilly, G. Martel, and K. Aït-Ameur, “Beam propagation factor of truncated Laguerre-Gauss beams,” J. Mod. Opt. 51, 2279–2286 (2004).

J. Opt. A Pure Appl. Opt.

Z. Mei and D. Zhao, “The generalized beam propagation factor of truncated standard and elegant Laguerre-Gaussian beams,” J. Opt. A Pure Appl. Opt. 6, 1005–1011.
[CrossRef]

Opt. Commun.

M. Ciofini, A. Labate, R. Meucci, and P. Y. Wang, “Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations,” Opt. Commun. 154, 307–312 (1998).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Aït-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

Z. Derrar-Kaddour, A. Taleb, K. Aït-Ameur, G. Martel, and E. Cagniot, “Alternative model for computing intensity patterns through apertured ABCD systems,” Opt. Commun. 281, 1384–1395 (2008).
[CrossRef]

P.-A. Bélanger, Y. Champagne, and C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

E. Cagniot, Z. Derrar-Kaddour, M. Fromager, and K. Aït-Ameur, “Improving both transverse mode discrimination and diffraction losses in a plano-concave cavity,” Opt. Commun. 281, 4449–4454 (2008).
[CrossRef]

R. de Saint Denis, N. Passilly, M. Fromager, E. Cagniot, and K. Ait-Ameur, “Diffraction properties of opaque disks outside and inside a laser cavity,” Opt. Commun. 281, 4758–4761 (2008).
[CrossRef]

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

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, “Three-dimensional superresolution by annular filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

R. de Saint Denis, N. Passilly, and K. Ait-Ameur, “Laser beam brightness of apertured optical resonators,” Opt. Commun. 264, 193–202 (2006).
[CrossRef]

K. Ait-Ameur, M. Brunel, and F. Sanchez, “High transverse mode discrimination in apertured resonators using diffractive binary optics,” Opt. Commun. 184, 73–78 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[CrossRef]

Other

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Elsevier, 2007), p. 106.

D. R. Hall and P. E. Jackson, The Physics and Technology of Laser Resonators (Institute of Physics, 1992), p. 137.

A. E. Siegman, Lasers (University Science, 1986), Chap. 17.

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Figures (11)

Fig. 1
Fig. 1

Opaque ring of internal (external) radius ρ A ( ρ B ).

Fig. 2
Fig. 2

Variations of the ring transmission as a function of normalized ring radius Y A = ρ A / W when the incident beam is a symmetrical Laguerre–Gauss mode TEM p 0 of order p and of width W = 1 mm , for Δ = 150 .

Fig. 3
Fig. 3

Variations of the single-pass discrimination factor T 00 / T 10 as a function of the normalized ring Y A radius for Δ = 150 and W = 1 mm .

Fig. 4
Fig. 4

Variations of the single-pass discrimination factor T 00 / T 10 as a function of the normalized ring Y A radius for Δ = 150 and 50, and W = 1 mm .

Fig. 5
Fig. 5

Variations of divergence ratio θ p / θ p 0 versus Y A , where θ p stands for the diffracted TEM p 0 beam upon the absorbing ring, and θ p 0 for the pure TEM p 0 beam, for Δ = 150 and W = 1 mm .

Fig. 6
Fig. 6

Variation of divergence ratios θ 1 / θ 0 and θ 2 / θ 0 versus Y A , for Δ = 150 and W = 1 mm .

Fig. 7
Fig. 7

Sketch of the plano–concave cavity of length d = 600 mm made up of an absorbing ring against the plane mirror, and a diaphragm against the concave mirror.

Fig. 8
Fig. 8

Variations of beam propagation factor M 2 , fundamental mode loss L FM , and TMD for a normalized ring radius Y R = 0.7 , as a function of the normalized diaphragm radius Y D , for Δ = 20 and g = 0.5 . For an ideal pure TEM 00 ( TEM 10 ) mode, the beam quality factor is M 2 = 1 ( M 2 = 3 ).

Fig. 9
Fig. 9

Variations of beam propagation factor M 2 , fundamental mode loss L FM and TMD for a normalized ring radius Y R = 1.3 , as a function of the normalized diaphragm radius Y D , for Δ = 20 and g = 0.5 . For an ideal pure TEM 00 ( TEM 10 ) mode, the beam quality factor is M 2 = 1 ( M 2 = 3 ).

Fig. 10
Fig. 10

TMD F C versus fundamental mode losses L FM ; solid curve, without absorbing ring; dotted curve, with absorbing ring of normalized radius Y R = 1.3 and normalized width Δ = 20 . Note that L FM is varied by changing the diaphragm radius.

Fig. 11
Fig. 11

Far-field pattern of the fundamental mode of the cavity including only an absorbing ring characterized by a normalized radius Y R .

Tables (1)

Tables Icon

Table 1 Roots of Laguerre Polynomials: L p ( ρ / W ) = 0

Equations (24)

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E in ( ρ ) = L p ( 2 ρ 2 W 2 ) exp ( ρ 2 W 2 ) ,
T p 0 = 0 ρ A I p 0 ( ρ ) ρ d ρ + ρ B I p 0 ( ρ ) ρ d ρ 0 I p 0 ( ρ ) ρ d ρ .
T p 0 = 1 + F p 0 ( Y A ) F p 0 ( Y B ) ,
F 00 = 1 exp [ 2 Y 2 ] ,
F 10 = 1 ( 1 + 4 Y 4 ) exp [ 2 Y 2 ] ,
F 20 = 1 ( 1 + 8 Y 4 8 Y 6 + 4 Y 8 ) exp [ 2 Y 2 ] .
θ p = W e D .
W p 2 = λ d π ( g 1 g ) 1 / 2 ,
W c 2 = W p 2 g .
Y R = ρ A W p , Y D = ρ D W c .
F C = | Γ 0 | 2 | Γ 1 | 2 ,
G f p ( ρ , z ) = ( 2 π ) 1 / 2 1 W ( z ) L p ( 2 ρ 2 W 2 ) exp ( ρ 2 W 2 ) exp { + i [ k ρ 2 2 R c ( z ) ( 2 p + 1 ) ϕ ( z ) ] } ,
G b p ( ρ , z ) = ( 2 π ) 1 / 2 1 W ( z ) L p ( 2 ρ 2 W 2 ) exp ( ρ 2 W 2 ) exp { i [ k ρ 2 2 R c ( z ) ( 2 p + 1 ) ϕ ( z ) ] } ,
W 2 ( z ) = W 0 2 [ 1 + ( z / z 0 ) 2 ] ,
R c ( z ) = z [ 1 + ( z 0 / z ) 2 ] ,
ϕ ( z ) = arctan ( z / z 0 ) ,
E f ( ρ , z ) = exp [ i ( k z ω t ) ] p f p G f p ( ρ , z ) ,
E b ( ρ , z ) = exp { i [ k ( 2 d z ) ω t ] } p b p G b p ( ρ , z ) .
f p = m M p m f m ,
M p m = r p r c exp [ 2 i k d ] n C p n R C n m D exp [ 2 i ( n + m + 1 ) ϕ ( d ) ] ,
C p n R = 0 2 Y A 2 exp [ X ] L p ( X ) L n ( X ) + 2 Y B 2 exp [ X ] L p ( X ) L n ( X ) ,
C n m D = 0 2 Y D 2 exp [ X ] L n ( X ) L m ( X ) .
E d ( ρ , z ) = p D p G f p ( ρ , z ) .
M 2 = [ { p ( 2 p + 1 ) | D p | 2 } 2 4 { p q p ( D p * D q ) r δ p , q + 1 } 2 ] 1 / 2 ,

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