Abstract

Excellent beam quality and divergence stability over a wide pump power range was demonstrated in a Q-switched, Nd:YAG, positive branch confocal unstable resonator by using a one degree-of-freedom, adaptive optic. Unlike single-element flexible-membrane mirrors, the variable radius mirror (VRM) consisted of a lens and mirror, whose separation determined the VRM’s effective radius of curvature. This simple method enabled low cost and efficient thermal focusing compensation. The VRM was demonstrated by producing a 300-mJ Q-switch or 1-J free-running at a beam quality factor M 2 that varied between 1.2 and 1.8 as the average output power varied between 0 and 33 W.

© 1998 Optical Society of America

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References

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  1. A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 858–922.
  2. A. Siegman, “Modes in unstable optical resonators and lens waveguides,” IEEE J. Quantum Electron. QE-3, 156–163 (1967).
    [CrossRef]
  3. S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
    [CrossRef]
  4. S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, “Q-Switched Nd:YAG laser with super-Gaussian resonators,” Opt. Lett. 16, 642–644 (1991).
    [CrossRef] [PubMed]
  5. P. A. Bélanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
    [CrossRef]
  6. S. A. Chetkin, G. V. Vdovin, “Deformable mirror correction of a thermal lens induced in the active rod of a solid state laser,” Opt. Commun. 100, 159–165 (1993).
    [CrossRef]
  7. K. Du, P. Loosen, H. Kochmann, “Properties of a high-power CO2 laser with an adaptive mirror,” Opt. Commun. 106, 269–277 (1994).
    [CrossRef]
  8. N. Pavel, T. Dascalu, V. Lupei, “Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation,” Opt. Commun. 123, 115–120 (1996).
    [CrossRef]
  9. S. Jackel, I. Moshe, “Method and apparatus for compensating thermal effects in laser resonators and multiple-pass amplifiers,” Israel Patent application121720 (1997).
  10. I. Moshe, S. Jackel, R. Lalluz, “Working beyond the static limits of laser stability by use of adaptive and polarization-conjugation optics,” Appl. Opt. 37, 6415–6420 (1998).
    [CrossRef]
  11. W. Koechner, Solid-State Laser Engineering, 4th ed. (Springer-Verlag, New York, 1996), pp. 204–205.
  12. A. Parent, M. Morin, P. Lavingne, “Propagation of Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
    [CrossRef]
  13. C. Swift, E. Bliss, D. Lenz, R. Miller, “Deformable mirror for zigzag solid-state lasers,” Opt. Eng. 29, 1199–1203 (1990).
    [CrossRef]
  14. A. V. Kuryashov, V. I. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
    [CrossRef]

1998 (1)

1996 (2)

A. V. Kuryashov, V. I. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
[CrossRef]

N. Pavel, T. Dascalu, V. Lupei, “Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation,” Opt. Commun. 123, 115–120 (1996).
[CrossRef]

1994 (2)

P. A. Bélanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
[CrossRef]

K. Du, P. Loosen, H. Kochmann, “Properties of a high-power CO2 laser with an adaptive mirror,” Opt. Commun. 106, 269–277 (1994).
[CrossRef]

1993 (1)

S. A. Chetkin, G. V. Vdovin, “Deformable mirror correction of a thermal lens induced in the active rod of a solid state laser,” Opt. Commun. 100, 159–165 (1993).
[CrossRef]

1992 (1)

A. Parent, M. Morin, P. Lavingne, “Propagation of Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

1991 (1)

1990 (2)

C. Swift, E. Bliss, D. Lenz, R. Miller, “Deformable mirror for zigzag solid-state lasers,” Opt. Eng. 29, 1199–1203 (1990).
[CrossRef]

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

1967 (1)

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

Bélanger, P. A.

P. A. Bélanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
[CrossRef]

Bliss, E.

C. Swift, E. Bliss, D. Lenz, R. Miller, “Deformable mirror for zigzag solid-state lasers,” Opt. Eng. 29, 1199–1203 (1990).
[CrossRef]

Chetkin, S. A.

S. A. Chetkin, G. V. Vdovin, “Deformable mirror correction of a thermal lens induced in the active rod of a solid state laser,” Opt. Commun. 100, 159–165 (1993).
[CrossRef]

Dascalu, T.

N. Pavel, T. Dascalu, V. Lupei, “Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation,” Opt. Commun. 123, 115–120 (1996).
[CrossRef]

De Silvestri, S.

S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, “Q-Switched Nd:YAG laser with super-Gaussian resonators,” Opt. Lett. 16, 642–644 (1991).
[CrossRef] [PubMed]

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Du, K.

K. Du, P. Loosen, H. Kochmann, “Properties of a high-power CO2 laser with an adaptive mirror,” Opt. Commun. 106, 269–277 (1994).
[CrossRef]

Jackel, S.

I. Moshe, S. Jackel, R. Lalluz, “Working beyond the static limits of laser stability by use of adaptive and polarization-conjugation optics,” Appl. Opt. 37, 6415–6420 (1998).
[CrossRef]

S. Jackel, I. Moshe, “Method and apparatus for compensating thermal effects in laser resonators and multiple-pass amplifiers,” Israel Patent application121720 (1997).

Kochmann, H.

K. Du, P. Loosen, H. Kochmann, “Properties of a high-power CO2 laser with an adaptive mirror,” Opt. Commun. 106, 269–277 (1994).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 4th ed. (Springer-Verlag, New York, 1996), pp. 204–205.

Kuryashov, A. V.

A. V. Kuryashov, V. I. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
[CrossRef]

Lalluz, R.

Lavingne, P.

A. Parent, M. Morin, P. Lavingne, “Propagation of Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

Lenz, D.

C. Swift, E. Bliss, D. Lenz, R. Miller, “Deformable mirror for zigzag solid-state lasers,” Opt. Eng. 29, 1199–1203 (1990).
[CrossRef]

Loosen, P.

K. Du, P. Loosen, H. Kochmann, “Properties of a high-power CO2 laser with an adaptive mirror,” Opt. Commun. 106, 269–277 (1994).
[CrossRef]

Lupei, V.

N. Pavel, T. Dascalu, V. Lupei, “Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation,” Opt. Commun. 123, 115–120 (1996).
[CrossRef]

Magni, V.

S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, “Q-Switched Nd:YAG laser with super-Gaussian resonators,” Opt. Lett. 16, 642–644 (1991).
[CrossRef] [PubMed]

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Miller, R.

C. Swift, E. Bliss, D. Lenz, R. Miller, “Deformable mirror for zigzag solid-state lasers,” Opt. Eng. 29, 1199–1203 (1990).
[CrossRef]

Morin, M.

A. Parent, M. Morin, P. Lavingne, “Propagation of Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

Moshe, I.

I. Moshe, S. Jackel, R. Lalluz, “Working beyond the static limits of laser stability by use of adaptive and polarization-conjugation optics,” Appl. Opt. 37, 6415–6420 (1998).
[CrossRef]

S. Jackel, I. Moshe, “Method and apparatus for compensating thermal effects in laser resonators and multiple-pass amplifiers,” Israel Patent application121720 (1997).

Paré, C.

P. A. Bélanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
[CrossRef]

Parent, A.

A. Parent, M. Morin, P. Lavingne, “Propagation of Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

Pavel, N.

N. Pavel, T. Dascalu, V. Lupei, “Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation,” Opt. Commun. 123, 115–120 (1996).
[CrossRef]

Shmalhausen, V. I.

A. V. Kuryashov, V. I. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
[CrossRef]

Siegman, A.

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

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 858–922.

Svelto, O.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Swift, C.

C. Swift, E. Bliss, D. Lenz, R. Miller, “Deformable mirror for zigzag solid-state lasers,” Opt. Eng. 29, 1199–1203 (1990).
[CrossRef]

Taccheo, S.

Valentini, G.

S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, “Q-Switched Nd:YAG laser with super-Gaussian resonators,” Opt. Lett. 16, 642–644 (1991).
[CrossRef] [PubMed]

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Vdovin, G. V.

S. A. Chetkin, G. V. Vdovin, “Deformable mirror correction of a thermal lens induced in the active rod of a solid state laser,” Opt. Commun. 100, 159–165 (1993).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

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

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Opt. Commun. (4)

P. A. Bélanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
[CrossRef]

S. A. Chetkin, G. V. Vdovin, “Deformable mirror correction of a thermal lens induced in the active rod of a solid state laser,” Opt. Commun. 100, 159–165 (1993).
[CrossRef]

K. Du, P. Loosen, H. Kochmann, “Properties of a high-power CO2 laser with an adaptive mirror,” Opt. Commun. 106, 269–277 (1994).
[CrossRef]

N. Pavel, T. Dascalu, V. Lupei, “Variable reflectivity mirror unstable resonator with deformable mirror thermal compensation,” Opt. Commun. 123, 115–120 (1996).
[CrossRef]

Opt. Eng. (2)

C. Swift, E. Bliss, D. Lenz, R. Miller, “Deformable mirror for zigzag solid-state lasers,” Opt. Eng. 29, 1199–1203 (1990).
[CrossRef]

A. V. Kuryashov, V. I. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

A. Parent, M. Morin, P. Lavingne, “Propagation of Gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[CrossRef]

Other (3)

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 858–922.

S. Jackel, I. Moshe, “Method and apparatus for compensating thermal effects in laser resonators and multiple-pass amplifiers,” Israel Patent application121720 (1997).

W. Koechner, Solid-State Laser Engineering, 4th ed. (Springer-Verlag, New York, 1996), pp. 204–205.

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Figures (8)

Fig. 1
Fig. 1

Magnification m of a static, positive branch, confocal, unstable resonator as a function of pump power P for a thermal lensing of 0.67 diopter/kW. Magnification decreases as the pump power increases and the resonator becomes stable (m = 1) at P = 145 W.

Fig. 2
Fig. 2

Adaptive optic’s effective radius of curvature ρVRM required to maintain a collimated output beam under variable pump power.

Fig. 3
Fig. 3

VRM mirror-to-lens separation; Δ as a function of pump power.

Fig. 4
Fig. 4

Experimental Q-switched unstable resonator layout.

Fig. 5
Fig. 5

Experimental system for beam quality measurements.

Fig. 6
Fig. 6

Beam quality (M 2) and output energy as functions of pump power for the Q-switched confocal unstable resonator with a dynamic VRM and with a static rear mirror. The PFN energy was 23 J.

Fig. 7
Fig. 7

(a) Near-field and (b) far-field beam profiles from the unstable resonator operating at a Q-switch condition at a pump power of 460 W.

Fig. 8
Fig. 8

Beam quality (M 2) and output energy as functions of pump power for the free-running confocal unstable resonator with a dynamic VRM and with a static rear mirror. The PFN energy was 46 J.

Equations (6)

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G 1 = g 1 - L 2 / f T 1 - L 1 / ρ 1 , G 2 = g 2 - L 1 / f T 1 - L 2 / ρ 2 ,
L * = L 1 + L 2 - L 1 L 2 / f T ,
A B C D = 4 G 1 G 2 - 2 G 1 a - 1 2 G 1 L * 4 G 1 G 2 a - 2 G 1 a 2 - 2 G 2 L * 2 G 1 a - 1 ,
m = | 2 G 1 G 2 - 1 | + 4 G 1 G 2 G 1 G 2 - 1 1 / 2 .
ρ VRM ρ 2 C = 0 = a 2 - 2 aG 1 L 1 + L 2 - L 1 L 2 / f T a 2 - 2 aG 1 1 - L 1 / f T + G 1 .
ρ VRM = f lens ρ mirror + Δ f lens - ρ mirror - Δ .

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