Abstract

We report that unidirectional lasing emission can be generated from a rounded isosceles triangular microcavity within a low nkD range, where n is the refractive index, k is the vacuum wave number, and D is the characteristic size of the microcavity. It is shown that unidirectional resonance modes have relatively high-Q values and in a nonlinear dynamic model appear as stationary lasing solutions with a low threshold. The formation of a whispering-gallery-type pattern along the rounded part on the symmetry axis is responsible for the unidirectionality of the resonances.

© 2004 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. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
    [CrossRef]
  3. R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
    [CrossRef]
  4. L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
    [CrossRef]
  5. J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
    [CrossRef]
  6. H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, and A. D. Stone, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” July 31, 2003, arXiv:physics/0308001, http://xxx.lanl.gov.
  7. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
    [CrossRef]
  8. The boundary shape is given in polar coordinates as follows: r(f)=r0[1+(e /2p)f], where e is the deformation parameter and r0 is the radius of the spiral at f=0. The shape jumps back to r0 at f=2p, creating a notch.
  9. J. Wiersig, J. Opt. A Pure Appl. Opt. 5, 53 (2003).
    [CrossRef]
  10. H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1976).
  11. T. Harayama, P. Davis, and K. S. Ikeda, Phys. Rev. Lett. 90, 063901 (2003).
    [CrossRef]
  12. T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, Phys. Rev. Lett. 91, 073903 (2003).
    [CrossRef]
  13. S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, Phys. Rev. A 70, 023809 (2004).
    [CrossRef]

2004

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, Phys. Rev. A 70, 023809 (2004).
[CrossRef]

2003

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

J. Wiersig, J. Opt. A Pure Appl. Opt. 5, 53 (2003).
[CrossRef]

T. Harayama, P. Davis, and K. S. Ikeda, Phys. Rev. Lett. 90, 063901 (2003).
[CrossRef]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, Phys. Rev. Lett. 91, 073903 (2003).
[CrossRef]

1997

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

1993

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
[CrossRef]

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

1992

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Baltes, H. P.

H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1976).

Brune, M.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Chang, R. K.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, and A. D. Stone, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” July 31, 2003, arXiv:physics/0308001, http://xxx.lanl.gov.

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Collot, L.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Davis, P.

T. Harayama, P. Davis, and K. S. Ikeda, Phys. Rev. Lett. 90, 063901 (2003).
[CrossRef]

Fukushima, T.

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, Phys. Rev. Lett. 91, 073903 (2003).
[CrossRef]

Harayama, T.

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, Phys. Rev. Lett. 91, 073903 (2003).
[CrossRef]

T. Harayama, P. Davis, and K. S. Ikeda, Phys. Rev. Lett. 90, 063901 (2003).
[CrossRef]

Haroche, S.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Hilf, E. R.

H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1976).

Ikeda, K. S.

T. Harayama, P. Davis, and K. S. Ikeda, Phys. Rev. Lett. 90, 063901 (2003).
[CrossRef]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, Phys. Rev. Lett. 91, 073903 (2003).
[CrossRef]

Johnson, N. M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Kim, C.-M.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Kneissl, M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Kurdoglyan, M. S.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Lee, S.-Y.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Lefevreseguin, V.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Levi, A. F. J.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Logan, R. A.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

McCall, S. L.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Mohideen, U.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
[CrossRef]

Nöckel, J. U.

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Pearton, S. J.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Raimond, J. M.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Rex, N. B.

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, and A. D. Stone, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” July 31, 2003, arXiv:physics/0308001, http://xxx.lanl.gov.

Rim, S.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Schwefel, H. G. L.

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, and A. D. Stone, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” July 31, 2003, arXiv:physics/0308001, http://xxx.lanl.gov.

Slusher, R. E.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Stone, A. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, and A. D. Stone, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” July 31, 2003, arXiv:physics/0308001, http://xxx.lanl.gov.

Sunada, S.

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, Phys. Rev. Lett. 91, 073903 (2003).
[CrossRef]

Tureci, H. E.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, and A. D. Stone, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” July 31, 2003, arXiv:physics/0308001, http://xxx.lanl.gov.

Wiersig, J.

J. Wiersig, J. Opt. A Pure Appl. Opt. 5, 53 (2003).
[CrossRef]

Appl. Phys. Lett.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 63, 1310 (1993).
[CrossRef]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Europhys. Lett.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

J. Opt. A Pure Appl. Opt.

J. Wiersig, J. Opt. A Pure Appl. Opt. 5, 53 (2003).
[CrossRef]

Nature

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Phys. Rev. A

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Phys. Rev. Lett.

T. Harayama, P. Davis, and K. S. Ikeda, Phys. Rev. Lett. 90, 063901 (2003).
[CrossRef]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, Phys. Rev. Lett. 91, 073903 (2003).
[CrossRef]

Other

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

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, and A. D. Stone, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” July 31, 2003, arXiv:physics/0308001, http://xxx.lanl.gov.

H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1976).

The boundary shape is given in polar coordinates as follows: r(f)=r0[1+(e /2p)f], where e is the deformation parameter and r0 is the radius of the spiral at f=0. The shape jumps back to r0 at f=2p, creating a notch.

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Figures (5)

Fig. 1
Fig. 1

Rounded-isosceles-triangle-shaped microcavity.

Fig. 2
Fig. 2

Resonance positions in the complex nkD plane. The circles and triangles represent the resonances of odd and even symmetry classes, respectively. The filled circles and triangles denote high-Q resonances showing unidirectional emission from the bottom. The high-Q resonances, denoted by A and B, are shown in Fig. 3.

Fig. 3
Fig. 3

Resonance patterns with unidirectional emission: (a) resonance A (odd symmetry), (b) resonance B (even symmetry).

Fig. 4
Fig. 4

(a) Near-field distribution at D/2 away from the boundary. (b) Far-field distribution. The dashed and solid curves denote resonances A and B, respectively.

Fig. 5
Fig. 5

Stationary lasing pattern in the Schrödinger–Bloch mode. Note that it matches well with resonance pattern A in Fig. 3(b).

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