Abstract

We report what is believed to be the first observation of a nonlinear mode in a cylindrical nonlinear Fabry–Perot cavity. The field enhancement from cavity buildup, as well as the large χ3 optical nonlinearity that is due to resonantly excited  85Rb vapor, allows the nonlinear mode to form at low incident optical powers of less than 1 mW. The mode is observed to occur for both self-focusing and self-defocusing nonlinearity.

© 1999 Optical Society of America

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  2. N. N. Akhmediev and A. Ankiewicz, Solitons:?Nonlinear Beams and Pulses (Chapman & Hall, London, 1997).
  3. A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
    [CrossRef]
  4. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, Opt. Lett. 15, 471 (1990).
    [CrossRef] [PubMed]
  5. R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
    [CrossRef]
  6. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  7. G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
    [CrossRef]
  8. H. M. Gibbs, Optical Bistability:?Controlling Light with Light (Academic, San Diego, Calif., 1985).
  9. I. H. Deutsch, R. Y. Chiao, and J. C. Garrison, Phys. Rev. Lett. 69, 3627 (1992).
    [CrossRef] [PubMed]
  10. L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
    [CrossRef] [PubMed]
  11. J. Boyce and R. Y. Chiao, Phys. Rev. A 59, 3953 (1999).
    [CrossRef]

1999

J. Boyce and R. Y. Chiao, Phys. Rev. A 59, 3953 (1999).
[CrossRef]

1996

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

1995

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

1993

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

1992

I. H. Deutsch, R. Y. Chiao, and J. C. Garrison, Phys. Rev. Lett. 69, 3627 (1992).
[CrossRef] [PubMed]

1990

1987

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

1985

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

1964

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Aitchison, J. S.

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, Solitons:?Nonlinear Beams and Pulses (Chapman & Hall, London, 1997).

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, Solitons:?Nonlinear Beams and Pulses (Chapman & Hall, London, 1997).

Baek, Y.

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Barthelemy, A.

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Boyce, J.

J. Boyce and R. Y. Chiao, Phys. Rev. A 59, 3953 (1999).
[CrossRef]

Chiao, R. Y.

J. Boyce and R. Y. Chiao, Phys. Rev. A 59, 3953 (1999).
[CrossRef]

I. H. Deutsch, R. Y. Chiao, and J. C. Garrison, Phys. Rev. Lett. 69, 3627 (1992).
[CrossRef] [PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Crosignani, B.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Deutsch, I. H.

I. H. Deutsch, R. Y. Chiao, and J. C. Garrison, Phys. Rev. Lett. 69, 3627 (1992).
[CrossRef] [PubMed]

Di Porto, P.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Duree, G. C.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Froehly, C.

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Garrison, J. C.

I. H. Deutsch, R. Y. Chiao, and J. C. Garrison, Phys. Rev. Lett. 69, 3627 (1992).
[CrossRef] [PubMed]

Gibbs, H. M.

H. M. Gibbs, Optical Bistability:?Controlling Light with Light (Academic, San Diego, Calif., 1985).

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Jackel, J. L.

Leaird, D. E.

Lefever, R.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

Lugiato, L. A.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

Maneuf, S.

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Neurgaonkar, R. R.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Oliver, M. K.

Salamo, G. J.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Schiek, R.

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Schultz, J. L.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Segev, M.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Sharp, E. J.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Silberberg, Y.

Smith, P. W. E.

Stegeman, G. I.

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torner, G. I.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Vogel, E. M.

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Weiner, A. M.

Yariv, A.

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

Opt. Commun.

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Opt. Lett.

Phys. Rev. A

J. Boyce and R. Y. Chiao, Phys. Rev. A 59, 3953 (1999).
[CrossRef]

Phys. Rev. E

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Phys. Rev. Lett.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Stryland, G. I. Torner, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

G. C. Duree, J. L. Schultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef]

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

I. H. Deutsch, R. Y. Chiao, and J. C. Garrison, Phys. Rev. Lett. 69, 3627 (1992).
[CrossRef] [PubMed]

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

Other

N. N. Akhmediev and A. Ankiewicz, Solitons:?Nonlinear Beams and Pulses (Chapman & Hall, London, 1997).

H. M. Gibbs, Optical Bistability:?Controlling Light with Light (Academic, San Diego, Calif., 1985).

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Figures (6)

Fig. 1
Fig. 1

Cylindrical Fabry–Perot cavity, showing the coordinate system used and an incident Gaussian (in x) beam.

Fig. 2
Fig. 2

Schematic of the experimental apparatus used to observe the spatial nonlinear mode. D1–D3, detectors.

Fig. 3
Fig. 3

Calculated linear absorption and n2 in natural-abundance rubidium vapor at 80 °C N=1.5×1012 cm-3, near the D2 transition at λ=780 nm, for circularly polarized light. The arrow indicates the line used in the experiment, the Doppler-broadened  85Rb, F=2 set of transitions.

Fig. 4
Fig. 4

Power transmitted through the nonlinear cavity as a function of laser frequency for a particular cavity length L and beam power. The frequency is relative to the  85Rb line indicated in Fig. 3.

Fig. 5
Fig. 5

Total power transmitted through the cavity as a function of laser frequency for two different cavity lengths L.

Fig. 6
Fig. 6

Transmitted intensity profiles of spatial nonlinear modes taken with the CCD camera, integrated over y, at the peaks of the nonlinear modes shown in Fig. 5.

Equations (1)

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Et=ic2n0k2Ex2+iωAn2n0E2E+icΔkn0E-ΓE-Ed,

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