Abstract

We develop an electromagnetic (EM) simulation method based on a finite-element method (FEM) for an exciton confined to a semiconductor nanostructure. The EM field inside the semiconductor excites two transverse exciton polariton and a single longitudinal exciton at a given frequency. Established EM simulation methods cannot be applied directly to semiconductor nanostructures because of this multimode excitation; however, the present method overcomes this difficulty by introducing an additional boundary condition. To avoid spurious solutions and enhance the precision, we propose a hybrid edge–nodal element formulation in which edge and nodal elements are employed to represent the transverse and longitudinal polarizations, respectively. We apply the developed method to the EM-field scattering and distributions of exciton polarizations of spherical and hexagonal-disk quantum dots.

© 2014 Optical Society of America

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References

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  1. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [Crossref]
  2. J.-M. Jin, The Finite Element Method in Electromagnetics (John Wiley, 2002).
  3. P. K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science (McGraw-Hill, 1981).
  4. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [Crossref] [PubMed]
  5. Y. Mizumoto and H. Ishihara, “Theory of resonant radiation force exerted on single organic molecules near metallic nanogap,” Proc. SPIE 8097, 80971C (2011).
    [Crossref]
  6. M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
    [Crossref]
  7. S. Uryu, H. Ajiki, and H. Ishihara, “Model of finite-momentum excitons driven by surface plasmons in photoexcited carbon nanotubes covered by gold metal films,” Phys. Rev. Lett. 110, 257401 (2013).
    [Crossref] [PubMed]
  8. H. Ajiki, “Calculation method for exciton wavefunctions with electron–hole exchange interaction: Application to carbon nanotubes,” J. Phys. Soc. Jpn. 82, 4701 (2013).
    [Crossref]
  9. S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958).
  10. J. Birman, E. Rashba, and M. Sturge, Excitons (North-Holland, 1982).
  11. V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons (Springer, 1984).
    [Crossref]
  12. A. d’Andrea and R. Del Sole, “Wannier-mott excitons in semi-infinite crystals: Wave functions and normal-incidence reflectivity,” Phys. Rev. B 25, 3714–3730 (1982).
    [Crossref]
  13. P. Halevi and R. Fuchs, “Generalized additional boundary condition for non-local dielectrics. I. Reflectivity,” J. Phys. C Sol. Stat. Phys. 17, 3869–3888 (1984).
    [Crossref]
  14. K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
    [Crossref]
  15. K. Cho, “Nonlocal theory of radiation-matter interaction: Boundary-condition-less treatment of Maxwell equations,” Prog. Theor. Phys. Suppl. 106, 225–233 (1991).
    [Crossref]
  16. K. Cho, Optical Response of Nanostructures: Microscopic Nonlocal Theory (Springer, 2003).
    [Crossref]
  17. Y. Sun, H. Ajiki, and G. Bao, “Computational modeling of optical response from excitons in a nano optical medium,” Commun. Comput. Phys. 4, 1051–1068 (2008).
  18. H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
    [Crossref]
  19. K. Cho and H. Ishihara, “ABC-theory of an exciton-polariton in a slab,” J. Phys. Soc. Jpn. 59, 754–764 (1990).
    [Crossref]
  20. J. Lagois, “Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23, 5511 (1981).
    [Crossref]
  21. M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
    [Crossref]
  22. A. Bossavit, “A rationale for ‘edge-elements’ in 3-D fields computations,” IEEE Trans. Mag. 24, 74–79 (1988).
    [Crossref]
  23. A. Bossavit, “Solving Maxwell equations in a closed cavity, and the question of ‘spurious modes’,” IEEE Trans. Mag. 26, 702–705 (1990).
    [Crossref]
  24. R. Ruppin, “Optical absorption by excitons in microcrystals,” J. Phys. Chem. Solids 50, 877–882 (1989).
    [Crossref]
  25. A. Ekimov, A. L. Efros, and A. Onushchenko, “Quantum size effect in semiconductor microcrystals,” Solid State Commun. 56, 921–924 (1985).
    [Crossref]
  26. K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
    [Crossref]
  27. Z. Tang, G. K. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett. 72, 3270–3272 (1998).
    [Crossref]

2013 (3)

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

S. Uryu, H. Ajiki, and H. Ishihara, “Model of finite-momentum excitons driven by surface plasmons in photoexcited carbon nanotubes covered by gold metal films,” Phys. Rev. Lett. 110, 257401 (2013).
[Crossref] [PubMed]

H. Ajiki, “Calculation method for exciton wavefunctions with electron–hole exchange interaction: Application to carbon nanotubes,” J. Phys. Soc. Jpn. 82, 4701 (2013).
[Crossref]

2011 (1)

Y. Mizumoto and H. Ishihara, “Theory of resonant radiation force exerted on single organic molecules near metallic nanogap,” Proc. SPIE 8097, 80971C (2011).
[Crossref]

2008 (1)

Y. Sun, H. Ajiki, and G. Bao, “Computational modeling of optical response from excitons in a nano optical medium,” Commun. Comput. Phys. 4, 1051–1068 (2008).

2006 (1)

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

2003 (1)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

2002 (1)

M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
[Crossref]

2000 (1)

H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
[Crossref]

1998 (1)

Z. Tang, G. K. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett. 72, 3270–3272 (1998).
[Crossref]

1991 (1)

K. Cho, “Nonlocal theory of radiation-matter interaction: Boundary-condition-less treatment of Maxwell equations,” Prog. Theor. Phys. Suppl. 106, 225–233 (1991).
[Crossref]

1990 (2)

A. Bossavit, “Solving Maxwell equations in a closed cavity, and the question of ‘spurious modes’,” IEEE Trans. Mag. 26, 702–705 (1990).
[Crossref]

K. Cho and H. Ishihara, “ABC-theory of an exciton-polariton in a slab,” J. Phys. Soc. Jpn. 59, 754–764 (1990).
[Crossref]

1989 (1)

R. Ruppin, “Optical absorption by excitons in microcrystals,” J. Phys. Chem. Solids 50, 877–882 (1989).
[Crossref]

1988 (1)

A. Bossavit, “A rationale for ‘edge-elements’ in 3-D fields computations,” IEEE Trans. Mag. 24, 74–79 (1988).
[Crossref]

1985 (2)

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[Crossref]

A. Ekimov, A. L. Efros, and A. Onushchenko, “Quantum size effect in semiconductor microcrystals,” Solid State Commun. 56, 921–924 (1985).
[Crossref]

1984 (1)

P. Halevi and R. Fuchs, “Generalized additional boundary condition for non-local dielectrics. I. Reflectivity,” J. Phys. C Sol. Stat. Phys. 17, 3869–3888 (1984).
[Crossref]

1982 (1)

A. d’Andrea and R. Del Sole, “Wannier-mott excitons in semi-infinite crystals: Wave functions and normal-incidence reflectivity,” Phys. Rev. B 25, 3714–3730 (1982).
[Crossref]

1981 (1)

J. Lagois, “Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23, 5511 (1981).
[Crossref]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

1958 (1)

S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958).

Agranovich, V. M.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons (Springer, 1984).
[Crossref]

Ajiki, H.

S. Uryu, H. Ajiki, and H. Ishihara, “Model of finite-momentum excitons driven by surface plasmons in photoexcited carbon nanotubes covered by gold metal films,” Phys. Rev. Lett. 110, 257401 (2013).
[Crossref] [PubMed]

H. Ajiki, “Calculation method for exciton wavefunctions with electron–hole exchange interaction: Application to carbon nanotubes,” J. Phys. Soc. Jpn. 82, 4701 (2013).
[Crossref]

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

Y. Sun, H. Ajiki, and G. Bao, “Computational modeling of optical response from excitons in a nano optical medium,” Commun. Comput. Phys. 4, 1051–1068 (2008).

H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
[Crossref]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Ashida, M.

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

Banerjee, P. K.

P. K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science (McGraw-Hill, 1981).

Bao, G.

Y. Sun, H. Ajiki, and G. Bao, “Computational modeling of optical response from excitons in a nano optical medium,” Commun. Comput. Phys. 4, 1051–1068 (2008).

Birman, J.

J. Birman, E. Rashba, and M. Sturge, Excitons (North-Holland, 1982).

Bossavit, A.

A. Bossavit, “Solving Maxwell equations in a closed cavity, and the question of ‘spurious modes’,” IEEE Trans. Mag. 26, 702–705 (1990).
[Crossref]

A. Bossavit, “A rationale for ‘edge-elements’ in 3-D fields computations,” IEEE Trans. Mag. 24, 74–79 (1988).
[Crossref]

Butterfield, R.

P. K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science (McGraw-Hill, 1981).

Cho, K.

H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
[Crossref]

K. Cho, “Nonlocal theory of radiation-matter interaction: Boundary-condition-less treatment of Maxwell equations,” Prog. Theor. Phys. Suppl. 106, 225–233 (1991).
[Crossref]

K. Cho and H. Ishihara, “ABC-theory of an exciton-polariton in a slab,” J. Phys. Soc. Jpn. 59, 754–764 (1990).
[Crossref]

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[Crossref]

K. Cho, Optical Response of Nanostructures: Microscopic Nonlocal Theory (Springer, 2003).
[Crossref]

d’Andrea, A.

A. d’Andrea and R. Del Sole, “Wannier-mott excitons in semi-infinite crystals: Wave functions and normal-incidence reflectivity,” Phys. Rev. B 25, 3714–3730 (1982).
[Crossref]

Del Sole, R.

A. d’Andrea and R. Del Sole, “Wannier-mott excitons in semi-infinite crystals: Wave functions and normal-incidence reflectivity,” Phys. Rev. B 25, 3714–3730 (1982).
[Crossref]

Efros, A. L.

A. Ekimov, A. L. Efros, and A. Onushchenko, “Quantum size effect in semiconductor microcrystals,” Solid State Commun. 56, 921–924 (1985).
[Crossref]

Ekimov, A.

A. Ekimov, A. L. Efros, and A. Onushchenko, “Quantum size effect in semiconductor microcrystals,” Solid State Commun. 56, 921–924 (1985).
[Crossref]

Fuchs, R.

P. Halevi and R. Fuchs, “Generalized additional boundary condition for non-local dielectrics. I. Reflectivity,” J. Phys. C Sol. Stat. Phys. 17, 3869–3888 (1984).
[Crossref]

Gil, B.

M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
[Crossref]

Ginzburg, V. L.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons (Springer, 1984).
[Crossref]

Halevi, P.

P. Halevi and R. Fuchs, “Generalized additional boundary condition for non-local dielectrics. I. Reflectivity,” J. Phys. C Sol. Stat. Phys. 17, 3869–3888 (1984).
[Crossref]

Ichimiya, M.

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

Iida, T.

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

Imaizumi, K.

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

Inaba, K.

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

Ishihara, H.

S. Uryu, H. Ajiki, and H. Ishihara, “Model of finite-momentum excitons driven by surface plasmons in photoexcited carbon nanotubes covered by gold metal films,” Phys. Rev. Lett. 110, 257401 (2013).
[Crossref] [PubMed]

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

Y. Mizumoto and H. Ishihara, “Theory of resonant radiation force exerted on single organic molecules near metallic nanogap,” Proc. SPIE 8097, 80971C (2011).
[Crossref]

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

K. Cho and H. Ishihara, “ABC-theory of an exciton-polariton in a slab,” J. Phys. Soc. Jpn. 59, 754–764 (1990).
[Crossref]

Itoh, T.

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

Jin, J.-M.

J.-M. Jin, The Finite Element Method in Electromagnetics (John Wiley, 2002).

Kaliteevski, M.

M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
[Crossref]

Katayama, K.

K. Inaba, K. Imaizumi, K. Katayama, M. Ichimiya, M. Ashida, T. Iida, H. Ishihara, and T. Itoh, “Optical manipulation of CuCl nanoparticles under an excitonic resonance condition in superfluid helium,” Phys. Stat. Solidi B 243, 3829–3833 (2006).
[Crossref]

Kavokin, A.

M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
[Crossref]

Kawasaki, M.

Z. Tang, G. K. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett. 72, 3270–3272 (1998).
[Crossref]

Kawata, M.

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[Crossref]

Koinuma, H.

Z. Tang, G. K. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett. 72, 3270–3272 (1998).
[Crossref]

Komeda, K.

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

Lagois, J.

J. Lagois, “Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23, 5511 (1981).
[Crossref]

Malpuech, G.

M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
[Crossref]

Mizumoto, Y.

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

Y. Mizumoto and H. Ishihara, “Theory of resonant radiation force exerted on single organic molecules near metallic nanogap,” Proc. SPIE 8097, 80971C (2011).
[Crossref]

Murakoshi, K.

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

Nabika, H.

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

Nara, M.

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

Noda, S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Ohtomo, A.

Z. Tang, G. K. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett. 72, 3270–3272 (1998).
[Crossref]

Onushchenko, A.

A. Ekimov, A. L. Efros, and A. Onushchenko, “Quantum size effect in semiconductor microcrystals,” Solid State Commun. 56, 921–924 (1985).
[Crossref]

Pekar, S. I.

S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958).

Rashba, E.

J. Birman, E. Rashba, and M. Sturge, Excitons (North-Holland, 1982).

Ruppin, R.

R. Ruppin, “Optical absorption by excitons in microcrystals,” J. Phys. Chem. Solids 50, 877–882 (1989).
[Crossref]

Segawa, Y.

Z. Tang, G. K. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett. 72, 3270–3272 (1998).
[Crossref]

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Sturge, M.

J. Birman, E. Rashba, and M. Sturge, Excitons (North-Holland, 1982).

Sun, Y.

Y. Sun, H. Ajiki, and G. Bao, “Computational modeling of optical response from excitons in a nano optical medium,” Commun. Comput. Phys. 4, 1051–1068 (2008).

Takase, M.

M. Takase, H. Ajiki, Y. Mizumoto, K. Komeda, M. Nara, H. Nabika, S. Yasuda, H. Ishihara, and K. Murakoshi, “Selection-rule breakdown in plasmon-induced electronic excitation of an isolated single-walled carbon nanotube,” Nat. Photonics 7, 550–554 (2013).
[Crossref]

Tang, Z.

Z. Tang, G. K. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett. 72, 3270–3272 (1998).
[Crossref]

Uryu, S.

S. Uryu, H. Ajiki, and H. Ishihara, “Model of finite-momentum excitons driven by surface plasmons in photoexcited carbon nanotubes covered by gold metal films,” Phys. Rev. Lett. 110, 257401 (2013).
[Crossref] [PubMed]

Wong, G. K.

Z. Tang, G. K. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films,” Appl. Phys. Lett. 72, 3270–3272 (1998).
[Crossref]

Yasuda, S.

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic illustration of a semiconductor nanostructure (region Ω1) surrounded by a dielectric (regions Ω0 and Ω). The interface between the semiconductor nanostructure and dielectric is denoted by Γ1, and an artificial spherical surface, denoted by Γ0, is introduced within which the region is subdivided into small volume elements for the numerical computation. Various wave modes are also depicted. (b) The dispersion relations of two transverse exciton polaritons and one longitudinal exciton in bulk CuCl (the CuCl parameters for the calculation are summarized in Table 1).

Fig. 2
Fig. 2

Example of the subdivision of the mesh by tetrahedral elements.

Fig. 3
Fig. 3

(a) Volume element mesh for a spherical QD. (b) Scattering cross section of a spherical QD of CuCl with a 10-nm diameter calculated by the present FEM (crosses) and by Mie theory (solid line). (c) Vector plots of the calculated electric field at the resonant photon energy indicated by the arrow in (b). (d) Vector plots of the calculated exciton polarization at the resonant photon energy indicated by the arrow in (b).

Fig. 4
Fig. 4

(a) Volume element mesh for a hexagonal-disk QD. (b) Scattering cross section calculated by the present FEM of a hexagonal-disk QD of ZnO with a length of 30 nm and a height of 10 nm. At the resonant photon energy of 3.39063 eV indicated by the left arrow in (b), (c) the magnitudes of the electric fields and the (d) x- and (e) y-components of the exciton polarization are plotted in the xy plane of the top surface of the QD. At the resonant photon energy of 3.39227 eV indicated by the right arrow in (b), (f) the magnitudes of the electric fields and the (g) x- and (h) y-components of the exciton polarization are plotted in the same plane.

Fig. 5
Fig. 5

Schematic illustrations of the (a) nodal-element basis L(e;i)(r) and (b) edge-element basis W(e;ij)(r).

Tables (1)

Tables Icon

Table 1 Parameters of the Z3 exciton of CuCl and Γ5(B) exciton of ZnO; me denotes the free electron mass.

Equations (53)

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ε ( k , ω ) = ε bg + ε bg Δ LT E G + ( h ¯ 2 / 2 M ) k 2 h ¯ ω i h ¯ γ ,
k 2 = ( ω c ) 2 ε ( k , ω ) .
E ( 1 ) = μ = 1 2 E ( t μ ) Φ ,
E ( ) = E ( inc ) + E ( scat ) ,
E ( scat ) ( r ) = n = 1 N c m = n n [ a m n M m n ( r ) + b m n N m n ( r ) ] ,
E ( inc ) = I 0 n = 1 N c m = ± 1 [ p m n M m n ( r ) + q m n N m n ( r ) ] ,
p 1 n = q 1 n = i n + 1 2 n + 1 2 n ( n + 1 ) ,
p 1 n = q 1 n = i n + 1 ( n + 1 2 ) .
n ^ 1 × E ( 0 ) = n ^ 1 × E ( 1 ) ,
n ^ 1 × × E ( 0 ) = n ^ 1 × × E ( 1 ) = μ = 1 2 n ^ 1 × × E ( t μ ) ,
μ = 1 2 χ ( k t μ , ω ) E ( t μ ) + χ ( k l , ω ) ( Φ ) = 0 .
n ^ 1 Φ = μ = 1 2 χ ( k t μ , ω ) χ ( k l , ω ) n ^ 1 E ( t μ ) ,
χ ( k l , ω ) n ^ 1 × Φ = μ = 1 2 χ ( k t μ , ω ) n ^ 1 × E ( t μ ) .
n ^ 0 × E ( 0 ) = n ^ 0 × E ( ) ,
n ^ 0 × × E ( 0 ) = n ^ 0 × × E ( ) = k n = 1 N c m = n n [ ( I 0 p m n δ m , ± 1 + a m n ) n ^ 0 × N m n ( r ) + ( I 0 q m n δ m , ± 1 + b m n ) n ^ 0 × M m n ( r ) ] ,
E ( ) = E ( 0 ) .
× × E ( 0 ) k 2 E ( 0 ) = 0 ,
0 [ E ( 0 ) ] = 1 2 Ω 0 d 3 r { [ × E ( 0 ) * ] [ × E ( 0 ) ] k 2 E ( 0 ) * E ( 0 ) } + 1 2 Ω 0 d 2 r E ( 0 ) * [ n ^ 0 × × E ( 0 ) ] ,
× × E ( t μ ) k t μ 2 E ( t μ ) = 0 ,
2 Φ + k l 2 Φ = 0 .
1 [ E ( t 1 ) , E ( t 2 ) , Φ ] = 1 2 μ = 1 2 Ω 1 d 3 r { [ × E ( t μ ) * ] [ × E ( t μ ) ] k t μ 2 E ( t μ ) * E ( t μ ) } + 1 2 μ = 1 2 Ω 1 d 2 r E ( t μ ) * [ n ^ 1 × × E ( t μ ) ] 1 2 Ω 1 d 3 r [ ( Φ * ) ( Φ ) k l 2 Φ * Φ ] + 1 2 Ω 1 d 2 r Φ * ( n ^ 1 Φ ) ,
Φ ( r ) = e Ω 1 i = 1 4 Φ s ( e ; i ) L ( e ; i ) ( r ) ,
E ( 0 ) ( r ) = e Ω 0 i j = 1 4 E s ( e ; i ) s ( e ; j ) ( 0 ) W ( e ; i j ) ( r ) ,
E ( t μ ) ( r ) = e Ω 1 i j = 1 4 E s ( e ; i ) s ( e ; j ) ( t μ ) W ( e ; i j ) ( r ) ,
α = { 0 , t 1 , t 2 } δ δ E s ( e ; i ) s ( e ; j ) ( α ) = 0 . [ for s ( e ; i ) , s ( e ; j ) Γ 1 ]
δ ˜ δ E s ( e ; i ) s ( e ; j ) ( α ) = 0 , [ for s ( e ; i ) , s ( e ; j ) Γ 1 ]
δ ˜ δ Φ s ( e ; i ) = 0 .
E s ( e ; i ) s ( e ; j ) ( t 1 ) + E s ( e ; i ) s ( e ; j ) ( t 2 ) Φ s ( e ; j ) Φ s ( e ; i ) l i j = E s ( e ; i ) s ( e ; j ) ( 0 ) , [ s ( e , i ) , s ( e , j ) Γ 1 ] .
χ ( k t 1 , ω ) E s ( e ; i ) s ( e ; j ) ( t 1 ) + χ ( k t 2 , ω ) E s ( e ; i ) s ( e ; j ) ( t 2 ) χ ( k l , ω ) Φ s ( e ; j ) Φ s ( e ; i ) l i j = 0 . [ s ( e , i ) , s ( e , j ) Γ 1 ]
( I 0 p u v δ u , ± 1 + a u v ) S u v ( M ) = e ; f e Γ 0 i j = 1 4 E s ( e ; i ) s ( e ; j ) ( 0 ) Γ ( f e ) d 2 r M u v * W ( e ; i j ) ,
( I 0 q u v δ u , ± 1 + b u v ) S u v ( N ) = e ; f e Γ 0 i j = 1 4 E s ( e ; i ) s ( e ; j ) ( 0 ) Γ ( f e ) d 2 r N u v * W ( e ; i j ) ,
σ s = 1 k 2 n = 1 N c m = n n D m n ( | a m n | 2 + | b m n | 2 ) ,
M m n ( r ) = × [ r Ψ m n ( r ) ] ,
N m n ( r ) = 1 k × × [ r Ψ m n ( r ) ] ,
Ψ m n ( r ) = h n ( 1 ) ( k r ) P n m ( cos θ ) e i m ϕ ,
M m n ( r ) = 0 , N m n ( r ) = 0 ,
× N m n ( r ) = k M m n ( r ) , × M m n ( r ) = k N m n ( r ) .
M m n ( r ) = i m sin θ h n ( 1 ) ( k r ) P n m ( cos θ ) e i m ϕ θ ^ h n ( 1 ) ( k r ) d P n m ( cos θ ) d θ e i m ϕ ϕ ^ ,
N m n ( r ) = n ( n + 1 ) k r h n ( 1 ) ( k r ) P n m ( cos θ ) e i m ϕ r ^ + 1 k r ξ n ( k r ) d P n m ( cos θ ) d θ e i m ϕ θ ^ + i 1 k r m sin θ ξ n ( k r ) P n m ( cos θ ) e i m ϕ ϕ ^ ,
Γ 0 d 2 r M m n * N m n = 0 ,
Γ 0 d 2 r M m n * M m n = δ m m δ n n | h n ( 1 ) ( k R ) | 2 R 2 D m n S m n ( M ) δ m m δ n n ,
Γ 0 d 2 r N m n * N m n = δ m m δ n n R 2 D m n [ | ξ ( k R ) k R | 2 + n ( n + 1 ) | h n ( 1 ) ( k R ) | 2 ] S m n ( N ) δ m m δ n n ,
D m n = 4 π n ( n + 1 ) 2 n + 1 ( n + m ) ! ( n m ) ! .
L ( e ; i ) ( r ) = a ( e ; i ) x + a ( e ; i ) y y + a ( e ; i ) z z + b ( e ; i ) ,
W ( e ; i j ) ( r ) = 1 l i j [ L ( e ; i ) ( r ) L ( e ; j ) ( r ) L ( e ; j ) ( r ) L ( e ; i ) ( r ) ] ,
Φ s ( e ; i ) = Φ [ r ( e ; i ) ] ,
E s ( e ; i ) s ( e ; j ) ( α ) = t ^ ( e ; i j ) E ( α ) [ r ( e ; i j ) ] ,
0 = 1 2 e Ω 0 i j k l = 1 4 K i j k l ( e ) ( k ) E s ( e ; i ) s ( e ; j ) ( 0 ) * E s ( e ; k ) s ( e ; l ) ( 0 ) + k 2 e ; f e Γ 0 i j = 1 4 n = 1 N c m = n n E s ( e ; i ) s ( e ; j ) ( 0 ) * × { ( I 0 p m n δ m , ± 1 + a m n ) Γ ( f e ) d 2 r W ( e ; i j ) [ n ^ 0 × N m n ( r ) ] f e + ( I 0 q m n δ m , ± 1 + b m n ) Γ ( f e ) d 2 r W ( e ; i j ) [ n ^ 0 × M m n ( r ) ] f e } + 1 2 e ; f e Γ 1 i j = 1 4 E s ( e ; i ) s ( e ; j ) ( 0 ) * Γ ( f e ) d 2 r W ( e ; i j ) [ n ^ 0 × × E ( 0 ) ] f e ,
K i j k l ( e ) ( k ) = Ω ( e ) d 3 r { [ × W ( e ; i j ) ] [ × W ( e ; k l ) ] k 2 W ( e ; i j ) W ( e ; k l ) } ,
1 = 1 2 μ = 1 2 e Ω 1 i j k l = 1 4 K i j k l ( e ) ( k t μ ) E s ( e ; i ) s ( e ; j ) ( t μ ) * E s ( e ; k ) s ( e ; l ) ( t μ ) + 1 2 μ = 1 2 e ; f e Γ 1 i j = 1 4 E s ( e ; i ) s ( e ; j ) ( t μ ) * Γ ( f e ) d 2 r W ( e ; i j ) [ n ^ 1 × × E ( t μ ) ] f e 1 2 e Ω 1 i j = 1 4 J i j ( e ) ( k l ) Φ s ( e ; i ) * Φ s ( e ; j ) + 1 2 μ = 1 2 e ; f e Γ 1 i j = 1 4 χ ( k t μ , ω ) χ ( k l , ω ) Φ s ( e ; i ) * E s ( e ; i ) s ( e ; j ) ( t μ ) Γ ( f e ) d 2 r L ( e ; i ) [ n ^ 1 W ( e ; i j ) ] f e ,
J i j ( e ) ( k l ) = Ω ( e ) d 3 r { [ L ( e ; i ) ] [ L ( e ; j ) ] k l 2 L ( e ; i ) L ( e ; j ) } .
˜ 0 = 1 2 e Ω 0 i j k l = 1 4 K i j k l ( e ) ( k ) E s ( e ; i ) s ( e ; j ) ( 0 ) * E s ( e ; k ) s ( e ; l ) ( 0 ) + k 2 e ; f e Γ 0 i j = 1 4 n = 1 N c m = n n E s ( e ; i ) s ( e ; j ) ( 0 ) * × { ( I 0 p m n δ m , ± 1 + a m n ) Γ ( f e ) d 2 r W ( e ; i j ) [ n ^ 0 × N m n ( r ) ] f e + ( I 0 q m n δ m , ± 1 + b m n ) Γ ( f e ) d 2 r W ( e ; i j ) [ n ^ 0 × M m n ( r ) ] f e } ,
˜ 1 = 1 2 μ = 1 2 e Ω 1 i j k l = 1 4 K i j k l ( e ) ( k t μ ) E s ( e ; i ) s ( e ; j ) ( t μ ) * E s ( e ; k ) s ( e ; l ) ( t μ ) 1 2 e Ω 1 i j = 1 4 J i j ( e ) ( k l ) Φ s ( e ; i ) * Φ s ( e ; j ) + 1 2 μ = 1 2 e ; f e Γ 1 i j = 1 4 χ ( k t μ , ω ) χ ( k l , ω ) Φ s ( e ; i ) * E s ( e ; i ) s ( e ; j ) ( t μ ) Γ ( f e ) d 2 r L ( e ; i ) [ n ^ 1 W ( e ; i j ) ] f e .

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