Abstract

An adaptive optical system for precise control of a laser beam’s mode structure has been developed. The system uses a dynamic lens based on controlled optical path deformation in a dichroic optical element that is heated with an auxiliary laser. Our method is essentially aberration free, has high dynamic range, and can be implemented with high average power laser beams where other adaptive optics methods fail. A quantitative model agrees well with our experimental data and demonstrates the potential of our method as a mode-matching and beam-shaping element for future large-scale gravitational wave detectors.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Wyss, M. Roth, T. Graf, and H. P. Weber, IEEE J. Quantum Electron. 38, 1620 (2002).
    [CrossRef]
  2. G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
    [CrossRef]
  3. H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
    [CrossRef]
  4. R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, Opt. Lett. 29, 2635 (2004).
    [CrossRef] [PubMed]
  5. J. Degallaix, C. N. Zhao, L. Ju, and D. Blair, Class. Quantum Grav. 21, 903 (2004).
    [CrossRef]
  6. B. Abbott and the LIGO Science Collaboration, Nucl. Instrum. Methods Phys. Res. A 517, 154 (2004).
    [CrossRef]
  7. E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, LIGO Technical Note T990080-00, http://www.ligo.caltech.edu/docs/T/T990080-00.pdf.
  8. J. D. Mansell, J. Hennawi, E. Gustafson, M. Fejer, R. L. Byer, D. Clubley, S. Yoshida, and D. H. Reitze, Appl. Opt. 40, 366 (2001).
    [CrossRef]
  9. OG515 datasheet, Schott North America, Inc., 555 Taxter Road, Elmsford, N.Y. 10523. There is some uncertainty in the literature regarding the magnitude of dn/dT as well as kappa for Schott OG515. However, a literature survey and our own measurements indicate that it can contribute no more than 20% to the overall thermal lensing.
  10. H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  11. D. Z. Anderson, Appl. Opt. 23, 2944 (1984).
    [CrossRef] [PubMed]
  12. E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
    [CrossRef]

2004

J. Degallaix, C. N. Zhao, L. Ju, and D. Blair, Class. Quantum Grav. 21, 903 (2004).
[CrossRef]

B. Abbott and the LIGO Science Collaboration, Nucl. Instrum. Methods Phys. Res. A 517, 154 (2004).
[CrossRef]

E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
[CrossRef]

R. Lawrence, D. Ottaway, M. Zucker, and P. Fritschel, Opt. Lett. 29, 2635 (2004).
[CrossRef] [PubMed]

2002

E. Wyss, M. Roth, T. Graf, and H. P. Weber, IEEE J. Quantum Electron. 38, 1620 (2002).
[CrossRef]

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

2001

2000

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

1984

1966

Abbott, B.

B. Abbott and the LIGO Science Collaboration, Nucl. Instrum. Methods Phys. Res. A 517, 154 (2004).
[CrossRef]

Amin, R.

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

Anderson, D. Z.

Aufmuth, P.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

Blair, D.

J. Degallaix, C. N. Zhao, L. Ju, and D. Blair, Class. Quantum Grav. 21, 903 (2004).
[CrossRef]

Byer, R. L.

Clubley, D.

D'Ambrosio, E.

E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
[CrossRef]

Danzmann, K.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

Degallaix, J.

J. Degallaix, C. N. Zhao, L. Ju, and D. Blair, Class. Quantum Grav. 21, 903 (2004).
[CrossRef]

Fejer, M.

Fritschel, P.

Graf, T.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, IEEE J. Quantum Electron. 38, 1620 (2002).
[CrossRef]

Guagliardo, D.

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

Gustafson, E.

J. D. Mansell, J. Hennawi, E. Gustafson, M. Fejer, R. L. Byer, D. Clubley, S. Yoshida, and D. H. Reitze, Appl. Opt. 40, 366 (2001).
[CrossRef]

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, LIGO Technical Note T990080-00, http://www.ligo.caltech.edu/docs/T/T990080-00.pdf.

Hennawi, J.

Ju, L.

J. Degallaix, C. N. Zhao, L. Ju, and D. Blair, Class. Quantum Grav. 21, 903 (2004).
[CrossRef]

Kogelnik, H.

Lawrence, R.

Li, T.

Lück, H.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

Lundock, R.

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

Mansell, J. D.

McFeron, D.

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

Mueller, G.

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

Müller, K.-O.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

O'Shaugnessy, R.

E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
[CrossRef]

Ottaway, D.

Reitze, D. H.

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

J. D. Mansell, J. Hennawi, E. Gustafson, M. Fejer, R. L. Byer, D. Clubley, S. Yoshida, and D. H. Reitze, Appl. Opt. 40, 366 (2001).
[CrossRef]

Roth, M.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, IEEE J. Quantum Electron. 38, 1620 (2002).
[CrossRef]

Shoemaker, D.

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, LIGO Technical Note T990080-00, http://www.ligo.caltech.edu/docs/T/T990080-00.pdf.

Strain, K.

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, LIGO Technical Note T990080-00, http://www.ligo.caltech.edu/docs/T/T990080-00.pdf.

Strigin, S.

E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
[CrossRef]

Tanner, D. B.

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

Thorne, K.

E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
[CrossRef]

Vyatchanin, S.

E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
[CrossRef]

Weber, H. P.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, IEEE J. Quantum Electron. 38, 1620 (2002).
[CrossRef]

Weiss, R.

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, LIGO Technical Note T990080-00, http://www.ligo.caltech.edu/docs/T/T990080-00.pdf.

Willems, P.

E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
[CrossRef]

Wyss, E.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, IEEE J. Quantum Electron. 38, 1620 (2002).
[CrossRef]

Yoshida, S.

Zhao, C. N.

J. Degallaix, C. N. Zhao, L. Ju, and D. Blair, Class. Quantum Grav. 21, 903 (2004).
[CrossRef]

Zucker, M.

Appl. Opt.

Class. Quantum Grav.

J. Degallaix, C. N. Zhao, L. Ju, and D. Blair, Class. Quantum Grav. 21, 903 (2004).
[CrossRef]

G. Mueller, R. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, Class. Quantum Grav. 19, 1793 (2002).
[CrossRef]

E. D'Ambrosio, R. O'Shaugnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, Class. Quantum Grav. 21, S867 (2004).
[CrossRef]

IEEE J. Quantum Electron.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, IEEE J. Quantum Electron. 38, 1620 (2002).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

B. Abbott and the LIGO Science Collaboration, Nucl. Instrum. Methods Phys. Res. A 517, 154 (2004).
[CrossRef]

Opt. Commun.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

Opt. Lett.

Other

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, LIGO Technical Note T990080-00, http://www.ligo.caltech.edu/docs/T/T990080-00.pdf.

OG515 datasheet, Schott North America, Inc., 555 Taxter Road, Elmsford, N.Y. 10523. There is some uncertainty in the literature regarding the magnitude of dn/dT as well as kappa for Schott OG515. However, a literature survey and our own measurements indicate that it can contribute no more than 20% to the overall thermal lensing.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(Color online) Calculated radial dependence of the optical path difference assuming 4 W of heating power in a 7.2 mm diameter beam. The solid curve results from an exact solution of the thermal diffusion equation; the dotted curve displays the OPL assuming a parabolic lens. Right inset, schematic view of laser adaptive mode control. Left inset, spatial dependence of the temperature profile Δ T ( r , z ) .

Fig. 2
Fig. 2

Measured lens power in diopters (circles) as a function of heating beam power. The solid line is the theoretically computed lens power for the parameters used in this experiment. Inset, raw divergence angle data along the y axis used to compute the lens power. For clarity only a reduced set of measurements is shown.

Fig. 3
Fig. 3

(Color online) Left, Experimentally measured mode content as a function of heating laser power, starting with optimal mode matching at 0 W . Right, Experimentally measured mode content as a function of laser power after changing the lens position to reoptimize the mode matching at each power setting. The squares, circles, and diamonds correspond to the experimentally measured bull’s-eye modes, first-order Hermite–Gauss modes ( HG 01 and HG 10 ) and the sum of all other higher-order modes.

Equations (5)

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

2 T ( r , z ) = 2 α P π K w 2 exp ( 2 r 2 w 2 ) exp ( α z ) ,
T ( r , z ) = n = 1 4 α P π K R 2 w 2 0 R exp ( 2 r 2 w 2 ) J 0 ( k n r R ) r d r [ J 0 ( k n ) ] 2 J 0 ( k n r R ) f n ( z ) + T 0 ,
f n = α R k n [ p k p α 1 p k 2 1 e ( k n R ) z p α p k 1 p α 2 1 e ( k n R ) z ] + e α z α 2 ( k n R ) 2 .
P ( r ) = [ d n d T + α T ( n 1 ) ] 0 L Δ T ( r , z ) d z ,
u o ( r , z ) = u p ( r , z ) exp [ i k P ( r ) ] = u p ( r , z ) exp { i k [ P ( 0 ) + P ( 0 ) ( r 2 / 2 ) + O ( r 4 ) ] } ,

Metrics