Abstract

We study spectral and far-field characteristics of lasing emission from stadium-shaped semiconductor (InGaAsP) microlasers. We demonstrate that the correspondence between a lasing far-field emission pattern and the result of a ray simulation becomes better as the number of lasing modes increases. This phenomenon is reproduced in the wave calculation of the cavity modes.

© 2008 Optical Society of America

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  1. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
    [Crossref] [PubMed]
  2. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
    [Crossref]
  3. H. G. L. Schwefel, H. E. Türeci, A. D. Stone, R. K. Chang, and K. Vahala“Progress in Asymmetric Resonant Cavities: Using Shape as a Design Parameter in Dielectric Microcavity Lasers,” in Optical Processes in Microcavities, K. Vahala ed. (World Scientific, Singapore, 2005), pp. 415–496.
  4. L. A. Bunimovich, “On the ergodic properties of nowhere dispersing billiards,” Commun. Math. Phys. 65, 295–312 (1977).
    [Crossref]
  5. T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
    [Crossref]
  6. S. Shinohara, T. Harayama, H. E. Türeci, A. D. Stone, S. Shinohara, and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
    [Crossref]
  7. S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A 77, 033807 (2008).
    [Crossref]
  8. T. Fukushima and T. Harayama, “Stadium and quasi-stadium laser diodes,” IEEE Sel. Top. Quantum Electron. 10, 1039–1051 (2004).
    [Crossref]
  9. W. Fang, H. Cao, and G. S. Solomon, “Control of lasing in fully chaotic open microcavities by tailoring the shape factor,” Appl. Phys. Lett. 90, 081108 (2007).
    [Crossref]
  10. H. -G. Park, F. Qian, C. J. Barrelet, and Y. Li, “Microstadium single-nanowire laser,” Appl. Phys. Lett. 91, 251115 (2007).
    [Crossref]
  11. M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
    [Crossref]
  12. T. Fukushima, T. Tanaka, and T. Harayama, “Ring and axis mode switching in multielectrode strained InGaAsP multiple-quantum-well quasistadium laser diodes,” Appl. Phys. Lett.,  87, 191103 (2005).
    [Crossref]
  13. J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5, 53–60 (2003).
    [Crossref]
  14. J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
    [Crossref]

2008 (1)

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A 77, 033807 (2008).
[Crossref]

2007 (3)

W. Fang, H. Cao, and G. S. Solomon, “Control of lasing in fully chaotic open microcavities by tailoring the shape factor,” Appl. Phys. Lett. 90, 081108 (2007).
[Crossref]

H. -G. Park, F. Qian, C. J. Barrelet, and Y. Li, “Microstadium single-nanowire laser,” Appl. Phys. Lett. 91, 251115 (2007).
[Crossref]

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

2005 (2)

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

T. Fukushima, T. Tanaka, and T. Harayama, “Ring and axis mode switching in multielectrode strained InGaAsP multiple-quantum-well quasistadium laser diodes,” Appl. Phys. Lett.,  87, 191103 (2005).
[Crossref]

2004 (1)

T. Fukushima and T. Harayama, “Stadium and quasi-stadium laser diodes,” IEEE Sel. Top. Quantum Electron. 10, 1039–1051 (2004).
[Crossref]

2003 (2)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5, 53–60 (2003).
[Crossref]

1997 (1)

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

1977 (1)

L. A. Bunimovich, “On the ergodic properties of nowhere dispersing billiards,” Commun. Math. Phys. 65, 295–312 (1977).
[Crossref]

An, K.

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

Barrelet, C. J.

H. -G. Park, F. Qian, C. J. Barrelet, and Y. Li, “Microstadium single-nanowire laser,” Appl. Phys. Lett. 91, 251115 (2007).
[Crossref]

Bogomolny, E.

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

Bunimovich, L. A.

L. A. Bunimovich, “On the ergodic properties of nowhere dispersing billiards,” Commun. Math. Phys. 65, 295–312 (1977).
[Crossref]

Cao, H.

W. Fang, H. Cao, and G. S. Solomon, “Control of lasing in fully chaotic open microcavities by tailoring the shape factor,” Appl. Phys. Lett. 90, 081108 (2007).
[Crossref]

Chang, R. K.

H. G. L. Schwefel, H. E. Türeci, A. D. Stone, R. K. Chang, and K. Vahala“Progress in Asymmetric Resonant Cavities: Using Shape as a Design Parameter in Dielectric Microcavity Lasers,” in Optical Processes in Microcavities, K. Vahala ed. (World Scientific, Singapore, 2005), pp. 415–496.

Fang, W.

W. Fang, H. Cao, and G. S. Solomon, “Control of lasing in fully chaotic open microcavities by tailoring the shape factor,” Appl. Phys. Lett. 90, 081108 (2007).
[Crossref]

Fukushima, T.

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A 77, 033807 (2008).
[Crossref]

T. Fukushima, T. Tanaka, and T. Harayama, “Ring and axis mode switching in multielectrode strained InGaAsP multiple-quantum-well quasistadium laser diodes,” Appl. Phys. Lett.,  87, 191103 (2005).
[Crossref]

T. Fukushima and T. Harayama, “Stadium and quasi-stadium laser diodes,” IEEE Sel. Top. Quantum Electron. 10, 1039–1051 (2004).
[Crossref]

Harayama, T.

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A 77, 033807 (2008).
[Crossref]

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

T. Fukushima, T. Tanaka, and T. Harayama, “Ring and axis mode switching in multielectrode strained InGaAsP multiple-quantum-well quasistadium laser diodes,” Appl. Phys. Lett.,  87, 191103 (2005).
[Crossref]

T. Fukushima and T. Harayama, “Stadium and quasi-stadium laser diodes,” IEEE Sel. Top. Quantum Electron. 10, 1039–1051 (2004).
[Crossref]

S. Shinohara, T. Harayama, H. E. Türeci, A. D. Stone, S. Shinohara, and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[Crossref]

S. Shinohara, T. Harayama, H. E. Türeci, A. D. Stone, S. Shinohara, and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[Crossref]

Hierle, R.

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

Ikeda, K. S.

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

Kim, S. W.

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

Lauret, J. S.

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

Lebental, M.

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

Lee, H.-W.

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

Lee, J.-H.

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

Lee, S.-B.

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

Li, Y.

H. -G. Park, F. Qian, C. J. Barrelet, and Y. Li, “Microstadium single-nanowire laser,” Appl. Phys. Lett. 91, 251115 (2007).
[Crossref]

Moon, S.

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[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]

Park, H. -G.

H. -G. Park, F. Qian, C. J. Barrelet, and Y. Li, “Microstadium single-nanowire laser,” Appl. Phys. Lett. 91, 251115 (2007).
[Crossref]

Qian, F.

H. -G. Park, F. Qian, C. J. Barrelet, and Y. Li, “Microstadium single-nanowire laser,” Appl. Phys. Lett. 91, 251115 (2007).
[Crossref]

Schmit, C.

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

Schwefel, H. G. L.

H. G. L. Schwefel, H. E. Türeci, A. D. Stone, R. K. Chang, and K. Vahala“Progress in Asymmetric Resonant Cavities: Using Shape as a Design Parameter in Dielectric Microcavity Lasers,” in Optical Processes in Microcavities, K. Vahala ed. (World Scientific, Singapore, 2005), pp. 415–496.

Shim, J.-B.

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

Shinohara, S.

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A 77, 033807 (2008).
[Crossref]

S. Shinohara, T. Harayama, H. E. Türeci, A. D. Stone, S. Shinohara, and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[Crossref]

S. Shinohara, T. Harayama, H. E. Türeci, A. D. Stone, S. Shinohara, and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[Crossref]

Solomon, G. S.

W. Fang, H. Cao, and G. S. Solomon, “Control of lasing in fully chaotic open microcavities by tailoring the shape factor,” Appl. Phys. Lett. 90, 081108 (2007).
[Crossref]

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]

H. G. L. Schwefel, H. E. Türeci, A. D. Stone, R. K. Chang, and K. Vahala“Progress in Asymmetric Resonant Cavities: Using Shape as a Design Parameter in Dielectric Microcavity Lasers,” in Optical Processes in Microcavities, K. Vahala ed. (World Scientific, Singapore, 2005), pp. 415–496.

S. Shinohara, T. Harayama, H. E. Türeci, A. D. Stone, S. Shinohara, and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[Crossref]

Sunada, S.

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

Tanaka, T.

T. Fukushima, T. Tanaka, and T. Harayama, “Ring and axis mode switching in multielectrode strained InGaAsP multiple-quantum-well quasistadium laser diodes,” Appl. Phys. Lett.,  87, 191103 (2005).
[Crossref]

Türeci, H. E.

S. Shinohara, T. Harayama, H. E. Türeci, A. D. Stone, S. Shinohara, and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[Crossref]

H. G. L. Schwefel, H. E. Türeci, A. D. Stone, R. K. Chang, and K. Vahala“Progress in Asymmetric Resonant Cavities: Using Shape as a Design Parameter in Dielectric Microcavity Lasers,” in Optical Processes in Microcavities, K. Vahala ed. (World Scientific, Singapore, 2005), pp. 415–496.

Vahala, K.

H. G. L. Schwefel, H. E. Türeci, A. D. Stone, R. K. Chang, and K. Vahala“Progress in Asymmetric Resonant Cavities: Using Shape as a Design Parameter in Dielectric Microcavity Lasers,” in Optical Processes in Microcavities, K. Vahala ed. (World Scientific, Singapore, 2005), pp. 415–496.

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

Wiersig, J.

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5, 53–60 (2003).
[Crossref]

Yang, J.

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

Zyss, J.

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

Appl. Phys. Lett. (3)

W. Fang, H. Cao, and G. S. Solomon, “Control of lasing in fully chaotic open microcavities by tailoring the shape factor,” Appl. Phys. Lett. 90, 081108 (2007).
[Crossref]

H. -G. Park, F. Qian, C. J. Barrelet, and Y. Li, “Microstadium single-nanowire laser,” Appl. Phys. Lett. 91, 251115 (2007).
[Crossref]

T. Fukushima, T. Tanaka, and T. Harayama, “Ring and axis mode switching in multielectrode strained InGaAsP multiple-quantum-well quasistadium laser diodes,” Appl. Phys. Lett.,  87, 191103 (2005).
[Crossref]

Commun. Math. Phys. (1)

L. A. Bunimovich, “On the ergodic properties of nowhere dispersing billiards,” Commun. Math. Phys. 65, 295–312 (1977).
[Crossref]

IEEE Sel. Top. Quantum Electron. (1)

T. Fukushima and T. Harayama, “Stadium and quasi-stadium laser diodes,” IEEE Sel. Top. Quantum Electron. 10, 1039–1051 (2004).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5, 53–60 (2003).
[Crossref]

J. Phys. Soc. Jpn. (1)

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, H.-W. Lee, and S. W. Kim, “Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity,” J. Phys. Soc. Jpn. 76, 114005 (2007).
[Crossref]

Nature (2)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

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

Phys. Rev. A (2)

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A 77, 033807 (2008).
[Crossref]

Other (3)

M. Lebental, J. S. Lauret, R. Hierle, J. Zyss, M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, “Directional emission of stadium-shaped microlasers,” Phys. Rev. A75, 033806 (2007).
[Crossref]

S. Shinohara, T. Harayama, H. E. Türeci, A. D. Stone, S. Shinohara, and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[Crossref]

H. G. L. Schwefel, H. E. Türeci, A. D. Stone, R. K. Chang, and K. Vahala“Progress in Asymmetric Resonant Cavities: Using Shape as a Design Parameter in Dielectric Microcavity Lasers,” in Optical Processes in Microcavities, K. Vahala ed. (World Scientific, Singapore, 2005), pp. 415–496.

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Figures (3)

Fig. 1.
Fig. 1.

Lasing spectra for the stadium-shaped InGaAsP microlaser. (a) Single-mode lasing at pumping current 90 mA. The inset shows the microscope image of the Bunimovich stadium. (b) Multi-mode lasing at 270 mA.

Fig. 2.
Fig. 2.

Far-field patterns for experiments (green curves in (a) and (b)) and for wave numerical simulations (green and black curves in (c), (d) and (e)). In (a)–(e), ray simulation data are plotted by a red broken curve. (a) Experimental single-mode lasing data for the pumping current 100 mA. (b) Experimental multi-mode lasing data for 270 mA. (c) Wave calculation data of a single cavity mode. (d) Wave calculation data of the average of 8 cavity modes. These wave calculations are performed for a cavity with R=15µm, which is the cavity size of our experiments. (e) Wave calculation data for a cavity with R=30µm, where the averaged far-field pattern for 8 cavity modes is plotted by a green curve, while that for 54 cavity modes is plotted by a black curve.

Fig. 3.
Fig. 3.

Far-field patterns for the 6 dominant lasing modes for the pumping current 270 mA. The data are measured by a monochromator. The labeling of the lasing modes corresponds to that in Fig. 1(b). The result of a ray simulation is plotted in dashed curves.

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