Abstract

Localization of light in a basic multiple photonic quantum well system (MPQWS) is investigated with the finite-difference time-domain method. Resonance tunneling and splitting are observed in a MPQWS, as electron waves to a superlattice. Our numerical results reveal a quite interesting hierarchic distribution of the field mode when the system is illuminated with plane waves at a specific frequency. That is, if the number of wells is odd (even), strong localized states occur in odd (even) indexed wells. Light localization in a MPQWS, however, seems to be confined only in a narrow incident frequency window.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. W. Ding, L. Chen, and S. Liu, "Localization properties and the effects on multi-mode switching in discrete mode CCWs," Opt. Commun. 248, 479-484 (2005).
    [CrossRef]
  16. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B 54, 11245-11251 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (3)

T. Zentgraf, A. Christ, J. Kuhl, N. A. Gippius, S. G. Tikhodeev, D. Nau, and H. Giessen, "Metallodielectric photonic crystal superlattices: influence of periodic defects on transmission properties," Phys. Rev. B 73, 115103 (2006).
[CrossRef]

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, "Surface electromagnetic waves in Fibonacci superlattices: theoretical and experimental results," Phys. Rev. B 74, 035314 (2006).
[CrossRef]

A. Yamilov, X. Wu, X. Liu, R. P. H. Chang, and H. Cao, "Self-optimization of optical confinement in an ultraviolet photonic crystal slab laser," Phys. Rev. Lett. 96, 083905 (2006).
[CrossRef] [PubMed]

2005 (2)

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, "Controlling the resonance of a photonic crystal microcavity by a near-field probe," Phys. Rev. Lett. 95, 153904 (2005).
[CrossRef] [PubMed]

W. Ding, L. Chen, and S. Liu, "Localization properties and the effects on multi-mode switching in discrete mode CCWs," Opt. Commun. 248, 479-484 (2005).
[CrossRef]

2000 (1)

F. Qiao, C. Zhang, J. Wan, and J. Zi, "Photonic quantum-well structures: multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

1999 (2)

Y. Jiang, C. Niu, and D. L. Lin, "Resonance tunneling through photonic quantum wells," Phys. Rev. B 59, 9981-9986 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

1996 (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B 54, 11245-11251 (1996).
[CrossRef]

1994 (2)

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

1984 (1)

J. K. Butler, D. E. Ackley, and D. Botez, "Coupled-mode analysis of phase-locked injection laser arrays," Appl. Phys. Lett. 44, 293-295 (1984).
[CrossRef]

1981 (1)

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

1973 (1)

R. Tsu and L. Esaki, "Tunneling in a finite superlattice," Appl. Phys. Lett. 22, 562-564 (1973).
[CrossRef]

Appl. Phys. Lett. (3)

F. Qiao, C. Zhang, J. Wan, and J. Zi, "Photonic quantum-well structures: multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

J. K. Butler, D. E. Ackley, and D. Botez, "Coupled-mode analysis of phase-locked injection laser arrays," Appl. Phys. Lett. 44, 293-295 (1984).
[CrossRef]

R. Tsu and L. Esaki, "Tunneling in a finite superlattice," Appl. Phys. Lett. 22, 562-564 (1973).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

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

Opt. Commun. (1)

W. Ding, L. Chen, and S. Liu, "Localization properties and the effects on multi-mode switching in discrete mode CCWs," Opt. Commun. 248, 479-484 (2005).
[CrossRef]

Phys. Rev. B (4)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B 54, 11245-11251 (1996).
[CrossRef]

T. Zentgraf, A. Christ, J. Kuhl, N. A. Gippius, S. G. Tikhodeev, D. Nau, and H. Giessen, "Metallodielectric photonic crystal superlattices: influence of periodic defects on transmission properties," Phys. Rev. B 73, 115103 (2006).
[CrossRef]

Y. El Hassouani, H. Aynaou, E. H. El Boudouti, B. Djafari-Rouhani, A. Akjouj, and V. R. Velasco, "Surface electromagnetic waves in Fibonacci superlattices: theoretical and experimental results," Phys. Rev. B 74, 035314 (2006).
[CrossRef]

Y. Jiang, C. Niu, and D. L. Lin, "Resonance tunneling through photonic quantum wells," Phys. Rev. B 59, 9981-9986 (1999).
[CrossRef]

Phys. Rev. Lett. (4)

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, "Controlling the resonance of a photonic crystal microcavity by a near-field probe," Phys. Rev. Lett. 95, 153904 (2005).
[CrossRef] [PubMed]

A. Yamilov, X. Wu, X. Liu, R. P. H. Chang, and H. Cao, "Self-optimization of optical confinement in an ultraviolet photonic crystal slab laser," Phys. Rev. Lett. 96, 083905 (2006).
[CrossRef] [PubMed]

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Science (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Other (4)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).
[CrossRef]

D. B. Ge and Y. B. Yan, Finite-Difference Time-Domain Method for Electromagnetic Waves, 2nd ed. (Xidian U. Press, 2005).

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

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Figures (5)

Fig. 1
Fig. 1

Schematics of photonic analog of electrons [(a) and (b)], and the two types of MPQWSs for simulation [(c) and (d)] are shown; (a) dynamic localization of light at resonance frequency; (b) dynamic localization of electrons in resonance tunneling (one-dimensional case); (c) y-infinite MPQWS; and (d) y-finite MPQWS. In (c) and (d), the dielectric columns have a radius of r = 0.2 a and a dielectric constant of ϵ = 8.9 . Plane waves are emitted from the connective boundary.

Fig. 2
Fig. 2

Resonance splitting effect at frequency ω = 0.408 ( 2 π c a ) with increasing numbers of barriers in the y-infinite system is shown. Here n is the number of wells (hence the number of barriers is n + 1 ).

Fig. 3
Fig. 3

Field distribution E z for the y-infinite MPQWS is shown, where n is the number of wells. All cases are normalized with the maximum E z of the n = 5 case.

Fig. 4
Fig. 4

(a) Transmission spectra of the y-finite MPQWS with 13 [solid (blue) curve] and 14 [dashed–dotted (green) curve] rows of dielectric columns for n = 5 , 6 , 7 wells are depicted. Along with them is a background case of the y-infinite MPQWS [dashed (red) curve] to mark the shift of resonance frequencies. All cases have a fixed well width of 3.4 a . The maximum magnitude of the spectra of the 14-row case for n = 5 [the dashed–dotted (green) curve in the bottom subfigure] is used to normalize the intensities for all y-finite cases; (b) transmission spectra of the y-finite MPQWS with 13 rows of dielectric columns for three different well widths of 3.3 a [dashed–dotted (green) curve], 3.4 a [solid (blue) curve], 3.5 a [dashed (red) curve] for n = 5 , 6 , 7 wells are depicted. All intensities are normalized with the maximum magnitude of the spectra of the case having a well width of 3.3 a for n = 6 [the dashed–dotted (green) curve in the middle subfigure]. These two plots (a) and (b), respectively, illustrate the size effect along the y and x directions.

Fig. 5
Fig. 5

Field distribution E z for the y-finite MPQWS is shown, where n is the number of wells. E z is normalized with the maximum E z of the n = 5 case in Fig. 3.

Equations (1)

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E z L ( x , y ) = m = 1 N sin ( m θ L ) v m ( y ) exp ( ( γ + γ L ) x ) ,

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