Abstract

We numerically performed wave dynamical simulations based on the Maxwell–Bloch (MB) model for a quadrupole-deformed microcavity laser with spatially selective pumping. We demonstrate the appearance of an asymmetric lasing mode whose spatial pattern violates both the x- and y-axes mirror symmetries of the cavity. Dynamical simulations revealed that a lasing mode consisting of a clockwise or counterclockwise rotating-wave component is a stable stationary solution of the MB model. From the results of a passive-cavity mode analysis, we interpret these asymmetric rotating-wave lasing modes by the locking of four nearly degenerate passive-cavity modes. For comparison, we carried out simulations for a uniform pumping case and found a different locking rule for the nearly degenerate modes. Our results demonstrate a nonlinear dynamical mechanism for the formation of a lasing mode that adjusts its pattern to a pumped area.

© 2017 Chinese Laser Press

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References

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    [Crossref]
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  3. T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (2011).
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  4. H. Cao and J. Wiersig, “Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
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  5. X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
    [Crossref]
  6. J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
    [Crossref]
  7. J. Wiersig, J. Unterhinninghofen, Q. H. Song, H. Cao, M. Hentschel, and S. Shinohara, “Review on unidirectional light emission from ultralow-loss modes in deformed microdisks,” in Trends in Nano- and Micro-cavities, O. Kwon, B. Lee, and K. An, eds. (Bentham Books, 2011), pp. 109–152.
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    [Crossref]
  9. H. G. L. 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).
    [Crossref]
  10. S.-Y. Lee, J.-W. Ryu, T.-Y. Kwon, S. Rim, and C.-M. Kim, “Scarred resonances and steady probability distribution in a chaotic microcavity,” Phys. Rev. A 72, 061801(R) (2005).
    [Crossref]
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    [Crossref]
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    [Crossref]
  22. 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, 1710–1712 (2003).
    [Crossref]
  23. T. Fukushima and T. Harayama, “Stadium and quasi-stadium laser diodes,” IEEE J. Sel. Top. Quantum Electron. 10, 1039–1051 (2004).
    [Crossref]
  24. M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, “Control of directional emission in quasistadium microcavity laser diodes with two electrodes,” Appl. Phys. Lett. 88, 211110 (2006).
    [Crossref]
  25. S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043828 (2015).
    [Crossref]
  26. L. I. Deych, “Effects of spatial nonuniformity on laser dynamics,” Phys. Rev. Lett. 95, 043902 (2005).
    [Crossref]
  27. T.-Y. Kwon, S.-Y. Lee, M. S. Kurdoglyan, S. Rim, C.-M. Kim, and Y.-J. Park, “Lasing modes in a spiral-shaped dielectric microcavity,” Opt. Lett. 31, 1250–1252 (2006).
    [Crossref]
  28. L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: Generalization and analytic results,” Phys. Rev. A 82, 063824 (2010).
    [Crossref]
  29. L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
    [Crossref]
  30. L. Ge, “Selective excitation of lasing modes by controlling modal interactions,” Opt. Express 23, 30049–30056 (2015).
    [Crossref]
  31. T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
    [Crossref]
  32. S. Sunada, T. Harayama, and K. S. Ikeda, “Nonlinear whispering-gallery modes in a microellipse cavity,” Opt. Lett. 29, 718–720 (2004).
    [Crossref]
  33. S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in two-dimensional fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
    [Crossref]
  34. S. Shinohara, S. Sunada, T. Harayama, and K. S. Ikeda, “Mode expansion description of stadium-cavity laser dynamics,” Phys. Rev. E 71, 036203 (2005).
    [Crossref]

2016 (1)

X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[Crossref]

2015 (4)

N. L. Aung, L. Ge, O. Malik, H. E. Türeci, and C. F. Gmachl, “Threshold current reduction and directional emission of deformed microdisk lasers via spatially selective electrical pumping,” Appl. Phys. Lett. 107, 151106 (2015).
[Crossref]

H. Cao and J. Wiersig, “Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043828 (2015).
[Crossref]

L. Ge, “Selective excitation of lasing modes by controlling modal interactions,” Opt. Express 23, 30049–30056 (2015).
[Crossref]

2014 (1)

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

2011 (1)

T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (2011).
[Crossref]

2010 (3)

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]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: Generalization and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

2008 (1)

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

2006 (4)

S. Shinohara, T. Harayama, H. E. Türeci, and A. D. Stone, “Ray-wave correspondence in the nonlinear description of stadium-cavity lasers,” Phys. Rev. A 74, 033820 (2006).
[Crossref]

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, “Control of directional emission in quasistadium microcavity laser diodes with two electrodes,” Appl. Phys. Lett. 88, 211110 (2006).
[Crossref]

T.-Y. Kwon, S.-Y. Lee, M. S. Kurdoglyan, S. Rim, C.-M. Kim, and Y.-J. Park, “Lasing modes in a spiral-shaped dielectric microcavity,” Opt. Lett. 31, 1250–1252 (2006).
[Crossref]

2005 (6)

L. I. Deych, “Effects of spatial nonuniformity on laser dynamics,” Phys. Rev. Lett. 95, 043902 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in two-dimensional fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

S. Shinohara, S. Sunada, T. Harayama, and K. S. Ikeda, “Mode expansion description of stadium-cavity laser dynamics,” Phys. Rev. E 71, 036203 (2005).
[Crossref]

V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett. 30, 474–476 (2005).
[Crossref]

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

S.-Y. Lee, J.-W. Ryu, T.-Y. Kwon, S. Rim, and C.-M. Kim, “Scarred resonances and steady probability distribution in a chaotic microcavity,” Phys. Rev. A 72, 061801(R) (2005).
[Crossref]

2004 (3)

2003 (4)

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, 1710–1712 (2003).
[Crossref]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

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

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside–outside duality for optical systems and beyond,” Europhys. Lett. 62, 636–642 (2003).
[Crossref]

2002 (2)

1997 (1)

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

Aida, T.

An, K.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

Aung, N. L.

N. L. Aung, L. Ge, O. Malik, H. E. Türeci, and C. F. Gmachl, “Threshold current reduction and directional emission of deformed microdisk lasers via spatially selective electrical pumping,” Appl. Phys. Lett. 107, 151106 (2015).
[Crossref]

Ben-Messaoud, T.

Cao, H.

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043828 (2015).
[Crossref]

H. Cao and J. Wiersig, “Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

J. Wiersig, J. Unterhinninghofen, Q. H. Song, H. Cao, M. Hentschel, and S. Shinohara, “Review on unidirectional light emission from ultralow-loss modes in deformed microdisks,” in Trends in Nano- and Micro-cavities, O. Kwon, B. Lee, and K. An, eds. (Bentham Books, 2011), pp. 109–152.

Chang, R. K.

H. G. L. 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).
[Crossref]

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, 1710–1712 (2003).
[Crossref]

H. G. L. Schwefel, H. E. Tureci, A. D. Stone, and R. K. Chang, “Progress in asymmetric resonant cavities: Using shape as a design parameter in dielectric microcavity lasers,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004), pp. 415–495.

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, 1710–1712 (2003).
[Crossref]

Choi, M.

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, “Control of directional emission in quasistadium microcavity laser diodes with two electrodes,” Appl. Phys. Lett. 88, 211110 (2006).
[Crossref]

Chong, Y. D.

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: Generalization and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Collier, B.

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

Dao, T. T. A.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

Davis, P.

Deych, L. I.

L. I. Deych, “Effects of spatial nonuniformity on laser dynamics,” Phys. Rev. Lett. 95, 043902 (2005).
[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]

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, “Control of directional emission in quasistadium microcavity laser diodes with two electrodes,” Appl. Phys. Lett. 88, 211110 (2006).
[Crossref]

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

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

T. Fukushima, T. Harayama, P. Davis, P. O. Vaccaro, T. Nishimura, and T. Aida, “Ring and axis mode lasing in quasi-stadium laser diodes with concentric end mirrors,” Opt. Lett. 27, 1430–1432 (2002).
[Crossref]

Ge, L.

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043828 (2015).
[Crossref]

L. Ge, “Selective excitation of lasing modes by controlling modal interactions,” Opt. Express 23, 30049–30056 (2015).
[Crossref]

N. L. Aung, L. Ge, O. Malik, H. E. Türeci, and C. F. Gmachl, “Threshold current reduction and directional emission of deformed microdisk lasers via spatially selective electrical pumping,” Appl. Phys. Lett. 107, 151106 (2015).
[Crossref]

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: Generalization and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Gmachl, C. F.

N. L. Aung, L. Ge, O. Malik, H. E. Türeci, and C. F. Gmachl, “Threshold current reduction and directional emission of deformed microdisk lasers via spatially selective electrical pumping,” Appl. Phys. Lett. 107, 151106 (2015).
[Crossref]

Gong, Q.

X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[Crossref]

Harayama, T.

T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (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]

S. Shinohara, T. Harayama, H. E. Türeci, and A. D. Stone, “Ray-wave correspondence in the nonlinear description of stadium-cavity lasers,” Phys. Rev. A 74, 033820 (2006).
[Crossref]

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, “Control of directional emission in quasistadium microcavity laser diodes with two electrodes,” Appl. Phys. Lett. 88, 211110 (2006).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in two-dimensional fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

S. Shinohara, S. Sunada, T. Harayama, and K. S. Ikeda, “Mode expansion description of stadium-cavity laser dynamics,” Phys. Rev. E 71, 036203 (2005).
[Crossref]

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

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

S. Sunada, T. Harayama, and K. S. Ikeda, “Nonlinear whispering-gallery modes in a microellipse cavity,” Opt. Lett. 29, 718–720 (2004).
[Crossref]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

T. Fukushima, T. Harayama, P. Davis, P. O. Vaccaro, T. Nishimura, and T. Aida, “Ring and axis mode lasing in quasi-stadium laser diodes with concentric end mirrors,” Opt. Lett. 27, 1430–1432 (2002).
[Crossref]

Hentschel, M.

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]

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

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside–outside duality for optical systems and beyond,” Europhys. Lett. 62, 636–642 (2003).
[Crossref]

J. Wiersig, J. Unterhinninghofen, Q. H. Song, H. Cao, M. Hentschel, and S. Shinohara, “Review on unidirectional light emission from ultralow-loss modes in deformed microdisks,” in Trends in Nano- and Micro-cavities, O. Kwon, B. Lee, and K. An, eds. (Bentham Books, 2011), pp. 109–152.

Ikeda, K. S.

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

S. Shinohara, S. Sunada, T. Harayama, and K. S. Ikeda, “Mode expansion description of stadium-cavity laser dynamics,” Phys. Rev. E 71, 036203 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in two-dimensional fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Nonlinear whispering-gallery modes in a microellipse cavity,” Opt. Lett. 29, 718–720 (2004).
[Crossref]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

Jiang, X.-F.

X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[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, 1710–1712 (2003).
[Crossref]

Kim, C.-M.

T.-Y. Kwon, S.-Y. Lee, M. S. Kurdoglyan, S. Rim, C.-M. Kim, and Y.-J. Park, “Lasing modes in a spiral-shaped dielectric microcavity,” Opt. Lett. 31, 1250–1252 (2006).
[Crossref]

S.-Y. Lee, J.-W. Ryu, T.-Y. Kwon, S. Rim, and C.-M. Kim, “Scarred resonances and steady probability distribution in a chaotic microcavity,” Phys. Rev. A 72, 061801(R) (2005).
[Crossref]

Kim, S. W.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[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, 1710–1712 (2003).
[Crossref]

Kurdoglyan, M. S.

Kwon, T.-Y.

T.-Y. Kwon, S.-Y. Lee, M. S. Kurdoglyan, S. Rim, C.-M. Kim, and Y.-J. Park, “Lasing modes in a spiral-shaped dielectric microcavity,” Opt. Lett. 31, 1250–1252 (2006).
[Crossref]

S.-Y. Lee, J.-W. Ryu, T.-Y. Kwon, S. Rim, and C.-M. Kim, “Scarred resonances and steady probability distribution in a chaotic microcavity,” Phys. Rev. A 72, 061801(R) (2005).
[Crossref]

Lee, J.-H.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

Lee, S.-B.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

Lee, S.-Y.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

T.-Y. Kwon, S.-Y. Lee, M. S. Kurdoglyan, S. Rim, C.-M. Kim, and Y.-J. Park, “Lasing modes in a spiral-shaped dielectric microcavity,” Opt. Lett. 31, 1250–1252 (2006).
[Crossref]

S.-Y. Lee, J.-W. Ryu, T.-Y. Kwon, S. Rim, and C.-M. Kim, “Scarred resonances and steady probability distribution in a chaotic microcavity,” Phys. Rev. A 72, 061801(R) (2005).
[Crossref]

Liew, S. F.

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043828 (2015).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford University, 2000).

Malik, O.

N. L. Aung, L. Ge, O. Malik, H. E. Türeci, and C. F. Gmachl, “Threshold current reduction and directional emission of deformed microdisk lasers via spatially selective electrical pumping,” Appl. Phys. Lett. 107, 151106 (2015).
[Crossref]

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

Moon, S.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

Narimanov, E. E.

Nishimura, T.

Nöckel, J. U.

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

Park, Y.-J.

Podolskiy, V. A.

Redding, B.

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043828 (2015).
[Crossref]

Rex, N. B.

Rim, S.

T.-Y. Kwon, S.-Y. Lee, M. S. Kurdoglyan, S. Rim, C.-M. Kim, and Y.-J. Park, “Lasing modes in a spiral-shaped dielectric microcavity,” Opt. Lett. 31, 1250–1252 (2006).
[Crossref]

S.-Y. Lee, J.-W. Ryu, T.-Y. Kwon, S. Rim, and C.-M. Kim, “Scarred resonances and steady probability distribution in a chaotic microcavity,” Phys. Rev. A 72, 061801(R) (2005).
[Crossref]

Ryu, J.-W.

S.-Y. Lee, J.-W. Ryu, T.-Y. Kwon, S. Rim, and C.-M. Kim, “Scarred resonances and steady probability distribution in a chaotic microcavity,” Phys. Rev. A 72, 061801(R) (2005).
[Crossref]

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]

Schomerus, H.

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside–outside duality for optical systems and beyond,” Europhys. Lett. 62, 636–642 (2003).
[Crossref]

Schubert, R.

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside–outside duality for optical systems and beyond,” Europhys. Lett. 62, 636–642 (2003).
[Crossref]

Schwefel, H. G. L.

Shinohara, S.

T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (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]

S. Shinohara, T. Harayama, H. E. Türeci, and A. D. Stone, “Ray-wave correspondence in the nonlinear description of stadium-cavity lasers,” Phys. Rev. A 74, 033820 (2006).
[Crossref]

S. Shinohara, S. Sunada, T. Harayama, and K. S. Ikeda, “Mode expansion description of stadium-cavity laser dynamics,” Phys. Rev. E 71, 036203 (2005).
[Crossref]

J. Wiersig, J. Unterhinninghofen, Q. H. Song, H. Cao, M. Hentschel, and S. Shinohara, “Review on unidirectional light emission from ultralow-loss modes in deformed microdisks,” in Trends in Nano- and Micro-cavities, O. Kwon, B. Lee, and K. An, eds. (Bentham Books, 2011), pp. 109–152.

Solomon, G. S.

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043828 (2015).
[Crossref]

Song, Q. H.

J. Wiersig, J. Unterhinninghofen, Q. H. Song, H. Cao, M. Hentschel, and S. Shinohara, “Review on unidirectional light emission from ultralow-loss modes in deformed microdisks,” in Trends in Nano- and Micro-cavities, O. Kwon, B. Lee, and K. An, eds. (Bentham Books, 2011), pp. 109–152.

Stone, A. D.

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: Generalization and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

S. Shinohara, T. Harayama, H. E. Türeci, and A. D. Stone, “Ray-wave correspondence in the nonlinear description of stadium-cavity lasers,” Phys. Rev. A 74, 033820 (2006).
[Crossref]

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

H. G. L. 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).
[Crossref]

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, 1710–1712 (2003).
[Crossref]

T. E. Tureci, H. G. L. Schwefel, A. D. Stone, and E. E. Narimanov, “Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities,” Opt. Express 10, 752–776 (2002).
[Crossref]

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

H. G. L. Schwefel, H. E. Tureci, A. D. Stone, and R. K. Chang, “Progress in asymmetric resonant cavities: Using shape as a design parameter in dielectric microcavity lasers,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004), pp. 415–495.

Sunada, S.

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

S. Shinohara, S. Sunada, T. Harayama, and K. S. Ikeda, “Mode expansion description of stadium-cavity laser dynamics,” Phys. Rev. E 71, 036203 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in two-dimensional fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Nonlinear whispering-gallery modes in a microellipse cavity,” Opt. Lett. 29, 718–720 (2004).
[Crossref]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

Tanaka, T.

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, “Control of directional emission in quasistadium microcavity laser diodes with two electrodes,” Appl. Phys. Lett. 88, 211110 (2006).
[Crossref]

Tureci, H. E.

H. G. L. 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).
[Crossref]

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, 1710–1712 (2003).
[Crossref]

H. G. L. Schwefel, H. E. Tureci, A. D. Stone, and R. K. Chang, “Progress in asymmetric resonant cavities: Using shape as a design parameter in dielectric microcavity lasers,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004), pp. 415–495.

Tureci, T. E.

Türeci, H. E.

N. L. Aung, L. Ge, O. Malik, H. E. Türeci, and C. F. Gmachl, “Threshold current reduction and directional emission of deformed microdisk lasers via spatially selective electrical pumping,” Appl. Phys. Lett. 107, 151106 (2015).
[Crossref]

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

S. Shinohara, T. Harayama, H. E. Türeci, and A. D. Stone, “Ray-wave correspondence in the nonlinear description of stadium-cavity lasers,” Phys. Rev. A 74, 033820 (2006).
[Crossref]

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

Unterhinninghofen, J.

J. Wiersig, J. Unterhinninghofen, Q. H. Song, H. Cao, M. Hentschel, and S. Shinohara, “Review on unidirectional light emission from ultralow-loss modes in deformed microdisks,” in Trends in Nano- and Micro-cavities, O. Kwon, B. Lee, and K. An, eds. (Bentham Books, 2011), pp. 109–152.

Vaccaro, P. O.

Wang, L.

X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[Crossref]

Wiersig, J.

H. Cao and J. Wiersig, “Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

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

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

J. Wiersig, J. Unterhinninghofen, Q. H. Song, H. Cao, M. Hentschel, and S. Shinohara, “Review on unidirectional light emission from ultralow-loss modes in deformed microdisks,” in Trends in Nano- and Micro-cavities, O. Kwon, B. Lee, and K. An, eds. (Bentham Books, 2011), pp. 109–152.

Xiao, Y.-F.

X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[Crossref]

Yang, J.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

Zou, C.-L.

X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[Crossref]

Zyss, J.

Appl. Phys. Lett. (3)

N. L. Aung, L. Ge, O. Malik, H. E. Türeci, and C. F. Gmachl, “Threshold current reduction and directional emission of deformed microdisk lasers via spatially selective electrical pumping,” Appl. Phys. Lett. 107, 151106 (2015).
[Crossref]

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, 1710–1712 (2003).
[Crossref]

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, “Control of directional emission in quasistadium microcavity laser diodes with two electrodes,” Appl. Phys. Lett. 88, 211110 (2006).
[Crossref]

Europhys. Lett. (1)

M. Hentschel, H. Schomerus, and R. Schubert, “Husimi functions at dielectric interfaces: Inside–outside duality for optical systems and beyond,” Europhys. Lett. 62, 636–642 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

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

J. Opt. A (1)

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

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (2)

T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (2011).
[Crossref]

X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[Crossref]

Nat. Photonics (1)

L. Ge, O. Malik, and H. E. Türeci, “Enhancement of laser power-efficiency by control of spatial hole burning interactions,” Nat. Photonics 8, 871–875 (2014).
[Crossref]

Nature (1)

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

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (6)

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

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

S.-Y. Lee, J.-W. Ryu, T.-Y. Kwon, S. Rim, and C.-M. Kim, “Scarred resonances and steady probability distribution in a chaotic microcavity,” Phys. Rev. A 72, 061801(R) (2005).
[Crossref]

S. Shinohara, T. Harayama, H. E. Türeci, and A. D. Stone, “Ray-wave correspondence in the nonlinear description of stadium-cavity lasers,” Phys. Rev. A 74, 033820 (2006).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: Generalization and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

S. F. Liew, L. Ge, B. Redding, G. S. Solomon, and H. Cao, “Pump-controlled modal interactions in microdisk lasers,” Phys. Rev. A 91, 043828 (2015).
[Crossref]

Phys. Rev. E (2)

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in two-dimensional fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

S. Shinohara, S. Sunada, T. Harayama, and K. S. Ikeda, “Mode expansion description of stadium-cavity laser dynamics,” Phys. Rev. E 71, 036203 (2005).
[Crossref]

Phys. Rev. Lett. (5)

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

L. I. Deych, “Effects of spatial nonuniformity on laser dynamics,” Phys. Rev. Lett. 95, 043902 (2005).
[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]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett. 104, 243601 (2010).
[Crossref]

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

Rev. Mod. Phys. (1)

H. Cao and J. Wiersig, “Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

Other (3)

H. G. L. Schwefel, H. E. Tureci, A. D. Stone, and R. K. Chang, “Progress in asymmetric resonant cavities: Using shape as a design parameter in dielectric microcavity lasers,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004), pp. 415–495.

J. Wiersig, J. Unterhinninghofen, Q. H. Song, H. Cao, M. Hentschel, and S. Shinohara, “Review on unidirectional light emission from ultralow-loss modes in deformed microdisks,” in Trends in Nano- and Micro-cavities, O. Kwon, B. Lee, and K. An, eds. (Bentham Books, 2011), pp. 109–152.

R. Loudon, The Quantum Theory of Light (Oxford University, 2000).

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Figures (10)

Fig. 1.
Fig. 1. (a) Double-triangle orbits in the quadrupole-deformed cavity. (b) Spatial selective pumping (yellow region) along the upward-pointing triangle orbit (red lines).
Fig. 2.
Fig. 2. Intensity distributions of the resonant modes for a passive quadrupole-deformed cavity with refractive index 3.3. The modes are four nearly degenerate modes associated with the double-triangle orbits. The double-triangle orbits (red and green lines) are superposed, and the intensities outside the cavity are plotted in log scale. (a) Even–even mode with scaled frequency Reω/ω0=1.0008278. (b) Even–odd mode with Reω/ω0=0.999085. (c) Odd–even mode with Reω/ω0=0.999075. (d) Odd–odd mode with Reω/ω0=1.0008277.
Fig. 3.
Fig. 3. Phase space of the ray dynamics for the quadrupole-deformed cavity. The islands of stability corresponding to the upward-pointing and downward-pointing triangle orbits are indicated by red and green points, respectively. The critical line for total internal reflection is indicated by a line at sinϕ=1/3.3. Husimi distribution for the eo mode shown in Fig. 2(b) is superposed.
Fig. 4.
Fig. 4. Distribution of the complex eigenfrequencies ω scaled by ω0, where ω0 is the gain center parameter. The four nearly degenerate modes associated with the double-triangle orbits are encircled by a green circle (the ee and oo modes are almost on top of each other, and so are the eo and oe modes). The modes indicated by filled circles (•) have positive linear gain [i.e., satisfying Eq. (9)] for the selective pumping with W=1.0×103, whereas those indicated by crosses (×) do not satisfy Eq. (9).
Fig. 5.
Fig. 5. Electric field intensity distributions. (a) An initial condition for the MB model simulation. (b) Time-averaged pattern of the stationary lasing state of the MB model for the selective pumping case with W=1.0×103. The intensity outside the cavity is plotted in log scale. The boundary of the pumped area is indicated by yellow lines.
Fig. 6.
Fig. 6. Results of the MB model simulation for the selective pumping case with W=1.0×103. (a) Time evolution of the total light intensity inside the cavity. (b) Power spectrum of the electric field for the stationary lasing regime. The peak frequency is around ω/ω0=0.9988.
Fig. 7.
Fig. 7. Intensity distributions of the superpositions of the resonant-mode wave functions. The triangle orbit is indicated by red lines, and the intensities outside the cavities are plotted in log scale. (a) ξ=ψee+ψeo. (b) η=ψoe+ψoo. (c) ΨCW=ξ+iη=(ψee+ψeo)+i(ψoe+ψoo). (d) ΨCCW=ξiη=(ψee+ψeo)i(ψoe+ψoo).
Fig. 8.
Fig. 8. Results of the MB model simulation for the uniform pumping case with W=3.0×104. (a) Time evolution of the total light intensity inside the cavity. (b) Power spectrum of the electric field for the stationary lasing regime. The frequencies of the primary and secondary peaks are ω/ω00.9990 and ω/ω01.0012, respectively.
Fig. 9.
Fig. 9. Time-averaged pattern of the stationary lasing state of the MB model for the uniform pumping case with W=3.0×104. The intensity outside the cavity is plotted in log scale.
Fig. 10.
Fig. 10. Intensity distribution of the superpositions of the resonant-mode wave functions. (a) ψeo+iψoe. (b) ψee+iψoo. The intensities outside the cavity are plotted in log scale.

Equations (14)

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2t2(Ez+4πεPz)=c2n22Ez2βtEz,
Pz=N(ρ+ρ*)κ,
tρ=iω0ρiκWEzγρ,
tW=2iκEz(ρρ*)γ(WW),
r(θ)=r0[1+ϵcos(2θ)],
(2+n2ω2c2)ψ(x,y)=0,
ψab(x,y)=aψab(x,y),
ψab(x,y)=bψab(x,y),
2πNκ2Wn2γReωs(Reωsω0)2+γ2>Imωs+β,
W=WDdxdy|ψ(x,y)|2Θ(x,y)Ddxdy|ψ(x,y)|2,
ξψee+ψeo,
ηψoe+ψoo.
ΨCWξ+iη=(ψee+ψeo)+i(ψoe+ψoo),
ΨCCWξiη=(ψee+ψeo)i(ψoe+ψoo).

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