Abstract

An optical surface of variable concave parabolic shape and a clear aperture of 30 mm was created using two rings to deform a flat 50.8 mm diameter mirror. The deformable mirror assembly was modeled using finite element analysis software as well as analytical solutions. Measured parabolic surface deformation showed good agreement with those models. Mirror performance was quantitatively studied using an interferometer and focal lengths from hundreds of meters down to the meter scale have been achieved. In this publication, the deformable mirror has been applied to compensate on shot thermal lensing in 16 mm diameter and 25 mm diameter Nd:Phosphate glass rod amplifiers by using only a single actuator. The possibility to rapidly change focal lengths across two to three orders of magnitude has applications for remote sensing, such as laser induced breakdown spectroscopy, LIDAR, and control of laser filament formation.

© 2006 Optical Society of America

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References

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  1. W. Koechner and B. Bass. Solid-State Lasers. (Springer, New York, 2003).
  2. P. H. Sarkies, "A stable yag resonator yielding a beam of very low divergence and high output energy," Opt. Commun. 31,189-92 (1979).
    [CrossRef]
  3. T. Graf, E. Wyss, M. Roth, and H. P. Weber, "Laser resonator with balanced thermal lenses," Opt. Commun. 190,327-31 (2001).
    [CrossRef]
  4. E. Wyss, M. Roth, T. Graf, and H. P. Weber, "Thermo optical compensation methods for high-power lasers," IEEE J. of Quantum Electron. 38,1620-8 (2002).
    [CrossRef]
  5. G. V. Vdovin and S. A. Chetkin, "Active correction of thermal lensing in solid-state lasers. II, use of a resonator with a controllable configuration," Kvantovaya Elektronika, Moskva Quantum Electronics 20,167-171 (1993).
  6. U. J. Greiner and H. H. Klingenberg, "Thermal lens correction of a diode-pumped Nd:YAG laser of high TEM00 power by an adjustable-curvature mirror," Opt. Lett. 19,1207-1209 (1994).
    [CrossRef] [PubMed]
  7. J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
    [CrossRef]
  8. S. K. Hawkes, A. Dunster, C. Hernandez-Gomez, and I. O. Musgrave. Pump induced aberration characterization and compensation for the vulcan petawatt beam. Central Laser Facility annual report 2004/2005, pps 194-196, 2004/2005.
  9. J. Schwarz, M. Ramsey, I. Smith, D. Headley, and J. Porter, "Low order adaptive optics on ZBeamlet using a single actuator deformable mirror," Opt. Commun. 264,203 - 212 (2006).
    [CrossRef]
  10. D. Headley, M. Ramsey, and J. Schwarz. Variable focal length deformable mirror. U.S. Patent Application No. 11,017,337, filed on 12/20/2004.
  11. P. K. Rambo, I. C. Smith, J. L. Porter, M. J. Hurst, C. S. Speas, R. G. Adams, A. J. Garcia, E. Dawson, B. D. Thurston, C. Wakefield, J. W. Kellogg, M. J. Slattery, H. C. Ives, R. S. Broyles, J. A. Caird, A. C. Erlandson, J. E. Murray,W. C. Behrendt, N. D. Neilsen, and J. M. Narduzzi, "Z-Beamlet: A multikilojoule, terawatt-class laser system," Appl. Opt. 44,2421-2430 (2005).
    [CrossRef] [PubMed]
  12. Y. C. Warren and B. G. Richard. Roark’s Formulas for Stress and Strain. McGraw-Hill, New York, seventh edition, 2002.
  13. Schott. Optical glass catalog. http://www.us.schott.com/sgt/english/download/n-bk7.pdf, 1996.

2006

J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
[CrossRef]

J. Schwarz, M. Ramsey, I. Smith, D. Headley, and J. Porter, "Low order adaptive optics on ZBeamlet using a single actuator deformable mirror," Opt. Commun. 264,203 - 212 (2006).
[CrossRef]

2005

2002

E. Wyss, M. Roth, T. Graf, and H. P. Weber, "Thermo optical compensation methods for high-power lasers," IEEE J. of Quantum Electron. 38,1620-8 (2002).
[CrossRef]

2001

T. Graf, E. Wyss, M. Roth, and H. P. Weber, "Laser resonator with balanced thermal lenses," Opt. Commun. 190,327-31 (2001).
[CrossRef]

1994

1993

G. V. Vdovin and S. A. Chetkin, "Active correction of thermal lensing in solid-state lasers. II, use of a resonator with a controllable configuration," Kvantovaya Elektronika, Moskva Quantum Electronics 20,167-171 (1993).

1979

P. H. Sarkies, "A stable yag resonator yielding a beam of very low divergence and high output energy," Opt. Commun. 31,189-92 (1979).
[CrossRef]

Adams, R. G.

Behrendt, W. C.

Broyles, R. S.

Caird, J. A.

Chetkin, S. A.

G. V. Vdovin and S. A. Chetkin, "Active correction of thermal lensing in solid-state lasers. II, use of a resonator with a controllable configuration," Kvantovaya Elektronika, Moskva Quantum Electronics 20,167-171 (1993).

Dawson, E.

Erlandson, A. C.

Garcia, A. J.

Graf, T.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, "Thermo optical compensation methods for high-power lasers," IEEE J. of Quantum Electron. 38,1620-8 (2002).
[CrossRef]

T. Graf, E. Wyss, M. Roth, and H. P. Weber, "Laser resonator with balanced thermal lenses," Opt. Commun. 190,327-31 (2001).
[CrossRef]

Greiner, U. J.

Headley, D.

J. Schwarz, M. Ramsey, I. Smith, D. Headley, and J. Porter, "Low order adaptive optics on ZBeamlet using a single actuator deformable mirror," Opt. Commun. 264,203 - 212 (2006).
[CrossRef]

J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
[CrossRef]

Hurst, M. J.

Ives, H. C.

Kellogg, J. W.

Klingenberg, H. H.

Murray, J. E.

Narduzzi, J. M.

Neilsen, N. D.

Porter, J.

J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
[CrossRef]

J. Schwarz, M. Ramsey, I. Smith, D. Headley, and J. Porter, "Low order adaptive optics on ZBeamlet using a single actuator deformable mirror," Opt. Commun. 264,203 - 212 (2006).
[CrossRef]

Porter, J. L.

Rambo, P.

J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
[CrossRef]

Rambo, P. K.

Ramsey, M.

J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
[CrossRef]

J. Schwarz, M. Ramsey, I. Smith, D. Headley, and J. Porter, "Low order adaptive optics on ZBeamlet using a single actuator deformable mirror," Opt. Commun. 264,203 - 212 (2006).
[CrossRef]

Roth, M.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, "Thermo optical compensation methods for high-power lasers," IEEE J. of Quantum Electron. 38,1620-8 (2002).
[CrossRef]

T. Graf, E. Wyss, M. Roth, and H. P. Weber, "Laser resonator with balanced thermal lenses," Opt. Commun. 190,327-31 (2001).
[CrossRef]

Sarkies, P. H.

P. H. Sarkies, "A stable yag resonator yielding a beam of very low divergence and high output energy," Opt. Commun. 31,189-92 (1979).
[CrossRef]

Schwarz, J.

J. Schwarz, M. Ramsey, I. Smith, D. Headley, and J. Porter, "Low order adaptive optics on ZBeamlet using a single actuator deformable mirror," Opt. Commun. 264,203 - 212 (2006).
[CrossRef]

J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
[CrossRef]

Slattery, M. J.

Smith, I.

J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
[CrossRef]

J. Schwarz, M. Ramsey, I. Smith, D. Headley, and J. Porter, "Low order adaptive optics on ZBeamlet using a single actuator deformable mirror," Opt. Commun. 264,203 - 212 (2006).
[CrossRef]

Smith, I. C.

Speas, C. S.

Thurston, B. D.

Vdovin, G. V.

G. V. Vdovin and S. A. Chetkin, "Active correction of thermal lensing in solid-state lasers. II, use of a resonator with a controllable configuration," Kvantovaya Elektronika, Moskva Quantum Electronics 20,167-171 (1993).

Wakefield, C.

Weber, H. P.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, "Thermo optical compensation methods for high-power lasers," IEEE J. of Quantum Electron. 38,1620-8 (2002).
[CrossRef]

T. Graf, E. Wyss, M. Roth, and H. P. Weber, "Laser resonator with balanced thermal lenses," Opt. Commun. 190,327-31 (2001).
[CrossRef]

Wyss, E.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, "Thermo optical compensation methods for high-power lasers," IEEE J. of Quantum Electron. 38,1620-8 (2002).
[CrossRef]

T. Graf, E. Wyss, M. Roth, and H. P. Weber, "Laser resonator with balanced thermal lenses," Opt. Commun. 190,327-31 (2001).
[CrossRef]

Appl. Opt.

Appl. Phys. B: Lasers and Optics

J. Schwarz, M. Ramsey, D. Headley, P. Rambo, I. Smith, and J. Porter, "Thermal lens compensation by convex deformation of a flat mirror with variable annular force," Appl. Phys. B: Lasers and Optics 82,275-281 (2006).
[CrossRef]

IEEE J. of Quantum Electron.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, "Thermo optical compensation methods for high-power lasers," IEEE J. of Quantum Electron. 38,1620-8 (2002).
[CrossRef]

Kvantovaya Elektronika, Moskva Quantum Electronics

G. V. Vdovin and S. A. Chetkin, "Active correction of thermal lensing in solid-state lasers. II, use of a resonator with a controllable configuration," Kvantovaya Elektronika, Moskva Quantum Electronics 20,167-171 (1993).

Opt. Commun.

P. H. Sarkies, "A stable yag resonator yielding a beam of very low divergence and high output energy," Opt. Commun. 31,189-92 (1979).
[CrossRef]

T. Graf, E. Wyss, M. Roth, and H. P. Weber, "Laser resonator with balanced thermal lenses," Opt. Commun. 190,327-31 (2001).
[CrossRef]

J. Schwarz, M. Ramsey, I. Smith, D. Headley, and J. Porter, "Low order adaptive optics on ZBeamlet using a single actuator deformable mirror," Opt. Commun. 264,203 - 212 (2006).
[CrossRef]

Opt. Lett.

Other

W. Koechner and B. Bass. Solid-State Lasers. (Springer, New York, 2003).

S. K. Hawkes, A. Dunster, C. Hernandez-Gomez, and I. O. Musgrave. Pump induced aberration characterization and compensation for the vulcan petawatt beam. Central Laser Facility annual report 2004/2005, pps 194-196, 2004/2005.

D. Headley, M. Ramsey, and J. Schwarz. Variable focal length deformable mirror. U.S. Patent Application No. 11,017,337, filed on 12/20/2004.

Y. C. Warren and B. G. Richard. Roark’s Formulas for Stress and Strain. McGraw-Hill, New York, seventh edition, 2002.

Schott. Optical glass catalog. http://www.us.schott.com/sgt/english/download/n-bk7.pdf, 1996.

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Figures (13)

Fig. 1.
Fig. 1.

Overview of the rod amplifier section.

Fig. 2.
Fig. 2.

(a) On-shot wavefront deviation for the 16 mm diameter rod amplifier. The black mesh depicts the 3-D spherical fit. (b) Residual wavefront deviation after mathematical subtraction of spherical aberration. Note that the wavefront deviation is shown in µm not waves.

Fig. 3.
Fig. 3.

(a) On-shot wavefront deviation for the 25 mm diameter rod amplifier. The black mesh depicts the 3-D spherical fit. (b) Residual wavefront deviation after mathematical subtraction of spherical aberration. Note that the wavefront deviation is shown in µm not waves.

Fig. 4.
Fig. 4.

Plot of PV wavefront deviation versus time for the 16 mm and 25 mm diameter amplifiers.

Fig. 5.
Fig. 5.

Temporal wavefront evolution of the cw alignment (probe) beam during a shot with the 25 mm diameter rod amplifier. The animated GIF file is 934 KB long.

Fig. 6.
Fig. 6.

Plot of focal length of the deformable mirror versus pusher/motor travel. The figure compares the calculated focal lengths from Eqs. 2 and 3 to the FEA model for a substrate thickness of 3 mm and pusher radii of 32.5 mm and 47.2 mm.

Fig. 7.
Fig. 7.

(a) Model of the deformable mirror assembly. (b) Cross-section view of contact regions.

Fig. 8.
Fig. 8.

(a) Tangential stress plot for the 76.2 mm diameter and 3mm thick BK7 optic. The plot is clipped to only show specific stress values, clearly showing the stress balance on the optic despite the asymmetric (different diameter) ring restraints. (b) Radial stress plot of the deformed optic.

Fig. 9.
Fig. 9.

Contour plot of a measured focal length of about 21 m using the polished pusher surfaces.

Fig. 10.
Fig. 10.

Animation of achievable focal length versus motor travel for polished pusher surfaces. The inset depicts the wavefront measured with a 4” interferometer. The GIF animation has a length of 473 KB.

Fig. 11.
Fig. 11.

Plot of achievable focal length versus motor travel (pusher force) for polished (red triangle) and unpolished (black square) pusher surfaces. The black line depicts calculated (not fitted) focal lengths using Eqs. 2 and 3.

Fig. 12.
Fig. 12.

(a) Contour plot of the residual RMS wavefront deviation from Fig. 9 after subtraction of piston, tilt, and spherical aberration. (b) Plot of RMS wavefront deviation versus focal length for polished pusher surfaces (red triangles) and unpolished surfaces (black squares).

Fig. 13.
Fig. 13.

(a) Focal spot at target chamber center using the cw alignment beam (b) focal spot quality of the 10 Hz OPCPA beam (c) spot size due to an uncompensated rod shot (d) spot size during a rod shot using the deformable mirror for on shot thermal lens compensation. The bars depict the FWHM of the focal spot size.

Tables (1)

Tables Icon

Table 1. List of focal spot parameters for different shot types.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Δ n ( r ) = Q 4 K dn dT r 2 ,
y ( r ) = y c + M c r 2 2 D ( 1 + ν ) , where y c = wa 3 2 D ( C 1 1 + ν 2 C 2 )
C 1 = r 0 a [ 1 + ν 2 ln a r 0 + 1 ν 4 [ 1 ( r 0 a ) 2 ] ] , C 2 = r 0 4 a [ [ ( r 0 a ) 2 + 1 ] ln a r 0 + ( r 0 a ) 2 1 ] .

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