Abstract

Roughness-induced scattering affects the performance of a resonator. We study the scattering of a single mirror first and compare the result with the losses of a two-mirror Fabry–Perot resonator. Besides some standard tools to characterize the losses, a new method based on the spectrally averaged transmission is introduced.

© 2007 Optical Society of America

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References

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  1. S. Haroche and D. Kleppner, "Cavity quantum electrodynamics," Phys. Today 42, 24-30 (1989).
    [CrossRef]
  2. K. D. Skeldon, J. Mackintosh, M. von Gradowski, S. Thieux, and R. Lee, "Qualification of supermirrors for ring-laser-gyros based on surface roughness and scatter measurements," J. Opt. A 3, 183-187 (2001).
    [CrossRef]
  3. http://www.ligo.caltech.edu.
  4. http://www.cascina.virgo.infn.it.
  5. http://tamago.mtk.nao.ac.jp.
  6. C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,"Phys. Rev. A 64, 033804 (2001).
    [CrossRef]
  7. N. Uehara, A. Ueda, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, and I Kataoka, "Ultralow-loss mirror of the parts-in-106 level at 1064 nm," Opt. Lett. 20, 530-532 (1995).
    [CrossRef] [PubMed]
  8. S. Sato, S. Miyoki, M. Ohashi, M. K. Fujimoto, T. Yamazaki, M. Fukushima, A. Ueda, K. Ueda, K. Watanabe, K. Nakamura, K. Etoh, N. Kitajima, K. Ito, and I. Kataoka, "Loss factors of mirrors for a gravitational wave antenna," Appl. Opt. 38, 2880-2885 (1999).
    [CrossRef]
  9. K. S. Repasky, L. E. Watson, and J. L. Carlsten, "High-finesse interferometers," Appl. Opt. 34, 2615-2618 (1995).
    [CrossRef] [PubMed]
  10. N. Uehara and K. Ueda, "Accurate measurement of the radius of curvature of a concave mirror and the power dependence in a high-finesse Fabry-Perot interferometer," Appl. Opt. 34, 5611-5619 (1995).
    [CrossRef] [PubMed]
  11. J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1999).
  12. J. C. Stover, Optical Scattering: Measurement and Analysis (SPIE Press, 1995).
    [CrossRef]
  13. We did not observe the scattering rings predicted by Amra et al. for dielectric mirrors. Possible reasons could be that the corrugations at the various interfaces of our multilayer mirror are not perfectly correlated or that the optical penetration depth of the incident field is small enough to shift the scattering rings to large angles and out of view.
  14. C. Amra, C. Grèzes-Besset, and L. Bruel, "Comparison of surface and bulk scattering in optical multilayers," Appl. Opt. 32, 5492-5503 (1993).
    [CrossRef] [PubMed]
  15. E. L. Church, "Fractal surface finish," Appl. Opt. 27, 1518-1526 (1988).
    [CrossRef] [PubMed]
  16. We have also tried to measure the surface roughness with a (WYKO RST-500) interferometer . This gave, however, a roughness of only σ = 0.4 nm, which is obviously much smaller compared with the scatter measurement. This discrepancy could originate from various effects. First, the multilayer coating is designed for a wavelength of 532 nm, whereas the WYKO beam profiler works at a wavelength of 633 nm. At this wavelength, the light penetrates the stack of layers much deeper than at 532 nm. Second, the beam profiler illuminates the mirror with a focused beam, whereas in the scatter experiment quasi-plane-wave illumination is used. Third, it is unknown whether the roughness of the consecutive dielectric layers adds up in a coherent or incoherent way. All this makes a comparison of the scattering-deduced surface roughness and the interferometrically deduced value rather difficult.
  17. TNO Science and Industry, Business Unit Opto-Mechanical Instrumentation (OMI), Delft, The Netherlands.
  18. K. V. Chance and R. J. D. Spurr, "Ring effect studies: Rayleigh scattering, including molecular parameters for rotational Raman scattering, and the Fraunhofer spectrum," Appl. Opt. 36, 5224-5230 (1997).
    [CrossRef] [PubMed]
  19. D. Z. Anderson, J. C. Frisch, and C. S. Masser, "Mirror reflectometer based on optical cavity decay time," Appl. Opt. 23, 1238-1245 (1984).
    [CrossRef] [PubMed]
  20. A. O'Keefe and D. A. G. Deacon, "Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources," Rev. Sci. Instrum. 59, 2544-2551 (1988).
    [CrossRef]
  21. N. Uehara and K. Ueda, "Accurate measurement of ultralow loss in a high-finesse Fabry-Perot interferometer using the frequency response functions," Appl. Phys. B 61, 9-15 (1995).
    [CrossRef]
  22. G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, "Measurement of ultralow losses in an optical interferometer," Opt. Lett. 17, 363-365 (1992).
    [CrossRef] [PubMed]
  23. J. M. Vaughan, Fabry-Perot Interferometer (Adam Hilger, 1989).
  24. T. Klaassen, J. de Jong, M. P. van Exter, and J. P. Woerdman, "Transverse mode coupling in an optical resonator," Opt. Lett. 30, 1959-1961 (2005).
    [CrossRef] [PubMed]

2005 (1)

2001 (2)

K. D. Skeldon, J. Mackintosh, M. von Gradowski, S. Thieux, and R. Lee, "Qualification of supermirrors for ring-laser-gyros based on surface roughness and scatter measurements," J. Opt. A 3, 183-187 (2001).
[CrossRef]

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,"Phys. Rev. A 64, 033804 (2001).
[CrossRef]

1999 (2)

1997 (1)

1995 (5)

1993 (1)

1992 (1)

1989 (2)

J. M. Vaughan, Fabry-Perot Interferometer (Adam Hilger, 1989).

S. Haroche and D. Kleppner, "Cavity quantum electrodynamics," Phys. Today 42, 24-30 (1989).
[CrossRef]

1988 (2)

E. L. Church, "Fractal surface finish," Appl. Opt. 27, 1518-1526 (1988).
[CrossRef] [PubMed]

A. O'Keefe and D. A. G. Deacon, "Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources," Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

1984 (1)

Amra, C.

Anderson, D. Z.

Bennett, J. M.

J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1999).

Bruel, L.

Carlsten, J. L.

Chance, K. V.

Church, E. L.

de Jong, J.

Deacon, D. A. G.

A. O'Keefe and D. A. G. Deacon, "Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources," Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

Etoh, K.

Frisch, J. C.

Fujimoto, M. K.

Fukushima, M.

Grèzes-Besset, C.

Haroche, S.

S. Haroche and D. Kleppner, "Cavity quantum electrodynamics," Phys. Today 42, 24-30 (1989).
[CrossRef]

Hood, C. J.

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,"Phys. Rev. A 64, 033804 (2001).
[CrossRef]

Ito, K.

Kataoka, I

Kataoka, I.

Kimble, H. J.

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,"Phys. Rev. A 64, 033804 (2001).
[CrossRef]

G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, "Measurement of ultralow losses in an optical interferometer," Opt. Lett. 17, 363-365 (1992).
[CrossRef] [PubMed]

Kitajima, N.

Klaassen, T.

Kleppner, D.

S. Haroche and D. Kleppner, "Cavity quantum electrodynamics," Phys. Today 42, 24-30 (1989).
[CrossRef]

Lalezari, R.

Lee, R.

K. D. Skeldon, J. Mackintosh, M. von Gradowski, S. Thieux, and R. Lee, "Qualification of supermirrors for ring-laser-gyros based on surface roughness and scatter measurements," J. Opt. A 3, 183-187 (2001).
[CrossRef]

Mackintosh, J.

K. D. Skeldon, J. Mackintosh, M. von Gradowski, S. Thieux, and R. Lee, "Qualification of supermirrors for ring-laser-gyros based on surface roughness and scatter measurements," J. Opt. A 3, 183-187 (2001).
[CrossRef]

Masser, C. S.

Mattsson, L.

J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1999).

Mitake, T.

Miyoki, S.

Nakamura, K.

Ohashi, M.

O'Keefe, A.

A. O'Keefe and D. A. G. Deacon, "Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources," Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

Rempe, G.

Repasky, K. S.

Sato, S.

Sekiguchi, H.

Skeldon, K. D.

K. D. Skeldon, J. Mackintosh, M. von Gradowski, S. Thieux, and R. Lee, "Qualification of supermirrors for ring-laser-gyros based on surface roughness and scatter measurements," J. Opt. A 3, 183-187 (2001).
[CrossRef]

Spurr, R. J. D.

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis (SPIE Press, 1995).
[CrossRef]

Thieux, S.

K. D. Skeldon, J. Mackintosh, M. von Gradowski, S. Thieux, and R. Lee, "Qualification of supermirrors for ring-laser-gyros based on surface roughness and scatter measurements," J. Opt. A 3, 183-187 (2001).
[CrossRef]

Thompson, R. J.

Ueda, A.

Ueda, K.

Uehara, N.

van Exter, M. P.

Vaughan, J. M.

J. M. Vaughan, Fabry-Perot Interferometer (Adam Hilger, 1989).

von Gradowski, M.

K. D. Skeldon, J. Mackintosh, M. von Gradowski, S. Thieux, and R. Lee, "Qualification of supermirrors for ring-laser-gyros based on surface roughness and scatter measurements," J. Opt. A 3, 183-187 (2001).
[CrossRef]

Watanabe, K.

Watson, L. E.

Woerdman, J. P.

Yamazaki, T.

Ye, J.

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,"Phys. Rev. A 64, 033804 (2001).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. B (1)

N. Uehara and K. Ueda, "Accurate measurement of ultralow loss in a high-finesse Fabry-Perot interferometer using the frequency response functions," Appl. Phys. B 61, 9-15 (1995).
[CrossRef]

J. Opt. A (1)

K. D. Skeldon, J. Mackintosh, M. von Gradowski, S. Thieux, and R. Lee, "Qualification of supermirrors for ring-laser-gyros based on surface roughness and scatter measurements," J. Opt. A 3, 183-187 (2001).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,"Phys. Rev. A 64, 033804 (2001).
[CrossRef]

Phys. Today (1)

S. Haroche and D. Kleppner, "Cavity quantum electrodynamics," Phys. Today 42, 24-30 (1989).
[CrossRef]

Rev. Sci. Instrum. (1)

A. O'Keefe and D. A. G. Deacon, "Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources," Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

Other (9)

J. M. Vaughan, Fabry-Perot Interferometer (Adam Hilger, 1989).

J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1999).

J. C. Stover, Optical Scattering: Measurement and Analysis (SPIE Press, 1995).
[CrossRef]

We did not observe the scattering rings predicted by Amra et al. for dielectric mirrors. Possible reasons could be that the corrugations at the various interfaces of our multilayer mirror are not perfectly correlated or that the optical penetration depth of the incident field is small enough to shift the scattering rings to large angles and out of view.

We have also tried to measure the surface roughness with a (WYKO RST-500) interferometer . This gave, however, a roughness of only σ = 0.4 nm, which is obviously much smaller compared with the scatter measurement. This discrepancy could originate from various effects. First, the multilayer coating is designed for a wavelength of 532 nm, whereas the WYKO beam profiler works at a wavelength of 633 nm. At this wavelength, the light penetrates the stack of layers much deeper than at 532 nm. Second, the beam profiler illuminates the mirror with a focused beam, whereas in the scatter experiment quasi-plane-wave illumination is used. Third, it is unknown whether the roughness of the consecutive dielectric layers adds up in a coherent or incoherent way. All this makes a comparison of the scattering-deduced surface roughness and the interferometrically deduced value rather difficult.

TNO Science and Industry, Business Unit Opto-Mechanical Instrumentation (OMI), Delft, The Netherlands.

http://www.ligo.caltech.edu.

http://www.cascina.virgo.infn.it.

http://tamago.mtk.nao.ac.jp.

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Figures (4)

Fig. 1
Fig. 1

Overview of the setup for measuring the scattering of a single mirror M. The mirror is illuminated by light diffracted from a pinhole P. Specular reflection from the concave mirror results in an image B. The dotted arrows indicate light scattered at the mirror under different scattering angles θ s . The distances between pinhole and mirror (PM) and mirror and image of the pinhole (MB) are 36 and 81 cm, respectively. The angle between both arms PMB is 12°. The image is blocked by a beam block B to prevent overexposure of the CCD.

Fig. 2
Fig. 2

(a) Angle-resolved scattering from a single mirror combined from 25 CCD images. In the center an obscuration blocks the direct beam. The speckles are formed by scattering from the surface roughness of the mirror. (b) The BRDF for a scattering angle θ s from 0.14° to 7.6°: dots, experimental data; line, fit of the data.

Fig. 3
Fig. 3

Conservation of energy for an optical resonator requires that a fraction of T / ( 2 T + 2 A ) = 1 / 2 η of the trapped light is transmitted (coupled out) through each mirror.

Fig. 4
Fig. 4

Transmission spectrum of the resonator for one FS Range.

Tables (1)

Tables Icon

Table 1 Overview of Resonator Efficiency η a

Equations (8)

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B R D F = 1 P 0 d P d Ω   cos   θ s ,
TIS = ( 4 π σ λ ) 2 ,
η = T / ( A + T ) ,
F = π 1 R = π A + T .
T ( ϕ ) = P T ( ϕ ) P i = ( T T + A ) 2 1 1 + ( 2 F π ) 2   sin   ϕ 2 ,
T ( 0 ) = ( T T + A ) 2 = η 2 .
T ( ϕ ) = P T ( ϕ ) P i = T 2 2 ( T + A ) = 1 / 2 T η ,
[ 1 + ( 2 F π ) 2 sin   ϕ 2 ] 1 = π / 2 F = ( A + T ) / 2

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