Abstract

The photonic analog of a semiconductor quantum well (QW) is constructed for the first time to our knowledge from two-dimensional periodic dielectric arrays. A sharp transmission peak is observed in the photonic band-gap spectral region of the barrier and is attributed to resonant transmission of an electromagnetic wave through a photonic bound state in this structure. In contrast with bound-state energy levels in semiconductor QW’s, the photonic bound state shifts to a higher frequency as the well width is increased, and a second bound state appears on the lower-frequency side.

© 1994 Optical Society of America

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  1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987); S. John and J. Wang, Phys. Rev. Lett. 64, 2418 (1990).
    [Crossref] [PubMed]
  2. M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
    [Crossref]
  3. H. S. Sozuer and J. W. Haus, J. Opt. Soc. Am. B 10, 296 (1993).
    [Crossref]
  4. S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
    [Crossref] [PubMed]
  5. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
    [Crossref] [PubMed]
  6. S. Y. Lin and G. Aijavalingam, Opt. Lett. 18, 1666 (1993).
    [Crossref] [PubMed]
  7. Y. Pastol, G. Ajavalingam, G. V. Kopcsay, and J.-M. Halbout, Appl. Phys. Lett. 55, 2277 (1989); G. Arjavalingam, N. Theophilou, Y. Pastol, G. V. Kopcsay, and M. Angelopoulos, J. Chem. Phys. 93, 6 (1990).
    [Crossref]
  8. G. Ajavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, IEEE Trans. Microwave Theory Tech. 38, 615 (1990).
    [Crossref]
  9. L. L. Chang, L. Esaki, and R. Tsu, Appl. Phys. Lett. 24, 593 (1974).
    [Crossref]
  10. G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Halsted, New York, 1989).
  11. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 328 (1993).
    [Crossref]
  12. See, for example, Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650 (1990); K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990); and K. M. Leung and Y. F. Liu, Phys. Rev. Lett. 65, 2646 (1990).
    [Crossref] [PubMed]

1993 (3)

1992 (1)

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
[Crossref] [PubMed]

1991 (2)

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
[Crossref] [PubMed]

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[Crossref]

1990 (2)

G. Ajavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, IEEE Trans. Microwave Theory Tech. 38, 615 (1990).
[Crossref]

See, for example, Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650 (1990); K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990); and K. M. Leung and Y. F. Liu, Phys. Rev. Lett. 65, 2646 (1990).
[Crossref] [PubMed]

1989 (1)

Y. Pastol, G. Ajavalingam, G. V. Kopcsay, and J.-M. Halbout, Appl. Phys. Lett. 55, 2277 (1989); G. Arjavalingam, N. Theophilou, Y. Pastol, G. V. Kopcsay, and M. Angelopoulos, J. Chem. Phys. 93, 6 (1990).
[Crossref]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987); S. John and J. Wang, Phys. Rev. Lett. 64, 2418 (1990).
[Crossref] [PubMed]

1974 (1)

L. L. Chang, L. Esaki, and R. Tsu, Appl. Phys. Lett. 24, 593 (1974).
[Crossref]

Aijavalingam, G.

Ajavalingam, G.

G. Ajavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, IEEE Trans. Microwave Theory Tech. 38, 615 (1990).
[Crossref]

Y. Pastol, G. Ajavalingam, G. V. Kopcsay, and J.-M. Halbout, Appl. Phys. Lett. 55, 2277 (1989); G. Arjavalingam, N. Theophilou, Y. Pastol, G. V. Kopcsay, and M. Angelopoulos, J. Chem. Phys. 93, 6 (1990).
[Crossref]

Arjavalingam, G.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
[Crossref] [PubMed]

Bastard, G.

G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Halsted, New York, 1989).

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 328 (1993).
[Crossref]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
[Crossref] [PubMed]

Chang, L. L.

L. L. Chang, L. Esaki, and R. Tsu, Appl. Phys. Lett. 24, 593 (1974).
[Crossref]

Dalichaouch, R.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
[Crossref] [PubMed]

Esaki, L.

L. L. Chang, L. Esaki, and R. Tsu, Appl. Phys. Lett. 24, 593 (1974).
[Crossref]

Halbout, J.-M.

G. Ajavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, IEEE Trans. Microwave Theory Tech. 38, 615 (1990).
[Crossref]

Y. Pastol, G. Ajavalingam, G. V. Kopcsay, and J.-M. Halbout, Appl. Phys. Lett. 55, 2277 (1989); G. Arjavalingam, N. Theophilou, Y. Pastol, G. V. Kopcsay, and M. Angelopoulos, J. Chem. Phys. 93, 6 (1990).
[Crossref]

Haus, J. W.

Joannopoulos, J. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 328 (1993).
[Crossref]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
[Crossref] [PubMed]

Kopcsay, G. V.

G. Ajavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, IEEE Trans. Microwave Theory Tech. 38, 615 (1990).
[Crossref]

Y. Pastol, G. Ajavalingam, G. V. Kopcsay, and J.-M. Halbout, Appl. Phys. Lett. 55, 2277 (1989); G. Arjavalingam, N. Theophilou, Y. Pastol, G. V. Kopcsay, and M. Angelopoulos, J. Chem. Phys. 93, 6 (1990).
[Crossref]

Lin, S. Y.

Maradudin, A. A.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[Crossref]

McCall, S. L.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
[Crossref] [PubMed]

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 328 (1993).
[Crossref]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
[Crossref] [PubMed]

Pastol, Y.

G. Ajavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, IEEE Trans. Microwave Theory Tech. 38, 615 (1990).
[Crossref]

Y. Pastol, G. Ajavalingam, G. V. Kopcsay, and J.-M. Halbout, Appl. Phys. Lett. 55, 2277 (1989); G. Arjavalingam, N. Theophilou, Y. Pastol, G. V. Kopcsay, and M. Angelopoulos, J. Chem. Phys. 93, 6 (1990).
[Crossref]

Platzman, P. M.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
[Crossref] [PubMed]

Plihal, M.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[Crossref]

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 328 (1993).
[Crossref]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
[Crossref] [PubMed]

Robertson, W. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
[Crossref] [PubMed]

Satpathy, S.

See, for example, Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650 (1990); K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990); and K. M. Leung and Y. F. Liu, Phys. Rev. Lett. 65, 2646 (1990).
[Crossref] [PubMed]

Schultz, S.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
[Crossref] [PubMed]

Shambrook, A.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[Crossref]

Sheng, P.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[Crossref]

Smith, D.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
[Crossref] [PubMed]

Sozuer, H. S.

Tsu, R.

L. L. Chang, L. Esaki, and R. Tsu, Appl. Phys. Lett. 24, 593 (1974).
[Crossref]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987); S. John and J. Wang, Phys. Rev. Lett. 64, 2418 (1990).
[Crossref] [PubMed]

Zhang, Z.

See, for example, Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650 (1990); K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990); and K. M. Leung and Y. F. Liu, Phys. Rev. Lett. 65, 2646 (1990).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

Y. Pastol, G. Ajavalingam, G. V. Kopcsay, and J.-M. Halbout, Appl. Phys. Lett. 55, 2277 (1989); G. Arjavalingam, N. Theophilou, Y. Pastol, G. V. Kopcsay, and M. Angelopoulos, J. Chem. Phys. 93, 6 (1990).
[Crossref]

L. L. Chang, L. Esaki, and R. Tsu, Appl. Phys. Lett. 24, 593 (1974).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

G. Ajavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, IEEE Trans. Microwave Theory Tech. 38, 615 (1990).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (4)

See, for example, Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650 (1990); K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990); and K. M. Leung and Y. F. Liu, Phys. Rev. Lett. 65, 2646 (1990).
[Crossref] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987); S. John and J. Wang, Phys. Rev. Lett. 64, 2418 (1990).
[Crossref] [PubMed]

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
[Crossref] [PubMed]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992); J. Opt. Soc. Am. B 10, 322 (1993).
[Crossref] [PubMed]

Other (1)

G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Halsted, New York, 1989).

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Figures (5)

Fig. 1
Fig. 1

Design of the photonic QW structure. The QW structure is constructed with n rows of empty lattice sandwiched between m rows of 2D photonic crystal, i.e., a mnm photonic QW structure. The photonic crystal consists of arrays of 10-cm-long alumina-ceramic cylindrical rods arranged parallel to one another in a 2D square lattice structure. (b) Schematic band diagram of the photonic QW structure. The continuous states in the well are quantized into a series of discrete states by the photonic band gaps of the barriers.

Fig. 2
Fig. 2

Experimental setup for COMITS measurements. The electric field is polarized parallel to the axes of the cylindrical rods. A/D, analog to digital.

Fig. 3
Fig. 3

(a) Reference spectrum taken without a sample in the beam path. It contains frequency components from 15 to 130 GHz. (b) Transmission spectrum of a thick photonic crystal of six rows, i.e., 6a0. The strong attenuation of EM waves between the first and the second allowed bands indicates the existence of a large photonic band gap Eg (labeled Eg) in the crystal. (c) Transmission spectrum of a 2–2–2 photonic QW structure. The sharp peak in the band-gap region of the barrier is attributed to resonant transmission of EM waves through a bound state of the structure. The position of the transmission peak is a direct measure of the bound-state level.

Fig. 4
Fig. 4

Transmission spectra taken from three photonic QW samples having the same barrier thickness but different QW thicknesses W = 1a0, 2a0, 3a0. For the W = 1a0 and W = 2a0 QW samples, we observe one transmission peak in the band gap. For the wider QW samples (W = 3a0), two transmission peaks were observed.

Fig. 5
Fig. 5

Frequency f of the transmission peak plotted as a function of QW thickness W. The solid dots are the measured bound-state levels, and the two horizontal lines are band edges of the fundamental band gap, i.e., the conduction-band edge and the valence-band edge. For W ≥ 3a0, an additional transmission peak moves to the band-gap region from the low-frequency side. As W is increased to 5a0, the bound-state level shifts toward the high-frequency side, or the conduction-band edge.

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