Abstract

It has become a significant challenge to accurately characterise the properties of recently developed very high finesse optical resonators (F>106). A similar challenge is encountered when trying to measure the properties of cavities in which either the probing laser or the cavity length is intrinsically unstable. We demonstrate in this article the means by which the finesse, mode-matching, free spectral range, mirror transmissions and dispersion may be measured easily and accurately even when the laser or cavity has a relatively poor intrinsic frequency stability.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Ringdown spectroscopy of stimulated Raman scattering in a whispering gallery mode resonator," Opt. Lett. 32,497-499, (2007).
    [CrossRef] [PubMed]
  2. Advanced Thin Films, www.atfilms.com 5733 Central Ave. Boulder, CO 80301
  3. J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
    [CrossRef]
  4. V. Collaboration, "Measurement of the optical parameters of the Virgo interferometer," Appl. Opt. 46,3466-3484 (2007).
    [PubMed]
  5. 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]
  6. Y. Gong, B. Li, and Y. Han, "Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity," Appl. Phys. B. 93,355-360 (2008).
    [CrossRef]
  7. Y. Dumeige, S. Trebaol, L. G. T. K. N. Nguyn, H. Tavernier, and P. Fron, "Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers," J. Opt. Soc. Am. B.  25, 2073-2080 (2008).
    [CrossRef]
  8. 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 1-7, (2001).
    [CrossRef]
  9. M. J. Thorpe, R. Jason Jones, K. D. Moll, and J. Ye, "Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs," Opt. Express 13, 882-888,(2005).
    [CrossRef] [PubMed]
  10. A. Schliesser, C. Gohle, T. Udem and T. W. Hänsch, "Complete characterization of a broadband high-finesse cavity using an optical frequency comb," Opt. Express 14, 5975-5983, (2006).
    [CrossRef] [PubMed]
  11. F. Bondu and O. Debieu, "Accurate measurement method of Fabry-Perot cavity parameters via optical transfer function," Appl. Opt. 46,2611-2614 (2007).
    [CrossRef] [PubMed]
  12. B. J. J. Slagmolen, M. B. Gray, K. G. Baigent, and D. E. McClelland, "Phase-sensitive reflection technique for characterization of a Fabry Perot interferometer," Appl. Opt. 39, 3638-3643 (2000).
    [CrossRef]
  13. A. E. Siegman, Lasers (University Science Books, Sausalito, California).
  14. I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72,1-29 (2001).
    [CrossRef]
  15. J Petersen and A. Luiten, "Short Pulses in Optical Resonators," Opt. Express 11, 2975-2981 (2003).
    [CrossRef] [PubMed]
  16. N. M. Sampas and D. Z. Anderson, "Stabilization of laser beam alignment to an optical resonator by heterodyne detection of off-axis modes," Appl. Opt. 29, 394-403 (1990).
    [CrossRef] [PubMed]
  17. P. Kwee, F. Seifert, B. Willke, and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 0731031-10 (2007).
    [CrossRef]
  18. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
    [CrossRef]

2009 (1)

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

2008 (2)

Y. Gong, B. Li, and Y. Han, "Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity," Appl. Phys. B. 93,355-360 (2008).
[CrossRef]

Y. Dumeige, S. Trebaol, L. G. T. K. N. Nguyn, H. Tavernier, and P. Fron, "Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers," J. Opt. Soc. Am. B.  25, 2073-2080 (2008).
[CrossRef]

2007 (4)

2006 (1)

2005 (1)

2003 (1)

2001 (2)

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 1-7, (2001).
[CrossRef]

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72,1-29 (2001).
[CrossRef]

2000 (1)

1992 (1)

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]

1990 (1)

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Anderson, D. Z.

Baigent, K. G.

Bize, S.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Bondu, F.

Collaboration, V.

Danzmann, K.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 0731031-10 (2007).
[CrossRef]

Debieu, O.

Dorrer, C.

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72,1-29 (2001).
[CrossRef]

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, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Dumeige, Y.

Y. Dumeige, S. Trebaol, L. G. T. K. N. Nguyn, H. Tavernier, and P. Fron, "Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers," J. Opt. Soc. Am. B.  25, 2073-2080 (2008).
[CrossRef]

English, E. M. L.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[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, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Fron, P.

Y. Dumeige, S. Trebaol, L. G. T. K. N. Nguyn, H. Tavernier, and P. Fron, "Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers," J. Opt. Soc. Am. B.  25, 2073-2080 (2008).
[CrossRef]

Gohle, C.

Gong, Y.

Y. Gong, B. Li, and Y. Han, "Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity," Appl. Phys. B. 93,355-360 (2008).
[CrossRef]

Gray, M. B.

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Han, Y.

Y. Gong, B. Li, and Y. Han, "Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity," Appl. Phys. B. 93,355-360 (2008).
[CrossRef]

Hänsch, T. W.

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 1-7, (2001).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Jason Jones, R.

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 1-7, (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]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Kwee, P.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 0731031-10 (2007).
[CrossRef]

Lalezari, R.

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]

Le Coq, Y.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Lemonde, P.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Li, B.

Y. Gong, B. Li, and Y. Han, "Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity," Appl. Phys. B. 93,355-360 (2008).
[CrossRef]

Lodewyck, J.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Luiten, A.

Magalhães, D. V.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Maleki, L.

Mandache, C.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Matsko, A. B.

McClelland, D. E.

Millo, J.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Moll, K. D.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Nguyn, L. G. T. K. N.

Y. Dumeige, S. Trebaol, L. G. T. K. N. Nguyn, H. Tavernier, and P. Fron, "Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers," J. Opt. Soc. Am. B.  25, 2073-2080 (2008).
[CrossRef]

Petersen, J

Rempe, G.

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]

Sampas, N. M.

Santarelli, G.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Savchenkov, A. A.

Schliesser, A.

Seifert, F.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 0731031-10 (2007).
[CrossRef]

Slagmolen, B. J. J.

Tavernier, H.

Y. Dumeige, S. Trebaol, L. G. T. K. N. Nguyn, H. Tavernier, and P. Fron, "Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers," J. Opt. Soc. Am. B.  25, 2073-2080 (2008).
[CrossRef]

Thompson, R. J.

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]

Thorpe, M. J.

Trebaol, S.

Y. Dumeige, S. Trebaol, L. G. T. K. N. Nguyn, H. Tavernier, and P. Fron, "Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers," J. Opt. Soc. Am. B.  25, 2073-2080 (2008).
[CrossRef]

Udem, T.

Walmsley, I.

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72,1-29 (2001).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Waxer, L.

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72,1-29 (2001).
[CrossRef]

Westergaard, P. G.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Willke, B.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 0731031-10 (2007).
[CrossRef]

Ye, J.

M. J. Thorpe, R. Jason Jones, K. D. Moll, and J. Ye, "Precise measurements of optical cavity dispersion and mirror coating properties via femtosecond combs," Opt. Express 13, 882-888,(2005).
[CrossRef] [PubMed]

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 1-7, (2001).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. B. (2)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B. 31, 97-105 (1983).
[CrossRef]

Y. Gong, B. Li, and Y. Han, "Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity," Appl. Phys. B. 93,355-360 (2008).
[CrossRef]

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

Y. Dumeige, S. Trebaol, L. G. T. K. N. Nguyn, H. Tavernier, and P. Fron, "Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers," J. Opt. Soc. Am. B.  25, 2073-2080 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Ringdown spectroscopy of stimulated Raman scattering in a whispering gallery mode resonator," Opt. Lett. 32,497-499, (2007).
[CrossRef] [PubMed]

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]

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 1-7, (2001).
[CrossRef]

Phys. Rev. A. (1)

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, "Ultrastable lasers based on vibration insensitive cavities," Phys. Rev. A. 79, 0538291-7 (2009).
[CrossRef]

Rev. Sci. Instrum. (2)

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72,1-29 (2001).
[CrossRef]

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 0731031-10 (2007).
[CrossRef]

Other (2)

A. E. Siegman, Lasers (University Science Books, Sausalito, California).

Advanced Thin Films, www.atfilms.com 5733 Central Ave. Boulder, CO 80301

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 (4)

Fig. 1.
Fig. 1.

Example of reflected field of a cavity mode scanned with a commercial cavitystabilized Ti:sapphire laser. The fit yields a 67±1 kHz linewidth.

Fig. 2.
Fig. 2.

Example of fractional transmitted (red) and reflected power (blue) in a scan of the modulation sidebands over a resonance, where we have assumed that the input beam is fully mode-matched. Here ϕ~1, δT ~0.03, T 1~0.009, T 2~0.01, δT ~0.03, and ϕs is the angular frequency detuning normalized in terms of the FSR,

Fig. 3.
Fig. 3.

Measured transmission (blue, upper) and reflection data (red, lower) of the ULE cavity. The upper curve in each case are fits to the data using the Eqs. 10 and 11 respectively. The fitted curves have been shifted upwards by 0.03 units so that they can be distinguished from the data.

Fig. 4.
Fig. 4.

A plot of the Free Spectral Range (FSR) and loss of the cavity as a function of wavelength for 24 modes in the cavity. The solid curves in the two curves are not fits but are based on the information provided by the manufacturer for the transmission of the mirrors and dispersion of the mirrors.

Equations (19)

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

E ˜ circ = g ˜ rt E ˜ circ + i T 1 E ˜ inc ,
E ˜ refl E ˜ inc = Γ = δ T 2 T 1 δ T ,
E ˜ trans E ˜ inc = T = 2 T 1 T 2 δ T ,
FSR = c L opt ,
𝓕 = 2 π δ T ,
P trans P inc = 4 T 1 T 2 δ T 2 = T 2 ,
C = 1 Γ 2 = 4 T 1 T 2 δ T 2 + 4 T 1 δ 0 δ T 2 = T 2 + Λ 2 ,
E ˜ inc ( t ) = E inc e j [ ω c t + ϕ sin ( 2 π f m t ) ]
E inc e j ω c t J 0 ( ϕ )
+ J 1 ( ϕ ) ( e j ( ω c + ω m ) t e j ( ω c ω m ) t )
+ J 2 ( ϕ ) ( e j ( ω c + 2 ω m ) t e j ( ω c 2 ω m ) t )
E ˜ trans , mm E ˜ inc 2 = T 2 S
E ˜ refl , mm E ˜ inc 2 = 1 ( T 2 + Λ 2 ) S
S = J 0 ( ϕ ) 2 + 2 J 1 ( ϕ ) 2 δ T 2 4 ϕ s 2 + δ T 2 + 2 J 2 ( ϕ ) 2 δ T 2 16 ϕ s 2 + δ T 2
E ˜ refl , mm E ˜ inc det uned 2 = Γ 2 J 0 ( ϕ ) 2 + 2 J 1 ( ϕ ) 2 + 2 J 2 ( ϕ ) 2
= 1 J 0 2 ( ϕ ) ( T 2 + Λ 2 )
E ˜ refl E ˜ inc 2 = 1 ε ( T 2 + Λ 2 ) S
= ( 1 S ε ) + ε Γ 2 S
E ˜ trans E ˜ inc 2 = ε T 2 S

Metrics