Abstract

The three-dimensional field distribution of the diffractive cavity mode structure in an active, open, unstable laser resonator is presented as a function of the equivalent Fresnel number of the cavity. The active cavity mode structures are compared to that of the corresponding passive cavity so that the effects of a spatially extended, homogeneously broadened, saturable gain medium on the cavity field structure may be ascertained. The qualitative structure of this intracavity field distribution, including the central intensity core (or oscillator filament), is explained in terms of the Fresnel zone structure defined over the cavity feedback aperture.

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References

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  1. A. E. Siegman, Lasers (University Science Books, 1986) Chapter 8.
  2. E. A. Sziklas and A. E. Siegman, Mode calculations in unstable resonators with flowing saturable gain. 2: fast Fourier transform method," Appl. Opt. 14, 1874-1889 (1975).
    [CrossRef] [PubMed]
  3. K. E. Oughstun, "Unstable resonator modes," in Progress in Optics, vol. xxiv, E. Wolf, ed. (North-Holland, 1987) pp. 165- 387.
    [CrossRef]
  4. D. B. Rensch, "Three-dimensional unstable resonator calculations with laser medium," Appl. Opt. 13, 2546-2561 (1974).
    [CrossRef] [PubMed]
  5. P. W. Milloni, "Criteria for the thin-sheet gain approximation," Appl. Opt. 16, 2794-2795 (1977).
    [CrossRef]
  6. C. C. Khamnei, Open Unstable Optical Resonator Mode Field Theory (Ph. D. dissertation, University of Vermont, 1998.
  7. Yu. A. Anan�v, "Angular divergence of radiation of solid-state lasers," Sov. Phys. Usp. 14, 197-215 (1971).
    [CrossRef]

Other (7)

A. E. Siegman, Lasers (University Science Books, 1986) Chapter 8.

E. A. Sziklas and A. E. Siegman, Mode calculations in unstable resonators with flowing saturable gain. 2: fast Fourier transform method," Appl. Opt. 14, 1874-1889 (1975).
[CrossRef] [PubMed]

K. E. Oughstun, "Unstable resonator modes," in Progress in Optics, vol. xxiv, E. Wolf, ed. (North-Holland, 1987) pp. 165- 387.
[CrossRef]

D. B. Rensch, "Three-dimensional unstable resonator calculations with laser medium," Appl. Opt. 13, 2546-2561 (1974).
[CrossRef] [PubMed]

P. W. Milloni, "Criteria for the thin-sheet gain approximation," Appl. Opt. 16, 2794-2795 (1977).
[CrossRef]

C. C. Khamnei, Open Unstable Optical Resonator Mode Field Theory (Ph. D. dissertation, University of Vermont, 1998.

Yu. A. Anan�v, "Angular divergence of radiation of solid-state lasers," Sov. Phys. Usp. 14, 197-215 (1971).
[CrossRef]

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Figures (14)

Fig. 1.
Fig. 1.

Unfolded cavity geometry for a positive branch half-symmetric unstable resonator.

Fig. 2.
Fig. 2.

Equivalent Fresnel number dependence of (a) the total intracavity power Pin incident upon the outcoupling aperture, (b) the outcoupled cavity power Pout , and (c) the flux eigenvalue for 1, 5, and 40

Fig. 3.
Fig. 3.

Relative intensity and phase of the intracavity mode structure incident upon the outcoupling aperture-feedback mirror of an M = 2, Neq = 2.5 half-symmetric unstable resonator with 1, 5, and 40 gain-phase sheets.

Fig. 4.
Fig. 4.

Convergence of the thin-sheet gain-phase approximation of the intracavity power Pin incident upon in the outcoupling aperture to the continuously extended limit (obtained in the limit as N → ∞) at several values of the cavity Fresnel number.

Fig. 5.
Fig. 5.

Active three-dimensional intracavity field distribution in an M=2 half-symmetric unstable cavity with Neq = 0.5 .

Fig. 6.
Fig. 6.

Active three-dimensional intracavity field distribution in an M=2 half-symmetric unstable cavity with Neq = 0.75.

Fig. 7.
Fig. 7.

Active three-dimensional intracavity field distribution in an M = 2 half-symmetric unstable cavity with Neq = 1.0.

Fig. 8.
Fig. 8.

Active three-dimensional intracavity field distribution in an M = 2 half-symmetric unstable cavity with Neq =1.25.

Fig. 9.
Fig. 9.

Active three-dimensional intracavity field distribution in an M = 2 half-symmetric unstable cavity with Neq = 1.5.

Fig. 10.
Fig. 10.

Active three-dimensional intracavity field distribution in an M = 2 half-symmetric unstable cavity with Neq =1.75.

Fig. 11.
Fig. 11.

Active three-dimensional intracavity field distribution in an M = 2 half-symmetric unstable cavity with Neq = 6.0.

Fig. 12.
Fig. 12.

Active three-dimensional intracavity field distribution in an M = 2 half-symmetric unstable cavity with Neq = 6.25.

Fig. 13.
Fig. 13.

Active three-dimensional intracavity field distribution in an M = 2 half-symmetric unstable cavity with Neq = 6.5.

Fig. 14.
Fig. 14.

Active three-dimensional intracavity field distribution in an M = 2 half-symmetric unstable cavity with Neq = 6.75.

Equations (5)

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g ( I , z ) = g 0 1 + I ( r , z ) / I s ,
g ( I , Z j ) = g 0 1 + I ( r , z ) / I s , j = 1,2 , , N g
N F = a 2 / ( 2 λ Δ Z )
T 2 ( g ( r , Z j ) u ( r , Z j ) ) g ( r , Z j ) u ( r , Z j ) 4 π ( λΔ Z ) , j = 1,2 , , N g ,
γ F = 1 ( P out P in ) ,

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