Abstract

We show that ominidirectional reflection is not a sufficient signature of a photonic bandgap. Although dramatic angular redistribution takes place, the mode density of the electromagnetic field is hardly altered within the ominidirectional reflection range but rather has characteristics typical of a waveguide. The strikingly large polarization anisotropy is due to the huge dielectric contrast but not to a photonic bandgap.

© 2000 Optical Society of America

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References

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  1. E. Yablanovitch, Phys. Rev. Lett. 58, 2059 (1987), S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  3. C. M. Soukolis, ed., Photonic Band Gap Materials (Kluwer, Dordrecht, The Netherlands, 1996), and references therein.
    [CrossRef]
  4. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998); Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
    [CrossRef] [PubMed]
  5. P. St. J. Russel, S. Tredwell, and P. J. Roberts, Opt. Commun. 160, 66 (1999).
    [CrossRef]
  6. In the context of Bragg mirrors in vertical-cavity surface-emitting lasers, many calculations regarding radiation patterns and waveguiding properties, as well as finite structures, have been performed. See, e.g., H. Rigneault and S. Monneret, Phys. Rev. A 54, 2356 (1996).
    [CrossRef] [PubMed]
  7. M. S. Tomas̆, Phys. Rev. A 51, 2545 (1995).
    [CrossRef]
  8. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964), Sect. 1.6.
  9. The optical thickness of a single layer is given by nd, where n is the refractive index of the layer and d is the physical thickness of the layer. By optically thick we mean that λ≪nd, and by optically thin we mean that λ≫nd.
  10. T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
    [CrossRef]

1999 (1)

P. St. J. Russel, S. Tredwell, and P. J. Roberts, Opt. Commun. 160, 66 (1999).
[CrossRef]

1998 (1)

1996 (2)

In the context of Bragg mirrors in vertical-cavity surface-emitting lasers, many calculations regarding radiation patterns and waveguiding properties, as well as finite structures, have been performed. See, e.g., H. Rigneault and S. Monneret, Phys. Rev. A 54, 2356 (1996).
[CrossRef] [PubMed]

T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
[CrossRef]

1995 (1)

M. S. Tomas̆, Phys. Rev. A 51, 2545 (1995).
[CrossRef]

1987 (1)

E. Yablanovitch, Phys. Rev. Lett. 58, 2059 (1987), S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Baets, R.

T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
[CrossRef]

Blok, H.

T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964), Sect. 1.6.

Demeulenaere, B.

T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
[CrossRef]

Fan, S.

Fink, Y.

Haus, J.

T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
[CrossRef]

Joannopoulos, J. D.

Lenstra, D.

T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Monneret, S.

In the context of Bragg mirrors in vertical-cavity surface-emitting lasers, many calculations regarding radiation patterns and waveguiding properties, as well as finite structures, have been performed. See, e.g., H. Rigneault and S. Monneret, Phys. Rev. A 54, 2356 (1996).
[CrossRef] [PubMed]

Rigneault, H.

In the context of Bragg mirrors in vertical-cavity surface-emitting lasers, many calculations regarding radiation patterns and waveguiding properties, as well as finite structures, have been performed. See, e.g., H. Rigneault and S. Monneret, Phys. Rev. A 54, 2356 (1996).
[CrossRef] [PubMed]

Roberts, P. J.

P. St. J. Russel, S. Tredwell, and P. J. Roberts, Opt. Commun. 160, 66 (1999).
[CrossRef]

Russel, P. St. J.

P. St. J. Russel, S. Tredwell, and P. J. Roberts, Opt. Commun. 160, 66 (1999).
[CrossRef]

Tomas?, M. S.

M. S. Tomas̆, Phys. Rev. A 51, 2545 (1995).
[CrossRef]

Tredwell, S.

P. St. J. Russel, S. Tredwell, and P. J. Roberts, Opt. Commun. 160, 66 (1999).
[CrossRef]

Visser, T. D.

T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
[CrossRef]

Winn, J. N.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964), Sect. 1.6.

Yablanovitch, E.

E. Yablanovitch, Phys. Rev. Lett. 58, 2059 (1987), S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

T. D. Visser, B. Demeulenaere, J. Haus, D. Lenstra, R. Baets, and H. Blok, J. Lightwave Technol. 14, 885 (1996).
[CrossRef]

Opt. Commun. (1)

P. St. J. Russel, S. Tredwell, and P. J. Roberts, Opt. Commun. 160, 66 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

In the context of Bragg mirrors in vertical-cavity surface-emitting lasers, many calculations regarding radiation patterns and waveguiding properties, as well as finite structures, have been performed. See, e.g., H. Rigneault and S. Monneret, Phys. Rev. A 54, 2356 (1996).
[CrossRef] [PubMed]

M. S. Tomas̆, Phys. Rev. A 51, 2545 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablanovitch, Phys. Rev. Lett. 58, 2059 (1987), S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Other (4)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

C. M. Soukolis, ed., Photonic Band Gap Materials (Kluwer, Dordrecht, The Netherlands, 1996), and references therein.
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964), Sect. 1.6.

The optical thickness of a single layer is given by nd, where n is the refractive index of the layer and d is the physical thickness of the layer. By optically thick we mean that λ≪nd, and by optically thin we mean that λ≫nd.

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Figures (4)

Fig. 1
Fig. 1

Mode density versus frequency ω [in c / d 1 ] for TE polarization for radiation modes, guided modes, and the sum of both (total).

Fig. 2
Fig. 2

Mode density versus ω [in c / d 1 ] for TM polarization for radiation modes, guided modes, and the sum of both (total).

Fig. 3
Fig. 3

Mode density versus ω [in c / d 1 ] for TM-polarized guided modes only, for configurations with layers of PS, ZnSe, or GaAs.

Fig. 4
Fig. 4

Wave vector k of the guided mode versus frequency ω [in c / d 2 ] for the 0th, 2nd, and 4th modes for TE and TM polarization.

Equations (3)

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Im G TE z 0 , ω = 1 4 π Re 0 d k k β j D TE 1 + r j + TE × exp 2 i β j d j - z 0 1 + r j - TE   exp 2 i β j z 0
Im G TM z 0 , ω = 1 4 π Re 0 d k k 3 k j 2 β j D TM 1 + r j + TM × exp 2 i β j d j - z 0 1 + r j - TM   exp 2 i β j z 0 + k β j k j 2 D TM × r j + TM   exp 2 i β j d j - z 0 - 1 r j - TM   exp 2 i β j z 0 - 1
r j ± q = M 11 + M 12 p a q p 1 q - M 21 + M 22 p a q M 11 + M 12 p a q p 1 q + M 21 + M 22 p a q ,

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