Abstract

Metal–dielectric–metal configurations of optical waveguides have a very high laterally packaging density at the cost of high optical loss. Photonic crystals based on refractive-index-modulation materials have been used in optics, e.g., two materials having different refractive indices form a well-defined Bragg refraction mirror. Such a waveguide has lower loss but also lower packaging density. From the outset of these two notions, we propose a photonic-crystal device based on the exciton-polariton effect in a three-dimensional array of semiconductor quantum dots (QDs) for ultradense optical planar circuit applications. Excitons are first photogenerated in the QDs by the incident electromagnetic field, the exciton–polariton effect in the QD photonic crystal then induces an extra optical dispersion in QDs. The high contrast ratio between the optical dispersions of the QDs and the background therefore creates clear photonic bandgaps. By carefully designing the QD size and the QD lattice structure, perfect electromagnetic field reflection can be obtained at a specific wavelength in the lossless case, thus providing the fundamental basis for ultradense optical waveguide applications.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  31. J. M. Vazquez, J.-Z. Zhang, and I. Galbraith, "Quantum dot versus quantum well semiconductor optical amplifiers for subpicosecond pulse amplification," Opt. Quantum Electron. 36, 539-549 (2004).
    [CrossRef]
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    [CrossRef]
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2006 (3)

Y. Zeng, X.-S. Chen, W. Lu, and Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313-318 (2006).
[CrossRef]

Y. Fu, T.-T. Han, Y. Luo, and H. Ågren, "Multiphoton excitation of quantum dots by ultra-short and ultra-intense laser pulse," Appl. Phys. Lett. 88, 221114 (2006).
[CrossRef]

L. Thylén and E. Berglind, "Nanophotonics and negative epsilon materials," J. Zhejiang Univ., Sci. 7, 41-44 (2006).
[CrossRef]

2005 (1)

H. H. Nilsson, J.-Z. Zhang, and I. Galbraith, "Homogeneous broadening in quantum dots due to Auger scattering with wetting layer carriers," Phys. Rev. B 72, 205331 (2005).
[CrossRef]

2004 (4)

J. M. Vazquez, J.-Z. Zhang, and I. Galbraith, "Quantum dot versus quantum well semiconductor optical amplifiers for subpicosecond pulse amplification," Opt. Quantum Electron. 36, 539-549 (2004).
[CrossRef]

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

T. Ishihara, "Optical response of semiconductor and metal-embedded photonic crystal slabs," Phys. Status Solidi A 201, 398-404 (2004).
[CrossRef]

2003 (3)

J. Ishi-Hayase and T. Ishihara, "Fundamental optical properties of photonic crystal slabs in the strong coupling regime," Semicond. Sci. Technol. 18, 411-418 (2003).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Field expulsion and reconfiguration in polaritonic photonic crystals," Phys. Rev. Lett. 90, 196402 (2003).
[CrossRef] [PubMed]

2002 (3)

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of polaritonic crystal slab," Phys. Status Solidi A 190, 413-419 (2002).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, "Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields," IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

M. Shimizu and T. Ishihara, "Subpicosecond transmission change in semiconductor-embedded photonic crystal slab: toward ultrafast optical switching," Appl. Phys. Lett. 80, 2836-2838 (2002).
[CrossRef]

2001 (3)

I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815-5875 (2001).
[CrossRef]

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

A. Yu. Sivachenko, M. E. Raikh, and Z. V. Vardeny, "Excitations in photonic crystals infiltrated with polarizable media," Phys. Rev. A 64, 13809-13816 (2001).
[CrossRef]

2000 (2)

E. L. Ivchenko, Y. Fu, and M. Willander, "Exciton polaritons in quantum-dot photonic crystals," Phys. Solid State 42, 1756-1765 (2000).
[CrossRef]

Y. Fu, M. Willander, and E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlattices Microstruct. 27, 255-264 (2000).
[CrossRef]

1999 (2)

Y. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. B 60, 1030-1035 (1999).
[CrossRef]

T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, "Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching," J. Vac. Sci. Technol. B 17, 2734-2739 (1999).
[CrossRef]

1998 (2)

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bendings of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

L. I. Deych, D. Livdan, and A. A. Lisyansky, "Resonant tunneling of electromagnetic waves through polariton gaps," Phys. Rev. E 57, 7254-7258 (1998).
[CrossRef]

1997 (2)

Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, "Existence of a photonic pseudogap for visible light in synthetic opals," Phys. Rev. B 55, R13357-R13360 (1997).
[CrossRef]

Y. Fu, M. Willander, E. L. Ivchenko, and A. A. Kiselev, "Four-wave mixing in microcavities with embedded quantum wells," Phys. Rev. B 55, 9872-9879 (1997).
[CrossRef]

1996 (1)

W. Zhang, A. Hu, X. Lei, N. Xu, and N. Ming, "Photonic band structures of a two-dimensional ionic dielectric medium," Phys. Rev. B 54, 10280-10283 (1996).
[CrossRef]

1993 (1)

A. R. McGurn and A. A. Maradudin, "Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays," Phys. Rev. B 48, 17576-17579 (1993).
[CrossRef]

1992 (1)

E. L. Ivchenko and A. V. Kavokin, "Reflection of light from structures with quantum wells, quantum wires and quantum dots," Fiz. Tverd. Tela (Leningrad) 34, 1815-1822 (1992); [E. L. Ivchenko and A. V. Kavokin,Sov. Phys. Solid State 34, 968-971 (1992)].

1991 (1)

E. L. Ivchenko, "Excitonic polaritons in periodic quantum-well structures," Sov. Phys. Solid State 33, 1344-1346 (1991).

Ågren, H.

Y. Fu, T.-T. Han, Y. Luo, and H. Ågren, "Multiphoton excitation of quantum dots by ultra-short and ultra-intense laser pulse," Appl. Phys. Lett. 88, 221114 (2006).
[CrossRef]

Alferov, Zh. I.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Astratov, V. N.

Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, "Existence of a photonic pseudogap for visible light in synthetic opals," Phys. Rev. B 55, R13357-R13360 (1997).
[CrossRef]

Berglind, E.

L. Thylén and E. Berglind, "Nanophotonics and negative epsilon materials," J. Zhejiang Univ., Sci. 7, 41-44 (2006).
[CrossRef]

L. Thylén and E. Berglind, "Integrated photonic nanometer-sized waveguides based on metals, a feasibility investigation" (submitted to IEEE J. Quantum Electron.).

Bienstman, P.

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Field expulsion and reconfiguration in polaritonic photonic crystals," Phys. Rev. Lett. 90, 196402 (2003).
[CrossRef] [PubMed]

Bimberg, D.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Bogomolov, V. N.

Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, "Existence of a photonic pseudogap for visible light in synthetic opals," Phys. Rev. B 55, R13357-R13360 (1997).
[CrossRef]

Borri, P.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Bristow, A. D.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Chen, X.-S.

Y. Zeng, X.-S. Chen, W. Lu, and Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313-318 (2006).
[CrossRef]

Chow, E.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bendings of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

de Dood, M. J. A.

T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, "Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching," J. Vac. Sci. Technol. B 17, 2734-2739 (1999).
[CrossRef]

Deych, L. I.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

L. I. Deych, D. Livdan, and A. A. Lisyansky, "Resonant tunneling of electromagnetic waves through polariton gaps," Phys. Rev. E 57, 7254-7258 (1998).
[CrossRef]

Dimmock, J. O.

J. O. Dimmock, "Introduction to the theory of exciton states in semiconductors," in Semiconductors and Semimetals (Academic, 1967), Vol. 3, Chap. 7, pp. 259-319.
[CrossRef]

Erementchouk, M. V.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Fan, S.

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Field expulsion and reconfiguration in polaritonic photonic crystals," Phys. Rev. Lett. 90, 196402 (2003).
[CrossRef] [PubMed]

Fan, W. H.

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Fox, A. M.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Fu, Y.

Y. Fu, T.-T. Han, Y. Luo, and H. Ågren, "Multiphoton excitation of quantum dots by ultra-short and ultra-intense laser pulse," Appl. Phys. Lett. 88, 221114 (2006).
[CrossRef]

Y. Zeng, X.-S. Chen, W. Lu, and Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313-318 (2006).
[CrossRef]

Y. Fu, M. Willander, and E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlattices Microstruct. 27, 255-264 (2000).
[CrossRef]

E. L. Ivchenko, Y. Fu, and M. Willander, "Exciton polaritons in quantum-dot photonic crystals," Phys. Solid State 42, 1756-1765 (2000).
[CrossRef]

Y. Fu, M. Willander, E. L. Ivchenko, and A. A. Kiselev, "Four-wave mixing in microcavities with embedded quantum wells," Phys. Rev. B 55, 9872-9879 (1997).
[CrossRef]

Galbraith, I.

H. H. Nilsson, J.-Z. Zhang, and I. Galbraith, "Homogeneous broadening in quantum dots due to Auger scattering with wetting layer carriers," Phys. Rev. B 72, 205331 (2005).
[CrossRef]

J. M. Vazquez, J.-Z. Zhang, and I. Galbraith, "Quantum dot versus quantum well semiconductor optical amplifiers for subpicosecond pulse amplification," Opt. Quantum Electron. 36, 539-549 (2004).
[CrossRef]

Garcia-Déniz, A. Z.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

Gippius, N. A.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of polaritonic crystal slab," Phys. Status Solidi A 190, 413-419 (2002).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, "Introduction to Maxwell's equations and the Yee algorithm," Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000), Chap. 3, pp. 67-107.

Haken, H.

H. Haken, Quantum Field Theory of Solids An Introduction (North-Holland, 1983), pp. 137-140.

Han, T.-T.

Y. Fu, T.-T. Han, Y. Luo, and H. Ågren, "Multiphoton excitation of quantum dots by ultra-short and ultra-intense laser pulse," Appl. Phys. Lett. 88, 221114 (2006).
[CrossRef]

Hietala, V.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bendings of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Hirlimann, Ch.

Y. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. B 60, 1030-1035 (1999).
[CrossRef]

Hönerlage, B.

Y. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. B 60, 1030-1035 (1999).
[CrossRef]

Hu, A.

W. Zhang, A. Hu, X. Lei, N. Xu, and N. Ming, "Photonic band structures of a two-dimensional ionic dielectric medium," Phys. Rev. B 54, 10280-10283 (1996).
[CrossRef]

Huang, K. C.

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Field expulsion and reconfiguration in polaritonic photonic crystals," Phys. Rev. Lett. 90, 196402 (2003).
[CrossRef] [PubMed]

Ishihara, T.

T. Ishihara, "Optical response of semiconductor and metal-embedded photonic crystal slabs," Phys. Status Solidi A 201, 398-404 (2004).
[CrossRef]

J. Ishi-Hayase and T. Ishihara, "Fundamental optical properties of photonic crystal slabs in the strong coupling regime," Semicond. Sci. Technol. 18, 411-418 (2003).
[CrossRef]

M. Shimizu and T. Ishihara, "Subpicosecond transmission change in semiconductor-embedded photonic crystal slab: toward ultrafast optical switching," Appl. Phys. Lett. 80, 2836-2838 (2002).
[CrossRef]

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of polaritonic crystal slab," Phys. Status Solidi A 190, 413-419 (2002).
[CrossRef]

Ishi-Hayase, J.

J. Ishi-Hayase and T. Ishihara, "Fundamental optical properties of photonic crystal slabs in the strong coupling regime," Semicond. Sci. Technol. 18, 411-418 (2003).
[CrossRef]

Ivchenko, E. L.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Y. Fu, M. Willander, and E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlattices Microstruct. 27, 255-264 (2000).
[CrossRef]

E. L. Ivchenko, Y. Fu, and M. Willander, "Exciton polaritons in quantum-dot photonic crystals," Phys. Solid State 42, 1756-1765 (2000).
[CrossRef]

Y. Fu, M. Willander, E. L. Ivchenko, and A. A. Kiselev, "Four-wave mixing in microcavities with embedded quantum wells," Phys. Rev. B 55, 9872-9879 (1997).
[CrossRef]

E. L. Ivchenko and A. V. Kavokin, "Reflection of light from structures with quantum wells, quantum wires and quantum dots," Fiz. Tverd. Tela (Leningrad) 34, 1815-1822 (1992); [E. L. Ivchenko and A. V. Kavokin,Sov. Phys. Solid State 34, 968-971 (1992)].

E. L. Ivchenko, "Excitonic polaritons in periodic quantum-well structures," Sov. Phys. Solid State 33, 1344-1346 (1991).

Joannopoulos, J. D.

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Field expulsion and reconfiguration in polaritonic photonic crystals," Phys. Rev. Lett. 90, 196402 (2003).
[CrossRef] [PubMed]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bendings of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Kaplyanskii, A. A.

Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, "Existence of a photonic pseudogap for visible light in synthetic opals," Phys. Rev. B 55, R13357-R13360 (1997).
[CrossRef]

Karimov, O. Z.

Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, "Existence of a photonic pseudogap for visible light in synthetic opals," Phys. Rev. B 55, R13357-R13360 (1997).
[CrossRef]

Kavokin, A. V.

E. L. Ivchenko and A. V. Kavokin, "Reflection of light from structures with quantum wells, quantum wires and quantum dots," Fiz. Tverd. Tela (Leningrad) 34, 1815-1822 (1992); [E. L. Ivchenko and A. V. Kavokin,Sov. Phys. Solid State 34, 968-971 (1992)].

Kawazoe, T.

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, "Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields," IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

Kiselev, A. A.

Y. Fu, M. Willander, E. L. Ivchenko, and A. A. Kiselev, "Four-wave mixing in microcavities with embedded quantum wells," Phys. Rev. B 55, 9872-9879 (1997).
[CrossRef]

Klein, G.

Y. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. B 60, 1030-1035 (1999).
[CrossRef]

Kobayashi, K.

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, "Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields," IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

Krauss, T. F.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Kundys, D. O.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

Langbein, W.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Ledentsov, N. N.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Lei, X.

W. Zhang, A. Hu, X. Lei, N. Xu, and N. Ming, "Photonic band structures of a two-dimensional ionic dielectric medium," Phys. Rev. B 54, 10280-10283 (1996).
[CrossRef]

Lin, S.-Y.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bendings of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Lisyansky, A. A.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

L. I. Deych, D. Livdan, and A. A. Lisyansky, "Resonant tunneling of electromagnetic waves through polariton gaps," Phys. Rev. E 57, 7254-7258 (1998).
[CrossRef]

Livdan, D.

L. I. Deych, D. Livdan, and A. A. Lisyansky, "Resonant tunneling of electromagnetic waves through polariton gaps," Phys. Rev. E 57, 7254-7258 (1998).
[CrossRef]

Lu, W.

Y. Zeng, X.-S. Chen, W. Lu, and Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313-318 (2006).
[CrossRef]

Luo, Y.

Y. Fu, T.-T. Han, Y. Luo, and H. Ågren, "Multiphoton excitation of quantum dots by ultra-short and ultra-intense laser pulse," Appl. Phys. Lett. 88, 221114 (2006).
[CrossRef]

Maradudin, A. A.

A. R. McGurn and A. A. Maradudin, "Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays," Phys. Rev. B 48, 17576-17579 (1993).
[CrossRef]

McGurn, A. R.

A. R. McGurn and A. A. Maradudin, "Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays," Phys. Rev. B 48, 17576-17579 (1993).
[CrossRef]

Meyer, J. R.

I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815-5875 (2001).
[CrossRef]

Ming, N.

W. Zhang, A. Hu, X. Lei, N. Xu, and N. Ming, "Photonic band structures of a two-dimensional ionic dielectric medium," Phys. Rev. B 54, 10280-10283 (1996).
[CrossRef]

Muljarov, E. A.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of polaritonic crystal slab," Phys. Status Solidi A 190, 413-419 (2002).
[CrossRef]

Nelson, K. A.

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Field expulsion and reconfiguration in polaritonic photonic crystals," Phys. Rev. Lett. 90, 196402 (2003).
[CrossRef] [PubMed]

Nilsson, H. H.

H. H. Nilsson, J.-Z. Zhang, and I. Galbraith, "Homogeneous broadening in quantum dots due to Auger scattering with wetting layer carriers," Phys. Rev. B 72, 205331 (2005).
[CrossRef]

Ohtsu, M.

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, "Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields," IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

Ouyang, D.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Petit, S.

Y. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. B 60, 1030-1035 (1999).
[CrossRef]

Polman, A.

T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, "Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching," J. Vac. Sci. Technol. B 17, 2734-2739 (1999).
[CrossRef]

Prokofiev, A. V.

Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, "Existence of a photonic pseudogap for visible light in synthetic opals," Phys. Rev. B 55, R13357-R13360 (1997).
[CrossRef]

Raikh, M. E.

A. Yu. Sivachenko, M. E. Raikh, and Z. V. Vardeny, "Excitations in photonic crystals infiltrated with polarizable media," Phys. Rev. A 64, 13809-13816 (2001).
[CrossRef]

Ram-Mohan, L. R.

I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815-5875 (2001).
[CrossRef]

Roberts, J. S.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Sangu, S.

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, "Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields," IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

Schneider, S.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Shimizu, M.

M. Shimizu and T. Ishihara, "Subpicosecond transmission change in semiconductor-embedded photonic crystal slab: toward ultrafast optical switching," Appl. Phys. Lett. 80, 2836-2838 (2002).
[CrossRef]

Sivachenko, A. Yu.

A. Yu. Sivachenko, M. E. Raikh, and Z. V. Vardeny, "Excitations in photonic crystals infiltrated with polarizable media," Phys. Rev. A 64, 13809-13816 (2001).
[CrossRef]

Skolnick, M. S.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Snoeks, E.

T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, "Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching," J. Vac. Sci. Technol. B 17, 2734-2739 (1999).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, "Introduction to Maxwell's equations and the Yee algorithm," Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000), Chap. 3, pp. 67-107.

Tahraoui, A.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Thylén, L.

L. Thylén and E. Berglind, "Nanophotonics and negative epsilon materials," J. Zhejiang Univ., Sci. 7, 41-44 (2006).
[CrossRef]

L. Thylén and E. Berglind, "Integrated photonic nanometer-sized waveguides based on metals, a feasibility investigation" (submitted to IEEE J. Quantum Electron.).

Tikhodeev, S. G.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of polaritonic crystal slab," Phys. Status Solidi A 190, 413-419 (2002).
[CrossRef]

Ustinov, V. M.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

van der Drift, E.

T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, "Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching," J. Vac. Sci. Technol. B 17, 2734-2739 (1999).
[CrossRef]

Vardeny, Z. V.

A. Yu. Sivachenko, M. E. Raikh, and Z. V. Vardeny, "Excitations in photonic crystals infiltrated with polarizable media," Phys. Rev. A 64, 13809-13816 (2001).
[CrossRef]

Vazquez, J. M.

J. M. Vazquez, J.-Z. Zhang, and I. Galbraith, "Quantum dot versus quantum well semiconductor optical amplifiers for subpicosecond pulse amplification," Opt. Quantum Electron. 36, 539-549 (2004).
[CrossRef]

Villeneuve, P. R.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bendings of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Vlasov, Y. A.

Y. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. B 60, 1030-1035 (1999).
[CrossRef]

Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, "Existence of a photonic pseudogap for visible light in synthetic opals," Phys. Rev. B 55, R13357-R13360 (1997).
[CrossRef]

Voronov, M. M.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Vurgaftman, I.

I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, "Band parameters for III-V compound semiconductors and their alloys," J. Appl. Phys. 89, 5815-5875 (2001).
[CrossRef]

Wells, J.-P. R.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Whittaker, D. M.

A. D. Bristow, D. O. Kundys, A. Z. Garcia-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption," J. Appl. Phys. 96, 4729-4734 (2004).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Willander, M.

Y. Fu, M. Willander, and E. L. Ivchenko, "Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices," Superlattices Microstruct. 27, 255-264 (2000).
[CrossRef]

E. L. Ivchenko, Y. Fu, and M. Willander, "Exciton polaritons in quantum-dot photonic crystals," Phys. Solid State 42, 1756-1765 (2000).
[CrossRef]

Y. Fu, M. Willander, E. L. Ivchenko, and A. A. Kiselev, "Four-wave mixing in microcavities with embedded quantum wells," Phys. Rev. B 55, 9872-9879 (1997).
[CrossRef]

Woggon, U.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Xu, N.

W. Zhang, A. Hu, X. Lei, N. Xu, and N. Ming, "Photonic band structures of a two-dimensional ionic dielectric medium," Phys. Rev. B 54, 10280-10283 (1996).
[CrossRef]

Yablonskii, A. L.

A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of polaritonic crystal slab," Phys. Status Solidi A 190, 413-419 (2002).
[CrossRef]

Yatsui, T.

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, "Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields," IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

Zeng, Y.

Y. Zeng, X.-S. Chen, W. Lu, and Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313-318 (2006).
[CrossRef]

Zhang, J.-Z.

H. H. Nilsson, J.-Z. Zhang, and I. Galbraith, "Homogeneous broadening in quantum dots due to Auger scattering with wetting layer carriers," Phys. Rev. B 72, 205331 (2005).
[CrossRef]

J. M. Vazquez, J.-Z. Zhang, and I. Galbraith, "Quantum dot versus quantum well semiconductor optical amplifiers for subpicosecond pulse amplification," Opt. Quantum Electron. 36, 539-549 (2004).
[CrossRef]

Zhang, W.

W. Zhang, A. Hu, X. Lei, N. Xu, and N. Ming, "Photonic band structures of a two-dimensional ionic dielectric medium," Phys. Rev. B 54, 10280-10283 (1996).
[CrossRef]

Zhukov, A. E.

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Zijlstra, T.

T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, "Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching," J. Vac. Sci. Technol. B 17, 2734-2739 (1999).
[CrossRef]

Appl. Phys. Lett. (4)

M. Shimizu and T. Ishihara, "Subpicosecond transmission change in semiconductor-embedded photonic crystal slab: toward ultrafast optical switching," Appl. Phys. Lett. 80, 2836-2838 (2002).
[CrossRef]

A. D. Bristow, J.-P. R. Wells, W. H. Fan, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, "Ultrafast nonlinear response of AlGaAs two-dimensional photonic crystal waveguides," Appl. Phys. Lett. 83, 851-853 (2003).
[CrossRef]

Y. Fu, T.-T. Han, Y. Luo, and H. Ågren, "Multiphoton excitation of quantum dots by ultra-short and ultra-intense laser pulse," Appl. Phys. Lett. 88, 221114 (2006).
[CrossRef]

P. Borri, S. Schneider, W. Langbein, U. Woggon, A. E. Zhukov, V. M. Ustinov, N. N. Ledentsov, Zh. I. Alferov, D. Ouyang, and D. Bimberg, "Ultrafast carrier dynamics and dephasing in InAs quantum-dot amplifiers emitting near 1.3-μm-wavelength at room temperature," Appl. Phys. Lett. 79, 2633-2635 (2001).
[CrossRef]

Eur. Phys. J. B (1)

Y. Zeng, X.-S. Chen, W. Lu, and Y. Fu, "Exciton polaritons of nano-spherical-particle photonic crystals in compound lattices," Eur. Phys. J. B 49, 313-318 (2006).
[CrossRef]

Fiz. Tverd. Tela (Leningrad) (1)

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

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T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, "Fabrication of two-dimensional photonic crystal waveguides for 1.5 μm in silicon by deep anisotropic dry etching," J. Vac. Sci. Technol. B 17, 2734-2739 (1999).
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Figures (5)

Fig. 1
Fig. 1

Schematic of a 2D QD photonic crystal.

Fig. 2
Fig. 2

Energy dispersion relation of a primitive cubic QD photonic crystal. ω LT ω a = 5 × 10 3 . A complete photonic stop band does not exist, while the prominent partial photonic stop band along the [001] direction is marked with arrows.

Fig. 3
Fig. 3

Reflectance from single (red dotted curves) and double (with a spatial separation of a, black solid curves) planes containing the quadratic QD lattice with two different periods. ω a = 1.0 eV , ω LT = 0.5 meV . (a) a = 198 nm and R = 50 nm . (b) a = 227 nm and R = 57 nm .

Fig. 4
Fig. 4

Optical waveguide by the excitonic QD array.

Fig. 5
Fig. 5

Spatial distributions of the E x field’s amplitude. ( a ) + ( a ) ω = ω a + 0.1 ω LT . ( b ) + ( b ) ω = ω a + 0.28 ω LT . ( c ) + ( c ) ω = ω a + 0.5 ω LT .

Equations (33)

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2 e 2 2 m 0 + U ( r e ) 2 h 2 2 m 0 + U ( r h ) e 2 4 π ϵ r e r h ,
Ψ n K ( r e , r h ) = k e , k h A n K ( k e , k h ) ψ k e ( r e ) ψ k h ( r h ) ,
ψ k e ( r e ) = 1 N e i k e r e u c ( r e ) , ψ k h ( r h ) = 1 N e i k h r h u v ( r h ) ,
H 0 ψ n K ( r e , r h ) = E n K ψ n K ( r e , r h ) ,
ψ n K ( r e , r h ) = 1 Ω k e , k h A n K ( k e , k h ) e i ( k e r e + k h r h ) ,
H 0 = [ E c ( i e ) E v ( i h ) e 2 4 π ϵ r e r h + V c ( r e ) + V v ( r h ) ] ,
ψ k e , k h ( r e , r h ) ψ k e ( r e ) ψ k h ( r h ) = α k e + β k h + Ψ 0 ( r e , r h ) ,
ψ n K ( r e , r h ) = k e , k h Ψ k e , k h Ψ k e , k h Ψ n K = k e , k h A n K ( k e , k h ) α k e + β k h + Ψ 0 .
V = d ( r ) E ( r , t ) d r ,
d ( r ) = e r e δ ( r r e ) + e r h δ ( r r h ) .
r e , r h , t = Ψ 0 ( r e , r h ) + c ( t ) Ψ n K ( r e , r h , t ) ,
i t r e , r h , t = ( H 0 + V ) r e , r h , t ,
i d c ( t ) d t = e i ( ω n K + i γ ) t Ψ n K ( r e , r h ) d ( r ) E ( r , t ) d r Ψ 0 ( r e , r h ) ,
P n K ( r , t ) = r e , r h , t d ( r ) r e , r h , t = Ψ n K ( r e , r h ) d ( r ) Ψ 0 ( r e , r h ) c * ( t ) + c.c.
c ( ) = 1 2 ( ω a ω + i γ ) Ψ a ( r e , r h ) d ( r ) E ( r ) d r Ψ 0 ( r e , r h ) ,
P a ( r ) = e 2 p cv ( ω ω a ) [ ( ω a ω ) 2 + γ 2 ] ω a 2 m 0 2 ψ a ( r , r ) ψ a ( r , r ) p ̇ cv E ( r ) d r ,
ψ a ( r e , r h ) = 1 2 π R a R a sin ( π R a R a ) 1 π a B 3 e ( r e r h a B )
× [ × E ( r ) ] = μ 0 ω 2 D ( r ) ,
D ( r ) = 0 ,
D ( r ) = ϵ E ( r ) + P ( r ) = ϵ E ( r ) + a P a ( r ) ,
ϵ a ( r ) = P a E = e 2 p cv 2 ( ω ω a ) ω a 2 m 0 2 ψ a ( r , r ) ψ a ( r , r ) d r = ϵ 2 ω LT ω ω a sin ( α a ) α a ,
E ( r ) = 1 ϵ P ( r ) ,
2 E ( r ) + k 2 E ( r ) = k 0 2 ϵ 0 { P ( r ) + 1 k 2 [ P ( r ) ] } ,
E q ( r + a ) = e i q a E q ( r ) ,
E ( z z L ) = e i k ( z z L ) E 0 + g e i g ( r r L ) E g ,
E ( z L < z z R ) = E q + E q ,
E ( z R z ) = g + e i g + ( r r R ) E g + .
g ± = [ 2 π l a , 2 π m a , ± k 2 ( 2 π a ) 2 ( l 2 + m 2 ) ] ,
E ( z z L ) = e i k ( z z L ) E 0 + e i k ( z z L ) E r ,
E ( z L < z z R ) = n [ e i ( q + b n ) z E q + b n A q + e i ( q + b n ) z E q + b n B q ] ,
E ( z R z ) = e i k ( z z R ) E t ,
i d c a ( t ) d t = e i ω a t ψ a ( r , r ) p cv E ( r , t ) d r ,
P ( r , t ) = a i e 2 p cv 2 ω a 2 m 0 2 ψ a ( r , r ) c a * ( t ) + c.c.

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