Abstract

The measured, angle-dependent, reflection spectra of a two-dimensional GaAs photonic crystal consist of an asymmetric peak on top of an oscillating background. At large angles of incidence (>70°), the asymmetry of the peak is observed to flip for p-polarized light. We explain the observed spectra with a Fano model that includes loss and interference between a resonant waveguide component and direct Fresnel reflection of the layered structure. We show that the reversal of the asymmetry of the line is due to a change in sign of the direct reflection at Brewster’s angle.

© 2007 Optical Society of America

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References

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  1. T. F. Krauss and R. M. De la Rue, Prog. Quantum Electron. 23, 51 (1999).
    [CrossRef]
  2. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
    [CrossRef]
  3. V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
    [CrossRef]
  4. L. Li, J. Opt. Soc. Am. A 14, 2758 (1997).
    [CrossRef]
  5. D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
    [CrossRef]
  6. A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, J. Opt. Soc. Am. A 18, 1160 (2001).
    [CrossRef]
  7. S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  8. U. Fano, Phys. Rev. 124, 1866 (1961).
    [CrossRef]
  9. S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
    [CrossRef]
  10. J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
    [CrossRef]
  11. J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 205, 237 (1906).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).
  13. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Vol. 1.
  14. L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
    [CrossRef]
  15. D. Gao and Z. Zhou, Appl. Phys. Lett. 88, 163105 (2006).
    [CrossRef]

2006 (2)

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
[CrossRef]

D. Gao and Z. Zhou, Appl. Phys. Lett. 88, 163105 (2006).
[CrossRef]

2003 (1)

2002 (1)

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

2001 (1)

1999 (3)

T. F. Krauss and R. M. De la Rue, Prog. Quantum Electron. 23, 51 (1999).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

1997 (2)

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

L. Li, J. Opt. Soc. Am. A 14, 2758 (1997).
[CrossRef]

1985 (1)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Vol. 1.

1980 (1)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

1961 (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

1906 (1)

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 205, 237 (1906).
[CrossRef]

1904 (1)

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

Andreani, L. C.

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
[CrossRef]

Astratov, V. N.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Busch, A.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Cowan, A. R.

Culshaw, I. S.

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

De la Rue, R. M.

T. F. Krauss and R. M. De la Rue, Prog. Quantum Electron. 23, 51 (1999).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Fan, S.

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Gao, D.

D. Gao and Z. Zhou, Appl. Phys. Lett. 88, 163105 (2006).
[CrossRef]

Gerace, D.

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
[CrossRef]

Joannopoulos, J. D.

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Johnson, S. R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Kanskar, M.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Krauss, T. F.

T. F. Krauss and R. M. De la Rue, Prog. Quantum Electron. 23, 51 (1999).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Li, L.

MacKenzie, J.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 205, 237 (1906).
[CrossRef]

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

Morin, R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Pacradouni, V.

A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, J. Opt. Soc. Am. A 18, 1160 (2001).
[CrossRef]

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Paddon, P.

A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, J. Opt. Soc. Am. A 18, 1160 (2001).
[CrossRef]

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Vol. 1.

Skolnick, M. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Stevenson, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Suh, W.

Tiedje, T.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Whittaker, D. M.

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Young, J. F.

A. R. Cowan, P. Paddon, V. Pacradouni, and J. F. Young, J. Opt. Soc. Am. A 18, 1160 (2001).
[CrossRef]

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Zhou, Z.

D. Gao and Z. Zhou, Appl. Phys. Lett. 88, 163105 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

D. Gao and Z. Zhou, Appl. Phys. Lett. 88, 163105 (2006).
[CrossRef]

J. Opt. Soc. Am. A (3)

Philos. Trans. R. Soc. London (2)

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London 205, 237 (1906).
[CrossRef]

Phys. Rev. (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Phys. Rev. B (4)

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Phys. Rev. B 60, R16255 (1999).
[CrossRef]

D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Prog. Quantum Electron. (1)

T. F. Krauss and R. M. De la Rue, Prog. Quantum Electron. 23, 51 (1999).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Vol. 1.

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Figures (3)

Fig. 1
Fig. 1

(a) SEM image of the photonic crystal (top view) showing a square lattice of holes with a lattice constant of 320 nm and a diameter of 100 nm . The arrow indicates the direction along which the reflectance is measured. (b) SEM image of the cross section of the photonic crystal slab (taken under an angle of 59°). The approximate shape of the holes is indicated with the black curves.

Fig. 2
Fig. 2

Experimental reflection spectra of the photonic crystal slab for three angles of incidence: (a) 50°, (b) 70°, and (c) 80°. The dashed curves are fits using the model discussed in the text. The insets show the reflection coefficient r 1 for an interface of air and n eff = 2.5 , as a function of angle of incidence. The circles indicate the angle of the measurement.

Fig. 3
Fig. 3

Model for the (a) nonresonant and (b) resonant pathways in the model. The numbers indicate the different channels in the scattering matrix model. (a) Nonresonant pathways are modeled by applying effective medium theory to the photonic crystal layer and calculating the Fresnel reflection and transmission coefficients of the layered system. (b) For the resonant pathway, the incident light is refracted into a waveguide mode, which can diffract back to channels 1 and 2, but can also propagate into the substrate (3) leading to loss.

Equations (5)

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C = [ r 1 t 0 t r 2 0 0 0 1 ] ,
U = d d T i ( ω ω 0 ) + 1 τ ,
C d * = d ,
d d = 2 τ .
R = i ( ω ω 0 ) r 1 + 1 τ [ Λ r 1 + ( 1 Λ ) t ] i ( ω ω 0 ) + 1 τ 2 .

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