Abstract

Small-angle scattering due to mirror surface roughness is shown to couple the optical modes and deform the transmission spectra in a frequency-degenerate optical cavity. A simple model based on a random scattering matrix clearly visualizes the mixing and avoided crossings between multiple transverse modes. These effects are visible only in the frequency-domain spectra; cavity ringdown experiments are unaffected by changes in the spatial coherence, as they probe just the intracavity photon lifetime.

© 2005 Optical Society of America

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References

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  1. S. Haroche and D. Kleppner, Phys. Today 42(1), 24 (1989).
    [CrossRef]
  2. S. Herriott, H. Kogelnik, and R. Kompfner, Appl. Opt. 3, 4 (1964).
    [CrossRef]
  3. A. E. Siegman, Lasers (University Science, 1986).
  4. P. Domokos and H. Ritsch, J. Opt. Soc. Am. B 20, 1098 (2003).
    [CrossRef]
  5. D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, Phys. Rev. Lett. 58, 1320 (1987).
    [CrossRef] [PubMed]
  6. G. Rempe, R. J. Thompson, and H. J. Kimble, Opt. Lett. 17, 363 (1992).
    [CrossRef] [PubMed]
  7. C. J. Hood, H. J. Kimble, and J. Ye, Phys. Rev. A 64, 033804 (2001).
    [CrossRef]
  8. J. C. Bergquist, W. M. Itano, and D. J. Wineland, in Proceedings of the International School of Physics Enrico Fermi CXX (North-Holland, 1994), p. 367.
  9. J. T. Hodges, J. P. Looney, and R. D. van Zee, J. Chem. Phys. 105, 10278 (1996).
    [CrossRef]
  10. D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
    [CrossRef]
  11. C. A. Schrama, D. Bouwmeester, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 51, 641 (1995).
    [CrossRef] [PubMed]
  12. J. C. Stover, Optical Scattering, Measurement, and Analysis (McGraw-Hill, 1990).
  13. H. J. Stöckmann, Quantum Chaos:?an Introduction (Cambridge U. Press, 1999).

2003 (1)

2002 (1)

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
[CrossRef]

2001 (1)

C. J. Hood, H. J. Kimble, and J. Ye, Phys. Rev. A 64, 033804 (2001).
[CrossRef]

1996 (1)

J. T. Hodges, J. P. Looney, and R. D. van Zee, J. Chem. Phys. 105, 10278 (1996).
[CrossRef]

1995 (1)

C. A. Schrama, D. Bouwmeester, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 51, 641 (1995).
[CrossRef] [PubMed]

1992 (1)

1989 (1)

S. Haroche and D. Kleppner, Phys. Today 42(1), 24 (1989).
[CrossRef]

1987 (1)

D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, Phys. Rev. Lett. 58, 1320 (1987).
[CrossRef] [PubMed]

1964 (1)

S. Herriott, H. Kogelnik, and R. Kompfner, Appl. Opt. 3, 4 (1964).
[CrossRef]

Bergquist, J. C.

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in Proceedings of the International School of Physics Enrico Fermi CXX (North-Holland, 1994), p. 367.

Bouwmeester, D.

C. A. Schrama, D. Bouwmeester, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 51, 641 (1995).
[CrossRef] [PubMed]

Childs, J. J.

D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, Phys. Rev. Lett. 58, 1320 (1987).
[CrossRef] [PubMed]

Domokos, P.

Feld, M. S.

D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, Phys. Rev. Lett. 58, 1320 (1987).
[CrossRef] [PubMed]

Hahn, J. W.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
[CrossRef]

Haroche, S.

S. Haroche and D. Kleppner, Phys. Today 42(1), 24 (1989).
[CrossRef]

Heinzen, D. J.

D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, Phys. Rev. Lett. 58, 1320 (1987).
[CrossRef] [PubMed]

Herriott, S.

S. Herriott, H. Kogelnik, and R. Kompfner, Appl. Opt. 3, 4 (1964).
[CrossRef]

Hodges, J. T.

J. T. Hodges, J. P. Looney, and R. D. van Zee, J. Chem. Phys. 105, 10278 (1996).
[CrossRef]

Hood, C. J.

C. J. Hood, H. J. Kimble, and J. Ye, Phys. Rev. A 64, 033804 (2001).
[CrossRef]

Itano, W. M.

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in Proceedings of the International School of Physics Enrico Fermi CXX (North-Holland, 1994), p. 367.

Kim, B.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
[CrossRef]

Kimble, H. J.

C. J. Hood, H. J. Kimble, and J. Ye, Phys. Rev. A 64, 033804 (2001).
[CrossRef]

G. Rempe, R. J. Thompson, and H. J. Kimble, Opt. Lett. 17, 363 (1992).
[CrossRef] [PubMed]

Kleppner, D.

S. Haroche and D. Kleppner, Phys. Today 42(1), 24 (1989).
[CrossRef]

Kogelnik, H.

S. Herriott, H. Kogelnik, and R. Kompfner, Appl. Opt. 3, 4 (1964).
[CrossRef]

Kompfner, R.

S. Herriott, H. Kogelnik, and R. Kompfner, Appl. Opt. 3, 4 (1964).
[CrossRef]

Lee, D.-H.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
[CrossRef]

Lee, J. Y.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
[CrossRef]

Looney, J. P.

J. T. Hodges, J. P. Looney, and R. D. van Zee, J. Chem. Phys. 105, 10278 (1996).
[CrossRef]

Nienhuis, G.

C. A. Schrama, D. Bouwmeester, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 51, 641 (1995).
[CrossRef] [PubMed]

Rempe, G.

Ritsch, H.

Schrama, C. A.

C. A. Schrama, D. Bouwmeester, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 51, 641 (1995).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Stöckmann, H. J.

H. J. Stöckmann, Quantum Chaos:?an Introduction (Cambridge U. Press, 1999).

Stover, J. C.

J. C. Stover, Optical Scattering, Measurement, and Analysis (McGraw-Hill, 1990).

Thomas, J. E.

D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, Phys. Rev. Lett. 58, 1320 (1987).
[CrossRef] [PubMed]

Thompson, R. J.

van Zee, R. D.

J. T. Hodges, J. P. Looney, and R. D. van Zee, J. Chem. Phys. 105, 10278 (1996).
[CrossRef]

Wineland, D. J.

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in Proceedings of the International School of Physics Enrico Fermi CXX (North-Holland, 1994), p. 367.

Woerdman, J. P.

C. A. Schrama, D. Bouwmeester, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 51, 641 (1995).
[CrossRef] [PubMed]

Ye, J.

C. J. Hood, H. J. Kimble, and J. Ye, Phys. Rev. A 64, 033804 (2001).
[CrossRef]

Yoo, Y. S.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
[CrossRef]

Yoon, Y.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
[CrossRef]

Appl. Opt. (1)

S. Herriott, H. Kogelnik, and R. Kompfner, Appl. Opt. 3, 4 (1964).
[CrossRef]

Appl. Phys. B (1)

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, Appl. Phys. B 74, 435 (2002).
[CrossRef]

J. Chem. Phys. (1)

J. T. Hodges, J. P. Looney, and R. D. van Zee, J. Chem. Phys. 105, 10278 (1996).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. A (2)

C. J. Hood, H. J. Kimble, and J. Ye, Phys. Rev. A 64, 033804 (2001).
[CrossRef]

C. A. Schrama, D. Bouwmeester, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 51, 641 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, Phys. Rev. Lett. 58, 1320 (1987).
[CrossRef] [PubMed]

Phys. Today (1)

S. Haroche and D. Kleppner, Phys. Today 42(1), 24 (1989).
[CrossRef]

Other (4)

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in Proceedings of the International School of Physics Enrico Fermi CXX (North-Holland, 1994), p. 367.

A. E. Siegman, Lasers (University Science, 1986).

J. C. Stover, Optical Scattering, Measurement, and Analysis (McGraw-Hill, 1990).

H. J. Stöckmann, Quantum Chaos:?an Introduction (Cambridge U. Press, 1999).

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Figures (2)

Fig. 1
Fig. 1

Relative spectral width of cavity resonances, expressed as finesse F, measured as a function of normalized cavity length δ, for a resonator with (dashed curve) and without (solid curve) a centered intracavity pinhole. Inset, two typical spectra measured at δ = 0 (solid curve) and δ = 1 × 10 3 (dashed curve).

Fig. 2
Fig. 2

(Color online). False color ( red = high , blue = low ) plot of the cavity transmission as a function of the normalized frequency detuning (horizontal) and frequency (vertical). Vertical cuts represent transmission spectra at a fixed cavity length. Both a, simulations and b, experimental data show how mode coupling leads to spectral broadening and a reduction in peak transmission around frequency-degenerate point ϵ = δ = 0 . Both effects result from level repulsion and mode mixing.

Equations (3)

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

E ( x , t ) = j a j ( t ) u j ( x ) .
P out ( ω ) j a j ( ω ) 2 j E in ( x ) u j * ( x ) d x 2 ( ω ω j ) 2 + Γ 2 ,
ω j u j = M u j = [ c 00 c 01 c 02 c 10 ϵ + c 11 c 12 c 20 c 21 2 ϵ + c 22 ] u j ,

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