Abstract

We experimentally show, for the first time to our knowledge, that a diode-pumped Nd:YVO4 laser can operate with multipass transverse (MPT) modes that self-reproduce after several round trips in a plano–concave cavity that has fractionally degenerate resonator configurations when the pump beam waist is sufficiently smaller than that of the fundamental cavity mode. The MPT mode is found to exhibit multiple beam waists located at different positions and to experience a lower pumping threshold than the single-pass transverse mode. With off-axis pumping, the N-pass transverse mode forms a symmetric pattern for even N and an asymmetric pattern for odd N. This result can be explained as being due to the introduction of MPT modes but not to superposition of the standard cavity modes.

© 2001 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 845.
  2. V. Kermene, A. Saviot, M. Vampouille, B. Colombeau, C. Froehly, and T. Dohnalik, “Flattening of the spatial laser beam profile with low losses and minimal beam divergence,” Opt. Lett. 17, 859–861 (1992).
    [CrossRef]
  3. F. Saviot, E. Mottay, M. Vampouille, and B. Colombeau, “Optical synthesis of a high-energy uniform and uniphase laser emission,” Opt. Lett. 18, 2117–2119 (1993).
    [CrossRef] [PubMed]
  4. V. Kermene, M. Vampouille, C. Froehly, and B. Colombeau, “Temporal laser beam construction under controlled mode filtering,” Opt. Commun. 97, 319–326 (1993).
    [CrossRef]
  5. B. Colombeau, M. Vampouille, V. Kermene, A. Desfarges, and C. Froehly, “Spatial shaping of coherent waves inside a confocal laser,” Pure Appl. Opt. 3, 757–773 (1994).
    [CrossRef]
  6. N. Hodgson, B. Ozygus, F. Schabert, and H. Weber, “Degenerated confocal resonator,” Appl. Opt. 32, 3190–3200 (1993).
    [CrossRef] [PubMed]
  7. V. Couderc, O. Guy, A. Barthelemy, C. Froehly, and F. Lourador, “Self-optimized resonator for optical pumping of solid-state lasers,” Opt. Lett. 19, 1134–1136 (1994).
    [CrossRef] [PubMed]
  8. A. Ramsay and J. J. Degnan, “A ray analysis of optical resonators formed by two spherical mirrors,” Appl. Opt. 9, 385–398 (1970).
    [CrossRef] [PubMed]
  9. Ref. 1, p. 580.
  10. H. H. Wu, C. C. Sheu, T. W. Chen, M. D. Wei, and W. F. Hsieh, “Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an end-pumped Nd:YVO4 laser,” Opt. Commun. 165, 225–229 (1999).
    [CrossRef]
  11. P. Laporta and M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
    [CrossRef]

1999

H. H. Wu, C. C. Sheu, T. W. Chen, M. D. Wei, and W. F. Hsieh, “Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an end-pumped Nd:YVO4 laser,” Opt. Commun. 165, 225–229 (1999).
[CrossRef]

1994

V. Couderc, O. Guy, A. Barthelemy, C. Froehly, and F. Lourador, “Self-optimized resonator for optical pumping of solid-state lasers,” Opt. Lett. 19, 1134–1136 (1994).
[CrossRef] [PubMed]

B. Colombeau, M. Vampouille, V. Kermene, A. Desfarges, and C. Froehly, “Spatial shaping of coherent waves inside a confocal laser,” Pure Appl. Opt. 3, 757–773 (1994).
[CrossRef]

1993

1992

1991

P. Laporta and M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
[CrossRef]

1970

Barthelemy, A.

Brussard, M.

P. Laporta and M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
[CrossRef]

Chen, T. W.

H. H. Wu, C. C. Sheu, T. W. Chen, M. D. Wei, and W. F. Hsieh, “Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an end-pumped Nd:YVO4 laser,” Opt. Commun. 165, 225–229 (1999).
[CrossRef]

Colombeau, B.

B. Colombeau, M. Vampouille, V. Kermene, A. Desfarges, and C. Froehly, “Spatial shaping of coherent waves inside a confocal laser,” Pure Appl. Opt. 3, 757–773 (1994).
[CrossRef]

F. Saviot, E. Mottay, M. Vampouille, and B. Colombeau, “Optical synthesis of a high-energy uniform and uniphase laser emission,” Opt. Lett. 18, 2117–2119 (1993).
[CrossRef] [PubMed]

V. Kermene, M. Vampouille, C. Froehly, and B. Colombeau, “Temporal laser beam construction under controlled mode filtering,” Opt. Commun. 97, 319–326 (1993).
[CrossRef]

V. Kermene, A. Saviot, M. Vampouille, B. Colombeau, C. Froehly, and T. Dohnalik, “Flattening of the spatial laser beam profile with low losses and minimal beam divergence,” Opt. Lett. 17, 859–861 (1992).
[CrossRef]

Couderc, V.

Degnan, J. J.

Desfarges, A.

B. Colombeau, M. Vampouille, V. Kermene, A. Desfarges, and C. Froehly, “Spatial shaping of coherent waves inside a confocal laser,” Pure Appl. Opt. 3, 757–773 (1994).
[CrossRef]

Dohnalik, T.

Froehly, C.

B. Colombeau, M. Vampouille, V. Kermene, A. Desfarges, and C. Froehly, “Spatial shaping of coherent waves inside a confocal laser,” Pure Appl. Opt. 3, 757–773 (1994).
[CrossRef]

V. Couderc, O. Guy, A. Barthelemy, C. Froehly, and F. Lourador, “Self-optimized resonator for optical pumping of solid-state lasers,” Opt. Lett. 19, 1134–1136 (1994).
[CrossRef] [PubMed]

V. Kermene, M. Vampouille, C. Froehly, and B. Colombeau, “Temporal laser beam construction under controlled mode filtering,” Opt. Commun. 97, 319–326 (1993).
[CrossRef]

V. Kermene, A. Saviot, M. Vampouille, B. Colombeau, C. Froehly, and T. Dohnalik, “Flattening of the spatial laser beam profile with low losses and minimal beam divergence,” Opt. Lett. 17, 859–861 (1992).
[CrossRef]

Guy, O.

Hodgson, N.

Hsieh, W. F.

H. H. Wu, C. C. Sheu, T. W. Chen, M. D. Wei, and W. F. Hsieh, “Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an end-pumped Nd:YVO4 laser,” Opt. Commun. 165, 225–229 (1999).
[CrossRef]

Kermene, V.

B. Colombeau, M. Vampouille, V. Kermene, A. Desfarges, and C. Froehly, “Spatial shaping of coherent waves inside a confocal laser,” Pure Appl. Opt. 3, 757–773 (1994).
[CrossRef]

V. Kermene, M. Vampouille, C. Froehly, and B. Colombeau, “Temporal laser beam construction under controlled mode filtering,” Opt. Commun. 97, 319–326 (1993).
[CrossRef]

V. Kermene, A. Saviot, M. Vampouille, B. Colombeau, C. Froehly, and T. Dohnalik, “Flattening of the spatial laser beam profile with low losses and minimal beam divergence,” Opt. Lett. 17, 859–861 (1992).
[CrossRef]

Laporta, P.

P. Laporta and M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
[CrossRef]

Lourador, F.

Mottay, E.

Ozygus, B.

Ramsay, A.

Saviot, A.

Saviot, F.

Schabert, F.

Sheu, C. C.

H. H. Wu, C. C. Sheu, T. W. Chen, M. D. Wei, and W. F. Hsieh, “Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an end-pumped Nd:YVO4 laser,” Opt. Commun. 165, 225–229 (1999).
[CrossRef]

Vampouille, M.

B. Colombeau, M. Vampouille, V. Kermene, A. Desfarges, and C. Froehly, “Spatial shaping of coherent waves inside a confocal laser,” Pure Appl. Opt. 3, 757–773 (1994).
[CrossRef]

V. Kermene, M. Vampouille, C. Froehly, and B. Colombeau, “Temporal laser beam construction under controlled mode filtering,” Opt. Commun. 97, 319–326 (1993).
[CrossRef]

F. Saviot, E. Mottay, M. Vampouille, and B. Colombeau, “Optical synthesis of a high-energy uniform and uniphase laser emission,” Opt. Lett. 18, 2117–2119 (1993).
[CrossRef] [PubMed]

V. Kermene, A. Saviot, M. Vampouille, B. Colombeau, C. Froehly, and T. Dohnalik, “Flattening of the spatial laser beam profile with low losses and minimal beam divergence,” Opt. Lett. 17, 859–861 (1992).
[CrossRef]

Weber, H.

Wei, M. D.

H. H. Wu, C. C. Sheu, T. W. Chen, M. D. Wei, and W. F. Hsieh, “Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an end-pumped Nd:YVO4 laser,” Opt. Commun. 165, 225–229 (1999).
[CrossRef]

Wu, H. H.

H. H. Wu, C. C. Sheu, T. W. Chen, M. D. Wei, and W. F. Hsieh, “Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an end-pumped Nd:YVO4 laser,” Opt. Commun. 165, 225–229 (1999).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

P. Laporta and M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
[CrossRef]

Opt. Commun.

H. H. Wu, C. C. Sheu, T. W. Chen, M. D. Wei, and W. F. Hsieh, “Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an end-pumped Nd:YVO4 laser,” Opt. Commun. 165, 225–229 (1999).
[CrossRef]

V. Kermene, M. Vampouille, C. Froehly, and B. Colombeau, “Temporal laser beam construction under controlled mode filtering,” Opt. Commun. 97, 319–326 (1993).
[CrossRef]

Opt. Lett.

Pure Appl. Opt.

B. Colombeau, M. Vampouille, V. Kermene, A. Desfarges, and C. Froehly, “Spatial shaping of coherent waves inside a confocal laser,” Pure Appl. Opt. 3, 757–773 (1994).
[CrossRef]

Other

Ref. 1, p. 580.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 845.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. The notation is defined in the text.

Fig. 2
Fig. 2

Sequence of transverse mode patterns for a Nd:YVO4 laser observed at the semiconfocal cavity (bottom row) and away from it (upper row) with on-axis pumping and the offset between the optic axis and the pump beam increasing from left to right.

Fig. 3
Fig. 3

Sequence of transverse mode patterns for an off-axis pumped Nd:YVO4 laser observed at 1/N-degenerate resonator configurations with some low values of N (N=3, 4, 5, 6 from left to right).

Fig. 4
Fig. 4

Experimental arrangement used for measuring the transformation of the laser output through a lens.

Fig. 5
Fig. 5

Schematic illustrating the MPT mode for a cavity with the 1/3-degenerate resonator configuration. Beam propagation (a) within a plano–concave cavity and (b) along an equivalent lens-guide cavity. Forward propagation of the MPT mode within a cavity and transformation of its output through the transform lens for (c) the first pass, (d) the second pass, and (e) the third pass.

Fig. 6
Fig. 6

Transformed beam spots observed at distances of (a) d3, (b) d1, and (c) d2 after the lens for the SPT mode and (d) d3, (e) d1, and (f) d2 for the MPT (N=3) mode. Because the original beam spot of (c) is too dark to be seen, we nonlinearly adjusted its gamma value to make it visible.

Fig. 7
Fig. 7

Output power as a function of absorbed pump power measured for cavity lengths (a) equivalent to a 1/4-degenerate resonator configuration and (b) 1 mm longer than it.

Fig. 8
Fig. 8

Dependence of the output power on the resonator G1G2 parameters with pump power slightly above the threshold of the MPT mode in a semiconfocal cavity. Some narrow power peaks occur at the cavity with G1G2 parameters corresponding to discrete fractionally degenerate resonator configurations (K/N=1/3, 3/10, 1/4, 1/5, and 1/6 from left to right).

Equations (4)

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abcd,
T=ABCD=2aG2-12bG22(2aG1G2-G1-a2G2)/b4G1G2-2aG2-1,
TN=ABCDN=1sin θA sin Nθ-sin(N-1)θB sin θC sin NθD sin Nθ-sin(N-1)θ,
T=0R/2-2/R0,

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