Abstract

We study both numerically and experimentally a specific geometric mode, named VW mode, in an end-pumped Nd:YVO4 laser with a plano-concave cavity near the 1/3-degeneracy. Three theoretical methods are used to analyze the transverse profiles, the operator method [J. Opt. Soc. Am. A 22, 1559 (2005)], the SU(2) wave representation [Phys. Rev. A 69, 053807 (2004)], and the Fox-Li approach. Some differences among them are addressed and clarified. Moreover, the generating conditions for VW mode are found peculiar and its propagation character is demonstrated. By comparing the experimental mode patterns with the three numerical results, we conclude that the field of a geometric mode in the operator method should be extended to include those of the reverse directional trajectories and the SU(2) coherent state representation is found too specific to produce the fringes within some transverse patterns.

© 2007 Optical Society of America

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References

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    [CrossRef]
  5. Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, "Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity," Phys. Rev. A 69, 053807 (2004).
    [CrossRef]
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    [CrossRef]
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2005 (1)

2004 (3)

2001 (1)

J. Dingjan, M. P. van Exter, and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser,’’Opt. Commun. 188, 345-351 (2001).
[CrossRef]

1999 (2)

R. Akis and D. K. Ferry, "Ballistic transport and scarring effects in coupled quantum dots," Phys. Rev. B 59, 7529-7536 (1999).
[CrossRef]

J. Banerji and G. S. Agarwal, "Non-linear wave packet dynamics of coherent states of various symmetry groups," Opt. Express 5,220-229 (1999).
[CrossRef] [PubMed]

1991 (1)

1989 (2)

1970 (2)

Agarwal, G. S.

Akis, R.

R. Akis and D. K. Ferry, "Ballistic transport and scarring effects in coupled quantum dots," Phys. Rev. B 59, 7529-7536 (1999).
[CrossRef]

Banerji, J.

Buzek, V.

Chen, C. H.

Chen, Y. F.

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, "Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity," Phys. Rev. A 69, 053807 (2004).
[CrossRef]

Collins, S. A.

Dagan, E.

Degnan, J. J.

Dick, D.

Dingjan, J.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser,’’Opt. Commun. 188, 345-351 (2001).
[CrossRef]

Ferry, D. K.

R. Akis and D. K. Ferry, "Ballistic transport and scarring effects in coupled quantum dots," Phys. Rev. B 59, 7529-7536 (1999).
[CrossRef]

Gabay, A.

Hanson, F.

Hsieh, W. F.

Huang, K. F.

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, "Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity," Phys. Rev. A 69, 053807 (2004).
[CrossRef]

Jiang, C. H.

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, "Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity," Phys. Rev. A 69, 053807 (2004).
[CrossRef]

Lan, Y. P.

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, "Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity," Phys. Rev. A 69, 053807 (2004).
[CrossRef]

Nienhuis, G.

Quang, T.

Ramsay, I. A.

Sterman, B.

Tai, P. T.

van Exter, M. P.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser,’’Opt. Commun. 188, 345-351 (2001).
[CrossRef]

Visser, J.

Woerdman, J. P.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser,’’Opt. Commun. 188, 345-351 (2001).
[CrossRef]

Yatsiv, S.

Zelders, N. J.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

J. Dingjan, M. P. van Exter, and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser,’’Opt. Commun. 188, 345-351 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, "Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity," Phys. Rev. A 69, 053807 (2004).
[CrossRef]

Phys. Rev. B (1)

R. Akis and D. K. Ferry, "Ballistic transport and scarring effects in coupled quantum dots," Phys. Rev. B 59, 7529-7536 (1999).
[CrossRef]

Other (1)

C. H. Chen, P. T. Tai, M. D. Wei, and W. F. Hsieh, "Multibeam-waist modes in an end-pumped Nd-YVO4 laser," J. Opt. Soc. Am. B 20, 1220-1226 (2003). There is lack of in the last term of equation (3) in this reference.
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a). Closed ray trajectories symmetric with the optical axis in a three-fold degenerate plano-concave cavity. (b) VW mode trajectories using the multibounce Gaussian beams model in [7]. (c) VW mode trajectories using the SU(2) representation in [5]. (d) VW mode trajectories using the Collins integral together with a rate equation.

Fig. 2.
Fig. 2.

Schematic diagram of the experimental setup: LD, laser diode; BS, beam splitter; M, reflective mirror; OC, output coupler; LF, line filter; TL, transform lens; other abbreviations defined in text.

Fig. 3.
Fig. 3.

The experimental mode patterns (a) and the numerical mode profile variation (b) after the transform lens.

Equations (2)

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Φ n ( x , y , z ; τ ) = 1 ( 1 + τ 2 ) n 2 p = 0 n ( n p ) 1 2 τ p Φ 3 p , 0 ( HG ) x y z ,
E m + 1 ( x ) = i B λ w w exp ( ik 2 L ) E m + ( x ) exp { ( i π / B λ ) ( A x′ 2 + Bxx′ + D x 2 ) } dx′ ,

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