Abstract

The optical properties of nanosize quantum-dot (QD) arrays are found to vary significantly around the exciton resonance frequency of the QDs. In order to simulate the interactions between electromagnetic waves and QD arrays, a general auxiliary-differential-equation, finite-difference time-domain approach is introduced and utilized in this article. Using this numerical method, the exciton-polariton resonances of single-layer and double-layer GaAs QD arrays are studied. The optical properties of a single-layer QD array are found to be characterized by the Mie resonance of its constituent QDs, while a double-layer QD array is characterized by the quasi-dipole formed by two QDs positioned in each of the two layers.

© 2008 Optical Society of America

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2007

S. Hughes, "Coupled-cavity QED using planar photonic crystals," Phys. Rev. Lett. 98, 083603 (2007).
[CrossRef] [PubMed]

L. Huang, C. Wang, L. Y. Lin, "A comparison of crosstalk effects between colloidal quantum dot waveguides and conventional waveguides," Opt. Lett. 32, 235 (2007).
[CrossRef] [PubMed]

V. S. C. Manga Rao, S. Hughes, "Single quantum-dot Purcell factor and ® factor in a photonic crystal waveguide," Phys. Rev. B 75, 205437 (2007).
[CrossRef]

2006

T. Iida, H. Ishihara, "Force control between quantum dots by light in polaritonic molecule states," Phys. Rev. Lett. 97, 117402 (2006).
[CrossRef] [PubMed]

J. A. Klugkist, M. Mostovoy, J. Knoester, "Mode Softening, Ferroelectric Transition, and Tunable Photonic Band Structures in a Point-Dipole Crystal," Phys. Rev. Lett. 96, 163903 (2006).
[CrossRef] [PubMed]

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-93 (2006).
[CrossRef] [PubMed]

Y. Fu, E. Berglind, L. Thyl’en, H. ° Agren, "Optical transmission and waveguiding by excitonic quantum dot lattices," J. Opt. Soc. Am. B 23, 2441 (2006).
[CrossRef]

Y. Zeng, Y. Fu, X. Chen, W. Lu, H. Agren, "Complete band gaps in three-dimensional quantum dot photonic crystals," Phys. Rev. B 74, 115325 (2006).
[CrossRef]

Y. Zeng, X. Chen, W. Lu, Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313 (2006).
[CrossRef]

H. Ajiki, T. Kaneno, H. Ishihara, "Vacuum-field Rabi splitting in semiconducting core-shell microsphere," Phys. Rev. B 73, 155322 (2006).
[CrossRef]

H. Mertens, J. S. Biteen, H. A. Atwater, A. Polman, "Polarization-Selective Plasmon-Enhanced Silicon Quantum-Dot Luminescence," Nano Lett. 6, 2622 (2006).
[CrossRef] [PubMed]

C. Wang, L. Huang, B. A. Parviz, L. Y. Lin, "Subdiffraction Photon Guidance by Quantum-Dot Cascades," Nano Lett. 6, 2549 (2006).
[CrossRef] [PubMed]

2005

O. Voskoboynikov, C. M. J. Wijers, J. L. Liu, C. P. Lee, "Magneto-optical response of layers of semiconductor quantum dots and nanorings," Phys. Rev. B 71, 245332 (2005).
[CrossRef]

V. Bondarenko, M. Zaluzny, Y. Zhao, "Interlevel electromagnetic response of systems of spherical quantum dots," Phys. Rev. B 71, 115304 (2005).
[CrossRef]

L. C. Andreani, D. Gerace, M. Agio, "Exciton-polaritons and nanoscale cavities in photonic crystal slab," Phys. Status Solidi B. 242, 2197 (2005).
[CrossRef]

C. Wang, L. Y. Lin, B. A. Parviz, "Modeling and simulation for a nano-photonic quantum dot waveguide fabricated by DNA-directed self-assembly," J. Sel. Top. Quantum Electron. 11, 500 (2005).
[CrossRef]

X. Zhang, P. Sharma, "Size dependency of strain in arbitrary shaped anisotropic embedded quantum dots due to nonlocal dispersive effects," Phys. Rev. B 72, 195345 (2005).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (2005).
[CrossRef]

K. Kempa, R. Ruppin, J. B. Pendry, "Electromagntic response of a point-dipole crystal," Phys. Rev. B 72, 205103 (2005).
[CrossRef]

2002

H. Ajiki, T. Tsuji, K. Kawano, K. Cho, "Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal," Phys. Rev. B 66, 245322 (2002).
[CrossRef]

2001

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, A. Hoffmann, D. Bimberg, "Effective boundary conditions for planar quantum dot structures," Phys. Rev. B 64, 125326 (2001).
[CrossRef]

F. Thiele, C. Fuchs, R. Baltz, "Optical absorption in semiconductor quantum dots: Nonlocal effects," Phys. Rev. B 64, 205309 (2001).
[CrossRef]

W. Guo, W. Li, Y. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation," IEEE Microwave and Wireless Components Lett. 11, 223 (2001).
[CrossRef]

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

2000

Y. Fu, M. Willander, E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlatt.Microstruct. 27, 255 (2000).
[CrossRef]

1999

S. Nojima, "Optical response of excitonic polaritons in photonic crystals," Phys. Rev. B 59, 5662 (1999).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

1998

S. Dey, R. Mittra, "Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation," IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
[CrossRef]

1995

L. Belleguie, S. Mukamel, "Nonlocal electrodynamics of arrays of quantum dots," Phys. Rev. B 52, 1936 (1995).
[CrossRef]

1992

J. A. Pereda, L. A. Vielva, A. Vegas, A. Prieto, "Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony’s methods," IEEE Microwave Guid. Wave Lett. 2, 431 (1992).
[CrossRef]

1989

Y. Hua, T. K. Sarkar, "Generalized pencil-of-function method for extracting poles of an EM system from its transient response," IEEE Trans. Antennas Propag. 37, 229 (1989).
[CrossRef]

1972

R. Zeyher, J. L. Birman, and W. Brenig, "Spatial Dispersion Effects in Resonant Polariton Scattering. I. Additional Boundary Conditions for Polarization Fields," Phys. Rev. B 6, 4613 (1972).
[CrossRef]

Agio, M.

L. C. Andreani, D. Gerace, M. Agio, "Exciton-polaritons and nanoscale cavities in photonic crystal slab," Phys. Status Solidi B. 242, 2197 (2005).
[CrossRef]

Ajiki, H.

H. Ajiki, T. Kaneno, H. Ishihara, "Vacuum-field Rabi splitting in semiconducting core-shell microsphere," Phys. Rev. B 73, 155322 (2006).
[CrossRef]

H. Ajiki, T. Tsuji, K. Kawano, K. Cho, "Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal," Phys. Rev. B 66, 245322 (2002).
[CrossRef]

Alferov, Zh. I.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

Andreani, L. C.

L. C. Andreani, D. Gerace, M. Agio, "Exciton-polaritons and nanoscale cavities in photonic crystal slab," Phys. Status Solidi B. 242, 2197 (2005).
[CrossRef]

Atwater, H. A.

H. Mertens, J. S. Biteen, H. A. Atwater, A. Polman, "Polarization-Selective Plasmon-Enhanced Silicon Quantum-Dot Luminescence," Nano Lett. 6, 2622 (2006).
[CrossRef] [PubMed]

Baltz, R.

F. Thiele, C. Fuchs, R. Baltz, "Optical absorption in semiconductor quantum dots: Nonlocal effects," Phys. Rev. B 64, 205309 (2001).
[CrossRef]

Belleguie, L.

L. Belleguie, S. Mukamel, "Nonlocal electrodynamics of arrays of quantum dots," Phys. Rev. B 52, 1936 (1995).
[CrossRef]

Berglind, E.

Bimberg, D.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, A. Hoffmann, D. Bimberg, "Effective boundary conditions for planar quantum dot structures," Phys. Rev. B 64, 125326 (2001).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

Birman, J. L.

R. Zeyher, J. L. Birman, and W. Brenig, "Spatial Dispersion Effects in Resonant Polariton Scattering. I. Additional Boundary Conditions for Polarization Fields," Phys. Rev. B 6, 4613 (1972).
[CrossRef]

Biteen, J. S.

H. Mertens, J. S. Biteen, H. A. Atwater, A. Polman, "Polarization-Selective Plasmon-Enhanced Silicon Quantum-Dot Luminescence," Nano Lett. 6, 2622 (2006).
[CrossRef] [PubMed]

Bondarenko, V.

V. Bondarenko, M. Zaluzny, Y. Zhao, "Interlevel electromagnetic response of systems of spherical quantum dots," Phys. Rev. B 71, 115304 (2005).
[CrossRef]

Brenig, W.

R. Zeyher, J. L. Birman, and W. Brenig, "Spatial Dispersion Effects in Resonant Polariton Scattering. I. Additional Boundary Conditions for Polarization Fields," Phys. Rev. B 6, 4613 (1972).
[CrossRef]

Chen, X.

Y. Zeng, Y. Fu, X. Chen, W. Lu, H. Agren, "Complete band gaps in three-dimensional quantum dot photonic crystals," Phys. Rev. B 74, 115325 (2006).
[CrossRef]

Y. Zeng, X. Chen, W. Lu, Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313 (2006).
[CrossRef]

Cho, K.

H. Ajiki, T. Tsuji, K. Kawano, K. Cho, "Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal," Phys. Rev. B 66, 245322 (2002).
[CrossRef]

Dey, S.

S. Dey, R. Mittra, "Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation," IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
[CrossRef]

Fu, Y.

Y. Zeng, Y. Fu, X. Chen, W. Lu, H. Agren, "Complete band gaps in three-dimensional quantum dot photonic crystals," Phys. Rev. B 74, 115325 (2006).
[CrossRef]

Y. Zeng, X. Chen, W. Lu, Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313 (2006).
[CrossRef]

Y. Fu, E. Berglind, L. Thyl’en, H. ° Agren, "Optical transmission and waveguiding by excitonic quantum dot lattices," J. Opt. Soc. Am. B 23, 2441 (2006).
[CrossRef]

Y. Fu, M. Willander, E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlatt.Microstruct. 27, 255 (2000).
[CrossRef]

Fuchs, C.

F. Thiele, C. Fuchs, R. Baltz, "Optical absorption in semiconductor quantum dots: Nonlocal effects," Phys. Rev. B 64, 205309 (2001).
[CrossRef]

Gerace, D.

L. C. Andreani, D. Gerace, M. Agio, "Exciton-polaritons and nanoscale cavities in photonic crystal slab," Phys. Status Solidi B. 242, 2197 (2005).
[CrossRef]

Guo, W.

W. Guo, W. Li, Y. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation," IEEE Microwave and Wireless Components Lett. 11, 223 (2001).
[CrossRef]

Herrmann, J.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

Hoffmann, A.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, A. Hoffmann, D. Bimberg, "Effective boundary conditions for planar quantum dot structures," Phys. Rev. B 64, 125326 (2001).
[CrossRef]

Hua, Y.

Y. Hua, T. K. Sarkar, "Generalized pencil-of-function method for extracting poles of an EM system from its transient response," IEEE Trans. Antennas Propag. 37, 229 (1989).
[CrossRef]

Huang, L.

Huang, Y.

W. Guo, W. Li, Y. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation," IEEE Microwave and Wireless Components Lett. 11, 223 (2001).
[CrossRef]

Hughes, S.

V. S. C. Manga Rao, S. Hughes, "Single quantum-dot Purcell factor and ® factor in a photonic crystal waveguide," Phys. Rev. B 75, 205437 (2007).
[CrossRef]

S. Hughes, "Coupled-cavity QED using planar photonic crystals," Phys. Rev. Lett. 98, 083603 (2007).
[CrossRef] [PubMed]

Iida, T.

T. Iida, H. Ishihara, "Force control between quantum dots by light in polaritonic molecule states," Phys. Rev. Lett. 97, 117402 (2006).
[CrossRef] [PubMed]

Ishihara, H.

T. Iida, H. Ishihara, "Force control between quantum dots by light in polaritonic molecule states," Phys. Rev. Lett. 97, 117402 (2006).
[CrossRef] [PubMed]

H. Ajiki, T. Kaneno, H. Ishihara, "Vacuum-field Rabi splitting in semiconducting core-shell microsphere," Phys. Rev. B 73, 155322 (2006).
[CrossRef]

Ivchenko, E. L.

Y. Fu, M. Willander, E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlatt.Microstruct. 27, 255 (2000).
[CrossRef]

Kalosha, V. P.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, A. Hoffmann, D. Bimberg, "Effective boundary conditions for planar quantum dot structures," Phys. Rev. B 64, 125326 (2001).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

Kaneno, T.

H. Ajiki, T. Kaneno, H. Ishihara, "Vacuum-field Rabi splitting in semiconducting core-shell microsphere," Phys. Rev. B 73, 155322 (2006).
[CrossRef]

Kawano, K.

H. Ajiki, T. Tsuji, K. Kawano, K. Cho, "Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal," Phys. Rev. B 66, 245322 (2002).
[CrossRef]

Kempa, K.

K. Kempa, R. Ruppin, J. B. Pendry, "Electromagntic response of a point-dipole crystal," Phys. Rev. B 72, 205103 (2005).
[CrossRef]

Klugkist, J. A.

J. A. Klugkist, M. Mostovoy, J. Knoester, "Mode Softening, Ferroelectric Transition, and Tunable Photonic Band Structures in a Point-Dipole Crystal," Phys. Rev. Lett. 96, 163903 (2006).
[CrossRef] [PubMed]

Knoester, J.

J. A. Klugkist, M. Mostovoy, J. Knoester, "Mode Softening, Ferroelectric Transition, and Tunable Photonic Band Structures in a Point-Dipole Crystal," Phys. Rev. Lett. 96, 163903 (2006).
[CrossRef] [PubMed]

Krestnikov, I. L.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

Ledentsov, N. N.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

Lee, C. P.

O. Voskoboynikov, C. M. J. Wijers, J. L. Liu, C. P. Lee, "Magneto-optical response of layers of semiconductor quantum dots and nanorings," Phys. Rev. B 71, 245332 (2005).
[CrossRef]

Li, W.

W. Guo, W. Li, Y. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation," IEEE Microwave and Wireless Components Lett. 11, 223 (2001).
[CrossRef]

Lin, L. Y.

L. Huang, C. Wang, L. Y. Lin, "A comparison of crosstalk effects between colloidal quantum dot waveguides and conventional waveguides," Opt. Lett. 32, 235 (2007).
[CrossRef] [PubMed]

C. Wang, L. Huang, B. A. Parviz, L. Y. Lin, "Subdiffraction Photon Guidance by Quantum-Dot Cascades," Nano Lett. 6, 2549 (2006).
[CrossRef] [PubMed]

C. Wang, L. Y. Lin, B. A. Parviz, "Modeling and simulation for a nano-photonic quantum dot waveguide fabricated by DNA-directed self-assembly," J. Sel. Top. Quantum Electron. 11, 500 (2005).
[CrossRef]

Liu, J. L.

O. Voskoboynikov, C. M. J. Wijers, J. L. Liu, C. P. Lee, "Magneto-optical response of layers of semiconductor quantum dots and nanorings," Phys. Rev. B 71, 245332 (2005).
[CrossRef]

Lu, W.

Y. Zeng, X. Chen, W. Lu, Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313 (2006).
[CrossRef]

Y. Zeng, Y. Fu, X. Chen, W. Lu, H. Agren, "Complete band gaps in three-dimensional quantum dot photonic crystals," Phys. Rev. B 74, 115325 (2006).
[CrossRef]

Maksimenko, S. A.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, A. Hoffmann, D. Bimberg, "Effective boundary conditions for planar quantum dot structures," Phys. Rev. B 64, 125326 (2001).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

Manga Rao, V. S. C.

V. S. C. Manga Rao, S. Hughes, "Single quantum-dot Purcell factor and ® factor in a photonic crystal waveguide," Phys. Rev. B 75, 205437 (2007).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (2005).
[CrossRef]

Mertens, H.

H. Mertens, J. S. Biteen, H. A. Atwater, A. Polman, "Polarization-Selective Plasmon-Enhanced Silicon Quantum-Dot Luminescence," Nano Lett. 6, 2622 (2006).
[CrossRef] [PubMed]

Meyer, J. R.

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

Mittra, R.

S. Dey, R. Mittra, "Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation," IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
[CrossRef]

Mostovoy, M.

J. A. Klugkist, M. Mostovoy, J. Knoester, "Mode Softening, Ferroelectric Transition, and Tunable Photonic Band Structures in a Point-Dipole Crystal," Phys. Rev. Lett. 96, 163903 (2006).
[CrossRef] [PubMed]

Mukamel, S.

L. Belleguie, S. Mukamel, "Nonlocal electrodynamics of arrays of quantum dots," Phys. Rev. B 52, 1936 (1995).
[CrossRef]

Nojima, S.

S. Nojima, "Optical response of excitonic polaritons in photonic crystals," Phys. Rev. B 59, 5662 (1999).
[CrossRef]

Ozbay, E.

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-93 (2006).
[CrossRef] [PubMed]

Parviz, B. A.

C. Wang, L. Huang, B. A. Parviz, L. Y. Lin, "Subdiffraction Photon Guidance by Quantum-Dot Cascades," Nano Lett. 6, 2549 (2006).
[CrossRef] [PubMed]

C. Wang, L. Y. Lin, B. A. Parviz, "Modeling and simulation for a nano-photonic quantum dot waveguide fabricated by DNA-directed self-assembly," J. Sel. Top. Quantum Electron. 11, 500 (2005).
[CrossRef]

Pendry, J. B.

K. Kempa, R. Ruppin, J. B. Pendry, "Electromagntic response of a point-dipole crystal," Phys. Rev. B 72, 205103 (2005).
[CrossRef]

Pereda, J. A.

J. A. Pereda, L. A. Vielva, A. Vegas, A. Prieto, "Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony’s methods," IEEE Microwave Guid. Wave Lett. 2, 431 (1992).
[CrossRef]

Polman, A.

H. Mertens, J. S. Biteen, H. A. Atwater, A. Polman, "Polarization-Selective Plasmon-Enhanced Silicon Quantum-Dot Luminescence," Nano Lett. 6, 2622 (2006).
[CrossRef] [PubMed]

Prieto, A.

J. A. Pereda, L. A. Vielva, A. Vegas, A. Prieto, "Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony’s methods," IEEE Microwave Guid. Wave Lett. 2, 431 (1992).
[CrossRef]

Ram-Mohan, L. R.

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

Ruppin, R.

K. Kempa, R. Ruppin, J. B. Pendry, "Electromagntic response of a point-dipole crystal," Phys. Rev. B 72, 205103 (2005).
[CrossRef]

Sarkar, T. K.

Y. Hua, T. K. Sarkar, "Generalized pencil-of-function method for extracting poles of an EM system from its transient response," IEEE Trans. Antennas Propag. 37, 229 (1989).
[CrossRef]

Sharma, P.

X. Zhang, P. Sharma, "Size dependency of strain in arbitrary shaped anisotropic embedded quantum dots due to nonlocal dispersive effects," Phys. Rev. B 72, 195345 (2005).
[CrossRef]

Slepyan, G. Ya.

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, A. Hoffmann, D. Bimberg, "Effective boundary conditions for planar quantum dot structures," Phys. Rev. B 64, 125326 (2001).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (2005).
[CrossRef]

Thiele, F.

F. Thiele, C. Fuchs, R. Baltz, "Optical absorption in semiconductor quantum dots: Nonlocal effects," Phys. Rev. B 64, 205309 (2001).
[CrossRef]

Thyl’en, L.

Tsuji, T.

H. Ajiki, T. Tsuji, K. Kawano, K. Cho, "Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal," Phys. Rev. B 66, 245322 (2002).
[CrossRef]

Vegas, A.

J. A. Pereda, L. A. Vielva, A. Vegas, A. Prieto, "Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony’s methods," IEEE Microwave Guid. Wave Lett. 2, 431 (1992).
[CrossRef]

Vielva, L. A.

J. A. Pereda, L. A. Vielva, A. Vegas, A. Prieto, "Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony’s methods," IEEE Microwave Guid. Wave Lett. 2, 431 (1992).
[CrossRef]

Voskoboynikov, O.

O. Voskoboynikov, C. M. J. Wijers, J. L. Liu, C. P. Lee, "Magneto-optical response of layers of semiconductor quantum dots and nanorings," Phys. Rev. B 71, 245332 (2005).
[CrossRef]

Vurgaftman, I.

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

Wang, C.

L. Huang, C. Wang, L. Y. Lin, "A comparison of crosstalk effects between colloidal quantum dot waveguides and conventional waveguides," Opt. Lett. 32, 235 (2007).
[CrossRef] [PubMed]

C. Wang, L. Huang, B. A. Parviz, L. Y. Lin, "Subdiffraction Photon Guidance by Quantum-Dot Cascades," Nano Lett. 6, 2549 (2006).
[CrossRef] [PubMed]

C. Wang, L. Y. Lin, B. A. Parviz, "Modeling and simulation for a nano-photonic quantum dot waveguide fabricated by DNA-directed self-assembly," J. Sel. Top. Quantum Electron. 11, 500 (2005).
[CrossRef]

Wijers, C. M. J.

O. Voskoboynikov, C. M. J. Wijers, J. L. Liu, C. P. Lee, "Magneto-optical response of layers of semiconductor quantum dots and nanorings," Phys. Rev. B 71, 245332 (2005).
[CrossRef]

Willander, M.

Y. Fu, M. Willander, E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlatt.Microstruct. 27, 255 (2000).
[CrossRef]

Zaluzny, M.

V. Bondarenko, M. Zaluzny, Y. Zhao, "Interlevel electromagnetic response of systems of spherical quantum dots," Phys. Rev. B 71, 115304 (2005).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (2005).
[CrossRef]

Zeng, Y.

Y. Zeng, Y. Fu, X. Chen, W. Lu, H. Agren, "Complete band gaps in three-dimensional quantum dot photonic crystals," Phys. Rev. B 74, 115325 (2006).
[CrossRef]

Y. Zeng, X. Chen, W. Lu, Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313 (2006).
[CrossRef]

Zeyher, R.

R. Zeyher, J. L. Birman, and W. Brenig, "Spatial Dispersion Effects in Resonant Polariton Scattering. I. Additional Boundary Conditions for Polarization Fields," Phys. Rev. B 6, 4613 (1972).
[CrossRef]

Zhang, X.

X. Zhang, P. Sharma, "Size dependency of strain in arbitrary shaped anisotropic embedded quantum dots due to nonlocal dispersive effects," Phys. Rev. B 72, 195345 (2005).
[CrossRef]

Zhao, Y.

V. Bondarenko, M. Zaluzny, Y. Zhao, "Interlevel electromagnetic response of systems of spherical quantum dots," Phys. Rev. B 71, 115304 (2005).
[CrossRef]

Eur. Phys. J. B

Y. Zeng, X. Chen, W. Lu, Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313 (2006).
[CrossRef]

IEEE Microwave and Wireless Components Lett.

W. Guo, W. Li, Y. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation," IEEE Microwave and Wireless Components Lett. 11, 223 (2001).
[CrossRef]

IEEE Microwave Guid. Wave Lett.

S. Dey, R. Mittra, "Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation," IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
[CrossRef]

J. A. Pereda, L. A. Vielva, A. Vegas, A. Prieto, "Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony’s methods," IEEE Microwave Guid. Wave Lett. 2, 431 (1992).
[CrossRef]

IEEE Trans. Antennas Propag.

Y. Hua, T. K. Sarkar, "Generalized pencil-of-function method for extracting poles of an EM system from its transient response," IEEE Trans. Antennas Propag. 37, 229 (1989).
[CrossRef]

J. Appl. Phys.

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Sel. Top. Quantum Electron.

C. Wang, L. Y. Lin, B. A. Parviz, "Modeling and simulation for a nano-photonic quantum dot waveguide fabricated by DNA-directed self-assembly," J. Sel. Top. Quantum Electron. 11, 500 (2005).
[CrossRef]

Microstruct.

Y. Fu, M. Willander, E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlatt.Microstruct. 27, 255 (2000).
[CrossRef]

Nano Lett.

H. Mertens, J. S. Biteen, H. A. Atwater, A. Polman, "Polarization-Selective Plasmon-Enhanced Silicon Quantum-Dot Luminescence," Nano Lett. 6, 2622 (2006).
[CrossRef] [PubMed]

C. Wang, L. Huang, B. A. Parviz, L. Y. Lin, "Subdiffraction Photon Guidance by Quantum-Dot Cascades," Nano Lett. 6, 2549 (2006).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rep.

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (2005).
[CrossRef]

Phys. Rev. B

Y. Zeng, Y. Fu, X. Chen, W. Lu, H. Agren, "Complete band gaps in three-dimensional quantum dot photonic crystals," Phys. Rev. B 74, 115325 (2006).
[CrossRef]

S. Nojima, "Optical response of excitonic polaritons in photonic crystals," Phys. Rev. B 59, 5662 (1999).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, A. Hoffmann, D. Bimberg, "Effective boundary conditions for planar quantum dot structures," Phys. Rev. B 64, 125326 (2001).
[CrossRef]

O. Voskoboynikov, C. M. J. Wijers, J. L. Liu, C. P. Lee, "Magneto-optical response of layers of semiconductor quantum dots and nanorings," Phys. Rev. B 71, 245332 (2005).
[CrossRef]

V. Bondarenko, M. Zaluzny, Y. Zhao, "Interlevel electromagnetic response of systems of spherical quantum dots," Phys. Rev. B 71, 115304 (2005).
[CrossRef]

L. Belleguie, S. Mukamel, "Nonlocal electrodynamics of arrays of quantum dots," Phys. Rev. B 52, 1936 (1995).
[CrossRef]

X. Zhang, P. Sharma, "Size dependency of strain in arbitrary shaped anisotropic embedded quantum dots due to nonlocal dispersive effects," Phys. Rev. B 72, 195345 (2005).
[CrossRef]

F. Thiele, C. Fuchs, R. Baltz, "Optical absorption in semiconductor quantum dots: Nonlocal effects," Phys. Rev. B 64, 205309 (2001).
[CrossRef]

H. Ajiki, T. Tsuji, K. Kawano, K. Cho, "Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal," Phys. Rev. B 66, 245322 (2002).
[CrossRef]

H. Ajiki, T. Kaneno, H. Ishihara, "Vacuum-field Rabi splitting in semiconducting core-shell microsphere," Phys. Rev. B 73, 155322 (2006).
[CrossRef]

R. Zeyher, J. L. Birman, and W. Brenig, "Spatial Dispersion Effects in Resonant Polariton Scattering. I. Additional Boundary Conditions for Polarization Fields," Phys. Rev. B 6, 4613 (1972).
[CrossRef]

G. Ya. Slepyan, S. A. Maksimenko, V. P. Kalosha, J. Herrmann, N. N. Ledentsov, I. L. Krestnikov, Zh. I. Alferov, D. Bimberg, "Polarization splitting of the gain band in quantum wire and quantum dot arrays," Phys. Rev. B 59, 12275 (1999).
[CrossRef]

K. Kempa, R. Ruppin, J. B. Pendry, "Electromagntic response of a point-dipole crystal," Phys. Rev. B 72, 205103 (2005).
[CrossRef]

V. S. C. Manga Rao, S. Hughes, "Single quantum-dot Purcell factor and ® factor in a photonic crystal waveguide," Phys. Rev. B 75, 205437 (2007).
[CrossRef]

Phys. Rev. Lett.

J. A. Klugkist, M. Mostovoy, J. Knoester, "Mode Softening, Ferroelectric Transition, and Tunable Photonic Band Structures in a Point-Dipole Crystal," Phys. Rev. Lett. 96, 163903 (2006).
[CrossRef] [PubMed]

T. Iida, H. Ishihara, "Force control between quantum dots by light in polaritonic molecule states," Phys. Rev. Lett. 97, 117402 (2006).
[CrossRef] [PubMed]

S. Hughes, "Coupled-cavity QED using planar photonic crystals," Phys. Rev. Lett. 98, 083603 (2007).
[CrossRef] [PubMed]

Phys. Status Solidi B.

L. C. Andreani, D. Gerace, M. Agio, "Exciton-polaritons and nanoscale cavities in photonic crystal slab," Phys. Status Solidi B. 242, 2197 (2005).
[CrossRef]

Science

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-93 (2006).
[CrossRef] [PubMed]

Other

H. Haug, S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1986).

G. A. Baker, Essentials of Pad’e approximants, (Academic Press, New York, 1975).

F. J. Taylor, Principles of signals and systems, (McGraw-Hill, New York, 1994).

M. Born, E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, (Pergamon Press 1959).
[PubMed]

A. Taflove, S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method, Second Edition, (Artech House Boston 2000).

Cited By

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic drawing of a freestanding dielectric film embedded with a square array of quantum dots. The quantum dot has a radius of R, the square array has a period of L, and the dielectric film has a thickness of 2R. (b) A cross section of the computational domain consisting of a single unit cell of the quantum-dot array. Periodic boundary conditions are imposed on the four surfaces perpendicular to the dielectric film, while perfect matched layers are imposed at the top and bottom surfaces. The input light wave is polarized along the z direction and propagates to the top dielectric surface along the x direction. The transmitted electric field is collected at the detector point.

Fig. 2.
Fig. 2.

The normalized amplitude spectra (at the center of the QD) of single-layer quantum-dot arrays with different period L. The dielectric film has a thickness of 40 nm.

Fig. 3.
Fig. 3.

The distribution of |E 2 z | of single-layer quantum-dot arrays at resonant frequencies, at vertical (x-y plane) cross section and cross section (y-z plane), respectively. (a) L=60 nm and the resonant frequency is ω 0 +0.404ω LT. (b) L=100 nm and the resonant frequency is ω 0+0.363ω LT. (c) L=150 nm and the resonant frequency is ω 0+0.345ω LT. The position of quantum dot is marked by dotted lines.

Fig. 4.
Fig. 4.

Variation of |E 2 z | along (a) z axis and (b) x axis including the center of quantum dot, for single-layer quantum-dot arrays with different period L. The position of quantum dot is marked by dash dotted lines.

Fig. 5.
Fig. 5.

The transmission spectrum of a single-layer quantum-dot array. The square array has a period of L=60 nm.

Fig. 6.
Fig. 6.

(a) The normalized spectrum of a double-layer quantum-dot array as well as that of the corresponding single-layer array. The square array has a period of L=60 nm, and the separation between the two layers is s=40 nm. Schematic drawing of a double-layer geometry (b) and a single-layer geometry (c). The quantum dot has a radius of R.

Fig. 7.
Fig. 7.

The distribution of |E 2 z | at a resonant frequency of ω 0+0.726ω LT, at (a,b) cross section (y-z plane) and (c) vertical (x-y plane) cross section, respectively. The double-layer quantum-dot array is same as that in Fig.(6b). The position of quantum dot is marked by dotted lines.

Fig. 8.
Fig. 8.

Variation of |E 2 z | along (a) x axis and (b) z axis including the center of quantum dot. The double-layer quantum-dot array is same as that in Fig.(6b). The position of quantum dot is marked by dash dotted lines.

Equations (24)

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

P ( r , ω ) = T ( ω ) Φ ( r ) Φ ( r ) E ( r , ω ) d r ,
Φ ( r e , r h ) = 1 r a 2 π R sin ( π r a R ) 1 π a B 3 e r e r h a B .
T ( ω ) = 2 π ε 0 ε b ω LT ω 0 a B 3 ω 0 2 ω 2 2 j ω δ .
ω 0 = E g h + h π 2 2 m 0 R 2 e ( 1 m e + 1 m h ) ,
× E = μ 0 H t , × H = ε 0 E t + J , J = P t .
P ( r , ω ) = A ω 0 2 ω 2 2 j ω δ E new ( r , ω ) ,
sinc ( π r a R ) sinc ( π r a R ) E ( r , ω ) d r R 3 ,
J ( r , ω ) j ω P ( r , ω ) = A j ω ω 0 2 ω 2 2 j ω δ E new ( r , ω ) ,
ω 0 2 J ( t ) + 2 δ d dt J ( t ) + d 2 dt 2 J ( t ) = A d dt E new ( t ) .
J n + 1 = a p J n + b p J n 1 + c p [ E new n + 1 2 E new n 1 2 ] ,
a p = 2 ω 0 2 Δ t 2 1 + δ Δ t , b p = δ Δ t 1 1 + δ Δ t , c p = A Δ t 1 + δ Δ t .
× H ( t ) = ε 0 ε b d dt E ( t ) + J ( t ) ,
E n + 3 2 = E n + 1 2 + Δ t ε 0 ε b [ × H n + 1 J n + 1 ] .
U ( N , ω ) = n = 0 N μ ( n Δ t ) exp ( i n ω Δ t ) ,
U ( , ω ) = n = μ ( n Δ t ) exp ( i n ω Δ t ) ,
U ( ω ) = μ ( t ) exp ( i ω t ) d t .
B Δ t < 1 ,
P ( ω ) = n = 0 N μ ( n Δ t ) exp ( in ω Δ t )
P ( ω ) = P p ( ω ) + P np ( ω ) ,
P ( ω ) = [ η N ( z ) θ N ( z ) ] z = e i ω Δ t ,
η N ( z ) = n = 0 N α n z n , θ N ( z ) = n = 0 N β n z n .
η 2 j ( z ) = η 2 j 2 ( z ) z η 2 j 1 ( z ) η ¯ 2 j 2 η 2 j 1 , θ 2 j ( z ) = θ 2 j 2 ( z ) z θ 2 j 1 ( z ) η ¯ 2 j 2 η 2 j 1 ,
η 2 j + 1 ( z ) = η ¯ 2 j η 2 j 1 ( z ) η ¯ 2 j 1 η 2 j ( z ) η 2 j η 2 j 1 , θ 2 j + 1 ( z ) = η ¯ 2 j θ 2 j 1 ( z ) η ¯ 2 j 1 θ 2 j ( z ) η 2 j η 2 j 1 ,
η 0 ( z ) = n = 0 N μ ( n Δ t ) z n , η 1 ( z ) = n = 0 N 1 μ ( n Δ t ) z n ,

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