Abstract

We report on a high-resolution wave-front sensor that measures the complete spatial profile of any frequency component of a laser field containing multiple frequencies. This probe technique was developed to address the necessity of measuring the spatial overlap of the carrier field with each sideband component of the field exiting the output port of a gravitational-wave interferometer. We present the results of an experimental test of the probe, where we were able to construct the spatial profile of a single radio-frequency sideband at the level of -50 dBc.

© 2004 Optical Society of America

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References

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  1. J. M. Geary, Introduction to Wave-front Sensors, Tutorial Text 18 (SPIE Press, Bellingham, Wash., 1995).
    [CrossRef]
  2. R. V. Shack and B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971) [abstract].
  3. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, Appl. Opt. 33, 5037 (1994).
    [CrossRef] [PubMed]
  4. Y. Hefetz, N. Mavalvala, and D. Sigg, J. Opt. Soc. Am. B 14, 1597 (1997).
    [CrossRef]
  5. G. Mueller, Q. Shu, R. Adhikari, D. B. Tanner, D. Reitze, D. Sigg, N. Mavalvala, and J. Camp, Opt. Lett. 25, 266 (2000).
    [CrossRef]
  6. B. Barish and R. Weiss, Phys. Today 52(10), 44 (1999).
    [CrossRef]
  7. P. Fritschel, R. Bork, G. González, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, and M. Zucker, Appl. Opt. 40, 4988 (2001).
    [CrossRef]
  8. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 746.
  9. P. Fritschel, N. Mavalvala, D. Shoemaker, D. Sigg, M. Zucker, and G. González, Appl. Opt. 37, 6734 (1998).
    [CrossRef]
  10. E. D’Ambrosio and W. Kells, California Institute of Technology, MS18-34, Pasadena, California 91125 (personal communication, 2002).
  11. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]

2001 (1)

2000 (1)

1999 (1)

B. Barish and R. Weiss, Phys. Today 52(10), 44 (1999).
[CrossRef]

1998 (1)

1997 (1)

1994 (1)

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

1971 (1)

R. V. Shack and B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971) [abstract].

Adhikari, R.

Barish, B.

B. Barish and R. Weiss, Phys. Today 52(10), 44 (1999).
[CrossRef]

Bork, R.

Camp, J.

D’Ambrosio, E.

E. D’Ambrosio and W. Kells, California Institute of Technology, MS18-34, Pasadena, California 91125 (personal communication, 2002).

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Fritschel, P.

Geary, J. M.

J. M. Geary, Introduction to Wave-front Sensors, Tutorial Text 18 (SPIE Press, Bellingham, Wash., 1995).
[CrossRef]

González, G.

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Hefetz, Y.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kells, W.

E. D’Ambrosio and W. Kells, California Institute of Technology, MS18-34, Pasadena, California 91125 (personal communication, 2002).

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Mavalvala, N.

Meers, B. J.

Morrison, E.

Mueller, G.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Ouimette, D.

Platt, B. C.

R. V. Shack and B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971) [abstract].

Reitze, D.

Robertson, D. I.

Rong, H.

Shack, R. V.

R. V. Shack and B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971) [abstract].

Shoemaker, D.

Shu, Q.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 746.

Sigg, D.

Tanner, D. B.

Ward, H.

E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, Appl. Opt. 33, 5037 (1994).
[CrossRef] [PubMed]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Weiss, R.

B. Barish and R. Weiss, Phys. Today 52(10), 44 (1999).
[CrossRef]

Zucker, M.

Appl. Opt. (3)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

R. V. Shack and B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971) [abstract].

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Phys. Today (1)

B. Barish and R. Weiss, Phys. Today 52(10), 44 (1999).
[CrossRef]

Other (3)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 746.

E. D’Ambrosio and W. Kells, California Institute of Technology, MS18-34, Pasadena, California 91125 (personal communication, 2002).

J. M. Geary, Introduction to Wave-front Sensors, Tutorial Text 18 (SPIE Press, Bellingham, Wash., 1995).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Schematic of the experimental test of the wave-front sensor. The test field generator is shown in the blue box, and the wave-front sensor is shown in the green box. The gray box shows the spectrum of light that is incident upon the wave-front sensor; only the 21.5-MHz beat is detected with aggressive bandpass filtering. REF., reference field; MC, mode-cleaner cavity; CIR, circulator; PM1, PM2, phase modulators; Gx, Gy, galvanometers scanned in the x and y directions. Other abbreviations defined in text.

Fig. 2
Fig. 2

Top maps: measured amplitude and phase of the first-order sideband in the TEM21 mode. Left, amplitude profile, color coded according to the bars at the right to show spatial variation in the relative amplitude. Right, phase profile, showing the sudden phase transitions that appear alternately as the amplitude changes polarity. Bottom maps: theoretical calculation of the amplitude and phase of the first-order sideband in the TEM21 mode, with color coding identical to that of the top maps and with no free parameters except an overall phase shift.

Equations (1)

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Ex,y=VIx,y2+VQx,y21/2,ϕx,y=argVIx,y+jVQx,y,

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