Abstract

We have devised and experimentally verified a method for observation of the optical Kerr effect in microcavities at room temperature. The technique discriminates against the much larger and typically dominant thermal component of nonlinearity by using its relatively slow frequency response. Measurement of the Kerr coefficient or equivalently of the third-order nonlinear susceptibility of the cavity material is demonstrated for a silica microcavity. With this approach, useful information about the characteristic thermal response time in microresonators can also be acquired.

© 2005 Optical Society of America

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References

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  1. R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
  2. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
    [CrossRef] [PubMed]
  3. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 92, 043903 (2004).
    [CrossRef]
  4. V. S. Ilchenko and M. L. Gorodetsky, Laser Phys. 2, 1004 (1992).
  5. F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
    [CrossRef]
  6. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  7. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
    [CrossRef]
  8. H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  9. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
    [CrossRef] [PubMed]
  10. M. Cai, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
    [CrossRef] [PubMed]
  11. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
    [CrossRef]

2004 (1)

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 92, 043903 (2004).
[CrossRef]

2003 (2)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

2002 (1)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

2000 (1)

M. Cai, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

1998 (1)

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

1992 (1)

V. S. Ilchenko and M. L. Gorodetsky, Laser Phys. 2, 1004 (1992).

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Cai, M.

M. Cai, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

Gorodetsky, M. L.

V. S. Ilchenko and M. L. Gorodetsky, Laser Phys. 2, 1004 (1992).

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Harche, S.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

Hare, J.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

Haus, H.

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Ilchenko, V. S.

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 92, 043903 (2004).
[CrossRef]

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

V. S. Ilchenko and M. L. Gorodetsky, Laser Phys. 2, 1004 (1992).

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

Lefevre-Seguin, V.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

Maleki, L.

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 92, 043903 (2004).
[CrossRef]

Matsko, A. B.

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 92, 043903 (2004).
[CrossRef]

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

M. Cai, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

Raimond, J. M.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

Roch, J.-F.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

Savchenkov, A. A.

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 92, 043903 (2004).
[CrossRef]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

Treussart, F.

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

Vahala, K. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

M. Cai, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

Eur. Phys. J. D (1)

F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Harche, Eur. Phys. J. D 1, 235 (1998).
[CrossRef]

Laser Phys. (1)

V. S. Ilchenko and M. L. Gorodetsky, Laser Phys. 2, 1004 (1992).

Nature (2)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Phys. Lett. A (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Phys. Rev. Lett. (3)

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 92, 043903 (2004).
[CrossRef]

M. Cai, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Other (3)

R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup used for characterizing the Kerr nonlinearity of microcavities. The picture is a top-view optical micrograph of a toroid microresonator that has been evanescently side coupled to a tapered optical fiber. Laser sources at 1550- and 1480-nm bands are used for pump and probe beams, respectively.

Fig. 2
Fig. 2

Measured amplitude modulation of the probe beam as a function of the modulation frequency of the pump power. The dotted lines show a 3-dB corner frequency of 25 kHz where the modulation of the pump power becomes comparable to or faster than the thermal response time of the resonator. The second roll-off is due to limited bandwidth of the cavity, which does not allow the pump power in the resonator to build up instantaneously. The flat response in the middle shows the fast Kerr effect.

Equations (4)

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

ΔPprobeΩPprobe=PpumpΩQprobetotalQpumpeff2n2λpumpπn2VeffCx,
PpumpcavityPpump=λpumpQpumpeffπ2nR,
Qpumpeff=Q0K1+K2.
τthermal=δR2D=1D2Rλ2π2n22/3,

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