Abstract

We report what is to our best knowledge the first observation of Mathieu–Gauss modes directly generated in an axicon-based stable resonator. By slightly breaking the symmetry of the cavity we were able to generate single lowest and high-order Mathieu–Gauss modes of high quality. The observed transverse modes have an inherent elliptic structure and exhibit remarkable agreement with theoretical predictions.

© 2008 Optical Society of America

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References

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  1. J. Rogel-Salazar, G. H.C. New, and S. Chávez-Cerda, "Bessel-Gauss beam optical resonator," Opt. Commun. 190,117-122 (2001).
    [CrossRef]
  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]
  3. 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]
  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," Proc. SPIE 5708, 323-331 (2005).
    [CrossRef]
  5. 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]
  6. 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]
  7. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Shaping soliton properties in Mathieu lattices," Opt. Lett. 31, 238-240 (2006).
    [CrossRef] [PubMed]
  8. C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne, and K. Dholakia, "Orbital angular momentum transfer in helical Mathieu beams," Opt. Express 14, 4182-4187 (2006).
    [CrossRef] [PubMed]
  9. C. A. Dartora and H. E. Hernández-Figueroa, "Properties of a localized Mathieu pulse," J. Opt. Soc. Am. A 21, 662-667 (2004).
    [CrossRef]
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    [CrossRef]
  11. C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006).
    [CrossRef]
  12. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, "Parabolic nondiffracting optical wave fields," Opt. Lett. 29, 44-46 (2004).
    [CrossRef] [PubMed]
  13. P. A. Bélanger and M. Rioux, "Ring pattern of a lens-axicon doublet illuminated by a Gaussian beam," Appl. Opt. 17, 1080-1086 (1978).
    [CrossRef] [PubMed]
  14. M. Rioux and P. A. Bélanger, "Linear, annular and radial focusing with axicons and application to laser machining," Appl. Opt. 17, 1532-1536 (1978).
    [CrossRef] [PubMed]
  15. J. C. Gutiérrez-Vega, R. Rodríguez-Masegosa, and S. Chávez-Cerda, "Focusing evolution of generalized propagation invariant optical fields," J. Opt. A 5, 276-282 (2003).
    [CrossRef]
  16. R. Akimoto, C. Saloma, T. Tanaka, and S. Kawata, "Imaging properties of axicon in a scanning optical system," Appl. Opt. 31, 6653-6657 (1992).
    [CrossRef]
  17. Z. Bin and Z. Zhu, "Diffraction property of an axicon in oblique illumination," Appl. Opt. 37, 1080-1086 (1978).
  18. A. Thanning, Z. Jaroszewicz, and A. T. Friberg, "Diffractive axicons in oblique illumination: analysis and experiments with comparison to elliptical axicons," Appl. Opt. 42, 9-17 (2003).
    [CrossRef]

2006 (3)

2005 (3)

J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005).
[CrossRef]

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," Proc. SPIE 5708, 323-331 (2005).
[CrossRef]

2004 (2)

2003 (3)

2001 (2)

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

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]

2000 (1)

1992 (1)

1978 (3)

Akimoto, R.

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," Proc. SPIE 5708, 323-331 (2005).
[CrossRef]

Bandres, M. A.

Bandrés, M. A.

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006).
[CrossRef]

Bélanger, P. A.

Bin, Z.

Z. Bin and Z. Zhu, "Diffraction property of an axicon in oblique illumination," Appl. Opt. 37, 1080-1086 (1978).

Chávez-Cerda, S.

Dartora, C. A.

Dholakia, K.

Egorov, A. A.

Friberg, A. T.

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," Proc. SPIE 5708, 323-331 (2005).
[CrossRef]

Gutiérrez-Vega, J. C.

C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne, and K. Dholakia, "Orbital angular momentum transfer in helical Mathieu beams," Opt. Express 14, 4182-4187 (2006).
[CrossRef] [PubMed]

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006).
[CrossRef]

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]

J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (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," Proc. SPIE 5708, 323-331 (2005).
[CrossRef]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, "Parabolic nondiffracting optical wave fields," Opt. Lett. 29, 44-46 (2004).
[CrossRef] [PubMed]

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]

J. C. Gutiérrez-Vega, R. Rodríguez-Masegosa, and S. Chávez-Cerda, "Focusing evolution of generalized propagation invariant optical fields," J. Opt. A 5, 276-282 (2003).
[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]

Hernández-Aranda, R. I.

Hernández-Figueroa, H. E.

Iturbe-Castillo, M. D.

Jaroszewicz, Z.

Kartashov, Y. V.

Katranji, E. G.

Kawata, S.

Khilo, A. N.

López-Mariscal, C.

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006).
[CrossRef]

C. López-Mariscal, J. C. Gutiérrez-Vega, G. Milne, and K. Dholakia, "Orbital angular momentum transfer in helical Mathieu beams," Opt. Express 14, 4182-4187 (2006).
[CrossRef] [PubMed]

Milne, G.

New, G. H.C.

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

Rioux, M.

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," Proc. SPIE 5708, 323-331 (2005).
[CrossRef]

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]

J. C. Gutiérrez-Vega, R. Rodríguez-Masegosa, and S. Chávez-Cerda, "Focusing evolution of generalized propagation invariant optical fields," J. Opt. A 5, 276-282 (2003).
[CrossRef]

Rogel-Salazar, J.

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.

Saloma, C.

Tanaka, T.

Thanning, A.

Torner, L.

Vysloukh, V. A.

Zhu, Z.

Z. Bin and Z. Zhu, "Diffraction property of an axicon in oblique illumination," Appl. Opt. 37, 1080-1086 (1978).

Appl. Opt. (5)

J. Opt. A (1)

J. C. Gutiérrez-Vega, R. Rodríguez-Masegosa, and S. Chávez-Cerda, "Focusing evolution of generalized propagation invariant optical fields," J. Opt. A 5, 276-282 (2003).
[CrossRef]

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

Opt. Commun. (1)

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

Opt. Eng. (1)

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (1)

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," Proc. SPIE 5708, 323-331 (2005).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Configuration of the axicon-based MG resonator. The conical wavefronts represent the geometric field distribution inside and outside of the cavity. The output beam preserves the nondiffracting behavior inside the conical green region. (b) Schematic of the CO2 slow flow laser system.

Fig. 2.
Fig. 2.

Transverse intensity patterns of the fundamental BG mode and the first high-order radial mode emitted by the cavity and their respective power spectra. The physical size of each image is 6.7×6.7 mm. Note that darker regions represent higher intensities to facilitate the observation.

Fig. 3.
Fig. 3.

Theoretical and experimental intensity patterns of even-parity MG beams and their power spectra for m={0,1,2,3}. The physical size of each image is 6.7×6.7 mm. Note that darker regions represent higher intensities to facilitate the observation.

Fig. 4.
Fig. 4.

Theoretical and experimental intensity patterns of odd-parity MG beams and their power spectra for m={1,2,3}. The physical size of each image is 6.7×6.7 mm. Note that darker regions represent higher intensities to facilitate the observation.

Fig. 5.
Fig. 5.

Output power as a function of the operating current for several gas pressures.

Equations (1)

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MG m ( r ) = exp ( i k t 2 2 k z μ ) GB ( r ) { Je m ( ξ , q ) ce m ( η , q ) , even parity , Jo m ( ξ , q ) se m ( η , q ) , odd parity ,

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