Abstract

A Mach–Zehnder interferometer was developed for accurately measuring relative phase shifts of light propagating in photonic colloidal crystals deep into the stop bands. These phase shifts can be used to determine the change in index of refraction and the optical dispersion relation from photonic band structure near the band edges. Phase measurements of colloidal crystals incorporating an impurity peak in the transmission spectrum are also presented.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
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  4. E. Yablonovitch, “Photonic band-gap crystals,” J. Phys. Condens. Matter 5, 2443 (1993).
    [CrossRef]
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    [CrossRef]
  6. W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
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  9. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. İ. İ. Tarhan, M. P. Zinkin, and G. H. Watson, “Interferometric technique for the measurement of photonic band structure in colloidal crystals,” Opt. Lett. 20, 1571 (1995).
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  29. P. Hariharan, “Modified Mach–Zehnder interferometer,” Appl. Opt. 8, 1925 (1969).
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  30. Omega Optical Inc., P.O. Box 573, Brattleboro, Vermont 05302.
  31. İ. İ. Tarhan, “Investigation of optical photonic band structure in fcc colloidal crystals,” Ph.D. dissertation (U. Delaware, Newark, Del., 1996).
  32. İ. İ. Tarhan and G. H. Watson, “Analytical expression for the optimized stop bands of fcc photonic crystals in the scalar-wave approximation,” Phys. Rev. B 54, 7593 (1996).
    [CrossRef]
  33. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
    [CrossRef] [PubMed]
  34. R. D. Pradhan, İ. İ. Tarhan, and G. H. Watson, “Impurity modes in the optical stop bands of doped colloidal crystals,” Phys. Rev. B 54, 13721 (1996).
    [CrossRef]
  35. S. A. Asher, J. Holtz, L. Liu, and Z. Wu, “Self-assembly motif for creating submicron periodic materials. Polymerized crystalline colloidal arrays,” J. Am. Chem. Soc. 116, 4997 (1994).
    [CrossRef]

1998 (1)

R. Biswas, M. M. Sigalas, G. Subramania, and K.-M. Ho, “Photonic band gaps in colloidal crystals,” Phys. Rev. B 57, 3701 (1998).
[CrossRef]

1997 (3)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143 (1997).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

R. D. Pradhan, J. A. Bloodgood, and G. H. Watson, “Photonic band structure of bcc colloidal crystals,” Phys. Rev. B 55, 9503 (1997).
[CrossRef]

1996 (8)

W. L. Vos, R. Sprik, A. vanBlaaderen, A. Imhof, A. Lagendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231 (1996).
[CrossRef]

İ. İ. Tarhan and G. H. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
[CrossRef] [PubMed]

C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, “Nanofabricated three dimensional photonic crystal operating at optical wavelengths,” Phys. Scr. T68, 17 (1996).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699 (1996).
[CrossRef]

U. Grüning, V. Lehmann, S. Ottow, and K. Busch, “Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm,” Appl. Phys. Lett. 68, 747 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

İ. İ. Tarhan and G. H. Watson, “Analytical expression for the optimized stop bands of fcc photonic crystals in the scalar-wave approximation,” Phys. Rev. B 54, 7593 (1996).
[CrossRef]

R. D. Pradhan, İ. İ. Tarhan, and G. H. Watson, “Impurity modes in the optical stop bands of doped colloidal crystals,” Phys. Rev. B 54, 13721 (1996).
[CrossRef]

1995 (3)

İ. İ. Tarhan, M. P. Zinkin, and G. H. Watson, “Interferometric technique for the measurement of photonic band structure in colloidal crystals,” Opt. Lett. 20, 1571 (1995).
[CrossRef] [PubMed]

C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. 13, 2696 (1995).
[CrossRef]

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

1994 (4)

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413 (1994).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron length scales,” Appl. Phys. Lett. 65, 1466 (1994).
[CrossRef]

S. A. Asher, J. Holtz, L. Liu, and Z. Wu, “Self-assembly motif for creating submicron periodic materials. Polymerized crystalline colloidal arrays,” J. Am. Chem. Soc. 116, 4997 (1994).
[CrossRef]

1993 (2)

E. Yablonovitch, “Photonic bandgap structures,” J. Opt. Soc. Am. B 10, 283 (1993).
[CrossRef]

E. Yablonovitch, “Photonic band-gap crystals,” J. Phys. Condens. Matter 5, 2443 (1993).
[CrossRef]

1992 (1)

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

1991 (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

1987 (2)

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

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

1985 (1)

I. Thormahlen, J. Straub, and U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933 (1985).
[CrossRef]

1983 (1)

P. Pieranski, “Colloidal crystals,” Contemp. Phys. 24, 25 (1983).
[CrossRef]

1981 (1)

P. Pieranski, E. Dubois-Violette, F. Rothen, and L. Strzelecki, “Geometry of Kossel lines in colloidal crystals,” J. Phys. (France) 42, 53 (1981).
[CrossRef]

1979 (1)

N. A. Clark, A. J. Hurd, and B. J. Ackerson, “Single colloidal crystals,” Nature (London) 281, 57 (1979).
[CrossRef]

1969 (1)

1959 (1)

J. B. Bateman, E. J. Weneck, and D. C. Eshler, “Determination of particle size and concentration from spectrophotometric transmission,” J. Colloid Sci. 14, 308 (1959).
[CrossRef]

Ackerson, B. J.

N. A. Clark, A. J. Hurd, and B. J. Ackerson, “Single colloidal crystals,” Nature (London) 281, 57 (1979).
[CrossRef]

Arbet-Engels, V.

C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, “Nanofabricated three dimensional photonic crystal operating at optical wavelengths,” Phys. Scr. T68, 17 (1996).
[CrossRef]

Arjavalingam, G.

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Asher, S. A.

S. A. Asher, J. Holtz, L. Liu, and Z. Wu, “Self-assembly motif for creating submicron periodic materials. Polymerized crystalline colloidal arrays,” J. Am. Chem. Soc. 116, 4997 (1994).
[CrossRef]

Bateman, J. B.

J. B. Bateman, E. J. Weneck, and D. C. Eshler, “Determination of particle size and concentration from spectrophotometric transmission,” J. Colloid Sci. 14, 308 (1959).
[CrossRef]

Biswas, R.

R. Biswas, M. M. Sigalas, G. Subramania, and K.-M. Ho, “Photonic band gaps in colloidal crystals,” Phys. Rev. B 57, 3701 (1998).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413 (1994).
[CrossRef]

Bloodgood, J. A.

R. D. Pradhan, J. A. Bloodgood, and G. H. Watson, “Photonic band structure of bcc colloidal crystals,” Phys. Rev. B 55, 9503 (1997).
[CrossRef]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699 (1996).
[CrossRef]

Brommer, K. D.

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Busch, K.

U. Grüning, V. Lehmann, S. Ottow, and K. Busch, “Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm,” Appl. Phys. Lett. 68, 747 (1996).
[CrossRef]

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413 (1994).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Cheng, C. C.

C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, “Nanofabricated three dimensional photonic crystal operating at optical wavelengths,” Phys. Scr. T68, 17 (1996).
[CrossRef]

C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. 13, 2696 (1995).
[CrossRef]

Clark, N. A.

N. A. Clark, A. J. Hurd, and B. J. Ackerson, “Single colloidal crystals,” Nature (London) 281, 57 (1979).
[CrossRef]

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699 (1996).
[CrossRef]

Dubois-Violette, E.

P. Pieranski, E. Dubois-Violette, F. Rothen, and L. Strzelecki, “Geometry of Kossel lines in colloidal crystals,” J. Phys. (France) 42, 53 (1981).
[CrossRef]

Eshler, D. C.

J. B. Bateman, E. J. Weneck, and D. C. Eshler, “Determination of particle size and concentration from spectrophotometric transmission,” J. Colloid Sci. 14, 308 (1959).
[CrossRef]

Fan, S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143 (1997).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron length scales,” Appl. Phys. Lett. 65, 1466 (1994).
[CrossRef]

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Grigul, U.

I. Thormahlen, J. Straub, and U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933 (1985).
[CrossRef]

Grüning, U.

U. Grüning, V. Lehmann, S. Ottow, and K. Busch, “Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm,” Appl. Phys. Lett. 68, 747 (1996).
[CrossRef]

Hariharan, P.

Ho, K. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413 (1994).
[CrossRef]

Ho, K.-M.

R. Biswas, M. M. Sigalas, G. Subramania, and K.-M. Ho, “Photonic band gaps in colloidal crystals,” Phys. Rev. B 57, 3701 (1998).
[CrossRef]

Holtz, J.

S. A. Asher, J. Holtz, L. Liu, and Z. Wu, “Self-assembly motif for creating submicron periodic materials. Polymerized crystalline colloidal arrays,” J. Am. Chem. Soc. 116, 4997 (1994).
[CrossRef]

Hurd, A. J.

N. A. Clark, A. J. Hurd, and B. J. Ackerson, “Single colloidal crystals,” Nature (London) 281, 57 (1979).
[CrossRef]

Imhof, A.

W. L. Vos, R. Sprik, A. vanBlaaderen, A. Imhof, A. Lagendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231 (1996).
[CrossRef]

Ippen, E. P.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

Joannopoulos, J. D.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143 (1997).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron length scales,” Appl. Phys. Lett. 65, 1466 (1994).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

John, S.

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

Kimerling, L. C.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

Kolodziejski, L. A.

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699 (1996).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Lagendijk, A.

W. L. Vos, R. Sprik, A. vanBlaaderen, A. Imhof, A. Lagendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231 (1996).
[CrossRef]

Lehmann, V.

U. Grüning, V. Lehmann, S. Ottow, and K. Busch, “Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm,” Appl. Phys. Lett. 68, 747 (1996).
[CrossRef]

Lim, K.-Y.

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

Liu, L.

S. A. Asher, J. Holtz, L. Liu, and Z. Wu, “Self-assembly motif for creating submicron periodic materials. Polymerized crystalline colloidal arrays,” J. Am. Chem. Soc. 116, 4997 (1994).
[CrossRef]

Meade, R. D.

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron length scales,” Appl. Phys. Lett. 65, 1466 (1994).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Ottow, S.

U. Grüning, V. Lehmann, S. Ottow, and K. Busch, “Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm,” Appl. Phys. Lett. 68, 747 (1996).
[CrossRef]

Petrich, G. S.

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

Pieranski, P.

P. Pieranski, “Colloidal crystals,” Contemp. Phys. 24, 25 (1983).
[CrossRef]

P. Pieranski, E. Dubois-Violette, F. Rothen, and L. Strzelecki, “Geometry of Kossel lines in colloidal crystals,” J. Phys. (France) 42, 53 (1981).
[CrossRef]

Pradhan, R. D.

R. D. Pradhan, J. A. Bloodgood, and G. H. Watson, “Photonic band structure of bcc colloidal crystals,” Phys. Rev. B 55, 9503 (1997).
[CrossRef]

R. D. Pradhan, İ. İ. Tarhan, and G. H. Watson, “Impurity modes in the optical stop bands of doped colloidal crystals,” Phys. Rev. B 54, 13721 (1996).
[CrossRef]

Rappe, A. M.

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Reif, R.

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

Robertson, W.

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

Rothen, F.

P. Pieranski, E. Dubois-Violette, F. Rothen, and L. Strzelecki, “Geometry of Kossel lines in colloidal crystals,” J. Phys. (France) 42, 53 (1981).
[CrossRef]

Scherer, A.

C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, “Nanofabricated three dimensional photonic crystal operating at optical wavelengths,” Phys. Scr. T68, 17 (1996).
[CrossRef]

C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. 13, 2696 (1995).
[CrossRef]

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413 (1994).
[CrossRef]

Sigalas, M. M.

R. Biswas, M. M. Sigalas, G. Subramania, and K.-M. Ho, “Photonic band gaps in colloidal crystals,” Phys. Rev. B 57, 3701 (1998).
[CrossRef]

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413 (1994).
[CrossRef]

Sprik, R.

W. L. Vos, R. Sprik, A. vanBlaaderen, A. Imhof, A. Lagendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231 (1996).
[CrossRef]

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

Straub, J.

I. Thormahlen, J. Straub, and U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933 (1985).
[CrossRef]

Strzelecki, L.

P. Pieranski, E. Dubois-Violette, F. Rothen, and L. Strzelecki, “Geometry of Kossel lines in colloidal crystals,” J. Phys. (France) 42, 53 (1981).
[CrossRef]

Subramania, G.

R. Biswas, M. M. Sigalas, G. Subramania, and K.-M. Ho, “Photonic band gaps in colloidal crystals,” Phys. Rev. B 57, 3701 (1998).
[CrossRef]

Tarhan, I. I.

İ. İ. Tarhan and G. H. Watson, “Analytical expression for the optimized stop bands of fcc photonic crystals in the scalar-wave approximation,” Phys. Rev. B 54, 7593 (1996).
[CrossRef]

İ. İ. Tarhan and G. H. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
[CrossRef] [PubMed]

R. D. Pradhan, İ. İ. Tarhan, and G. H. Watson, “Impurity modes in the optical stop bands of doped colloidal crystals,” Phys. Rev. B 54, 13721 (1996).
[CrossRef]

İ. İ. Tarhan, M. P. Zinkin, and G. H. Watson, “Interferometric technique for the measurement of photonic band structure in colloidal crystals,” Opt. Lett. 20, 1571 (1995).
[CrossRef] [PubMed]

Thoen, E. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

Thormahlen, I.

I. Thormahlen, J. Straub, and U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933 (1985).
[CrossRef]

vanBlaaderen, A.

W. L. Vos, R. Sprik, A. vanBlaaderen, A. Imhof, A. Lagendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231 (1996).
[CrossRef]

Villeneuve, P. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143 (1997).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron length scales,” Appl. Phys. Lett. 65, 1466 (1994).
[CrossRef]

Vos, W. L.

W. L. Vos, R. Sprik, A. vanBlaaderen, A. Imhof, A. Lagendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231 (1996).
[CrossRef]

Watson, G. H.

R. D. Pradhan, J. A. Bloodgood, and G. H. Watson, “Photonic band structure of bcc colloidal crystals,” Phys. Rev. B 55, 9503 (1997).
[CrossRef]

R. D. Pradhan, İ. İ. Tarhan, and G. H. Watson, “Impurity modes in the optical stop bands of doped colloidal crystals,” Phys. Rev. B 54, 13721 (1996).
[CrossRef]

İ. İ. Tarhan and G. H. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
[CrossRef] [PubMed]

İ. İ. Tarhan and G. H. Watson, “Analytical expression for the optimized stop bands of fcc photonic crystals in the scalar-wave approximation,” Phys. Rev. B 54, 7593 (1996).
[CrossRef]

İ. İ. Tarhan, M. P. Zinkin, and G. H. Watson, “Interferometric technique for the measurement of photonic band structure in colloidal crystals,” Opt. Lett. 20, 1571 (1995).
[CrossRef] [PubMed]

Wegdam, G. H.

W. L. Vos, R. Sprik, A. vanBlaaderen, A. Imhof, A. Lagendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231 (1996).
[CrossRef]

Weneck, E. J.

J. B. Bateman, E. J. Weneck, and D. C. Eshler, “Determination of particle size and concentration from spectrophotometric transmission,” J. Colloid Sci. 14, 308 (1959).
[CrossRef]

Wu, Z.

S. A. Asher, J. Holtz, L. Liu, and Z. Wu, “Self-assembly motif for creating submicron periodic materials. Polymerized crystalline colloidal arrays,” J. Am. Chem. Soc. 116, 4997 (1994).
[CrossRef]

Yablonovitch, E.

C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, “Nanofabricated three dimensional photonic crystal operating at optical wavelengths,” Phys. Scr. T68, 17 (1996).
[CrossRef]

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173 (1994).
[CrossRef]

E. Yablonovitch, “Photonic band-gap crystals,” J. Phys. Condens. Matter 5, 2443 (1993).
[CrossRef]

E. Yablonovitch, “Photonic bandgap structures,” J. Opt. Soc. Am. B 10, 283 (1993).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

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

Zinkin, M. P.

Appl. Opt. (1)

Appl. Phys. Lett. (3)

U. Grüning, V. Lehmann, S. Ottow, and K. Busch, “Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm,” Appl. Phys. Lett. 68, 747 (1996).
[CrossRef]

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air–bridge microcavities,” Appl. Phys. Lett. 67, 167 (1995).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron length scales,” Appl. Phys. Lett. 65, 1466 (1994).
[CrossRef]

Contemp. Phys. (1)

P. Pieranski, “Colloidal crystals,” Contemp. Phys. 24, 25 (1983).
[CrossRef]

J. Am. Chem. Soc. (1)

S. A. Asher, J. Holtz, L. Liu, and Z. Wu, “Self-assembly motif for creating submicron periodic materials. Polymerized crystalline colloidal arrays,” J. Am. Chem. Soc. 116, 4997 (1994).
[CrossRef]

J. Colloid Sci. (1)

J. B. Bateman, E. J. Weneck, and D. C. Eshler, “Determination of particle size and concentration from spectrophotometric transmission,” J. Colloid Sci. 14, 308 (1959).
[CrossRef]

J. Mod. Opt. (1)

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173 (1994).
[CrossRef]

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

J. Phys. (France) (1)

P. Pieranski, E. Dubois-Violette, F. Rothen, and L. Strzelecki, “Geometry of Kossel lines in colloidal crystals,” J. Phys. (France) 42, 53 (1981).
[CrossRef]

J. Phys. Chem. Ref. Data (1)

I. Thormahlen, J. Straub, and U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933 (1985).
[CrossRef]

J. Phys. Condens. Matter (1)

E. Yablonovitch, “Photonic band-gap crystals,” J. Phys. Condens. Matter 5, 2443 (1993).
[CrossRef]

J. Vac. Sci. Technol. (1)

C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. 13, 2696 (1995).
[CrossRef]

Nature (London) (4)

N. A. Clark, A. J. Hurd, and B. J. Ackerson, “Single colloidal crystals,” Nature (London) 281, 57 (1979).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature (London) 390, 143 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699 (1996).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (5)

R. D. Pradhan, İ. İ. Tarhan, and G. H. Watson, “Impurity modes in the optical stop bands of doped colloidal crystals,” Phys. Rev. B 54, 13721 (1996).
[CrossRef]

İ. İ. Tarhan and G. H. Watson, “Analytical expression for the optimized stop bands of fcc photonic crystals in the scalar-wave approximation,” Phys. Rev. B 54, 7593 (1996).
[CrossRef]

R. D. Pradhan, J. A. Bloodgood, and G. H. Watson, “Photonic band structure of bcc colloidal crystals,” Phys. Rev. B 55, 9503 (1997).
[CrossRef]

W. L. Vos, R. Sprik, A. vanBlaaderen, A. Imhof, A. Lagendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231 (1996).
[CrossRef]

R. Biswas, M. M. Sigalas, G. Subramania, and K.-M. Ho, “Photonic band gaps in colloidal crystals,” Phys. Rev. B 57, 3701 (1998).
[CrossRef]

Phys. Rev. Lett. (6)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

İ. İ. Tarhan and G. H. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76, 315 (1996).
[CrossRef] [PubMed]

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

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

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Phys. Scr. (1)

C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, “Nanofabricated three dimensional photonic crystal operating at optical wavelengths,” Phys. Scr. T68, 17 (1996).
[CrossRef]

Solid State Commun. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413 (1994).
[CrossRef]

Other (4)

R. H. Boundy and R. F. Boyer, Styrene: Its Polymers, Copolymers and Derivatives (Hafner, New York, 1965).

Duke Scientific Corporation, 2463 Faber Place, Palo Alto, Calif. 94303.

Omega Optical Inc., P.O. Box 573, Brattleboro, Vermont 05302.

İ. İ. Tarhan, “Investigation of optical photonic band structure in fcc colloidal crystals,” Ph.D. dissertation (U. Delaware, Newark, Del., 1996).

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Figures (11)

Fig. 1
Fig. 1

Transmission spectrum along the fcc [111] direction of a colloidal crystal made of polystyrene microspheres and water, with 0.173-μm-diameter particles and 7% volume fraction.

Fig. 2
Fig. 2

Experimental setup for gathering phase information with a dye laser or a Ti:Sa laser as tunable laser sources. F1 and F2 are neutral-density filters, RM1RM4 are removable mirrors, MA1 and MA2 are mirror assemblies for beam steering, and P1 and P2 are pinholes for alignment purposes. Solid lines indicate laser beam paths, while dashed lines show the data flow.

Fig. 3
Fig. 3

Modified Mach–Zehnder interferometer. The fringe pattern is positioned in front of the CCD camera by adjustment of pentaprism PP1. The optical paths are equalized by adjustment of pentaprism PP2 along a line perpendicular to PP1. The relative intensity in the reference arm is optimized for maximum fringe visibility before and during the scan via the neutral attenuation wheels AW1AW3. The cell WC contains water, while the crystal cell CC contains the photonic crystal. PO, polarizer and objective; BS, beam splitter.

Fig. 4
Fig. 4

Typical interferometer fringe pattern with optimized fringe visibility V=0.59. The solid curve is the resulting nonlinear least-squares fit of Eq. (1).

Fig. 5
Fig. 5

Effect of the attenuation wheels AW1 and AW2. The top plot shows the visibility of the fringe pattern in comparison with the lower plot, which shows a transmission scan through the reference sample used. It can be observed that the visibility stays at a high value of 0.5–0.6 up to 2.5 orders of magnitude into the stop band.

Fig. 6
Fig. 6

Phase shift without a photonic crystal. Owing to slightly unequal optical path lengths, a phase shift is introduced as the wavelength is changed. This graph shows multiple scans with all three mirror sets of the Ti:Sa laser spanning the entire wavelength range. The number of data points was reduced for clarity. The line is a least-squares fit of Eq. (4).

Fig. 7
Fig. 7

Raw data ΔΦ(λ) and the best fit of the fit function Δϕ0(λ) are shown in part (a). Subtracting the fitted phase from the raw phase data gives the phase-shift difference Δϕ in (b) arising solely from the photonic stop band. Far away from the stop band, the free-photon limit is approached.

Fig. 8
Fig. 8

Deviation of the index of refraction near the stop band, calculated from the phase data in Fig. 7(b) with Eq. (9). The phase information is lost when the stop-band center is approached because of a strongly decreased signal-to-noise ratio.

Fig. 9
Fig. 9

Transmission spectrum along the fcc [111] direction of a doped photonic crystal. The impurity peak is located at 920 nm with an intensity of one order of magnitude above the stop-band transmission minimum. The colloidal crystal consists of 0.173-μm polystyrene host particles with 7% of the host particles replaced with 0.203-μm impurity particles.

Fig. 10
Fig. 10

Phase change (circles) and transmission curve (line) of a doped colloidal photonic crystal. The phase data were acquired with the medium-wave output coupler (black circles) and the long-wave output coupler (open circles).

Fig. 11
Fig. 11

Data from Fig. 10, shown in (a), compared with previously acquired data28 in (b). The wide tuning range and the high dynamic range of the improved instrument are necessary to obtain the free-photon limit and the phase data of the impurity peak, respectively. For ease of comparison, all axes have the same scaling.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

I=Iavg exp-x-μw2[1+V cos(2πfx+ΔΦ)].
Δϕ12π=Δxλv1,
Δϕ22π=Δxλv2.
Δϕ02π=Δϕ1-Δϕ22π=Δx1λv1-1λv2.
Δϕ0(λv1)0.
Δx(λv)=Δxphys+Δxdisp(λv).
Δϕ(λv)=ΔΦ(λv)-Δϕ0(λv).
nc(λv)=nc0(λv)+Δnc(λv),
Δnc(λv)=Δϕ(λv)2π λvdsample.
2πk=λ=λvnc(λv).
k(ω)=ωc+Δϕ(ω)dsample.

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