Abstract

Asymmetric resonant cavities with highly noncircular but convex cross sections are predicted theoretically to have high-Q whispering gallery modes with highly anisotropic emission. We develop a ray dynamics model for the emission pattern and present numerical and experimental confirmation of the theory.

© 1996 Optical Society of America

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References

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  1. J. U. Nöckel, A. D. Stone, R. K. Chang, Opt. Lett. 19, 1693 (1994).
    [CrossRef] [PubMed]
  2. A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, R. K. Chang, Phys. Rev. Lett. 75, 2682 (1995).
    [CrossRef] [PubMed]
  3. J. U. Nöckel, A. D. Stone, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).
  4. J. N. Mather, Ergodic Theor. Dynam. Syst. 2, 397 (1982).
  5. M. Robnik, M. V. Berry, J. Phys. A 18, 1361 (1985).
    [CrossRef]
  6. E. S. C. Ching, P. T. Leung, K. Young, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).
    [CrossRef]
  7. R. F. Millar, Electron. Lett. 5, 416 (1969).
    [CrossRef]

1995 (1)

A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, R. K. Chang, Phys. Rev. Lett. 75, 2682 (1995).
[CrossRef] [PubMed]

1994 (1)

1985 (1)

M. Robnik, M. V. Berry, J. Phys. A 18, 1361 (1985).
[CrossRef]

1982 (1)

J. N. Mather, Ergodic Theor. Dynam. Syst. 2, 397 (1982).

1969 (1)

R. F. Millar, Electron. Lett. 5, 416 (1969).
[CrossRef]

Berry, M. V.

M. Robnik, M. V. Berry, J. Phys. A 18, 1361 (1985).
[CrossRef]

Chang, R. K.

A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, R. K. Chang, Phys. Rev. Lett. 75, 2682 (1995).
[CrossRef] [PubMed]

J. U. Nöckel, A. D. Stone, R. K. Chang, Opt. Lett. 19, 1693 (1994).
[CrossRef] [PubMed]

Chen, G.

A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, R. K. Chang, Phys. Rev. Lett. 75, 2682 (1995).
[CrossRef] [PubMed]

Ching, E. S. C.

E. S. C. Ching, P. T. Leung, K. Young, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).
[CrossRef]

Leung, P. T.

E. S. C. Ching, P. T. Leung, K. Young, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).
[CrossRef]

Mather, J. N.

J. N. Mather, Ergodic Theor. Dynam. Syst. 2, 397 (1982).

Mekis, A.

A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, R. K. Chang, Phys. Rev. Lett. 75, 2682 (1995).
[CrossRef] [PubMed]

Millar, R. F.

R. F. Millar, Electron. Lett. 5, 416 (1969).
[CrossRef]

Nöckel, J. U.

A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, R. K. Chang, Phys. Rev. Lett. 75, 2682 (1995).
[CrossRef] [PubMed]

J. U. Nöckel, A. D. Stone, R. K. Chang, Opt. Lett. 19, 1693 (1994).
[CrossRef] [PubMed]

J. U. Nöckel, A. D. Stone, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).

Robnik, M.

M. Robnik, M. V. Berry, J. Phys. A 18, 1361 (1985).
[CrossRef]

Stone, A. D.

A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, R. K. Chang, Phys. Rev. Lett. 75, 2682 (1995).
[CrossRef] [PubMed]

J. U. Nöckel, A. D. Stone, R. K. Chang, Opt. Lett. 19, 1693 (1994).
[CrossRef] [PubMed]

J. U. Nöckel, A. D. Stone, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).

Young, K.

E. S. C. Ching, P. T. Leung, K. Young, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).
[CrossRef]

Electron. Lett. (1)

R. F. Millar, Electron. Lett. 5, 416 (1969).
[CrossRef]

Ergodic Theor. Dynam. Syst. (1)

J. N. Mather, Ergodic Theor. Dynam. Syst. 2, 397 (1982).

J. Phys. A (1)

M. Robnik, M. V. Berry, J. Phys. A 18, 1361 (1985).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, R. K. Chang, Phys. Rev. Lett. 75, 2682 (1995).
[CrossRef] [PubMed]

Other (2)

J. U. Nöckel, A. D. Stone, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).

E. S. C. Ching, P. T. Leung, K. Young, in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

SOS for the quadrupole at = 0.072, showing four chaotic trajectories followed for 100–200 reflections. Superimposed are the curves given by Eq. (2). The thick horizontal lines indicate sin χc for different refractive indices n.

Fig. 2
Fig. 2

Far-field emission directionality from (a), (b) a quadrupole and (c) an ellipse with distortion = 0.09 for a resonance m = 68. Solid curves, intensity from solution of the wave equation; histograms, classical prediction. The refractive index is n = 2 in (a) and n = 1.54 in (b) and (c). The size parameter at this is kR = 45.2 in (a), kR = 48.1 in (b), and kR = 48.0 in (c). The insets show the shapes.

Fig. 3
Fig. 3

Lasing emission from a liquid dye column created by (a) rectangular and (b) circular orifices. Simultaneous images taken at 0° and 90° angles with respect to the pump beam are shown side by side.

Equations (2)

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r ( ϕ ) = 1 ( 1 + 2 / 2 ) 1 / 2 ( 1 + cos 2 ϕ ) .
sin χ ( ϕ ) = [ 1 ( 1 S 2 ) κ ( ϕ ) 2 / 3 ] 1 / 2 ,

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