Abstract

We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-Hänchen effect. The V-shaped modes, which have purely TE or TM polarization, are well described by a 2D billiard map with the Goos-Hänchen shift included. A phase space plot of this augmented billiard map reveals a saddle-node bifurcation; the stable periodic orbit that is created in the bifurcation corresponds to the numerically calculated eigenmode, dictating the angle of its 'V.' A transition from a fundamental Gaussian to a TM V mode has been observed as the cavity is lengthened to become nearly hemispherical.

© 2007 Optical Society of America

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  1. F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).
  2. N. H. Tran, L. Dutriaux, P. Balcou, A. Le Floch, and F. Bretenaker, Opt. Lett. 20, 1233 (1995).
  3. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
    [CrossRef]
  4. L. Dutriaux, A. Le Floch, and F. Bretenaker, J. Opt. Soc. Am. B 12, 2283 (1992).
  5. D. Q. Chowdhurry, D. H. Leach, and R. K. Chang, J. Opt. Soc. Am. A 11, 1110 (1994).
  6. D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1950 (1993).
    [CrossRef]
  7. D. H. Foster and J. U. Nöckel, Opt. Commun. 234, 351 (2004).
  8. K. V. Artmann, Ann. Phys. 2, 87 (1948).
  9. W. Nasalski, J. Opt. Soc. Am. A 13, 172 (1996).
  10. D. H. Foster and J. U. Nöckel, Opt. Lett. 29, 2788 (2004).
    [CrossRef]
  11. D. H. Foster, 'Fabry-Perot and whispering gallery modes in realistic resonator models,' Ph.D. thesis, (University of Oregon, 2006), http://hdl.handle.net/1794/3778.
  12. R. Blümel, T. M. Antonsen, B. Georgeot, E. Ott, and R. E. Prange, Phys. Rev. Lett. 76, 2476 (1996).
    [CrossRef]

2004 (2)

D. H. Foster and J. U. Nöckel, Opt. Commun. 234, 351 (2004).

D. H. Foster and J. U. Nöckel, Opt. Lett. 29, 2788 (2004).
[CrossRef]

1996 (2)

W. Nasalski, J. Opt. Soc. Am. A 13, 172 (1996).

R. Blümel, T. M. Antonsen, B. Georgeot, E. Ott, and R. E. Prange, Phys. Rev. Lett. 76, 2476 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1950 (1993).
[CrossRef]

1992 (2)

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef]

L. Dutriaux, A. Le Floch, and F. Bretenaker, J. Opt. Soc. Am. B 12, 2283 (1992).

1948 (1)

K. V. Artmann, Ann. Phys. 2, 87 (1948).

1947 (1)

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).

Antonsen, T. M.

R. Blümel, T. M. Antonsen, B. Georgeot, E. Ott, and R. E. Prange, Phys. Rev. Lett. 76, 2476 (1996).
[CrossRef]

Artmann, K. V.

K. V. Artmann, Ann. Phys. 2, 87 (1948).

Babic, D. I.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1950 (1993).
[CrossRef]

Balcou, P.

Blümel, R.

R. Blümel, T. M. Antonsen, B. Georgeot, E. Ott, and R. E. Prange, Phys. Rev. Lett. 76, 2476 (1996).
[CrossRef]

Bowers, J. E.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1950 (1993).
[CrossRef]

Bretenaker, F.

N. H. Tran, L. Dutriaux, P. Balcou, A. Le Floch, and F. Bretenaker, Opt. Lett. 20, 1233 (1995).

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef]

L. Dutriaux, A. Le Floch, and F. Bretenaker, J. Opt. Soc. Am. B 12, 2283 (1992).

Chang, R. K.

Chowdhurry, D. Q.

Chung, Y.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1950 (1993).
[CrossRef]

Dagli, N.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1950 (1993).
[CrossRef]

Dutriaux, L.

N. H. Tran, L. Dutriaux, P. Balcou, A. Le Floch, and F. Bretenaker, Opt. Lett. 20, 1233 (1995).

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef]

L. Dutriaux, A. Le Floch, and F. Bretenaker, J. Opt. Soc. Am. B 12, 2283 (1992).

Foster, D. H.

D. H. Foster and J. U. Nöckel, Opt. Commun. 234, 351 (2004).

D. H. Foster and J. U. Nöckel, Opt. Lett. 29, 2788 (2004).
[CrossRef]

D. H. Foster, 'Fabry-Perot and whispering gallery modes in realistic resonator models,' Ph.D. thesis, (University of Oregon, 2006), http://hdl.handle.net/1794/3778.

Georgeot, B.

R. Blümel, T. M. Antonsen, B. Georgeot, E. Ott, and R. E. Prange, Phys. Rev. Lett. 76, 2476 (1996).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).

Le Floch, A.

N. H. Tran, L. Dutriaux, P. Balcou, A. Le Floch, and F. Bretenaker, Opt. Lett. 20, 1233 (1995).

L. Dutriaux, A. Le Floch, and F. Bretenaker, J. Opt. Soc. Am. B 12, 2283 (1992).

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef]

Leach, D. H.

Nasalski, W.

Nöckel, J. U.

D. H. Foster and J. U. Nöckel, Opt. Lett. 29, 2788 (2004).
[CrossRef]

D. H. Foster and J. U. Nöckel, Opt. Commun. 234, 351 (2004).

Ott, E.

R. Blümel, T. M. Antonsen, B. Georgeot, E. Ott, and R. E. Prange, Phys. Rev. Lett. 76, 2476 (1996).
[CrossRef]

Prange, R. E.

R. Blümel, T. M. Antonsen, B. Georgeot, E. Ott, and R. E. Prange, Phys. Rev. Lett. 76, 2476 (1996).
[CrossRef]

Tran, N. H.

Ann. Phys. (2)

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).

K. V. Artmann, Ann. Phys. 2, 87 (1948).

IEEE J. Quantum Electron. (1)

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1950 (1993).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

L. Dutriaux, A. Le Floch, and F. Bretenaker, J. Opt. Soc. Am. B 12, 2283 (1992).

Opt. Commun. (1)

D. H. Foster and J. U. Nöckel, Opt. Commun. 234, 351 (2004).

Opt. Lett. (2)

Phys. Rev. Lett. (2)

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef]

R. Blümel, T. M. Antonsen, B. Georgeot, E. Ott, and R. E. Prange, Phys. Rev. Lett. 76, 2476 (1996).
[CrossRef]

Other (1)

D. H. Foster, 'Fabry-Perot and whispering gallery modes in realistic resonator models,' Ph.D. thesis, (University of Oregon, 2006), http://hdl.handle.net/1794/3778.

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