Abstract

Large-aperture vertical-cavity surface-emitting lasers with an equilateral triangular lateral confinement are fabricated to investigate the formation of high-order resonant modes. The experimental lasing patterns are composed of the superscar mode, honeycomb eigenstate, and chaotic mode. Experimental results confirm the theoretical predictions that tiny symmetry breaking can cause the high-order modes to reveal miscellaneous states of integrable and chaotic systems.

© 2008 Optical Society of America

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  1. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  6. Y. F. Chen, K. F. Huang, and Y. P. Lan, Phys. Rev. E 66, 066210 (2002).
    [Crossref]
  7. Y. F. Chen and K. F. Huang, Phys. Rev. E 68, 066207 (2003).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  17. J. C. Marinace, A. E. Michel, and M. I. Nathan, Proc. IEEE 52, 722 (1964)
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    [Crossref] [PubMed]
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    [Crossref]

2007 (3)

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[Crossref]

J. Yoon, S.-J. An, K. Kim, J. K. Ku, and O. Kwon, Appl. Opt. 46, 2969 (2007).
[Crossref] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[Crossref]

2006 (2)

E. Bogomolny, B. Dietz, T. Friedrich, M. Miski-Oglu, A. Richter, F. Schäfer, and C. Schmit, Phys. Rev. Lett. 97, 254102 (2006).
[Crossref]

C. C. Liu, T. H. Lu, Y. F. Chen, and K. F. Huang, Phys. Rev. E 74, 046214 (2006).
[Crossref]

2005 (1)

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[Crossref] [PubMed]

2003 (1)

Y. F. Chen and K. F. Huang, Phys. Rev. E 68, 066207 (2003).
[Crossref]

2002 (3)

K. F. Huang, Y. F. Chen, H. C. Lai, and Y. P. Lan, Phys. Rev. Lett. 89, 224102 (2002).
[Crossref] [PubMed]

Y. F. Chen, K. F. Huang, and Y. P. Lan, Phys. Rev. E 66, 066210 (2002).
[Crossref]

N. B. Rex, H. E. Tureci, H. G. L. Schwefel, R. K. Chang, and A. D. Stone, Phys. Rev. Lett. 88, 094102 (2002).
[Crossref] [PubMed]

2001 (1)

2000 (1)

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Haetty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, Phys. Rev. A 62, 013816 (2000).
[Crossref]

1999 (1)

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[Crossref]

1998 (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[Crossref] [PubMed]

1997 (1)

L. Christensson, H. Linke, P. Omling, P. E. Lindelof, I. V. Zozoulenko, and K. F. Berggren, Phys. Rev. B 57, 12306 (1997).
[Crossref]

1994 (1)

P. Bellomo and T. Uzer, Phys. Rev. E 50, 1886 (1994).
[Crossref]

1987 (1)

P. O'Connor, J. Gehlen, and E. J. Heller, Phys. Rev. Lett. 58, 1296 (1987).
[Crossref] [PubMed]

1984 (1)

E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
[Crossref]

1964 (1)

J. C. Marinace, A. E. Michel, and M. I. Nathan, Proc. IEEE 52, 722 (1964)
[Crossref]

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photon. Technol. Lett. 19, 963 (2007).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (2)

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Haetty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, Phys. Rev. A 62, 013816 (2000).
[Crossref]

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[Crossref]

Phys. Rev. B (1)

L. Christensson, H. Linke, P. Omling, P. E. Lindelof, I. V. Zozoulenko, and K. F. Berggren, Phys. Rev. B 57, 12306 (1997).
[Crossref]

Phys. Rev. E (4)

Y. F. Chen, K. F. Huang, and Y. P. Lan, Phys. Rev. E 66, 066210 (2002).
[Crossref]

Y. F. Chen and K. F. Huang, Phys. Rev. E 68, 066207 (2003).
[Crossref]

C. C. Liu, T. H. Lu, Y. F. Chen, and K. F. Huang, Phys. Rev. E 74, 046214 (2006).
[Crossref]

P. Bellomo and T. Uzer, Phys. Rev. E 50, 1886 (1994).
[Crossref]

Phys. Rev. Lett. (7)

E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
[Crossref]

E. Bogomolny, B. Dietz, T. Friedrich, M. Miski-Oglu, A. Richter, F. Schäfer, and C. Schmit, Phys. Rev. Lett. 97, 254102 (2006).
[Crossref]

N. B. Rex, H. E. Tureci, H. G. L. Schwefel, R. K. Chang, and A. D. Stone, Phys. Rev. Lett. 88, 094102 (2002).
[Crossref] [PubMed]

P. O'Connor, J. Gehlen, and E. J. Heller, Phys. Rev. Lett. 58, 1296 (1987).
[Crossref] [PubMed]

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, Phys. Rev. Lett. 82, 1434 (1999).
[Crossref]

K. F. Huang, Y. F. Chen, H. C. Lai, and Y. P. Lan, Phys. Rev. Lett. 89, 224102 (2002).
[Crossref] [PubMed]

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[Crossref] [PubMed]

Proc. IEEE (1)

J. C. Marinace, A. E. Michel, and M. I. Nathan, Proc. IEEE 52, 722 (1964)
[Crossref]

Science (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[Crossref] [PubMed]

Other (1)

H. J. Stöckmann, Quantum Chaos: an Introduction (Cambridge U. Press, 1999), and references cited therein.

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Figures (4)

Fig. 1
Fig. 1

Optical microscope image of the device with pattern of spontaneous emission to display the equilateral-triangular aperture.

Fig. 2
Fig. 2

Intensity patterns of transerse near-field patterns at temperatures of (a) 295 (room temperature), (b) 275, (c) 195, (d) 175, (e) 155, and (f) 125 K .

Fig. 3
Fig. 3

(a) Numerical wave pattern S 5 , 58 ( x , y ) 2 corresponding to the experimental honeycomb pattern shown in Fig. 2c. (b), (c) Numerical wave patterns of C 36 , 9 + ( x , y ; 1 , 0 , 0.23 π ) 2 and C 22 , 6 + ( x , y ; 1 , 1 , 0.35 π ) 2 corresponding to the experimental patterns shown in Figs. 2b, 2f, respectively. The geometrical POs are shown in the insets.

Fig. 4
Fig. 4

Histogram: intensity statistics of the experimental pattern shown in Fig. 2d; straight curve, Porter–Thomas distribution.

Equations (2)

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Φ m , n ± ( x , y ) = 16 a 2 3 3 { e ± i ( m + n ) ( 2 π 3 a ) x sin [ ( m n ) 2 π 3 a y ] + e i ( 2 m n ) ( 2 π 3 a ) x sin [ n 2 π 3 a y ] e i ( 2 n m ) ( 2 π 3 a ) x sin [ m 2 π 3 a y ] } ,
Ψ N , M ± ( x , y ; p , q , ϕ ) = 1 M K = 0 M 1 e ± i K ϕ Φ m o + p K , n o + q ( M 1 K ) ± ( x , y ) ,

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