Abstract

Chirality of a resonance localized on an islands chain is studied in a deformed Reuleaux triangular-shaped microcavity, where clockwise and counter clockwise traveling rays are classically separated. A resonance localized on a period-5 islands chain exhibits chiral emission due to the asymmetric cavity shape. Chirality is experimentally proved in a InGaAsP multi-quantum-well semiconductor laser by showing that the experimental emission characteristics well coincide with the wave dynamical ones.

© 2017 Optical Society of America

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References

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  1. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710 (2003).
    [Crossref]
  2. J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators: Comment,” Opt. Express 16, 5874 (2008).
    [Crossref] [PubMed]
  3. S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
    [Crossref] [PubMed]
  4. J. Lee, S. Rim, J. Cho, and C. M. Kim, “Resonances near the classical separatrix of a weakly deformed circular microcavity,” Phys. Rev. Lett. 101, 064101 (2008).
    [Crossref] [PubMed]
  5. J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78, 053809 (2008).
    [Crossref]
  6. J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (2011).
    [Crossref]
  7. B. Gutkin, “Dynamical ‘breaking’ of time reversal symmetry,” J. Phys. A: Math. Theor. 40, F761 (2007).
    [Crossref]
  8. Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
    [Crossref]
  9. B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
    [Crossref] [PubMed]
  10. R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
    [Crossref] [PubMed]
  11. J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A. 84, 063828 (2011).
    [Crossref]
  12. M. Kim, K. Kwon, J. Shim, Y. Jung, and K. Yu, “Partially directional microdisk laser with two Rayleigh scatterers,” Opt. Lett. 39, 2423 (2014).
    [Crossref] [PubMed]
  13. J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112, 203901 (2014).
    [Crossref]
  14. W. D. Heiss and H. L. Harney, “The chirality of exceptional points,” Eur. Phys. J. D 17, 149 (2001).
    [Crossref]
  15. D. D. Scott and Y. N. Joglekar, “PT-symmetry breaking and ubiquitous maximal chirality in a PT-symmetric ring,” Phys. Rev. A 85, 062105 (2012).
    [Crossref]
  16. M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys. 75, 246 (1981)
    [Crossref]
  17. D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274 (2001).
    [Crossref] [PubMed]
  18. S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
    [Crossref] [PubMed]
  19. M.-W. Kim, S. Rim, C.-H. Yi, and C.-M. Kim, “Chaos-assisted tunneling in a deformed microcavity laser,” Opt. Express 21, 32508 (2013).
    [Crossref]
  20. J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5, 53 (2003).
    [Crossref]
  21. 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]
  22. 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(R) (2011).
    [Crossref]

2015 (1)

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref] [PubMed]

2014 (3)

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112, 203901 (2014).
[Crossref]

M. Kim, K. Kwon, J. Shim, Y. Jung, and K. Yu, “Partially directional microdisk laser with two Rayleigh scatterers,” Opt. Lett. 39, 2423 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (2)

D. D. Scott and Y. N. Joglekar, “PT-symmetry breaking and ubiquitous maximal chirality in a PT-symmetric ring,” Phys. Rev. A 85, 062105 (2012).
[Crossref]

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

2011 (3)

J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A. 84, 063828 (2011).
[Crossref]

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (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(R) (2011).
[Crossref]

2010 (1)

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
[Crossref] [PubMed]

2009 (1)

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]

2008 (3)

J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators: Comment,” Opt. Express 16, 5874 (2008).
[Crossref] [PubMed]

J. Lee, S. Rim, J. Cho, and C. M. Kim, “Resonances near the classical separatrix of a weakly deformed circular microcavity,” Phys. Rev. Lett. 101, 064101 (2008).
[Crossref] [PubMed]

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78, 053809 (2008).
[Crossref]

2007 (1)

B. Gutkin, “Dynamical ‘breaking’ of time reversal symmetry,” J. Phys. A: Math. Theor. 40, F761 (2007).
[Crossref]

2004 (1)

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref] [PubMed]

2003 (2)

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

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

2001 (2)

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274 (2001).
[Crossref] [PubMed]

W. D. Heiss and H. L. Harney, “The chirality of exceptional points,” Eur. Phys. J. D 17, 149 (2001).
[Crossref]

1981 (1)

M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys. 75, 246 (1981)
[Crossref]

Cao, H.

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref] [PubMed]

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

Chang, R. K.

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

Chen, Z.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83, 1710 (2003).
[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(R) (2011).
[Crossref]

J. Lee, S. Rim, J. Cho, and C. M. Kim, “Resonances near the classical separatrix of a weakly deformed circular microcavity,” Phys. Rev. Lett. 101, 064101 (2008).
[Crossref] [PubMed]

Choi, M.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref] [PubMed]

Davis, M. J.

M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys. 75, 246 (1981)
[Crossref]

Eberspächer, A.

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (2011).
[Crossref]

Fukushima, T.

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
[Crossref] [PubMed]

Ge, L.

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref] [PubMed]

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

Gu, Z.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Gutkin, B.

B. Gutkin, “Dynamical ‘breaking’ of time reversal symmetry,” J. Phys. A: Math. Theor. 40, F761 (2007).
[Crossref]

Harayama, T.

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
[Crossref] [PubMed]

Harney, H. L.

W. D. Heiss and H. L. Harney, “The chirality of exceptional points,” Eur. Phys. J. D 17, 149 (2001).
[Crossref]

Heiss, W. D.

W. D. Heiss and H. L. Harney, “The chirality of exceptional points,” Eur. Phys. J. D 17, 149 (2001).
[Crossref]

Heller, E. J.

M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys. 75, 246 (1981)
[Crossref]

Hentschel, M.

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (2011).
[Crossref]

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
[Crossref] [PubMed]

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78, 053809 (2008).
[Crossref]

Joglekar, Y. N.

D. D. Scott and Y. N. Joglekar, “PT-symmetry breaking and ubiquitous maximal chirality in a PT-symmetric ring,” Phys. Rev. A 85, 062105 (2012).
[Crossref]

Johnson, N. M.

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

Jung, Y.

Kim, C. M.

J. Lee, S. Rim, J. Cho, and C. M. Kim, “Resonances near the classical separatrix of a weakly deformed circular microcavity,” Phys. Rev. Lett. 101, 064101 (2008).
[Crossref] [PubMed]

Kim, C.-M.

M.-W. Kim, S. Rim, C.-H. Yi, and C.-M. Kim, “Chaos-assisted tunneling in a deformed microcavity laser,” Opt. Express 21, 32508 (2013).
[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(R) (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]

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref] [PubMed]

Kim, M.

Kim, M.-W.

M.-W. Kim, S. Rim, C.-H. Yi, and C.-M. Kim, “Chaos-assisted tunneling in a deformed microcavity laser,” Opt. Express 21, 32508 (2013).
[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(R) (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]

Kim, S. W.

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78, 053809 (2008).
[Crossref]

Kneissl, M.

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

Kwon, K.

Kwon, T.-Y.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref] [PubMed]

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(R) (2011).
[Crossref]

J. Lee, S. Rim, J. Cho, and C. M. Kim, “Resonances near the classical separatrix of a weakly deformed circular microcavity,” Phys. Rev. Lett. 101, 064101 (2008).
[Crossref] [PubMed]

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(R) (2011).
[Crossref]

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(R) (2011).
[Crossref]

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref] [PubMed]

Li, M.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Liu, S.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Narimanov, E. E.

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
[Crossref] [PubMed]

Oskay, W. H.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274 (2001).
[Crossref] [PubMed]

Raizen, M. G.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274 (2001).
[Crossref] [PubMed]

Redding, B.

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

Rim, S.

M.-W. Kim, S. Rim, C.-H. Yi, and C.-M. Kim, “Chaos-assisted tunneling in a deformed microcavity laser,” Opt. Express 21, 32508 (2013).
[Crossref]

J. Lee, S. Rim, J. Cho, and C. M. Kim, “Resonances near the classical separatrix of a weakly deformed circular microcavity,” Phys. Rev. Lett. 101, 064101 (2008).
[Crossref] [PubMed]

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref] [PubMed]

Ryu, J. W.

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (2011).
[Crossref]

Ryu, J.-W.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref] [PubMed]

Sarma, R.

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref] [PubMed]

Sasaki, T.

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
[Crossref] [PubMed]

Schomerus, H.

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (2011).
[Crossref]

Scott, D. D.

D. D. Scott and Y. N. Joglekar, “PT-symmetry breaking and ubiquitous maximal chirality in a PT-symmetric ring,” Phys. Rev. A 85, 062105 (2012).
[Crossref]

Shim, J.

Shim, J. B.

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (2011).
[Crossref]

Shinohara, S.

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (2011).
[Crossref]

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
[Crossref] [PubMed]

Solomon, G. S.

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

Song, Q.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

Steck, D. A.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274 (2001).
[Crossref] [PubMed]

Stone, A. D.

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

Sun, S.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Tureci, H. E.

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

Wang, K.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Wiersig, J.

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref] [PubMed]

J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112, 203901 (2014).
[Crossref]

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (2011).
[Crossref]

J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A. 84, 063828 (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(R) (2011).
[Crossref]

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78, 053809 (2008).
[Crossref]

J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators: Comment,” Opt. Express 16, 5874 (2008).
[Crossref] [PubMed]

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

Xiao, S.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Yi, C.-H.

M.-W. Kim, S. Rim, C.-H. Yi, and C.-M. Kim, “Chaos-assisted tunneling in a deformed microcavity laser,” Opt. Express 21, 32508 (2013).
[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(R) (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, K.

Zhai, H.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Zhang, N.

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Appl. Phys. Lett. (2)

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

Eur. Phys. J. D (1)

W. D. Heiss and H. L. Harney, “The chirality of exceptional points,” Eur. Phys. J. D 17, 149 (2001).
[Crossref]

J. Chem. Phys. (1)

M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys. 75, 246 (1981)
[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 (2003).
[Crossref]

J. Phys. A: Math. Theor. (1)

B. Gutkin, “Dynamical ‘breaking’ of time reversal symmetry,” J. Phys. A: Math. Theor. 40, F761 (2007).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (4)

D. D. Scott and Y. N. Joglekar, “PT-symmetry breaking and ubiquitous maximal chirality in a PT-symmetric ring,” Phys. Rev. A 85, 062105 (2012).
[Crossref]

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78, 053809 (2008).
[Crossref]

J. Wiersig, A. Eberspächer, J. B. Shim, J. W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus, “Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities,” Phys. Rev. A 84, 023845 (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(R) (2011).
[Crossref]

Phys. Rev. A. (1)

J. Wiersig, “Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles,” Phys. Rev. A. 84, 063828 (2011).
[Crossref]

Phys. Rev. Lett. (6)

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104, 163902 (2010).
[Crossref] [PubMed]

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref] [PubMed]

J. Lee, S. Rim, J. Cho, and C. M. Kim, “Resonances near the classical separatrix of a weakly deformed circular microcavity,” Phys. Rev. Lett. 101, 064101 (2008).
[Crossref] [PubMed]

J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112, 203901 (2014).
[Crossref]

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref] [PubMed]

Sci. Rep. (1)

Q. Song, N. Zhang, H. Zhai, S. Liu, Z. Gu, K. Wang, S. Sun, Z. Chen, M. Li, and S. Xiao, “The combination of high Q factor and chirality in twin cavities and microcavity chain,” Sci. Rep. 4, 06493 (2014).
[Crossref]

Science (1)

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274 (2001).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 The shape of a microcavity and the positons of resonances. (a) is the shape of a microcavity according to Eq. (1). (b) is a fabricated laser. (c) is the positions of resonances. The red big dots are resonances localized on a period-5 islands chain. The inset is the resonance positions around A, which shows a pair of resonances. In (a), l is the reflection position on the boundary from x-axis, and χ is the incident angle.
Fig. 2
Fig. 2 Emission of a resonance localized on a period-5 islands chain. (a) is the angular momentum distribution for |αm|2 versus m. The inner (two red dashed curves) and the outer (two blue solid curves) distributions are the spatial modal distribution outside and inside of the cavity, respectively. (b) is the resonance localized on a period-5 islands chain. (c) and (d) are the CCW and the CW propagating wave, respectively. (e) is the FFP of the resonance. (f) and (g) are the FFP of the CCW and the CW propagating wave, respectively.
Fig. 3
Fig. 3 Husimi function and the classical trajectories on Birkhoff coordinate. (a) is the Husimi function superimposed on classical trajectories. (b) and (c) are the enlarged structures of two corresponding islands, which are marked by A and C in (a), respectively. The insets show islands of a period-5 periodic orbit. D and E are the main emission directions of the CCW and the CW propagating wave, respectively. Here, S = l/L.
Fig. 4
Fig. 4 Experimental results in our microcavity laser. (a) is the FFP at the injection current of 35 mA. The black and the red curve are the resonance and the experimental FFP, respectively. (b) and (c) are the optical spectrum of directions A and B, respectively. A and B are the CCW and the CW propagating wave.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

r 1 = r 0 ( 1 + ) , r 2 = r 1 r 0 sin θ 1 sin ( π θ 1 θ 2 ) , r 3 = r 2 + r 0 sin θ 2 sin ( π θ 1 θ 2 ) , r 4 = r 0 + r 3 r 1 , r 5 = r 0 + r 3 r 2 ,
ψ in ( r , ϕ ) = m = α m J m ( n in k r ) exp ( i m ϕ ) ,
ψ out ( r , ϕ ) = m = α m H m ( 1 ) ( n out k r ) exp ( i m ϕ ) ,
α = 1 min { inf 1 | α m | 2 , 1 inf | α m | 2 } max { inf 1 | α m | 2 , 1 inf | α m | 2 }
L = 1 N 1 i = 1 N 1 { ( λ i + λ i + 1 ) / 2 } 2 n g ( λ i + 1 λ i ) ,

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