Abstract

The three-dimensional field distribution of the diffractive cavity mode structure in a passive, open, unstable resonator is presented as a function of the equivalent Fresnel number of the cavity. The qualitative structure of this intracavity field distribution, including the central intensity core (or oscillator filament), is characterized in terms of the Fresnel zone structure that is defined over the cavity feedback aperture. Previous related research is reviewed.

© 1999 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science Books, 1986) Chapters 21–23.
  2. A. E. Siegman and R. Arrathoon, “Modes in unstable optical resonators and lens waveguides,” IEEE J. Quant. Electron. QE-3, 156–163 (1967).
    [Crossref]
  3. K. E. Oughstun, “Unstable resonator modes,” in Progress in Optics, vol. xxiv, E. Wolf, ed. (North-Holland, 1987) pp. 165–387.
    [Crossref]
  4. E. A. Sziklas and A. E. Siegman, “Diffraction calculations using fast Fourier transform methods,” IEEE Proc. 62, 410–412 (1974).
    [Crossref]
  5. Yu. A. Anan’ev, “Unstable resonators and their applications (Review),” Sov. J. Quant. Electron. 1, 565–586 (1972).
    [Crossref]
  6. Yu. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Adam Hilger, 1992).
  7. W. H. Steier and G. L. McAllister, “A simplified method for predicting unstable resonator mode profiles,” IEEE J. Quant. Electron. QE-11, 725–728 (1975).
    [Crossref]
  8. K. E. Oughstun, “Passive cavity transverse mode stability and its influence on the active cavity mode properties for unstable optical resonators,” in Optical Resonators, SPIE Proceedingsvol. 1224, D. A. Holmes, ed. (SPIE, 1990) pp. 80–98.
    [Crossref]
  9. Yu. A. Anan’ev, “Angular divergence of radiation of solid-state lasers,” Sov. Phys. Usp. 14, 197–215 (1971).
    [Crossref]
  10. Yu. A. Anan’ev, “Establishment of oscillations in unstable resonators,” Sov. J. Quant. Electron. 5, 615–617 (1975).
    [Crossref]
  11. C. C. Khamnei, Open Unstable Optical Resonator Mode Field Theory (Ph.D. dissertation, University of Vermont, 1998).

1998 (1)

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

1975 (2)

Yu. A. Anan’ev, “Establishment of oscillations in unstable resonators,” Sov. J. Quant. Electron. 5, 615–617 (1975).
[Crossref]

W. H. Steier and G. L. McAllister, “A simplified method for predicting unstable resonator mode profiles,” IEEE J. Quant. Electron. QE-11, 725–728 (1975).
[Crossref]

1974 (1)

E. A. Sziklas and A. E. Siegman, “Diffraction calculations using fast Fourier transform methods,” IEEE Proc. 62, 410–412 (1974).
[Crossref]

1972 (1)

Yu. A. Anan’ev, “Unstable resonators and their applications (Review),” Sov. J. Quant. Electron. 1, 565–586 (1972).
[Crossref]

1971 (1)

Yu. A. Anan’ev, “Angular divergence of radiation of solid-state lasers,” Sov. Phys. Usp. 14, 197–215 (1971).
[Crossref]

1967 (1)

A. E. Siegman and R. Arrathoon, “Modes in unstable optical resonators and lens waveguides,” IEEE J. Quant. Electron. QE-3, 156–163 (1967).
[Crossref]

Anan’ev, Yu. A.

Yu. A. Anan’ev, “Establishment of oscillations in unstable resonators,” Sov. J. Quant. Electron. 5, 615–617 (1975).
[Crossref]

Yu. A. Anan’ev, “Unstable resonators and their applications (Review),” Sov. J. Quant. Electron. 1, 565–586 (1972).
[Crossref]

Yu. A. Anan’ev, “Angular divergence of radiation of solid-state lasers,” Sov. Phys. Usp. 14, 197–215 (1971).
[Crossref]

Yu. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Adam Hilger, 1992).

Arrathoon, R.

A. E. Siegman and R. Arrathoon, “Modes in unstable optical resonators and lens waveguides,” IEEE J. Quant. Electron. QE-3, 156–163 (1967).
[Crossref]

Khamnei, C. C.

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

McAllister, G. L.

W. H. Steier and G. L. McAllister, “A simplified method for predicting unstable resonator mode profiles,” IEEE J. Quant. Electron. QE-11, 725–728 (1975).
[Crossref]

Oughstun, K. E.

K. E. Oughstun, “Passive cavity transverse mode stability and its influence on the active cavity mode properties for unstable optical resonators,” in Optical Resonators, SPIE Proceedingsvol. 1224, D. A. Holmes, ed. (SPIE, 1990) pp. 80–98.
[Crossref]

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

Siegman, A. E.

E. A. Sziklas and A. E. Siegman, “Diffraction calculations using fast Fourier transform methods,” IEEE Proc. 62, 410–412 (1974).
[Crossref]

A. E. Siegman and R. Arrathoon, “Modes in unstable optical resonators and lens waveguides,” IEEE J. Quant. Electron. QE-3, 156–163 (1967).
[Crossref]

A. E. Siegman, Lasers (University Science Books, 1986) Chapters 21–23.

Steier, W. H.

W. H. Steier and G. L. McAllister, “A simplified method for predicting unstable resonator mode profiles,” IEEE J. Quant. Electron. QE-11, 725–728 (1975).
[Crossref]

Sziklas, E. A.

E. A. Sziklas and A. E. Siegman, “Diffraction calculations using fast Fourier transform methods,” IEEE Proc. 62, 410–412 (1974).
[Crossref]

IEEE J. Quant. Electron. (2)

A. E. Siegman and R. Arrathoon, “Modes in unstable optical resonators and lens waveguides,” IEEE J. Quant. Electron. QE-3, 156–163 (1967).
[Crossref]

W. H. Steier and G. L. McAllister, “A simplified method for predicting unstable resonator mode profiles,” IEEE J. Quant. Electron. QE-11, 725–728 (1975).
[Crossref]

IEEE Proc. (1)

E. A. Sziklas and A. E. Siegman, “Diffraction calculations using fast Fourier transform methods,” IEEE Proc. 62, 410–412 (1974).
[Crossref]

Sov. J. Quant. Electron. (2)

Yu. A. Anan’ev, “Unstable resonators and their applications (Review),” Sov. J. Quant. Electron. 1, 565–586 (1972).
[Crossref]

Yu. A. Anan’ev, “Establishment of oscillations in unstable resonators,” Sov. J. Quant. Electron. 5, 615–617 (1975).
[Crossref]

Sov. Phys. Usp. (1)

Yu. A. Anan’ev, “Angular divergence of radiation of solid-state lasers,” Sov. Phys. Usp. 14, 197–215 (1971).
[Crossref]

Other (5)

A. E. Siegman, Lasers (University Science Books, 1986) Chapters 21–23.

K. E. Oughstun, “Passive cavity transverse mode stability and its influence on the active cavity mode properties for unstable optical resonators,” in Optical Resonators, SPIE Proceedingsvol. 1224, D. A. Holmes, ed. (SPIE, 1990) pp. 80–98.
[Crossref]

Yu. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Adam Hilger, 1992).

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

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

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Figures (11)

Fig. 1.
Fig. 1.

Half-symmetric, positive branch unstable cavity geometry with magnification M.

Fig. 1.
Fig. 1.

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

Fig. 2.
Fig. 2.

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

Fig. 3.
Fig. 3.

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

Fig. 4.
Fig. 4.

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

Fig. 5.
Fig. 5.

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

Fig. 6.
Fig. 6.

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

Fig. 7.
Fig. 7.

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

Fig. 8.
Fig. 8.

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

Fig. 9.
Fig. 9.

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

Fig. 10.
Fig. 10.

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

Equations (13)

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γ ˜ nl u nl ( r ) = 2 π e i ( l + 1 ) π / 2 N c M 0 1 u nl ( r 0 ) J l ( 2 π N c r r 0 / M ) exp [ N c ( r 0 2 + r 2 / M 2 ) ] r 0 d r 0 ,
N c = M a 2
γ ˜ nl ( G ) u nl ( G ) ( r ) = f l M u nl ( G ) ( r / M ) ; r < M
γ ˜ nl ( 1 ) u nl ( 1 ) = f l M u nl ( 1 ) ( r / M )
e iπl π ( M N c r ) 1 / 2 u nl ( 1 ) ( 1 ) 1 ( r / M ) 2 exp [ N c ( 1 + ( r / M ) 2 ) ]
· { cos ( 2 π N c r / M l π / 2 π / 4 ) i r M sin ( 2 π N c r / M l π / 2 π / 4 ) }
γ ˜ nl u nl ( r ) 2 π e i ( l + 1 ) π 2 N c M exp ( N c r 2 M 2 ) 0 1 u nl ( r 0 ) J l ( 2 π N c M r r 0 ) r 0 d r 0 ,
N eq = M 2 1 2 M 2 N c
Δ ( r ) 1 2 ( 1 r + 1 r ) r 2
Δ ( r ) M 2 1 2 MB r 2 .
N eq ( r ) Δ ( r ) λ N eq r 2 a 2
N eq ( r n ) = n + f N eq n = 0,1,2,3 , ,
r n = a ( n + f N eq ) 1 2 , n = 0,1,2,3 , ,

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