Abstract

Monochromaticity and directionality are two key characteristics of lasers. However, the combination of directional emission and single-mode operation is quite challenging, especially for the on-chip devices. Here we propose a microdisk laser with single-mode operation and directional emissions by exploiting the recent developments associated with parity-time (PT) symmetry. This is accomplished by introducing one-dimensional periodic gain and loss into a circular microdisk, which induces a coupling between whispering gallery modes with different radial numbers. The lowest threshold mode is selected at the positions with least initial wavelength difference. And the directional emissions are formed by the introduction of additional grating vectors by the periodic distribution of gain and loss regions. We believe this research will impact the practical applications of on-chip microdisk lasers.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
    [Crossref]
  5. A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38(9), L171–L176 (2005).
    [Crossref]
  6. Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  38. Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
    [Crossref] [PubMed]
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    [Crossref]
  40. L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
    [Crossref]
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    [Crossref] [PubMed]

2014 (6)

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
[Crossref] [PubMed]

L. Ge and A. D. Stone, “Parity-time symmetry breaking beyond one dimension: The role of degeneracy,” Phys. Rev. X 4(3), 031101 (2014).
[Crossref]

L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by Parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

2013 (2)

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

L. Ge, Q. H. Song, B. Redding, and H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87(2), 023833 (2013).
[Crossref]

2012 (3)

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(35), OP260 (2012).
[Crossref] [PubMed]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108(24), 243902 (2012).
[Crossref] [PubMed]

X. Tu, X. Wu, M. Li, L. Liu, and L. Xu, “Ultraviolet single-frequency coupled optofluidic ring resonator dye laser,” Opt. Express 20(18), 19996–20001 (2012).
[Crossref] [PubMed]

2011 (3)

P. Q. Liu, X. Wang, J. Y. Fan, and C. F. Gmachl, “Single-mode quantum cascade lasers based on a folded Fabry-Perot cavity,” Appl. Phys. Lett. 98(6), 061110 (2011).
[Crossref]

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023802 (2011).

2010 (4)

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref] [PubMed]

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

2009 (5)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80(4), 041807 (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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

Q. H. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavlength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009).
[Crossref]

Q. Song, L. Liu, and L. Xu, “Directional random-laser emission from Bragg gratings with irregular perturbation,” Opt. Lett. 34(3), 344–346 (2009).
[Crossref] [PubMed]

2008 (4)

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, “Directional emission InP/GaInAsP square-resonator microlasers,” Opt. Lett. 33(19), 2170–2172 (2008).
[Crossref] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008).
[Crossref] [PubMed]

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78(5), 053809 (2008).
[Crossref]

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100(3), 033901 (2008).
[Crossref] [PubMed]

2007 (2)

2005 (1)

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38(9), L171–L176 (2005).
[Crossref]

2004 (1)

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 (2004).
[Crossref]

2003 (1)

G. D. Chern, H. E. Türeci, 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(9), 1710–1712 (2003).
[Crossref]

2002 (1)

D. Lo, L. Shi, J. Wang, G. X. Zhang, and X. L. Zhu, “Zirconia and zirconia-organically modified silicate distributed feedback waveguide lasers tunable in the visible,” Appl. Phys. Lett. 81(15), 2707–2709 (2002).
[Crossref]

1998 (2)

C. Bender and S. Boettcher, “Real spectra of non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 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(6611), 45–47 (1997).
[Crossref]

1993 (1)

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62(6), 561–563 (1993).
[Crossref]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[Crossref]

Almeida, V. R.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Beere, H. E.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

Beltram, F.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

Bender, C.

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

C. Bender and S. Boettcher, “Real spectra of non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]

Bender, C. M.

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

Boettcher, S.

C. Bender and S. Boettcher, “Real spectra of non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]

Cao, H.

L. Ge, Q. H. Song, B. Redding, and H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87(2), 023833 (2013).
[Crossref]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108(24), 243902 (2012).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref] [PubMed]

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80(4), 041807 (2009).
[Crossref]

Q. H. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavlength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009).
[Crossref]

Capasso, F.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Chang, R. K.

G. D. Chern, H. E. Türeci, 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(9), 1710–1712 (2003).
[Crossref]

Che, K. J.

Chen, H.

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
[Crossref] [PubMed]

Chen, Y.-F.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Chern, G. D.

G. D. Chern, H. E. Türeci, 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(9), 1710–1712 (2003).
[Crossref]

Cho, A. Y.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Chong, Y. D.

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023802 (2011).

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref] [PubMed]

Christodoulides, D. N.

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008).
[Crossref] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007).
[Crossref] [PubMed]

Delgado, F.

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38(9), L171–L176 (2005).
[Crossref]

Diehl, L.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

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(35), OP260 (2012).
[Crossref] [PubMed]

Du, Y.

Edamura, T.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008).
[Crossref] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007).
[Crossref] [PubMed]

Faist, J.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Fan, J. Y.

P. Q. Liu, X. Wang, J. Y. Fan, and C. F. Gmachl, “Single-mode quantum cascade lasers based on a folded Fabry-Perot cavity,” Appl. Phys. Lett. 98(6), 061110 (2011).
[Crossref]

Fan, S. H.

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

Fan, Z. C.

Fang, W.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80(4), 041807 (2009).
[Crossref]

Fegadolli, W. S.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Feng, L.

L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by Parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Ge, L.

L. Ge and A. D. Stone, “Parity-time symmetry breaking beyond one dimension: The role of degeneracy,” Phys. Rev. X 4(3), 031101 (2014).
[Crossref]

L. Ge, Q. H. Song, B. Redding, and H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87(2), 023833 (2013).
[Crossref]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108(24), 243902 (2012).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023802 (2011).

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref] [PubMed]

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

Gianfreda, M.

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

Glass, J. L.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62(6), 561–563 (1993).
[Crossref]

Gmachl, C.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Gmachl, C. F.

P. Q. Liu, X. Wang, J. Y. Fan, and C. F. Gmachl, “Single-mode quantum cascade lasers based on a folded Fabry-Perot cavity,” Appl. Phys. Lett. 98(6), 061110 (2011).
[Crossref]

Gong, Q.

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(35), OP260 (2012).
[Crossref] [PubMed]

He, 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(35), OP260 (2012).
[Crossref] [PubMed]

Heinrich, M.

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

Hentschel, M.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100(3), 033901 (2008).
[Crossref] [PubMed]

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78(5), 053809 (2008).
[Crossref]

Ho, S. T.

Q. H. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavlength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009).
[Crossref]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80(4), 041807 (2009).
[Crossref]

Hodaei, H.

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

Huang, Y. Z.

Jiang, X. 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(35), OP260 (2012).
[Crossref] [PubMed]

Johnson, N. M.

G. D. Chern, H. E. Türeci, 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(9), 1710–1712 (2003).
[Crossref]

Kan, H.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

Khajavikhan, M.

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

Kim, G. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 (2004).
[Crossref]

Kim, S. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 (2004).
[Crossref]

Kim, S. K.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 (2004).
[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(5), 053809 (2008).
[Crossref]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Kneissl, M.

G. D. Chern, H. E. Türeci, 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(9), 1710–1712 (2003).
[Crossref]

Lee, Y. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 (2004).
[Crossref]

Lei, F. C.

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

Levi, A. F. J.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62(6), 561–563 (1993).
[Crossref]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[Crossref]

Li, B. B.

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(35), OP260 (2012).
[Crossref] [PubMed]

Li, H. Q.

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
[Crossref] [PubMed]

Li, J.

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
[Crossref] [PubMed]

Li, M.

Li, Y.

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(35), OP260 (2012).
[Crossref] [PubMed]

Liertzer, M.

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

Liu, B. Y.

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80(4), 041807 (2009).
[Crossref]

Liu, L.

Liu, P. Q.

P. Q. Liu, X. Wang, J. Y. Fan, and C. F. Gmachl, “Single-mode quantum cascade lasers based on a folded Fabry-Perot cavity,” Appl. Phys. Lett. 98(6), 061110 (2011).
[Crossref]

Lo, D.

D. Lo, L. Shi, J. Wang, G. X. Zhang, and X. L. Zhu, “Zirconia and zirconia-organically modified silicate distributed feedback waveguide lasers tunable in the visible,” Appl. Phys. Lett. 81(15), 2707–2709 (2002).
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Logan, R. A.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62(6), 561–563 (1993).
[Crossref]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[Crossref]

Long, G. L.

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
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Longhi, S.

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

Lu, M.-H.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Luo, X.

Ma, R.-M.

L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by Parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

Mahler, L.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008).
[Crossref] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007).
[Crossref] [PubMed]

McCall, S. L.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62(6), 561–563 (1993).
[Crossref]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[Crossref]

Miri, M. A.

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

Monifi, F.

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

Muga, J. G.

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38(9), L171–L176 (2005).
[Crossref]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008).
[Crossref] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007).
[Crossref] [PubMed]

Narimanov, E. E.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Nockel, J. U.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Nöckel, J. U.

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385(6611), 45–47 (1997).
[Crossref]

Nori, F.

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

Oliveira, J. E. B.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Özdemir, S. K.

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

Park, H. G.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 (2004).
[Crossref]

Pearton, S. J.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62(6), 561–563 (1993).
[Crossref]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[Crossref]

Peng, B.

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

Pflügl, C.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

Poon, A. W.

Redding, B.

L. Ge, Q. H. Song, B. Redding, and H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87(2), 023833 (2013).
[Crossref]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108(24), 243902 (2012).
[Crossref] [PubMed]

Ritchie, D. A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

Rotter, S.

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

Ruschhaupt, A.

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38(9), L171–L176 (2005).
[Crossref]

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Scherer, A.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Shi, L.

D. Lo, L. Shi, J. Wang, G. X. Zhang, and X. L. Zhu, “Zirconia and zirconia-organically modified silicate distributed feedback waveguide lasers tunable in the visible,” Appl. Phys. Lett. 81(15), 2707–2709 (2002).
[Crossref]

Shim, J. B.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

Shin, D. J.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 (2004).
[Crossref]

Sivco, D. L.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Slusher, R. E.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62(6), 561–563 (1993).
[Crossref]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[Crossref]

Solomon, G. S.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

Q. H. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavlength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009).
[Crossref]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80(4), 041807 (2009).
[Crossref]

Song, Q.

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108(24), 243902 (2012).
[Crossref] [PubMed]

Q. Song, L. Liu, and L. Xu, “Directional random-laser emission from Bragg gratings with irregular perturbation,” Opt. Lett. 34(3), 344–346 (2009).
[Crossref] [PubMed]

Song, Q. H.

L. Ge, Q. H. Song, B. Redding, and H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87(2), 023833 (2013).
[Crossref]

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80(4), 041807 (2009).
[Crossref]

Q. H. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavlength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009).
[Crossref]

Stone, A. D.

L. Ge and A. D. Stone, “Parity-time symmetry breaking beyond one dimension: The role of degeneracy,” Phys. Rev. X 4(3), 031101 (2014).
[Crossref]

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023802 (2011).

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref] [PubMed]

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

G. D. Chern, H. E. Türeci, 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(9), 1710–1712 (2003).
[Crossref]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385(6611), 45–47 (1997).
[Crossref]

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(35), OP260 (2012).
[Crossref] [PubMed]

Sun, Y.

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
[Crossref] [PubMed]

Tan, W.

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
[Crossref] [PubMed]

Tredicucci, A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

Tu, X.

Türeci, H. E.

G. D. Chern, H. E. Türeci, 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(9), 1710–1712 (2003).
[Crossref]

Unterhinninghofen, J.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

Walther, C.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

Wang, J.

D. Lo, L. Shi, J. Wang, G. X. Zhang, and X. L. Zhu, “Zirconia and zirconia-organically modified silicate distributed feedback waveguide lasers tunable in the visible,” Appl. Phys. Lett. 81(15), 2707–2709 (2002).
[Crossref]

Wang, Q. J.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

Wang, S. J.

Wang, X.

P. Q. Liu, X. Wang, J. Y. Fan, and C. F. Gmachl, “Single-mode quantum cascade lasers based on a folded Fabry-Perot cavity,” Appl. Phys. Lett. 98(6), 061110 (2011).
[Crossref]

Wang, Y.

L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by Parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

Wiersig, J.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78(5), 053809 (2008).
[Crossref]

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100(3), 033901 (2008).
[Crossref] [PubMed]

Witzigmann, B.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

Wong, Z. J.

L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by Parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

Wu, X.

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(35), OP260 (2012).
[Crossref] [PubMed]

Xu, L.

Xu, Y.-L.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Yamanishi, M.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

Yan, C.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

Yang, L.

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[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(35), OP260 (2012).
[Crossref] [PubMed]

Yang, Y. D.

Yilmaz, H.

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

Yu, N.

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

Zhang, G. X.

D. Lo, L. Shi, J. Wang, G. X. Zhang, and X. L. Zhu, “Zirconia and zirconia-organically modified silicate distributed feedback waveguide lasers tunable in the visible,” Appl. Phys. Lett. 81(15), 2707–2709 (2002).
[Crossref]

Zhang, X.

L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by Parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

Zhu, X. L.

D. Lo, L. Shi, J. Wang, G. X. Zhang, and X. L. Zhu, “Zirconia and zirconia-organically modified silicate distributed feedback waveguide lasers tunable in the visible,” Appl. Phys. Lett. 81(15), 2707–2709 (2002).
[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(35), OP260 (2012).
[Crossref] [PubMed]

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(35), OP260 (2012).
[Crossref] [PubMed]

Appl. Phys. Lett. (8)

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 behaviors from semiconductor lasers with limaçon-shaped microcavity,” Appl. Phys. Lett. 94(25), 251101 (2009).

P. Q. Liu, X. Wang, J. Y. Fan, and C. F. Gmachl, “Single-mode quantum cascade lasers based on a folded Fabry-Perot cavity,” Appl. Phys. Lett. 98(6), 061110 (2011).
[Crossref]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[Crossref]

Q. H. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavlength microdisk lasers,” Appl. Phys. Lett. 94(6), 061109 (2009).
[Crossref]

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 (2004).
[Crossref]

G. D. Chern, H. E. Türeci, 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(9), 1710–1712 (2003).
[Crossref]

D. Lo, L. Shi, J. Wang, G. X. Zhang, and X. L. Zhu, “Zirconia and zirconia-organically modified silicate distributed feedback waveguide lasers tunable in the visible,” Appl. Phys. Lett. 81(15), 2707–2709 (2002).
[Crossref]

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62(6), 561–563 (1993).
[Crossref]

J. Phys. A (1)

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38(9), L171–L176 (2005).
[Crossref]

Nat. Mater. (1)

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

Nat. Phys. (2)

B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. Bender, and L. Yang, “Parity-time-symmetric whispering gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Nature (1)

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385(6611), 45–47 (1997).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (5)

L. Ge, Q. H. Song, B. Redding, and H. Cao, “Extreme output sensitivity to subwavelength boundary deformation in microcavities,” Phys. Rev. A 87(2), 023833 (2013).
[Crossref]

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023802 (2011).

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A 80(4), 041807 (2009).
[Crossref]

J. Wiersig, S. W. Kim, and M. Hentschel, “Asymmetric scattering and nonorthogonal mode patterns in optical microspirals,” Phys. Rev. A 78(5), 053809 (2008).
[Crossref]

Phys. Rev. Lett. (8)

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100(3), 033901 (2008).
[Crossref] [PubMed]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108(24), 243902 (2012).
[Crossref] [PubMed]

Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112(14), 143903 (2014).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008).
[Crossref] [PubMed]

C. Bender and S. Boettcher, “Real spectra of non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J. Wiersig, J. B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon, “Directional laser emission from a wavelength-scale chaotic microcavity,” Phys. Rev. Lett. 105(10), 103902 (2010).
[Crossref] [PubMed]

Phys. Rev. X (1)

L. Ge and A. D. Stone, “Parity-time symmetry breaking beyond one dimension: The role of degeneracy,” Phys. Rev. X 4(3), 031101 (2014).
[Crossref]

Science (4)

L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by Parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 (1998).
[Crossref] [PubMed]

Other (3)

L. Ge and H. E. Türeci, “Inversed Vernier effect in coupled lasers,” arXiv:1503.04382 (2015).

M. Li, N. Zhang, K. Y. Wang, J. K. Li, S. M. Xiao, and Q. H. Song, “Inversed Vernier effect based single-mode laser emission in coupled microdisks,” arXiv: 1504.03436 (2015).

Z. Y. Gu, N. Zhang, Q. Lyu, M. Li, S. M. Xiao, and Q. H. Song, “Experimental demonstration of PT-symmetric stripe lasers,” arXiv: 1504.03937 (2015).

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Figures (4)

Fig. 1
Fig. 1 (a) and (b) shows the PT symmetric behaviors of real and imaginary parts of lasing and absorptive modes. (c) shows the field patterns of modes 1-6 marked in (a). Inset in (b) is the schematic picture of the gain and loss distribution. The position around modes 3 and 4 is defined as the bifurcating point, where the imaginary parts of two modes starts to bifurcate. The field distributions of two modes are dramatically changed after the bifurcating point.
Fig. 2
Fig. 2 (a) and (b) are the wavelength and (b) of mode at 938.6nm as a function of n”. Due to the larger wavelength difference, bifurcating point of lasing and absorptive modes shifts to larger n”. (c) The bifurcating point and wavelength detuning in passive cavity as a function of wavelength. (d) The β values of different resonances with n” = 0.005. It is easy to see that the mode at 919.8nm reaches the threshold first and always experiences the highest gain.
Fig. 3
Fig. 3 Far field patterns of lasing mode with n” = 0.000 (a), n” = 0.0017 (b), and n” = 0.009 (c). (d) shows the dependence of directionality U on n”. U is defined as (d). Here ϕFF and I(ϕFF) are the far field angle and its corresponding field intensity.
Fig. 4
Fig. 4 (a) The values of the same whispering gallery modes as Fig. 2(d). (b) The far field pattern of the mode at 919.8 nm. Here the imaginary part of refractive index n” is 0.007 and the period is increased to 4000 nm.

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