Angle-resolved reflectivity of single-domain photonic crystals: Effects of disorder

Juan F. Galisteo Lòpez; Willem L. Vos

doi:10.1103/PhysRevE.66.036616

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Angle-resolved reflectivity of single-domain photonic crystals: Effects of disorder

Juan F. Galisteo Lòpez^* and Willem L. Vos^†,‡

Van der Waals–Zeeman Instituut, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

^*Permanent address: Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Cientificas (CSIC), Cantoblanco 28049 (Madrid), Spain.
^†Permanent address: Faculty of Applied Physics and MESA+ Research Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands; email address: w.l.vos@tn.utwente.nl
^‡URL: www.photonicbandgaps.com

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Phys. Rev. E 66, 036616 – Published 25 September, 2002

DOI: https://doi.org/10.1103/PhysRevE.66.036616

Abstract

Angle-resolved reflectivity has been measured from single-domain photonic crystals consisting of air spheres in a ${TiO}_{2}$ backbone. Monochromatic beams are focused to a $10 μ m$ spot, and kept on the rotation axis with a precision better than $10 μ m .$ We report high reflectivity up to 94% and surface domains as large as $200 μ m,$ with a mosaic spread of $\pm 3 ° .$ The maximum reflectivity at normal incidence agrees well with theoretical calculations in the scalar-wave approximation, extended to include an extinction length due to diffuse scattering, that is obtained from independent experiments. The angle-resolved stop bands compare favorably with previous measurements using coarse beams as well as with prior theoretical calculations. Inhomogeneous broadening introduced by coarse beams in previous measurements is found to be small. Our results can only be understood if we assume multiple Bragg diffraction from more than one family of planes simultaneously to take place.

References (27)

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J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton University Press, Princeton, 1995).
A.F. Koenderink, P.M. Johnson, J.F. Galisteo Lòpez, and W.L. Vos, C. R. Phys. 3, 67 (2002).
W.L. Vos, H.M. van Driel, M. Megens, A.F. Koenderink, and A. Imhof, in Photonic Crystals and Light Localization in the 21st Century (Ref. [2]), pp. 191–218.
W.L. Vos, R. Sprik, A. van Blaaderen, A. Imhof, A. Lagendijk, and G.H, Wegdam, Phys. Rev. B 53, 16 231 (1996); ibid.55, 1903 (1997).
H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10 096 (1998).
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M.S. Thijssen, R. Sprik, J.E.G.J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W.L. Vos, Phys. Rev. Lett. 83, 2730 (1999).
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J.E.G.J. Wijnhoven and W.L. Vos, Science 281, 802 (1998).
J.E.G.J. Wijnhoven, L. Bechger, and W.L. Vos, Chem. Mater. 13, 4486 (2001).
H.M. van Driel and W.L. Vos, Phys. Rev. B 62, 9872 (2000).
W.L. Vos and H.M. van Driel, Phys. Lett. A 272, 101 (2000).
K.M. Ho, C.T. Chan, and C.M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
K.W.K. Shung and Y.C. Tsai, Phys. Rev. B 48, 11265 (1993).
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A.F. Koenderink, M. Megens, G. van Soest, W.L. Vos, and A. Lagendijk, Phys. Lett. A 268, 104 (2000).
P. Münstermann, T. Fischer, P. Maunz, P.W.H. Pinkse, and G. Rempe, Phys. Rev. Lett. 82, 3791 (1999).
H. Benisty, D. Labilloy, C. Weisbuch, C.J.M. Smith, T.F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, Appl. Phys. Lett. 76, 532 (2000).
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A. Imhof, W.L. Vos, R. Sprik, and A. Lagendijk, Phys. Rev. Lett. 83, 2942 (1999).

[c1] E.M. Purcell, Phys. Rev. 69, 2059 (1946).

[c2] Photonic Crystals and Light Localization in the 21st Century, Vol. 563 of Nato Advanced Studies Institute, Series C: Mathematical and Physical Sciences, edited by C.M. Soukoulis (Kluwer, Dordrecht, 2001).

[c3] J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton University Press, Princeton, 1995).

[c4] A.F. Koenderink, P.M. Johnson, J.F. Galisteo Lòpez, and W.L. Vos, C. R. Phys. 3, 67 (2002).

[c5] W.L. Vos, H.M. van Driel, M. Megens, A.F. Koenderink, and A. Imhof, in Photonic Crystals and Light Localization in the 21st Century (Ref. [2]), pp. 191–218.

[c6] W.L. Vos, R. Sprik, A. van Blaaderen, A. Imhof, A. Lagendijk, and G.H, Wegdam, Phys. Rev. B 53, 16 231 (1996); ibid.55, 1903 (1997).

[c7] H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10 096 (1998).

[c8] O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O’Brien, P.D. Dapkus, and I. Kim, Science 284, 1819 (1999).

[c9] C.J.M. Smith, R.M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T.F. Krauss, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).

[c10] R.W. James, The Optical Principles of the Diffraction of X-Rays (Bell, London, 1954).

[c11] W.H. Zachariasen, Theory of X-ray Diffraction in Crystals (Wiley, New York, 1945).

[c12] M.S. Thijssen, R. Sprik, J.E.G.J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W.L. Vos, Phys. Rev. Lett. 83, 2730 (1999).

[c13] Y.A. Vlasov, M. Deutsch, and D.J. Norris, Appl. Phys. Lett. 76, 1627 (2000).

[c14] J.F. Bertone, P. Jiang, K.S. Hwang, D.M. Mittleman, and V.L. Colvin, Phys. Rev. Lett. 83, 300 (1999).

[c15] Y.A. Vlasov, X.Z. Bo, J.C. Sturm, and D.J. Norris, Nature (London) 414, 289 (2001).

[c16] J.E.G.J. Wijnhoven and W.L. Vos, Science 281, 802 (1998).

[c17] J.E.G.J. Wijnhoven, L. Bechger, and W.L. Vos, Chem. Mater. 13, 4486 (2001).

[c18] H.M. van Driel and W.L. Vos, Phys. Rev. B 62, 9872 (2000).

[c19] W.L. Vos and H.M. van Driel, Phys. Lett. A 272, 101 (2000).

[c20] K.M. Ho, C.T. Chan, and C.M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).

[c21] K.W.K. Shung and Y.C. Tsai, Phys. Rev. B 48, 11265 (1993).

[c22] D.M. Mittleman, J.F. Bertone, P. Jiang, K.S. Hwang, and V.L. Colvin, J. Chem. Phys. 111, 345 (2000).

[c23] A.F. Koenderink, M. Megens, G. van Soest, W.L. Vos, and A. Lagendijk, Phys. Lett. A 268, 104 (2000).

[c24] P. Münstermann, T. Fischer, P. Maunz, P.W.H. Pinkse, and G. Rempe, Phys. Rev. Lett. 82, 3791 (1999).

[c25] H. Benisty, D. Labilloy, C. Weisbuch, C.J.M. Smith, T.F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, Appl. Phys. Lett. 76, 532 (2000).

[c26] Y.A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and C. Hirlimann, Phys. Rev. E 60, 1030 (1999).

[c27] A. Imhof, W.L. Vos, R. Sprik, and A. Lagendijk, Phys. Rev. Lett. 83, 2942 (1999).

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