Abstract

We propose a deformed microcavity laser, where a high-Q mode group emits unidirectionally. The cavity comprises three circular arcs and one linear section. To minimize diffraction effects from the boundary, three circular arcs and one linear section are tangentially connected. By adjusting the sizes and the positions of the two sub-circular arcs, unidirectionality is maximized. In an experiment with an InP based InGaAsP semiconductor microcavity laser, a lasing mode group localized on aperiod-7 unstable periodic orbit emits unidirectionally. In our resonance calculation, a high-Q factor is confirmed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2017 (1)

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192 (2017).
[Crossref] [PubMed]

2016 (2)

I.-G. Lee, S.-M. Go, J.-H. Ryu, C.-H. Yi, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Unidirectional emission from a cardioid-shaped microcavity laser,” Opt. Express 24, 2253–2258 (2016).
[Crossref] [PubMed]

J. Kullig and J. Wiersig, “Frobenius–perron eigenstates in deformed microdisk cavities: non-hermitian physics and asymmetric backscattering in ray dynamics,” New J. Phys. 18, 015005 (2016).
[Crossref]

2015 (2)

H.-H. Yu, C.-H. Yi, and C.-M. Kim, “Mechanism of Q-spoiling in deformed optical microcavities,” Opt. Express 23, 11054–11062 (2015).
[Crossref] [PubMed]

T. Harayama and S. Shinohara, “Ray-wave correspondence in chaotic dielectric billiards,” Phys. Rev. E 92, 042916 (2015).
[Crossref]

2013 (1)

E. G. Altmann, J. S. Portela, and T. Tél, “Leaking chaotic systems,” Rev. Mod. Phys. 85, 869 (2013).
[Crossref]

2012 (2)

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
[PubMed]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369 (2012).
[Crossref]

2011 (2)

J. Lee, S. Rim, J. Cho, and C.-M. Kim, “Unidirectional resonance modes supported by secondary islands in a microcavity comprised of two half-ellipses,” Physical review A 83, 033815 (2011).
[Crossref]

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
[Crossref]

2010 (2)

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
[Crossref]

2009 (4)

C.-H. Yi, M.-W. Kim, and C.-M. Kim, “Lasing characteristics of a limaçon-shaped microcavity laser,” Appl. Phys. Lett. 95, 141107 (2009).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limaçon-shaped semiconductor microcavities,” Phys. Rev. A 80, 031801 (2009).
[Crossref]

E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79, 013830 (2009).
[Crossref]

2008 (4)

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[Crossref] [PubMed]

E. G. Altmann, T. Friedrich, A. Motter, H. Kantz, and A. Richter, “Prevalence of marginally unstable periodic orbits in chaotic billiards,” Phys. Rev. E 77, 016205 (2008).
[Crossref]

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591 (2008).
[Crossref] [PubMed]

2007 (1)

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref] [PubMed]

2006 (1)

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73, 031802 (2006).
[Crossref]

2004 (2)

2003 (4)

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside-outside duality for optical systems and beyond,” Europhysics Letters 62, 636 (2003).
[Crossref]

L. Zhang and E. Hu, “Lasing from InGaAs quantum dots in an injection microdisk,” Appl. Phys. Lett. 82, 319–321 (2003).
[Crossref]

G. Chern, H. Tureci, A. D. Stone, R. Chang, M. Kneissl, and N. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710–1712 (2003).
[Crossref]

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

2002 (2)

S. Spillane, T. Kippenberg, and K. Vahala, “Ultralow-threshold raman laser using a spherical dielectric microcavity,” Nature 415, 621 (2002).
[Crossref] [PubMed]

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5, 53 (2002).
[Crossref]

1998 (1)

C. Gmachl, F. Capasso, E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref] [PubMed]

1997 (1)

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

1996 (1)

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69, 2456–2458 (1996).
[Crossref]

1992 (1)

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

1980 (1)

R. Benner, P. Barber, J. Owen, and R. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

1961 (1)

C. Garrett, W. Kaiser, and W. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807 (1961).
[Crossref]

Altmann, E. G.

E. G. Altmann, J. S. Portela, and T. Tél, “Leaking chaotic systems,” Rev. Mod. Phys. 85, 869 (2013).
[Crossref]

E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79, 013830 (2009).
[Crossref]

E. G. Altmann, T. Friedrich, A. Motter, H. Kantz, and A. Richter, “Prevalence of marginally unstable periodic orbits in chaotic billiards,” Phys. Rev. E 77, 016205 (2008).
[Crossref]

Armani, A. M.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref] [PubMed]

Armani, D.

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

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591 (2008).
[Crossref] [PubMed]

Barber, P.

R. Benner, P. Barber, J. Owen, and R. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

Belkin, M. A.

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

Ben-Messaoud, T.

Benner, R.

R. Benner, P. Barber, J. Owen, and R. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

Bond, W.

C. Garrett, W. Kaiser, and W. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807 (1961).
[Crossref]

Campillo, A. J.

R. K. Chang and A. J. Campillo, Optical processes in microcavities(World scientific, 1996).
[Crossref]

Capasso, F.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

C. Gmachl, F. Capasso, E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref] [PubMed]

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69, 2456–2458 (1996).
[Crossref]

Chang, R.

G. Chern, H. Tureci, A. D. Stone, R. Chang, M. Kneissl, and N. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710–1712 (2003).
[Crossref]

R. Benner, P. Barber, J. Owen, and R. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

Chang, R. K.

Chen, D.-R.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
[Crossref]

Chen, T.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369 (2012).
[Crossref]

Chen, W.

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192 (2017).
[Crossref] [PubMed]

Chern, G.

G. Chern, H. Tureci, A. D. Stone, R. Chang, M. Kneissl, and N. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710–1712 (2003).
[Crossref]

Cho, A. Y.

C. Gmachl, F. Capasso, E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref] [PubMed]

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69, 2456–2458 (1996).
[Crossref]

Cho, J.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
[Crossref]

J. Lee, S. Rim, J. Cho, and C.-M. Kim, “Unidirectional resonance modes supported by secondary islands in a microcavity comprised of two half-ellipses,” Physical review A 83, 033815 (2011).
[Crossref]

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
[Crossref]

Cui, J.-M.

C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” arXiv preprint arXiv:0908.3531 (2009).

Diehl, L.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

Dong, C.-H.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
[PubMed]

C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” arXiv preprint arXiv:0908.3531 (2009).

Edamura, T.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

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A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
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A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
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X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
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C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” arXiv preprint arXiv:0908.3531 (2009).

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J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
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X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
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G. Chern, H. Tureci, A. D. Stone, R. Chang, M. Kneissl, and N. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710–1712 (2003).
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C. Garrett, W. Kaiser, and W. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807 (1961).
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Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
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C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
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E. G. Altmann, T. Friedrich, A. Motter, H. Kantz, and A. Richter, “Prevalence of marginally unstable periodic orbits in chaotic billiards,” Phys. Rev. E 77, 016205 (2008).
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I.-G. Lee, S.-M. Go, J.-H. Ryu, C.-H. Yi, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Unidirectional emission from a cardioid-shaped microcavity laser,” Opt. Express 24, 2253–2258 (2016).
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J. Lee, S. Rim, J. Cho, and C.-M. Kim, “Unidirectional resonance modes supported by secondary islands in a microcavity comprised of two half-ellipses,” Physical review A 83, 033815 (2011).
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C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
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C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
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M. Kurdoglyan, S.-Y. Lee, S. Rim, and C.-M. Kim, “Unidirectional lasing from a microcavity with a rounded isosceles triangle shape,” Opt. Lett. 29, 2758–2760 (2004).
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Kim, J. H.

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
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Kim, M.-W.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
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C.-H. Yi, M.-W. Kim, and C.-M. Kim, “Lasing characteristics of a limaçon-shaped microcavity laser,” Appl. Phys. Lett. 95, 141107 (2009).
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Kippenberg, T.

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925 (2003).
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S. Spillane, T. Kippenberg, and K. Vahala, “Ultralow-threshold raman laser using a spherical dielectric microcavity,” Nature 415, 621 (2002).
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G. Chern, H. Tureci, A. D. Stone, R. Chang, M. Kneissl, and N. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710–1712 (2003).
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Kulkarni, R. P.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
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Lee, H.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369 (2012).
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Lee, I.-G.

Lee, J.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
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J. Lee, S. Rim, J. Cho, and C.-M. Kim, “Unidirectional resonance modes supported by secondary islands in a microcavity comprised of two half-ellipses,” Physical review A 83, 033815 (2011).
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C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
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Lee, S. H.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
[Crossref]

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
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Lee, S.-Y.

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
[Crossref]

M. Kurdoglyan, S.-Y. Lee, S. Rim, and C.-M. Kim, “Unidirectional lasing from a microcavity with a rounded isosceles triangle shape,” Opt. Lett. 29, 2758–2760 (2004).
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S. McCall, A. Levi, R. Slusher, S. Pearton, and R. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
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X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
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Li, J.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369 (2012).
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J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
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X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
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S. McCall, A. Levi, R. Slusher, S. Pearton, and R. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
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S. McCall, A. Levi, R. Slusher, S. Pearton, and R. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
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E. G. Altmann, T. Friedrich, A. Motter, H. Kantz, and A. Richter, “Prevalence of marginally unstable periodic orbits in chaotic billiards,” Phys. Rev. E 77, 016205 (2008).
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C. Gmachl, F. Capasso, E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
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C. Gmachl, F. Capasso, E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
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J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45 (1997).
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Oh, K. R.

I.-G. Lee, S.-M. Go, J.-H. Ryu, C.-H. Yi, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Unidirectional emission from a cardioid-shaped microcavity laser,” Opt. Express 24, 2253–2258 (2016).
[Crossref] [PubMed]

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
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J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
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W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192 (2017).
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H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369 (2012).
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Pearton, S.

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

Pflügl, C.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
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E. G. Altmann, J. S. Portela, and T. Tél, “Leaking chaotic systems,” Rev. Mod. Phys. 85, 869 (2013).
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Richter, A.

E. G. Altmann, T. Friedrich, A. Motter, H. Kantz, and A. Richter, “Prevalence of marginally unstable periodic orbits in chaotic billiards,” Phys. Rev. E 77, 016205 (2008).
[Crossref]

Rim, S.

J. Lee, S. Rim, J. Cho, and C.-M. Kim, “Unidirectional resonance modes supported by secondary islands in a microcavity comprised of two half-ellipses,” Physical review A 83, 033815 (2011).
[Crossref]

C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
[Crossref]

M. Kurdoglyan, S.-Y. Lee, S. Rim, and C.-M. Kim, “Unidirectional lasing from a microcavity with a rounded isosceles triangle shape,” Opt. Lett. 29, 2758–2760 (2004).
[Crossref] [PubMed]

Ryu, J.-H.

Sasaki, T.

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limaçon-shaped semiconductor microcavities,” Phys. Rev. A 80, 031801 (2009).
[Crossref]

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M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside-outside duality for optical systems and beyond,” Europhysics Letters 62, 636 (2003).
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Schubert, R.

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside-outside duality for optical systems and beyond,” Europhysics Letters 62, 636 (2003).
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Shinohara, S.

T. Harayama and S. Shinohara, “Ray-wave correspondence in chaotic dielectric billiards,” Phys. Rev. E 92, 042916 (2015).
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S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limaçon-shaped semiconductor microcavities,” Phys. Rev. A 80, 031801 (2009).
[Crossref]

Sirtori, C.

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69, 2456–2458 (1996).
[Crossref]

Sivco, D. L.

C. Gmachl, F. Capasso, E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref] [PubMed]

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69, 2456–2458 (1996).
[Crossref]

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

Spillane, S.

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

S. Spillane, T. Kippenberg, and K. Vahala, “Ultralow-threshold raman laser using a spherical dielectric microcavity,” Nature 415, 621 (2002).
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H. G. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B 21, 923–934 (2004).
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G. Chern, H. Tureci, A. D. Stone, R. Chang, M. Kneissl, and N. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710–1712 (2003).
[Crossref]

C. Gmachl, F. Capasso, E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref] [PubMed]

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

Striccoli, M.

J. Faist, C. Gmachl, M. Striccoli, C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, “Quantum cascade disk lasers,” Appl. Phys. Lett. 69, 2456–2458 (1996).
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Sun, F.-W.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
[PubMed]

C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” arXiv preprint arXiv:0908.3531 (2009).

Tél, T.

E. G. Altmann, J. S. Portela, and T. Tél, “Leaking chaotic systems,” Rev. Mod. Phys. 85, 869 (2013).
[Crossref]

Tureci, H.

G. Chern, H. Tureci, A. D. Stone, R. Chang, M. Kneissl, and N. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710–1712 (2003).
[Crossref]

Tureci, H. E.

Unterhinninghofen, J.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

Vahala, K.

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

S. Spillane, T. Kippenberg, and K. Vahala, “Ultralow-threshold raman laser using a spherical dielectric microcavity,” Nature 415, 621 (2002).
[Crossref] [PubMed]

Vahala, K. J.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369 (2012).
[Crossref]

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref] [PubMed]

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591 (2008).
[Crossref] [PubMed]

Wang, Q. J.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

Wiersig, J.

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192 (2017).
[Crossref] [PubMed]

J. Kullig and J. Wiersig, “Frobenius–perron eigenstates in deformed microdisk cavities: non-hermitian physics and asymmetric backscattering in ray dynamics,” New J. Phys. 18, 015005 (2016).
[Crossref]

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
[Crossref]

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limaçon-shaped semiconductor microcavities,” Phys. Rev. A 80, 031801 (2009).
[Crossref]

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
[Crossref] [PubMed]

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73, 031802 (2006).
[Crossref]

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5, 53 (2002).
[Crossref]

Wu, X.-W.

C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” arXiv preprint arXiv:0908.3531 (2009).

Xiao, Y.-F.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
[PubMed]

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
[Crossref]

Yamanishi, M.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

Yan, C.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

Yang, K. Y.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369 (2012).
[Crossref]

Yang, L.

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192 (2017).
[Crossref] [PubMed]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
[PubMed]

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
[Crossref]

Yang, Y.

C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” arXiv preprint arXiv:0908.3531 (2009).

Yi, C.-H.

I.-G. Lee, S.-M. Go, J.-H. Ryu, C.-H. Yi, S.-B. Kim, K. R. Oh, and C.-M. Kim, “Unidirectional emission from a cardioid-shaped microcavity laser,” Opt. Express 24, 2253–2258 (2016).
[Crossref] [PubMed]

H.-H. Yu, C.-H. Yi, and C.-M. Kim, “Mechanism of Q-spoiling in deformed optical microcavities,” Opt. Express 23, 11054–11062 (2015).
[Crossref] [PubMed]

C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
[Crossref]

C.-H. Yi, M.-W. Kim, and C.-M. Kim, “Lasing characteristics of a limaçon-shaped microcavity laser,” Appl. Phys. Lett. 95, 141107 (2009).
[Crossref]

Yu, H.-H.

Yu, N.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
[Crossref]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
[Crossref]

Zhang, L.

L. Zhang and E. Hu, “Lasing from InGaAs quantum dots in an injection microdisk,” Appl. Phys. Lett. 82, 319–321 (2003).
[Crossref]

Zhao, G.

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192 (2017).
[Crossref] [PubMed]

Zhu, J.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
[Crossref]

Zou, C.-L.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
[PubMed]

C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” arXiv preprint arXiv:0908.3531 (2009).

Zyss, J.

Adv. Mater. (1)

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
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L. Zhang and E. Hu, “Lasing from InGaAs quantum dots in an injection microdisk,” Appl. Phys. Lett. 82, 319–321 (2003).
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C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflügl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94, 251101 (2009).
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C.-M. Kim, J. Cho, J. Lee, S. Rim, S. H. Lee, K. R. Oh, and J. H. Kim, “Continuous wave operation of a spiral-shaped microcavity laser,” Appl. Phys. Lett. 92, 131110 (2008).
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C.-H. Yi, M.-W. Kim, and C.-M. Kim, “Lasing characteristics of a limaçon-shaped microcavity laser,” Appl. Phys. Lett. 95, 141107 (2009).
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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 (2002).
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J. Opt. Soc. Am. B (1)

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591 (2008).
[Crossref] [PubMed]

Nat. Photonics (2)

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46 (2010).
[Crossref]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369 (2012).
[Crossref]

Nature (4)

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192 (2017).
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J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45 (1997).
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J. Kullig and J. Wiersig, “Frobenius–perron eigenstates in deformed microdisk cavities: non-hermitian physics and asymmetric backscattering in ray dynamics,” New J. Phys. 18, 015005 (2016).
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J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73, 031802 (2006).
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C.-H. Yi, S. H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A 84, 041803 (2011).
[Crossref]

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limaçon-shaped semiconductor microcavities,” Phys. Rev. A 80, 031801 (2009).
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Proceedings of the National Academy of Sciences (1)

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proceedings of the National Academy of Sciences 107, 22407–22412 (2010).
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A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
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C. Gmachl, F. Capasso, E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
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C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” arXiv preprint arXiv:0908.3531 (2009).

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Figures (6)

Fig. 1
Fig. 1 The design of the cavity and ray dynamics in Birkhoff coordinate. (a) is the shape of the cavity and (b) is the Poincaré surface of section. The thick black lines are marginally unstable periodic orbits. The seven big dots indicate the period-7 unstable periodic orbit, where the lasing modes are localized. The solid line at p = 0.96 indicates the outside region of the electrode of our laser and the dashed line at p = 1 / 3.3 is the critical line.
Fig. 2
Fig. 2 Scanning electron microscope image of (a) top and (b) side view. R and R in (a) are the radius of the microdisk and the p-contac electrode which are 50 μ m and 48 μ m, respectively. The p-contact electrode defines the area where the injection current is applied into the microdisk. The angle χ = sin 1 ( 48 / 50 = 0.96 ) in (a) is the lowest incident angle of rays traveling outside of the electrode area. In (b), the vertical lines mark the edge of the cavity and the electrode indicated by the arrows R and R in (a), and their gap 2 μ m is shown by the bidirectional arrow.
Fig. 3
Fig. 3 The emission characteristics of our laser. (a) is the emission intensity depending on the injection current, which shows the threshold around 35 mA which correspond to the lasing threshold current density 0.4835 kA / c m 2. (b) is the optical spectrum around 1570 nm at 60 mA injection current. There are four lasing modes belonging to a mode group localized on the period-7 unstable periodic orbit.
Fig. 4
Fig. 4 A resonance localized on the period-7 unstable periodic orbit. (a) is the even resonance, whose eigenvalue is Re ( n k R ) = 100.359 and Im ( n k R ) = 1.442 × 10 5. (b) is the Husimi function h ( s , p ) superimposed on the survival probability distribution. The main and the minor emission tongue are around s / s m a x = 0.4 and s / s m a x = 0.95, respectively. The Husimi function exhibits localization of the resonance on the period-7 unstable periodic orbit. Weak intensities around the tongues indicate the emission of the resonance by following the unstable manifolds of the chaotic saddle. The green polygonal line in (a) is superimposed on the resonance to guide eyes the period-7 unstable periodic orbit. (c) is the projection of the Husimi distribution on the p-axis. The arrows at p = 0.5 and p = 0.707 in (c) mark the period-3 and the period-4 MUPOs, respectively. In (b), the Husimi function intensity is in the color-bar scale above the figure while the intensity of the survival probability distribution of the background is in the gray-scale from white to black ranged as 0 to 1.
Fig. 5
Fig. 5 Far-field patterns. The black curve in (a) and (b) is the experimental data showing the divergence of Δ θ 26 . (a) is the far-field pattern of an odd resonance (blue) and an even resonance (red). The subemission angles are θ 20 and 60 . (b) is the ray dynamical far-field pattern (dashed blue), whose divergence angle is Δ θ 26 and the summation of the even and the odd resonance (dashed red). The ray dynamics and the summation of the field intensities exhibit subemission directions at around θ 20 and 60 . The inset in (a) illustrates the angle of far-field measurement.
Fig. 6
Fig. 6 Emission characteristics of rays depending on α. In (a), the emission direction difference is presented by circles and the full width at half maximum for total divergence is presented by triangles. The left, the center, and the right inset are the emission of rays at α = 10 , at 30 , and at 50 , respectively. (b) and (c) show the definitions of the emission direction difference D θ and the full width at half maximum Δ θ. Note that in the region α < 30 , the emission exhibit two lobes so that Δ θ does not give the exact meaning of the full width at half maximum.

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