Abstract

Numerical calculations recently published [J. Opt. Soc. Am. A 23, 912 (2006) ] on the eigenmodes in axicon-based Bessel–Gauss resonators revealed significant inconsistencies regarding the modal patterns, the mode losses, the mode ordering by loss, and the intracavity field distributions. We show that the results are inaccurate mainly because (a) it was overlooked in the derivation of the matrix equations that light crosses twice through the axicon in a complete round-trip and (b) the numerical method used to evaluate the diffraction integral equations cannot resolve the eigenvalues and eigenfields for the given resonator configuration.

© 2007 Optical Society of America

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References

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  1. D. Ling, J. Li, and J. Chen, "Analysis of eigenfields in the axicon-based Bessel-Gauss resonator by the transfer-matrix method," J. Opt. Soc. Am. A 23, 912-918 (2006).
    [CrossRef]
  2. J. C. Gutiérrez-Vega, R. Rodríguez-Masegosa, and S. Chávez-Cerda, "Bessel-Gauss resonator with spherical output mirror: geometrical and wave-optics analysis," J. Opt. Soc. Am. A 20, 2113-2122 (2003).
    [CrossRef]
  3. R. I. Hernández-Aranda, S. Chávez-Cerda, and J. C. Gutiérrez-Vega, "Theory of the unstable Bessel resonator," J. Opt. Soc. Am. A 22, 1909-1917 (2005).
    [CrossRef]
  4. M. Alvarez, M. Guizar-Sicairos, R. Rodríguez-Masegosa, and J. C. Gutiérrez-Vega, "Construction and characterization of CO2 laser with an axicon based Bessel-Gauss resonator," in Laser Resonators and Beam Control VIII, A.V.Kudrayashov and A.H.Paxton, eds., Proc. SPIE 5708, 323-331 (2005).
  5. J. Rogel-Salazar, G. H. C. New, and S. Chávez-Cerda, "Bessel-Gauss beam optical resonator," Opt. Commun. 190, 117-122 (2001).
    [CrossRef]
  6. A. N. Khilo, E. G. Katranji, and A. A. Ryzhevich, "Axicon-based Bessel resonator: analytical description and experiment," J. Opt. Soc. Am. A 18, 1986-1992 (2001).
    [CrossRef]
  7. P. Muys and E. Vandamme, "Direct generation of Bessel beams," Appl. Opt. 41, 6375-6379 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
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  10. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, "Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields," J. Opt. Soc. Am. A 21, 53-58 (2004).
    [CrossRef]
  11. A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
    [CrossRef]
  12. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1992).
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2006 (1)

2005 (2)

R. I. Hernández-Aranda, S. Chávez-Cerda, and J. C. Gutiérrez-Vega, "Theory of the unstable Bessel resonator," J. Opt. Soc. Am. A 22, 1909-1917 (2005).
[CrossRef]

M. Alvarez, M. Guizar-Sicairos, R. Rodríguez-Masegosa, and J. C. Gutiérrez-Vega, "Construction and characterization of CO2 laser with an axicon based Bessel-Gauss resonator," in Laser Resonators and Beam Control VIII, A.V.Kudrayashov and A.H.Paxton, eds., Proc. SPIE 5708, 323-331 (2005).

2004 (2)

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

M. Guizar-Sicairos and J. C. Gutiérrez-Vega, "Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields," J. Opt. Soc. Am. A 21, 53-58 (2004).
[CrossRef]

2003 (2)

2002 (1)

2001 (2)

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

J. Rogel-Salazar, G. H. C. New, and S. Chávez-Cerda, "Bessel-Gauss beam optical resonator," Opt. Commun. 190, 117-122 (2001).
[CrossRef]

1992 (1)

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1992).

1980 (1)

1978 (1)

1969 (1)

1961 (1)

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

Alvarez, M.

M. Alvarez, M. Guizar-Sicairos, R. Rodríguez-Masegosa, and J. C. Gutiérrez-Vega, "Construction and characterization of CO2 laser with an axicon based Bessel-Gauss resonator," in Laser Resonators and Beam Control VIII, A.V.Kudrayashov and A.H.Paxton, eds., Proc. SPIE 5708, 323-331 (2005).

Bernabe, M. L.

Buchter, S. C.

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

Chávez-Cerda, S.

Chen, J.

Dente, G. C.

Elfstrom, H.

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1992).

Fox, A. G.

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

Guizar-Sicairos, M.

M. Alvarez, M. Guizar-Sicairos, R. Rodríguez-Masegosa, and J. C. Gutiérrez-Vega, "Construction and characterization of CO2 laser with an axicon based Bessel-Gauss resonator," in Laser Resonators and Beam Control VIII, A.V.Kudrayashov and A.H.Paxton, eds., Proc. SPIE 5708, 323-331 (2005).

M. Guizar-Sicairos and J. C. Gutiérrez-Vega, "Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields," J. Opt. Soc. Am. A 21, 53-58 (2004).
[CrossRef]

Gutiérrez-Vega, J. C.

Hakola, A.

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

Hernández-Aranda, R. I.

Kajava, T.

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

Katranji, E. G.

Khilo, A. N.

Latham, W. P.

Li, J.

Li, T.

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

Ling, D.

Murphy, W. D.

Muys, P.

New, G. H. C.

C. L. Tsangaris, G. H. C. New, and J. Rogel-Salazar, "Unstable Bessel beam resonator," Opt. Commun. 223, 233-238 (2003).
[CrossRef]

J. Rogel-Salazar, G. H. C. New, and S. Chávez-Cerda, "Bessel-Gauss beam optical resonator," Opt. Commun. 190, 117-122 (2001).
[CrossRef]

Paakkonen, P.

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1992).

Rodríguez-Masegosa, R.

M. Alvarez, M. Guizar-Sicairos, R. Rodríguez-Masegosa, and J. C. Gutiérrez-Vega, "Construction and characterization of CO2 laser with an axicon based Bessel-Gauss resonator," in Laser Resonators and Beam Control VIII, A.V.Kudrayashov and A.H.Paxton, eds., Proc. SPIE 5708, 323-331 (2005).

J. C. Gutiérrez-Vega, R. Rodríguez-Masegosa, and S. Chávez-Cerda, "Bessel-Gauss resonator with spherical output mirror: geometrical and wave-optics analysis," J. Opt. Soc. Am. A 20, 2113-2122 (2003).
[CrossRef]

Rogel-Salazar, J.

C. L. Tsangaris, G. H. C. New, and J. Rogel-Salazar, "Unstable Bessel beam resonator," Opt. Commun. 223, 233-238 (2003).
[CrossRef]

J. Rogel-Salazar, G. H. C. New, and S. Chávez-Cerda, "Bessel-Gauss beam optical resonator," Opt. Commun. 190, 117-122 (2001).
[CrossRef]

Ryzhevich, A. A.

Sanderson, R. L.

Simonen, J.

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

Streifer, W.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1992).

Tsangaris, C. L.

C. L. Tsangaris, G. H. C. New, and J. Rogel-Salazar, "Unstable Bessel beam resonator," Opt. Commun. 223, 233-238 (2003).
[CrossRef]

Turunen, J.

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

Vandamme, E.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1992).

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

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

J. Opt. Soc. Am. A (5)

Opt. Commun. (3)

A. Hakola, S. C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, and J. Turunen, "Bessel-Gauss output beam from a diode-pumped Nd:YAG laser," Opt. Commun. 238, 335-340 (2004).
[CrossRef]

J. Rogel-Salazar, G. H. C. New, and S. Chávez-Cerda, "Bessel-Gauss beam optical resonator," Opt. Commun. 190, 117-122 (2001).
[CrossRef]

C. L. Tsangaris, G. H. C. New, and J. Rogel-Salazar, "Unstable Bessel beam resonator," Opt. Commun. 223, 233-238 (2003).
[CrossRef]

Other (2)

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1992).

M. Alvarez, M. Guizar-Sicairos, R. Rodríguez-Masegosa, and J. C. Gutiérrez-Vega, "Construction and characterization of CO2 laser with an axicon based Bessel-Gauss resonator," in Laser Resonators and Beam Control VIII, A.V.Kudrayashov and A.H.Paxton, eds., Proc. SPIE 5708, 323-331 (2005).

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L = a 2 ( n 1 ) α ,

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