Dynamical localization in microdisk lasers

W. Fang; H. Cao; V. A. Podolskiy; E. E. Narimanov

doi:10.1364/OPEX.13.005641

Optics Express
Vol. 13,
Issue 15,
pp. 5641-5652
(2005)
•https://doi.org/10.1364/OPEX.13.005641

Dynamical localization in microdisk lasers

W. Fang, H. Cao, V. A. Podolskiy, and E. E. Narimanov

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W. Fang, H. Cao, V. A. Podolskiy, and E. E. Narimanov, "Dynamical localization in microdisk lasers," Opt. Express 13, 5641-5652 (2005)

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Abstract

We demonstrate the lasing action from a dynamically localized mode in a microdisk resonator with rough boundary. Although substantial boundary roughness and surface defects in our devices imply strong light scattering and destroy the regular whispering gallery modes, the destructive interference of the scattered light leads to the dynamical Anderson localization in the phase space of the system and the formation of a different type of high-Q modes. Using direct optical imaging of the lasing mode and theoretical calculations, we show that the lasing modes in our devices has dynamical localization origin. This behavior, although demonstrated here in GaAs-InAs microdisk laser, should be applicable to any lasers and sensors based on semiconductor or polymer materials.

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References

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Year
Author
Publication

S.X. Qian, J. Snow, H.M. Tzeng, and R.K. Chang, “Lasing droplets - highlighting the liquid-air interface by lasere-mission,” Science 231, 486–488 (1986).
[Crossref] [PubMed]
K. Djordjev, S. Choi, S. Choi, and P. Dapkus, “High-Q vertically coupled InP microdisk resonators,” IEEE Photonics Technol. Lett. 14, 331–333 (2002).
[Crossref]
B. Gayral, J. M. Gerard, A. Lemaitre, C. Dupuis, L. Manin, and J. L. Pelouard, “High-Q wet-etched GaAs microdisks containing InAs quantum boxes,” Appl. Phys. Lett. 75, 1908–1910 (1999).
[Crossref]
B. Corbett, J. Justice, L. Considint, S. Walsh, and W.M. Kelly, “Low-threshold lasing in novel microdisk geometries,” IEEE Photonics Technol. Lett. 8, 855–857 (1996).
[Crossref]
T. Kipp, L. Rolf, C. Schuller, D. Endler, Ch. Heyn, and D. Heitmann, “Selectively enhanced inelastic light scattering of electronic excitations in a semiconductor microcavity,” Phys. Rev. B 63, 195304 (2001).
[Crossref]
J. U. Nöckel, A. D. Stone, G. Chen, H. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609–1611 (1996).
[Crossref]
E. E. Narimanov, G. Hackenbroich, P. Jacquod, and A. D. Stone, “Semiclassical theory of the emission properties of wave-chaotic resonant cavities,” Phys. Rev. Lett. 83, 4991–4994 (1999).
[Crossref]
It can be shown that in 2D the small wavelength approximation to the solutions of Maxwell equations is essentially equivalent to the standard semiclassical limit of Shrödinger Equation.
J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997)
[Crossref]
K.M. Frahm and D.L. Shepelyansky, “Quantum localization in rough billiards,” Phys. Rev. Lett 78, 1440–1443 (1997).
[Crossref]
S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]
M. Berry, “Regular and irregular semiclassical wavefunctions,” J. Phys. A 10, 2083 (1977).
[Crossref]
M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York, 1991).
G. Casati, B. V. Chirikov, J. Ford, and F. M. Izrailev, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Lecture Notes in PhysicsVol. 93 (Springer, Berlin, 1979), p. 334.
[Crossref]
S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett 49, 509–512 (1982).
[Crossref]
J. Ringor, P. Szriftgiser, J. C. Carreau, and D. Delande, “Experimental evidence of dynamical localization and delocalization in a quasiperiodic driven system,” Phys. Rev. Lett 85, 2741–2744 (2000).
[Crossref]
L. Sirko, Sz. Bauch, Y. Hlushchuk, P.M. Koch, R. Blümel, M. Barth, U. Kuhl, and H.-J. Stöckmann, “Observation of dynamical localization in a rough microwave cavity,” Phys. Lett. A 266, 331–335 (2000).
[Crossref]
O.A. Starykh, P.R.J. Jacquod, E.E. Narimanov, and A.D. Stone, “Signature of dynamical localization in the resonance width distribution of wave-chaotic dielectric cavities,” Phys. Rev. E 62, 2078–2084 (2000).
[Crossref]
V.A. Podolskiy, E.E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proceedings of Nat. Acad. of Sci. 101, 10498–10500 (2004).
[Crossref]
H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]
D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref] [PubMed]
G. Casati, I. Guarneri, and D. Shepelyansky, “Exponential photonic localization for the hydrogen atom in a monochromatic field,” Phys. Rev. A 36, 3501–3504 (1987).
[Crossref] [PubMed]
F. HaakeQuantum Signatures of Chaos Springer NY (2000).
E. Doron and U. Smilansky, “Chaotic spectroscopy,” Phys. Rev. Lett. 68, 1255–1258 (1992).
[Crossref] [PubMed]
H.E. Tureci, H.G.L. Schwefel, P. Jacquod, and A.D. Stone, “Modes of wave-chaotic dielectric resonators,” ArXiv: physics/0308016 (2003)

2004 (1)

V.A. Podolskiy, E.E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proceedings of Nat. Acad. of Sci. 101, 10498–10500 (2004).
[Crossref]

2003 (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref] [PubMed]

2002 (1)

K. Djordjev, S. Choi, S. Choi, and P. Dapkus, “High-Q vertically coupled InP microdisk resonators,” IEEE Photonics Technol. Lett. 14, 331–333 (2002).
[Crossref]

2001 (1)

T. Kipp, L. Rolf, C. Schuller, D. Endler, Ch. Heyn, and D. Heitmann, “Selectively enhanced inelastic light scattering of electronic excitations in a semiconductor microcavity,” Phys. Rev. B 63, 195304 (2001).
[Crossref]

2000 (4)

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

J. Ringor, P. Szriftgiser, J. C. Carreau, and D. Delande, “Experimental evidence of dynamical localization and delocalization in a quasiperiodic driven system,” Phys. Rev. Lett 85, 2741–2744 (2000).
[Crossref]

L. Sirko, Sz. Bauch, Y. Hlushchuk, P.M. Koch, R. Blümel, M. Barth, U. Kuhl, and H.-J. Stöckmann, “Observation of dynamical localization in a rough microwave cavity,” Phys. Lett. A 266, 331–335 (2000).
[Crossref]

O.A. Starykh, P.R.J. Jacquod, E.E. Narimanov, and A.D. Stone, “Signature of dynamical localization in the resonance width distribution of wave-chaotic dielectric cavities,” Phys. Rev. E 62, 2078–2084 (2000).
[Crossref]

1999 (2)

B. Gayral, J. M. Gerard, A. Lemaitre, C. Dupuis, L. Manin, and J. L. Pelouard, “High-Q wet-etched GaAs microdisks containing InAs quantum boxes,” Appl. Phys. Lett. 75, 1908–1910 (1999).
[Crossref]

E. E. Narimanov, G. Hackenbroich, P. Jacquod, and A. D. Stone, “Semiclassical theory of the emission properties of wave-chaotic resonant cavities,” Phys. Rev. Lett. 83, 4991–4994 (1999).
[Crossref]

1997 (2)

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997)
[Crossref]

K.M. Frahm and D.L. Shepelyansky, “Quantum localization in rough billiards,” Phys. Rev. Lett 78, 1440–1443 (1997).
[Crossref]

1996 (2)

B. Corbett, J. Justice, L. Considint, S. Walsh, and W.M. Kelly, “Low-threshold lasing in novel microdisk geometries,” IEEE Photonics Technol. Lett. 8, 855–857 (1996).
[Crossref]

J. U. Nöckel, A. D. Stone, G. Chen, H. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609–1611 (1996).
[Crossref]

1992 (2)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

E. Doron and U. Smilansky, “Chaotic spectroscopy,” Phys. Rev. Lett. 68, 1255–1258 (1992).
[Crossref] [PubMed]

1987 (1)

G. Casati, I. Guarneri, and D. Shepelyansky, “Exponential photonic localization for the hydrogen atom in a monochromatic field,” Phys. Rev. A 36, 3501–3504 (1987).
[Crossref] [PubMed]

1986 (1)

S.X. Qian, J. Snow, H.M. Tzeng, and R.K. Chang, “Lasing droplets - highlighting the liquid-air interface by lasere-mission,” Science 231, 486–488 (1986).
[Crossref] [PubMed]

1982 (1)

S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett 49, 509–512 (1982).
[Crossref]

1977 (1)

M. Berry, “Regular and irregular semiclassical wavefunctions,” J. Phys. A 10, 2083 (1977).
[Crossref]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref] [PubMed]

Barth, M.

Bauch, Sz.

Berry, M.

M. Berry, “Regular and irregular semiclassical wavefunctions,” J. Phys. A 10, 2083 (1977).
[Crossref]

Blümel, R.

Cao, H.

V.A. Podolskiy, E.E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proceedings of Nat. Acad. of Sci. 101, 10498–10500 (2004).
[Crossref]

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

Carreau, J. C.

Casati, G.

G. Casati, I. Guarneri, and D. Shepelyansky, “Exponential photonic localization for the hydrogen atom in a monochromatic field,” Phys. Rev. A 36, 3501–3504 (1987).
[Crossref] [PubMed]

G. Casati, B. V. Chirikov, J. Ford, and F. M. Izrailev, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Lecture Notes in PhysicsVol. 93 (Springer, Berlin, 1979), p. 334.
[Crossref]

Chang, R. K.

J. U. Nöckel, A. D. Stone, G. Chen, H. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609–1611 (1996).
[Crossref]

Chang, R.K.

S.X. Qian, J. Snow, H.M. Tzeng, and R.K. Chang, “Lasing droplets - highlighting the liquid-air interface by lasere-mission,” Science 231, 486–488 (1986).
[Crossref] [PubMed]

Chang, S.-H.

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

Chen, G.

J. U. Nöckel, A. D. Stone, G. Chen, H. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609–1611 (1996).
[Crossref]

Chirikov, B. V.

Choi, S.

K. Djordjev, S. Choi, S. Choi, and P. Dapkus, “High-Q vertically coupled InP microdisk resonators,” IEEE Photonics Technol. Lett. 14, 331–333 (2002).
[Crossref]

Considint, L.

B. Corbett, J. Justice, L. Considint, S. Walsh, and W.M. Kelly, “Low-threshold lasing in novel microdisk geometries,” IEEE Photonics Technol. Lett. 8, 855–857 (1996).
[Crossref]

Corbett, B.

B. Corbett, J. Justice, L. Considint, S. Walsh, and W.M. Kelly, “Low-threshold lasing in novel microdisk geometries,” IEEE Photonics Technol. Lett. 8, 855–857 (1996).
[Crossref]

Dapkus, P.

K. Djordjev, S. Choi, S. Choi, and P. Dapkus, “High-Q vertically coupled InP microdisk resonators,” IEEE Photonics Technol. Lett. 14, 331–333 (2002).
[Crossref]

Delande, D.

Djordjev, K.

K. Djordjev, S. Choi, S. Choi, and P. Dapkus, “High-Q vertically coupled InP microdisk resonators,” IEEE Photonics Technol. Lett. 14, 331–333 (2002).
[Crossref]

Doron, E.

E. Doron and U. Smilansky, “Chaotic spectroscopy,” Phys. Rev. Lett. 68, 1255–1258 (1992).
[Crossref] [PubMed]

Dupuis, C.

Endler, D.

Fang, W.

V.A. Podolskiy, E.E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proceedings of Nat. Acad. of Sci. 101, 10498–10500 (2004).
[Crossref]

Fishman, S.

S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett 49, 509–512 (1982).
[Crossref]

Ford, J.

Frahm, K.M.

K.M. Frahm and D.L. Shepelyansky, “Quantum localization in rough billiards,” Phys. Rev. Lett 78, 1440–1443 (1997).
[Crossref]

Gayral, B.

Gerard, J. M.

Grempel, D. R.

S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett 49, 509–512 (1982).
[Crossref]

Grossman, H.

J. U. Nöckel, A. D. Stone, G. Chen, H. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609–1611 (1996).
[Crossref]

Guarneri, I.

G. Casati, I. Guarneri, and D. Shepelyansky, “Exponential photonic localization for the hydrogen atom in a monochromatic field,” Phys. Rev. A 36, 3501–3504 (1987).
[Crossref] [PubMed]

Gutzwiller, M.

M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York, 1991).

Haake, F.

F. HaakeQuantum Signatures of Chaos Springer NY (2000).

Hackenbroich, G.

Heitmann, D.

Heyn, Ch.

Hlushchuk, Y.

Ho, S. T.

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

Izrailev, F. M.

Jacquod, P.

H.E. Tureci, H.G.L. Schwefel, P. Jacquod, and A.D. Stone, “Modes of wave-chaotic dielectric resonators,” ArXiv: physics/0308016 (2003)

Jacquod, P.R.J.

Justice, J.

B. Corbett, J. Justice, L. Considint, S. Walsh, and W.M. Kelly, “Low-threshold lasing in novel microdisk geometries,” IEEE Photonics Technol. Lett. 8, 855–857 (1996).
[Crossref]

Kelly, W.M.

B. Corbett, J. Justice, L. Considint, S. Walsh, and W.M. Kelly, “Low-threshold lasing in novel microdisk geometries,” IEEE Photonics Technol. Lett. 8, 855–857 (1996).
[Crossref]

Kipp, T.

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref] [PubMed]

Koch, P.M.

Kuhl, U.

Lemaitre, A.

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

Ma, Y.

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

Manin, L.

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

Narimanov, E. E.

Narimanov, E.E.

V.A. Podolskiy, E.E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proceedings of Nat. Acad. of Sci. 101, 10498–10500 (2004).
[Crossref]

Nöckel, J. U.

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997)
[Crossref]

J. U. Nöckel, A. D. Stone, G. Chen, H. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609–1611 (1996).
[Crossref]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

Pelouard, J. L.

Podolskiy, V.A.

V.A. Podolskiy, E.E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proceedings of Nat. Acad. of Sci. 101, 10498–10500 (2004).
[Crossref]

Prange, R. E.

S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett 49, 509–512 (1982).
[Crossref]

Qian, S.X.

S.X. Qian, J. Snow, H.M. Tzeng, and R.K. Chang, “Lasing droplets - highlighting the liquid-air interface by lasere-mission,” Science 231, 486–488 (1986).
[Crossref] [PubMed]

Ringor, J.

Rolf, L.

Schuller, C.

Schwefel, H.G.L.

H.E. Tureci, H.G.L. Schwefel, P. Jacquod, and A.D. Stone, “Modes of wave-chaotic dielectric resonators,” ArXiv: physics/0308016 (2003)

Shepelyansky, D.

G. Casati, I. Guarneri, and D. Shepelyansky, “Exponential photonic localization for the hydrogen atom in a monochromatic field,” Phys. Rev. A 36, 3501–3504 (1987).
[Crossref] [PubMed]

Shepelyansky, D.L.

K.M. Frahm and D.L. Shepelyansky, “Quantum localization in rough billiards,” Phys. Rev. Lett 78, 1440–1443 (1997).
[Crossref]

Sirko, L.

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

Smilansky, U.

E. Doron and U. Smilansky, “Chaotic spectroscopy,” Phys. Rev. Lett. 68, 1255–1258 (1992).
[Crossref] [PubMed]

Snow, J.

S.X. Qian, J. Snow, H.M. Tzeng, and R.K. Chang, “Lasing droplets - highlighting the liquid-air interface by lasere-mission,” Science 231, 486–488 (1986).
[Crossref] [PubMed]

Solomon, G.S.

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref] [PubMed]

Starykh, O.A.

Stöckmann, H.-J.

Stone, A. D.

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997)
[Crossref]

J. U. Nöckel, A. D. Stone, G. Chen, H. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609–1611 (1996).
[Crossref]

Stone, A.D.

H.E. Tureci, H.G.L. Schwefel, P. Jacquod, and A.D. Stone, “Modes of wave-chaotic dielectric resonators,” ArXiv: physics/0308016 (2003)

Szriftgiser, P.

Tureci, H.E.

H.E. Tureci, H.G.L. Schwefel, P. Jacquod, and A.D. Stone, “Modes of wave-chaotic dielectric resonators,” ArXiv: physics/0308016 (2003)

Tzeng, H.M.

S.X. Qian, J. Snow, H.M. Tzeng, and R.K. Chang, “Lasing droplets - highlighting the liquid-air interface by lasere-mission,” Science 231, 486–488 (1986).
[Crossref] [PubMed]

Vahala, K. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref] [PubMed]

Walsh, S.

B. Corbett, J. Justice, L. Considint, S. Walsh, and W.M. Kelly, “Low-threshold lasing in novel microdisk geometries,” IEEE Photonics Technol. Lett. 8, 855–857 (1996).
[Crossref]

Xiang, W.H.

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

Xu, J.Y.

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

Appl. Phys. Lett. (3)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[Crossref]

H. Cao, J.Y. Xu, W.H. Xiang, Y. Ma, S.-H. Chang, S. T. Ho, and G.S. Solomon, “Optically pumped InAs quantum dot microdisk lasers,” Appl. Phys. Lett. 76, 3519–3521 (2000).
[Crossref]

IEEE Photonics Technol. Lett. (2)

B. Corbett, J. Justice, L. Considint, S. Walsh, and W.M. Kelly, “Low-threshold lasing in novel microdisk geometries,” IEEE Photonics Technol. Lett. 8, 855–857 (1996).
[Crossref]

K. Djordjev, S. Choi, S. Choi, and P. Dapkus, “High-Q vertically coupled InP microdisk resonators,” IEEE Photonics Technol. Lett. 14, 331–333 (2002).
[Crossref]

J. Phys. A (1)

M. Berry, “Regular and irregular semiclassical wavefunctions,” J. Phys. A 10, 2083 (1977).
[Crossref]

Nature (2)

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997)
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref] [PubMed]

Opt. Lett. (1)

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Fig. 1. The typical ray trajectory in circular (a) and rough (b, c) resonators. The resonator geometry in (b) corresponds to the adiabatic regime (Κ ≈ 0.06), the geometry in (c) corresponds to the device studied in our experiments (Κ ≈ 0.2).

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Fig. 2. Top (a) and side (b) view SEM images of a GaAs microdisk on an Al_0.7Ga_0.3 pedestal.

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Fig. 3. (a) Spectrum of emission from the GaAs microdisk shown in Fig. 2. The incident pump power is 44μW. (b) The emission intensity and linewidth of the mode at 855.5nm as a function of the incident pump power.

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Fig. 4. The blue curve I and the inset I are the spectrum and near-field image taken when the bandpass filter is tuned to the mode at 855.5nm. The red curve II and the inset II are the spectrum and image taken when the bandpass filter is tuned away from any cavity resonance. The incident pump power is 44μW.

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Fig. 5. (a) Radial distribution of the emission intensity when the bandpass filter is tuned to the mode at 855.5nm. The incident pump powers are marked next to the curves. (b) The blue (red) curve represents the radial distribution of the laser emission (or amplified spontaneous emission) intensity obtained from the inset I (II) in Fig. 4.

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Fig. 6. (a) Two-dimensional spatial-spectral image of the emission from the microdisk in Fig. 2. The incident pump power is 44μW. (b) Blue (red) curve is the spectrum of emission collected from the edge (center) part of the disk, corresponding to the horizontal strip marked by 1 (2) in (a). (c) Blue (red) line represents the emission intensity distribution across the disk diameter inside the vertical strip marked by α (β) in (a).

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Fig. 7. Poincare surface of section (SOS) in (a) a circular microcavity and (b) the microdisk of rough boundary shown in Fig. 2. Note the chaotic dynamics in the fabricated microcavity.

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Fig. 8. (a) Angle-averaged radial structure of the mode obtained in numerical calculations (solid line) and in experiments (dots) (constant ASE background subtracted). the inset shows the real-space mode structure. (b) The angular-momentum distribution of the lasing mode obtained from our numerical simulations in logarithmic scale (dots) and its fit to exponential (solid lines).

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Equations (5)

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κ = {〈 {(\frac{d R}{d ϕ})}^{2} 〉}^{\frac{1}{2}}

κ ≪ \frac{λ}{R_{0}}

I_{r} (r) = \frac{1}{2 π} \int_{0}^{2 π} I (r, θ) d θ

ψ_{m} \propto \exp (- \frac{∣ m - m_{0} ∣}{l}),

κ ≪ \frac{1}{\sqrt{{n k R}_{0}}}