Abstract

The formation of the given low loss and large beamwidth doughnut-like fundamental mode of stable resonator by an intracavity flexible mirror is discussed. The mirror is a bimorph one with one round and two ring controlling electrodes. An inverse propagation method is used to determine the appropriate shape of the controlled mirror. The mirror reproduces the shape with minimal RMS error by combining weights of experimentally measured response functions of the mirror sample. The voltages applied to each mirror electrode are calculated. The calculations are carried out for industrial CW CO2 laser.

© 1998 Optical Society of America

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References

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  1. Yu. A. Anan’ev,“Laser Resonators and Beam Divergence Problem,” A. Higler, Ed.Bristol (1992).
  2. E.F. Ishenko and E.F. Reshetin, “Aspherical open optical cavity,” Opt. Spectros. (USSR)  51, 581–583 (1981).
  3. M. Lax, C. E. Greninger, W. H. Louisell, and W.B. McKKnight, “Large-mode-volume stable resonators,” J. Opt. Soc. Am. 65, 642–648 (1975).
    [Crossref]
  4. P. A. Bélanger and C. Paré, “Optical resonators using graded phase mirrors,” Opt. Lett. 16, 1057–1059 (1991).
    [Crossref] [PubMed]
  5. C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors: circular geometry,” IEEE J.Quantum Electron. 30, 1141–1148 (1994).
    [Crossref]
  6. P. A. Bélanger, R. L. Lachance, and C. Paré, “Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator,” Opt. Lett. 17, 739–741 (1992).
    [Crossref] [PubMed]
  7. R. van Neste, C. Paré, R. L. Lachance, and P. A. Bélanger, “Graded-phase mirror resonator with a super-gaussian output in a CW-CO2 laser,” IEEE J. Quantum Electron. 30, 2663–2669, (1994).
    [Crossref]
  8. R. van Neste. “Résonateurs Laser À Miroir De Phase: Vérification De Principe,” Thesis M. Sc., 1994, (in French).
  9. E. R. McClure,“Manufacturers turn precision optics with diamond,” Laser Focus World 27(2), 95–105 (1991).
  10. A. V. Kudryashov and V. I. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
    [Crossref]
  11. M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, and V. I. Shmalhausen, “Flexible mirror for adaptive light - beam formation systems,” Sov. J. Quantum Electron. 14 (16), 839–841 (1984).
    [Crossref]
  12. T. Yu. Cherezova, L. N. Kaptsov, and A. V. Kudryashov, “Cw industrial rod YAG:Nd3+ laser with an intracavity active bimorph mirror,” Appl. Opt. 35, 2554–2561 (1996).
    [Crossref] [PubMed]
  13. A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” The Bell Syst. Tech. J. 40, March, 453–488 (1961).
  14. T. Li, “Diffraction loss and selection of modes in maser resonators with circular mirrors,” The Bell Syst. Tech. J. May, 917–932 (1965).
  15. G. Zakharova, Yu. N. Karamzin, and V. A. Trofimov, “Some problems of optical radiation nonlinear distortions compensation. Blooming and random phase distortions of profiled beams,” Atmospheric Optics and Climate 8, 706–712 (1995)
  16. S. A. Ahmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Syhorykov, and S. S. Chesnokov, “Thermal self-action of light beams and methods of its compensation,” Izv. Visshih Uchebnih Vavedenii,  XXIII, 1–37 (1980) (in Russian).

1996 (2)

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

T. Yu. Cherezova, L. N. Kaptsov, and A. V. Kudryashov, “Cw industrial rod YAG:Nd3+ laser with an intracavity active bimorph mirror,” Appl. Opt. 35, 2554–2561 (1996).
[Crossref] [PubMed]

1995 (1)

G. Zakharova, Yu. N. Karamzin, and V. A. Trofimov, “Some problems of optical radiation nonlinear distortions compensation. Blooming and random phase distortions of profiled beams,” Atmospheric Optics and Climate 8, 706–712 (1995)

1994 (2)

C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors: circular geometry,” IEEE J.Quantum Electron. 30, 1141–1148 (1994).
[Crossref]

R. van Neste, C. Paré, R. L. Lachance, and P. A. Bélanger, “Graded-phase mirror resonator with a super-gaussian output in a CW-CO2 laser,” IEEE J. Quantum Electron. 30, 2663–2669, (1994).
[Crossref]

1992 (1)

1991 (2)

P. A. Bélanger and C. Paré, “Optical resonators using graded phase mirrors,” Opt. Lett. 16, 1057–1059 (1991).
[Crossref] [PubMed]

E. R. McClure,“Manufacturers turn precision optics with diamond,” Laser Focus World 27(2), 95–105 (1991).

1984 (1)

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, and V. I. Shmalhausen, “Flexible mirror for adaptive light - beam formation systems,” Sov. J. Quantum Electron. 14 (16), 839–841 (1984).
[Crossref]

1981 (1)

E.F. Ishenko and E.F. Reshetin, “Aspherical open optical cavity,” Opt. Spectros. (USSR)  51, 581–583 (1981).

1980 (1)

S. A. Ahmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Syhorykov, and S. S. Chesnokov, “Thermal self-action of light beams and methods of its compensation,” Izv. Visshih Uchebnih Vavedenii,  XXIII, 1–37 (1980) (in Russian).

1975 (1)

1961 (1)

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” The Bell Syst. Tech. J. 40, March, 453–488 (1961).

Ahmanov, S. A.

S. A. Ahmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Syhorykov, and S. S. Chesnokov, “Thermal self-action of light beams and methods of its compensation,” Izv. Visshih Uchebnih Vavedenii,  XXIII, 1–37 (1980) (in Russian).

Anan’ev, Yu. A.

Yu. A. Anan’ev,“Laser Resonators and Beam Divergence Problem,” A. Higler, Ed.Bristol (1992).

Bélanger, P. A.

C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors: circular geometry,” IEEE J.Quantum Electron. 30, 1141–1148 (1994).
[Crossref]

R. van Neste, C. Paré, R. L. Lachance, and P. A. Bélanger, “Graded-phase mirror resonator with a super-gaussian output in a CW-CO2 laser,” IEEE J. Quantum Electron. 30, 2663–2669, (1994).
[Crossref]

P. A. Bélanger, R. L. Lachance, and C. Paré, “Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator,” Opt. Lett. 17, 739–741 (1992).
[Crossref] [PubMed]

P. A. Bélanger and C. Paré, “Optical resonators using graded phase mirrors,” Opt. Lett. 16, 1057–1059 (1991).
[Crossref] [PubMed]

Cherezova, T. Yu.

Chesnokov, S. S.

S. A. Ahmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Syhorykov, and S. S. Chesnokov, “Thermal self-action of light beams and methods of its compensation,” Izv. Visshih Uchebnih Vavedenii,  XXIII, 1–37 (1980) (in Russian).

Fox, A. G.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” The Bell Syst. Tech. J. 40, March, 453–488 (1961).

Greninger, C. E.

Ishenko, E.F.

E.F. Ishenko and E.F. Reshetin, “Aspherical open optical cavity,” Opt. Spectros. (USSR)  51, 581–583 (1981).

Kandidov, V. P.

S. A. Ahmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Syhorykov, and S. S. Chesnokov, “Thermal self-action of light beams and methods of its compensation,” Izv. Visshih Uchebnih Vavedenii,  XXIII, 1–37 (1980) (in Russian).

Kaptsov, L. N.

Karamzin, Yu. N.

G. Zakharova, Yu. N. Karamzin, and V. A. Trofimov, “Some problems of optical radiation nonlinear distortions compensation. Blooming and random phase distortions of profiled beams,” Atmospheric Optics and Climate 8, 706–712 (1995)

Kudryashov, A. V.

T. Yu. Cherezova, L. N. Kaptsov, and A. V. Kudryashov, “Cw industrial rod YAG:Nd3+ laser with an intracavity active bimorph mirror,” Appl. Opt. 35, 2554–2561 (1996).
[Crossref] [PubMed]

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

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, and V. I. Shmalhausen, “Flexible mirror for adaptive light - beam formation systems,” Sov. J. Quantum Electron. 14 (16), 839–841 (1984).
[Crossref]

Lachance, R. L.

R. van Neste, C. Paré, R. L. Lachance, and P. A. Bélanger, “Graded-phase mirror resonator with a super-gaussian output in a CW-CO2 laser,” IEEE J. Quantum Electron. 30, 2663–2669, (1994).
[Crossref]

P. A. Bélanger, R. L. Lachance, and C. Paré, “Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator,” Opt. Lett. 17, 739–741 (1992).
[Crossref] [PubMed]

Lax, M.

Li, T.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” The Bell Syst. Tech. J. 40, March, 453–488 (1961).

T. Li, “Diffraction loss and selection of modes in maser resonators with circular mirrors,” The Bell Syst. Tech. J. May, 917–932 (1965).

Louisell, W. H.

McClure, E. R.

E. R. McClure,“Manufacturers turn precision optics with diamond,” Laser Focus World 27(2), 95–105 (1991).

McKKnight, W.B.

Nazarkin, S. I.

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, and V. I. Shmalhausen, “Flexible mirror for adaptive light - beam formation systems,” Sov. J. Quantum Electron. 14 (16), 839–841 (1984).
[Crossref]

Paré, C.

C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors: circular geometry,” IEEE J.Quantum Electron. 30, 1141–1148 (1994).
[Crossref]

R. van Neste, C. Paré, R. L. Lachance, and P. A. Bélanger, “Graded-phase mirror resonator with a super-gaussian output in a CW-CO2 laser,” IEEE J. Quantum Electron. 30, 2663–2669, (1994).
[Crossref]

P. A. Bélanger, R. L. Lachance, and C. Paré, “Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator,” Opt. Lett. 17, 739–741 (1992).
[Crossref] [PubMed]

P. A. Bélanger and C. Paré, “Optical resonators using graded phase mirrors,” Opt. Lett. 16, 1057–1059 (1991).
[Crossref] [PubMed]

Reshetin, E.F.

E.F. Ishenko and E.F. Reshetin, “Aspherical open optical cavity,” Opt. Spectros. (USSR)  51, 581–583 (1981).

Shmalhausen, V. I.

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

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, and V. I. Shmalhausen, “Flexible mirror for adaptive light - beam formation systems,” Sov. J. Quantum Electron. 14 (16), 839–841 (1984).
[Crossref]

Syhorykov, A. P.

S. A. Ahmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Syhorykov, and S. S. Chesnokov, “Thermal self-action of light beams and methods of its compensation,” Izv. Visshih Uchebnih Vavedenii,  XXIII, 1–37 (1980) (in Russian).

Trofimov, V. A.

G. Zakharova, Yu. N. Karamzin, and V. A. Trofimov, “Some problems of optical radiation nonlinear distortions compensation. Blooming and random phase distortions of profiled beams,” Atmospheric Optics and Climate 8, 706–712 (1995)

van Neste, R.

R. van Neste, C. Paré, R. L. Lachance, and P. A. Bélanger, “Graded-phase mirror resonator with a super-gaussian output in a CW-CO2 laser,” IEEE J. Quantum Electron. 30, 2663–2669, (1994).
[Crossref]

R. van Neste. “Résonateurs Laser À Miroir De Phase: Vérification De Principe,” Thesis M. Sc., 1994, (in French).

Vorontsov, M. A.

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, and V. I. Shmalhausen, “Flexible mirror for adaptive light - beam formation systems,” Sov. J. Quantum Electron. 14 (16), 839–841 (1984).
[Crossref]

S. A. Ahmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Syhorykov, and S. S. Chesnokov, “Thermal self-action of light beams and methods of its compensation,” Izv. Visshih Uchebnih Vavedenii,  XXIII, 1–37 (1980) (in Russian).

Zakharova, G.

G. Zakharova, Yu. N. Karamzin, and V. A. Trofimov, “Some problems of optical radiation nonlinear distortions compensation. Blooming and random phase distortions of profiled beams,” Atmospheric Optics and Climate 8, 706–712 (1995)

Appl. Opt. (1)

Atmospheric Optics and Climate (1)

G. Zakharova, Yu. N. Karamzin, and V. A. Trofimov, “Some problems of optical radiation nonlinear distortions compensation. Blooming and random phase distortions of profiled beams,” Atmospheric Optics and Climate 8, 706–712 (1995)

IEEE J. Quantum Electron. (1)

R. van Neste, C. Paré, R. L. Lachance, and P. A. Bélanger, “Graded-phase mirror resonator with a super-gaussian output in a CW-CO2 laser,” IEEE J. Quantum Electron. 30, 2663–2669, (1994).
[Crossref]

IEEE J.Quantum Electron. (1)

C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors: circular geometry,” IEEE J.Quantum Electron. 30, 1141–1148 (1994).
[Crossref]

Izv. Visshih Uchebnih Vavedenii (1)

S. A. Ahmanov, M. A. Vorontsov, V. P. Kandidov, A. P. Syhorykov, and S. S. Chesnokov, “Thermal self-action of light beams and methods of its compensation,” Izv. Visshih Uchebnih Vavedenii,  XXIII, 1–37 (1980) (in Russian).

J. Opt. Soc. Am. (1)

Laser Focus World (1)

E. R. McClure,“Manufacturers turn precision optics with diamond,” Laser Focus World 27(2), 95–105 (1991).

Opt. Eng. (1)

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

Opt. Lett. (2)

Opt. Spectros. (1)

E.F. Ishenko and E.F. Reshetin, “Aspherical open optical cavity,” Opt. Spectros. (USSR)  51, 581–583 (1981).

Sov. J. Quantum Electron. (1)

M. A. Vorontsov, A. V. Kudryashov, S. I. Nazarkin, and V. I. Shmalhausen, “Flexible mirror for adaptive light - beam formation systems,” Sov. J. Quantum Electron. 14 (16), 839–841 (1984).
[Crossref]

The Bell Syst. Tech. J. (1)

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” The Bell Syst. Tech. J. 40, March, 453–488 (1961).

Other (3)

T. Li, “Diffraction loss and selection of modes in maser resonators with circular mirrors,” The Bell Syst. Tech. J. May, 917–932 (1965).

Yu. A. Anan’ev,“Laser Resonators and Beam Divergence Problem,” A. Higler, Ed.Bristol (1992).

R. van Neste. “Résonateurs Laser À Miroir De Phase: Vérification De Principe,” Thesis M. Sc., 1994, (in French).

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Figures (7)

Fig. 1.
Fig. 1.

Bimorph deformable mirror

Fig.2
Fig.2

Surface profiles of adaptive mirror: (a) for central electrode “e1” - (P-V)=0.81 μm for applied voltage 20V, (b) for second ring “e3” - (P-V)=0.35 μm for applied voltage 40V, (c) for first ring of electrodes “e2” -(P-V)=0.79 μm for applied voltage 40V.

Fig.3.
Fig.3.

Schematic setup of the CW CO2 laser with adaptive mirror

Fig. 4.
Fig. 4.

Formation of a doughnut-like beam: Ψ(r)= (r+0.1)2 Exp(-((r+0.1)/3.1)4), N1=1, N2=4.7, G=0.5. (a) lilac curve - the phase profile of laser beam to be reconstructed and blue - the phase profile of active mirror; (b) - the normalizzed intensity profile of the given doughnut-like beam on the flexible back mirror; (c) - normalized intensity distributions on plane coupler: lilac - the given initial intensity profile, black (dashed) - intensity formed by GPM, blue - by flexible mirror.

Fig.5.
Fig.5.

Intensity distributions in far-field zone: lilac - far field pattern of a gaussian fundamental mode, blue - far field pattern of the beam formed by flexible corrector

Fig.6.
Fig.6.

The fragment of the intensity distributions shown in Fig.5.

Fig.7.
Fig.7.

Formation of a doughnut-like beam: Ψ(r)= (r+0.01)1/2 Exp(-((r+0.01)/3.1)4), N1=1, N2=4.7, G=0.5. (a) lilac curve - the phase profile of laser beam to be reconstructed and blue - the phase profile of active mirror; (b) - normalized intensity distributions on plane coupler: lilac - the given initial intensity profile, black (solid) - intensity formed by GPM, black (dashed) - by flexible mirror.

Tables (1)

Tables Icon

Table1. Voltages (in V) applied to the electrodes of adaptive mirror

Equations (4)

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γ 2 Ψ 2 ( r 2 ) = 0 b K 1 ( r 1 , r 2 ) Ψ 1 ( r 1 ) r 1 d r 1
γ 1 Ψ 1 ( r 1 ) = 0 a K 2 ( r 2 , r 1 ) Ψ 2 ( r 2 ) r 2 d r 2
K 1 ( r 1 , r 2 ) = j B J 0 ( k r 1 r 2 B ) exp ( j k 2 B ( A r 1 2 + D r 2 2 ) )
K 2 ( r 2 , r 1 ) = j B J 0 ( k r 1 r 2 B ) exp ( j k 2 B ( A r 1 2 + D r 2 2 ) ) exp ( j k φ m irror ( r 2 ) ) .

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