Abstract

We formulated an efficient numerical method for the dispersion relation of polaritonic channel waveguides and applied it to ZnO (wurzite) and ZnSe (zinc-blende) waveguides. The dispersion relation obtained by our calculations is distinct from that of bulk crystals. We found that important contributions to light propagation were made by two modes in the frequency range below the transverse exciton frequency, which was confirmed by comparing the group index obtained by our calculation with Fabry-Perot interference experiments. The numerical error of our method was estimated to be less than 1 % by comparing it with an analytical solution for a model structure. Our calculations predict an extremely small bending loss, which was estimated from the spatial decay rate of evanescent waves outside of the waveguide.

© 2017 Optical Society of America

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  1. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
    [Crossref]
  2. S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
    [Crossref] [PubMed]
  3. S. Kéna-Cohen and S. R. Forrest, “Room-temperature polariton lasing in an organic single-crystal microcavity,” Nat. Photonics 4, 371–375 (2010).
    [Crossref]
  4. J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton polaritons in a polymer,” Nat. Mater. 13, 247–252 (2014).
    [Crossref]
  5. L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
    [Crossref] [PubMed]
  6. S. Rühle, L. K. van Vugt, H.-Y. Li, N. A. Keizer, L. Kuipers, and D. Vanmaekelbergh, “Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire,” Nano Lett. 8, 119–123 (2008).
    [Crossref]
  7. H.-Y. Li, S. Rühle, R. Khedoe, A. F. Koenderink, and D. Vanmaekelbergh, “Polarization, microscopic origin, and mode structure of luminescence and lasing from single ZnO nanowires,” Nano Lett. 9, 3515–3520 (2009).
    [Crossref] [PubMed]
  8. L. K. van Vugt, B. Zhang, B. Piccione, A. A. Spector, and R. Agarwal, “Size-dependent waveguide dispersion in nanowire optical cavities: slowed light and dispersionless guiding,” Nano Lett. 9, 1684–1688 (2009).
    [Crossref] [PubMed]
  9. H. Yoshikawa and S. Adachi, “Optical constants of ZnO,” Jpn. J. Appl. Phys. 36, 6237–6243 (1997).
    [Crossref]
  10. G. E. Jellison and L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
    [Crossref]
  11. S. Adachi and T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
    [Crossref]
  12. C. C. Kim and S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
    [Crossref]
  13. H. Takeda and K. Sakoda, “Exciton polariton mediated light propagation in anisotropic waveguides,” Phys. Rev. B 86, 205319 (2012).
    [Crossref]
  14. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  15. P. R. Karmel, G. D. Colef, and R. L. Camisa, Introduction to Electromagnetic and Microwave Engineering (Wiley Series in Microwave and Optical Engineering), 1st ed. (Wiley-Interscience, 1998).
  16. J. Lagois, “Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23, 5511–5520 (1981).
    [Crossref]
  17. H. Takeda and K. Sakoda, “Bending losses of optically anisotropic exciton polaritons in organic molecular-crystal nanofibers,” Opt. Express 21, 31420–31429 (2013).
    [Crossref]
  18. X. T. Zhang, Z. Liu, Y. P. Leung, Q. Li, and S. K. Harka, “Growth and luminescence of zinc-blende-structured ZnSe nanowires by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 83, 5533–5535 (2003).
    [Crossref]

2014 (1)

J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton polaritons in a polymer,” Nat. Mater. 13, 247–252 (2014).
[Crossref]

2013 (1)

2012 (1)

H. Takeda and K. Sakoda, “Exciton polariton mediated light propagation in anisotropic waveguides,” Phys. Rev. B 86, 205319 (2012).
[Crossref]

2010 (1)

S. Kéna-Cohen and S. R. Forrest, “Room-temperature polariton lasing in an organic single-crystal microcavity,” Nat. Photonics 4, 371–375 (2010).
[Crossref]

2009 (2)

H.-Y. Li, S. Rühle, R. Khedoe, A. F. Koenderink, and D. Vanmaekelbergh, “Polarization, microscopic origin, and mode structure of luminescence and lasing from single ZnO nanowires,” Nano Lett. 9, 3515–3520 (2009).
[Crossref] [PubMed]

L. K. van Vugt, B. Zhang, B. Piccione, A. A. Spector, and R. Agarwal, “Size-dependent waveguide dispersion in nanowire optical cavities: slowed light and dispersionless guiding,” Nano Lett. 9, 1684–1688 (2009).
[Crossref] [PubMed]

2008 (1)

S. Rühle, L. K. van Vugt, H.-Y. Li, N. A. Keizer, L. Kuipers, and D. Vanmaekelbergh, “Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire,” Nano Lett. 8, 119–123 (2008).
[Crossref]

2007 (1)

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

2006 (1)

L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

2003 (1)

X. T. Zhang, Z. Liu, Y. P. Leung, Q. Li, and S. K. Harka, “Growth and luminescence of zinc-blende-structured ZnSe nanowires by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 83, 5533–5535 (2003).
[Crossref]

1998 (1)

G. E. Jellison and L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[Crossref]

1997 (1)

H. Yoshikawa and S. Adachi, “Optical constants of ZnO,” Jpn. J. Appl. Phys. 36, 6237–6243 (1997).
[Crossref]

1996 (1)

C. C. Kim and S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
[Crossref]

1991 (1)

S. Adachi and T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
[Crossref]

1981 (1)

J. Lagois, “Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23, 5511–5520 (1981).
[Crossref]

1958 (1)

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
[Crossref]

Adachi, S.

H. Yoshikawa and S. Adachi, “Optical constants of ZnO,” Jpn. J. Appl. Phys. 36, 6237–6243 (1997).
[Crossref]

S. Adachi and T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
[Crossref]

Agarwal, R.

L. K. van Vugt, B. Zhang, B. Piccione, A. A. Spector, and R. Agarwal, “Size-dependent waveguide dispersion in nanowire optical cavities: slowed light and dispersionless guiding,” Nano Lett. 9, 1684–1688 (2009).
[Crossref] [PubMed]

Baldassarri Höger von Högersthal, G.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Baumberg, J. J.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Boatner, L. A.

G. E. Jellison and L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[Crossref]

Butte, R.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Camisa, R. L.

P. R. Karmel, G. D. Colef, and R. L. Camisa, Introduction to Electromagnetic and Microwave Engineering (Wiley Series in Microwave and Optical Engineering), 1st ed. (Wiley-Interscience, 1998).

Carlin, J.-F.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Christmann, G.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Christopoulos, S.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Colef, G. D.

P. R. Karmel, G. D. Colef, and R. L. Camisa, Introduction to Electromagnetic and Microwave Engineering (Wiley Series in Microwave and Optical Engineering), 1st ed. (Wiley-Interscience, 1998).

Feltin, E.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Forrest, S. R.

S. Kéna-Cohen and S. R. Forrest, “Room-temperature polariton lasing in an organic single-crystal microcavity,” Nat. Photonics 4, 371–375 (2010).
[Crossref]

Gerritsen, H. C.

L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Grandjean, N.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Grundy, A. J. D.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Harka, S. K.

X. T. Zhang, Z. Liu, Y. P. Leung, Q. Li, and S. K. Harka, “Growth and luminescence of zinc-blende-structured ZnSe nanowires by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 83, 5533–5535 (2003).
[Crossref]

Hopfield, J. J.

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
[Crossref]

Jellison, G. E.

G. E. Jellison and L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[Crossref]

Karmel, P. R.

P. R. Karmel, G. D. Colef, and R. L. Camisa, Introduction to Electromagnetic and Microwave Engineering (Wiley Series in Microwave and Optical Engineering), 1st ed. (Wiley-Interscience, 1998).

Kavokin, A. V.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Keizer, N. A.

S. Rühle, L. K. van Vugt, H.-Y. Li, N. A. Keizer, L. Kuipers, and D. Vanmaekelbergh, “Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire,” Nano Lett. 8, 119–123 (2008).
[Crossref]

Kéna-Cohen, S.

S. Kéna-Cohen and S. R. Forrest, “Room-temperature polariton lasing in an organic single-crystal microcavity,” Nat. Photonics 4, 371–375 (2010).
[Crossref]

Khedoe, R.

H.-Y. Li, S. Rühle, R. Khedoe, A. F. Koenderink, and D. Vanmaekelbergh, “Polarization, microscopic origin, and mode structure of luminescence and lasing from single ZnO nanowires,” Nano Lett. 9, 3515–3520 (2009).
[Crossref] [PubMed]

Kim, C. C.

C. C. Kim and S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
[Crossref]

Koenderink, A. F.

H.-Y. Li, S. Rühle, R. Khedoe, A. F. Koenderink, and D. Vanmaekelbergh, “Polarization, microscopic origin, and mode structure of luminescence and lasing from single ZnO nanowires,” Nano Lett. 9, 3515–3520 (2009).
[Crossref] [PubMed]

Kuipers, L.

S. Rühle, L. K. van Vugt, H.-Y. Li, N. A. Keizer, L. Kuipers, and D. Vanmaekelbergh, “Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire,” Nano Lett. 8, 119–123 (2008).
[Crossref]

L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Lagois, J.

J. Lagois, “Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23, 5511–5520 (1981).
[Crossref]

Lagoudakis, P. G.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Leung, Y. P.

X. T. Zhang, Z. Liu, Y. P. Leung, Q. Li, and S. K. Harka, “Growth and luminescence of zinc-blende-structured ZnSe nanowires by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 83, 5533–5535 (2003).
[Crossref]

Li, H.-Y.

H.-Y. Li, S. Rühle, R. Khedoe, A. F. Koenderink, and D. Vanmaekelbergh, “Polarization, microscopic origin, and mode structure of luminescence and lasing from single ZnO nanowires,” Nano Lett. 9, 3515–3520 (2009).
[Crossref] [PubMed]

S. Rühle, L. K. van Vugt, H.-Y. Li, N. A. Keizer, L. Kuipers, and D. Vanmaekelbergh, “Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire,” Nano Lett. 8, 119–123 (2008).
[Crossref]

Li, Q.

X. T. Zhang, Z. Liu, Y. P. Leung, Q. Li, and S. K. Harka, “Growth and luminescence of zinc-blende-structured ZnSe nanowires by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 83, 5533–5535 (2003).
[Crossref]

Liu, Z.

X. T. Zhang, Z. Liu, Y. P. Leung, Q. Li, and S. K. Harka, “Growth and luminescence of zinc-blende-structured ZnSe nanowires by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 83, 5533–5535 (2003).
[Crossref]

Mahrt, R. F.

J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton polaritons in a polymer,” Nat. Mater. 13, 247–252 (2014).
[Crossref]

Mai, L.

J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton polaritons in a polymer,” Nat. Mater. 13, 247–252 (2014).
[Crossref]

Piccione, B.

L. K. van Vugt, B. Zhang, B. Piccione, A. A. Spector, and R. Agarwal, “Size-dependent waveguide dispersion in nanowire optical cavities: slowed light and dispersionless guiding,” Nano Lett. 9, 1684–1688 (2009).
[Crossref] [PubMed]

Plumhof, J. D.

J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton polaritons in a polymer,” Nat. Mater. 13, 247–252 (2014).
[Crossref]

Ravindran, P.

L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Rühle, S.

H.-Y. Li, S. Rühle, R. Khedoe, A. F. Koenderink, and D. Vanmaekelbergh, “Polarization, microscopic origin, and mode structure of luminescence and lasing from single ZnO nanowires,” Nano Lett. 9, 3515–3520 (2009).
[Crossref] [PubMed]

S. Rühle, L. K. van Vugt, H.-Y. Li, N. A. Keizer, L. Kuipers, and D. Vanmaekelbergh, “Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire,” Nano Lett. 8, 119–123 (2008).
[Crossref]

L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Sakoda, K.

H. Takeda and K. Sakoda, “Bending losses of optically anisotropic exciton polaritons in organic molecular-crystal nanofibers,” Opt. Express 21, 31420–31429 (2013).
[Crossref]

H. Takeda and K. Sakoda, “Exciton polariton mediated light propagation in anisotropic waveguides,” Phys. Rev. B 86, 205319 (2012).
[Crossref]

Scherf, U.

J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton polaritons in a polymer,” Nat. Mater. 13, 247–252 (2014).
[Crossref]

Sivananthan, S.

C. C. Kim and S. Sivananthan, “Optical properties of ZnSe and its modeling,” Phys. Rev. B 53, 1475–1484 (1996).
[Crossref]

Spector, A. A.

L. K. van Vugt, B. Zhang, B. Piccione, A. A. Spector, and R. Agarwal, “Size-dependent waveguide dispersion in nanowire optical cavities: slowed light and dispersionless guiding,” Nano Lett. 9, 1684–1688 (2009).
[Crossref] [PubMed]

Stöferle, T.

J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton polaritons in a polymer,” Nat. Mater. 13, 247–252 (2014).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Taguchi, T.

S. Adachi and T. Taguchi, “Optical properties of ZnSe,” Phys. Rev. B 43, 9569–9577 (1991).
[Crossref]

Takeda, H.

H. Takeda and K. Sakoda, “Bending losses of optically anisotropic exciton polaritons in organic molecular-crystal nanofibers,” Opt. Express 21, 31420–31429 (2013).
[Crossref]

H. Takeda and K. Sakoda, “Exciton polariton mediated light propagation in anisotropic waveguides,” Phys. Rev. B 86, 205319 (2012).
[Crossref]

van Vugt, L. K.

L. K. van Vugt, B. Zhang, B. Piccione, A. A. Spector, and R. Agarwal, “Size-dependent waveguide dispersion in nanowire optical cavities: slowed light and dispersionless guiding,” Nano Lett. 9, 1684–1688 (2009).
[Crossref] [PubMed]

S. Rühle, L. K. van Vugt, H.-Y. Li, N. A. Keizer, L. Kuipers, and D. Vanmaekelbergh, “Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire,” Nano Lett. 8, 119–123 (2008).
[Crossref]

L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Vanmaekelbergh, D.

H.-Y. Li, S. Rühle, R. Khedoe, A. F. Koenderink, and D. Vanmaekelbergh, “Polarization, microscopic origin, and mode structure of luminescence and lasing from single ZnO nanowires,” Nano Lett. 9, 3515–3520 (2009).
[Crossref] [PubMed]

S. Rühle, L. K. van Vugt, H.-Y. Li, N. A. Keizer, L. Kuipers, and D. Vanmaekelbergh, “Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire,” Nano Lett. 8, 119–123 (2008).
[Crossref]

L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Yoshikawa, H.

H. Yoshikawa and S. Adachi, “Optical constants of ZnO,” Jpn. J. Appl. Phys. 36, 6237–6243 (1997).
[Crossref]

Zhang, B.

L. K. van Vugt, B. Zhang, B. Piccione, A. A. Spector, and R. Agarwal, “Size-dependent waveguide dispersion in nanowire optical cavities: slowed light and dispersionless guiding,” Nano Lett. 9, 1684–1688 (2009).
[Crossref] [PubMed]

Zhang, X. T.

X. T. Zhang, Z. Liu, Y. P. Leung, Q. Li, and S. K. Harka, “Growth and luminescence of zinc-blende-structured ZnSe nanowires by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 83, 5533–5535 (2003).
[Crossref]

Appl. Phys. Lett. (1)

X. T. Zhang, Z. Liu, Y. P. Leung, Q. Li, and S. K. Harka, “Growth and luminescence of zinc-blende-structured ZnSe nanowires by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 83, 5533–5535 (2003).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 The (real) dielectric constants of bulk wurzite ZnO for Ec and Ec at room temperature [10]. The electronic band gap of ZnO is approximately 3.4 eV, and the imaginary part of the dielectric constant is less than 0.04 for ω < 3.25 eV.
Fig. 2
Fig. 2 Dispersion curves of the ZnO nanowire for R = 100 nm on a glass substrate. The solid lines denote the numerical solutions. The upper and lower dashed lines denote the approximate analytical solutions for the uniform backgrounds of air and SiO2, respectively. The green line denotes the bulk dispersion curve.
Fig. 3
Fig. 3 Group refractive index of the ZnO nanowire for R = 100 nm on a glass substrate. The solid and dashed lines were derived from vg of the numerical and analytical solutions, respectively. The upper and lower dashed lines stand for the uniform backgrounds of air and SiO2, respectively. The green line stands for bulk ZnO.
Fig. 4
Fig. 4 Electric-field distribution of the first, second and third lowest bands for ħω = 3.21 eV in Fig. 2. Figures (a)–(c) are x, y and z components of the electric field of the first lowest band, respectively. Similarly, Figs. (d)–(f) and (g)–(i) are the second and third bands, respectively.
Fig. 5
Fig. 5 The (real) dielectric constant of bulk zinc-blende ZnSe at room temperature [11].
Fig. 6
Fig. 6 Dispersion curves of the ZnSe nanowire for R = 100 nm on a glass substrate. The solid lines denote the numerical solutions. The upper and lower dashed lines denote the approximate analytical solutions for the uniform backgrounds of air and SiO2, respectively. The green line denotes the bulk dispersion curve.
Fig. 7
Fig. 7 Group refractive index of the ZnSe nanowire for R = 100 nm on a glass substrate. The solid and dashed lines are derived from vg of the numerical and analytical solutions, respectively. The upper and lower dashed lines are for the uniform backgrounds of air and SiO2, respectively. The green line is for bulk.
Fig. 8
Fig. 8 Dispersion curves for the isotropic ZnO nanowire for R = 100 nm in a uniform background of (a) air and (b) SiO2. The solid lines and black circles denote the analytical and numerical solutions, respectively.

Equations (23)

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ε ( ω ) = ε ω L 2 ω 2 ω T 2 ω 2 ,
× × E ( r ) = ω 2 c 2 ε ( r ; ω ) E ( r ) ,
E ( r ) = E ( x , y ) exp ( i β z ) ,
E z ( x , y ) = i ε z z 1 ( x , y ; ω ) β [ { ε x x ( x , y ; ω ) E x ( x , y ) } x + { ε y y ( x , y ; ω ) E y ( x , y ) } y ] ,
ε i i ( x , y ; ω ) = G ε i i ; G ( ω ) exp [ i ( G x x + G y y ) ] ,
E i ( x , y ) = G E i ; G exp [ i ( G x x + G y y ) ] ,
[ M x x ( ω ) M x y ( ω ) M y x ( ω ) M y y ( ω ) ] [ E ˜ x E ˜ y ] = β 2 [ E ˜ x E ˜ y ] ,
κ = β 2 β 0 2 ,
ε ω 2 + ω T 2 ε ( ω ) ε ω L 2 ω 2 ε ( ω ) = 0 .
f ( A , B , C ) = 1 N i = 1 N [ A ω i 2 + B ε i + C ω i 2 ε i ] 2 .
[ i = 1 N ω i 4 i = 1 N ω i 2 ε i i = 1 N ω i 2 i = 1 N ω i 2 ε i i = 1 N ε i 2 i = 1 N ε i i = 1 N ε i 2 i = 1 N ε i N ] [ A B C ] = [ i = 1 N ω i 4 ε i i = 1 N ω i 2 ε i 2 i = 1 N ω i 2 ε i ] .
ε i i ; G ( ω ) = 1 L x L y L x / 2 L x / 2 d x L y / 2 L y / 2 d y ε i i ( x , y ; ω ) exp [ i ( G x x + G y y ) ] = ε i i ; 2 L x L y L x / 2 L x / 2 d x L y / 2 L y / 2 d y exp [ i ( G x x + G y y ) ] + ε i i ; 1 ( ω ) ε i i ; 2 L x L y x 2 + y 2 R 2 d x d y exp [ i ( G x x + G y y ) ] + ε i i ; 3 ε i i ; 2 L x L y L x / 2 L x / 2 d x L y / 2 R d y exp [ i ( G x x + G y y ) ] = ε i i ; 2 δ G x , 0 δ G y , 0 + 2 [ ε i i ; 1 ( ω ) ε i i ; 2 ] J 1 ( G R ) G R π R 2 L x L y + [ ε i i ; 3 ε i i ; 2 ] δ G x , 0 e i G y L y / 2 e i G y R i G y ( L y / 2 R ) L y 2 R 2 L y ,
ω 2 c 2 ε x x E x + x [ ε z z 1 ( ε x x E x ) x ] + 2 E x y 2 2 E y x y + x [ ε z z 1 ( ε y y E y ) y ] = β 2 E x ,
2 E x y x + x [ ε z z 1 ( ε x x E x ) x ] + ω 2 c 2 ε y y E y + 2 E y x 2 + y [ ε z z 1 ( ε y y E y ) y ] = β 2 E y .
G M x x G , G ( ω ) E x ; G + G M x y ; G , G ( ω ) E y ; G = β 2 E x ; G ,
G M y x ; G , G ( ω ) E x ; G + G M y y ; G , G ( ω ) E y ; G = β 2 E y ; G ,
M x x ; G , G ( ω ) = ω 2 c 2 ε x x ; G G ( ω ) G ε z z ; G G 1 ( ω ) ε x x ; G G ( ω ) G x G x G y 2 δ G G ,
M x y ; G , G ( ω ) = G x G y δ G , G G ε z z ; G G 1 ( ω ) ε y y ; G G ( ω ) G x G y ,
M y x ; G , G ( ω ) = G x G y δ G , G G ε z z ; G G 1 ( ω ) ε x x ; G G ( ω ) G y G x ,
M y y ; G , G ( ω ) = ω 2 c 2 ε y y ; G G ( ω ) G x 2 δ G , G G ε z z ; G G 1 ( ω ) ε y y ; G G ( ω ) G y G y .
[ J n ( p ) p J n ( p ) + K n ( q ) q K n ( q ) ] [ ε 1 J n ( p ) p J n ( p ) + ε 2 K n ( q ) q K n ( q ) ] = n 2 [ 1 p 2 + 1 q 2 ] [ ε 1 p 2 + ε 2 q 2 ] ,
J 1 ( p ) [ q K 0 ( q ) ] + [ p J 0 ( p ) ] K 1 ( q ) = 0
ε 1 J 1 ( p ) [ q K 0 ( q ) ] + ε 2 [ p J 0 ( p ) ] K 1 ( q ) = 0 ,

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