Abstract

We report the increase in optical absorption in a finite three-dimensional photonic crystal through the dependence of the crystal film’s thickness. Varying thicknesses of TiO2 inverse opal electrodes were assembled in dye-sensitized solar cells and their optical properties were characterized. Through measuring the enhancement in the incident photon-to-electricity conversion efficiency over the reference cell, we show that optical absorption of a photosensitive dye coupled to a finite ordered structure can be influenced by the spatial properties of the structure. This report provides an insight into the changes in optical absorption of an atom when the space surrounding that atom is modified.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  36. S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
    [CrossRef] [PubMed]

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

2009 (1)

2008 (6)

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78, 023825 (2008).
[CrossRef]

D. Duché, L. Escoubas, J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92, 193310 (2008).
[CrossRef]

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
[CrossRef]

C. H. Yip, Y. M. Chiang, and C. C. Wong, “Dielectric band edge enhancement of energy conversion efficiency in photonic crystal dye-sensitized solar cell,” J. Phys. Chem. C 112, 8735–8740 (2008).
[CrossRef]

A. Mihi, M. E. Calvo, J. A. Anta, and H. Miguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112, 13–17 (2008).
[CrossRef]

S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
[CrossRef] [PubMed]

2006 (2)

J. Chen, G. Von Freymann, S. Y. Choi, V. Kitaev, and G. A. Ozin, “Amplified photochemistry with slow photons,” Adv. Mater. 18, 1915–1919 (2006).
[CrossRef]

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

2005 (2)

M. Gratzel, “Solar energy conversion by dye-sensitized photovoltaic cells,” Inorg. Chem. 44, 6841–6851 (2005).
[CrossRef] [PubMed]

A. Mihi and H. Miguez, “Origin of light-harvesting enhancement in colloidal-photonic-crystal-based dye-sensitized solar cells,” J. Phys. Chem. B 109, 15968–15976 (2005).
[CrossRef]

2004 (6)

X. Zhou and X. S. Zhao, “Flow-controlled vertical deposition method for the fabrication of photonic crystals,” Langmuir 20, 1524–1526 (2004).
[CrossRef]

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

R. Wang and S. John, “Engineering the electromagnetic vacuum for controlling light with light in a photonic-band-gap microchip,” Phys. Rev. A 70, 043805 (2004).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69, 057601 (2004).
[CrossRef]

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, “Photonic bands and group-velocity dispersion in Si/SiO2 photonic crystals from white-light interferometry,” Phys. Rev. B 69, 115107 (2004).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: A comprehensive analysis,” Phys. Rev. E 70, 016612 (2004).
[CrossRef]

2003 (5)

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, “Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal,” J. Opt. Soc. Am. B 20, 1538–1541 (2003).
[CrossRef]

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67, 155114 (2003).
[CrossRef]

J. F. Galisteo-Lopez, E. Palacios-Lidon, E. Castillo-Martinez, and C. Lopez, “Optical study of the pseudogap in thickness and orientation controlled artificial opals,” Phys. Rev. B 68, 115109 (2003).
[CrossRef]

Y. J. Lee and P. V. Braun, “Tunable inverse opal hydrogel pH sensors,” Adv. Mater. 15, 563–566 (2003).
[CrossRef]

2002 (1)

S. Nishimura, A. Shishido, N. Abrams, and T. E. Mallouk, “Fabrication technique for filling-factor tunable titanium dioxide colloidal crystal replicas,” Appl. Phys. Lett. 81, 4532–4534 (2002).
[CrossRef]

2001 (1)

1999 (1)

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60, 1030–1035 (1999).
[CrossRef]

1998 (1)

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

1995 (1)

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser—a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

1991 (1)

B. O’Regan and M. Gratzel, “A low-cost, high efficiency solar-cell based on dye-sensitized colloidal TiO2 films,” Nature 353, 737–740 (1991).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Lett. Rev. 58, 2486–2489 (1987).
[CrossRef]

1982 (1)

Abrams, N.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

S. Nishimura, A. Shishido, N. Abrams, and T. E. Mallouk, “Fabrication technique for filling-factor tunable titanium dioxide colloidal crystal replicas,” Appl. Phys. Lett. 81, 4532–4534 (2002).
[CrossRef]

Abrams, N. M.

S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
[CrossRef] [PubMed]

Alamariu, B. A.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

Andreani, L. C.

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, “Photonic bands and group-velocity dispersion in Si/SiO2 photonic crystals from white-light interferometry,” Phys. Rev. B 69, 115107 (2004).
[CrossRef]

Anta, J. A.

A. Mihi, M. E. Calvo, J. A. Anta, and H. Miguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112, 13–17 (2008).
[CrossRef]

Avniel, Y.

Bajoni, D.

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, “Photonic bands and group-velocity dispersion in Si/SiO2 photonic crystals from white-light interferometry,” Phys. Rev. B 69, 115107 (2004).
[CrossRef]

Barber, G. D.

S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
[CrossRef] [PubMed]

Benkstein, K. D.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

M. Ghebrebrhan, P. Bermel, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, “Global optimization of silicon photovoltaic cell front coatings,” Opt. Express 17, 7505–7518 (2009).
[CrossRef] [PubMed]

Biswas, R.

Bloemer, M. J.

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: A comprehensive analysis,” Phys. Rev. E 70, 016612 (2004).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69, 057601 (2004).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser—a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser—a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

Braun, P. V.

Y. J. Lee and P. V. Braun, “Tunable inverse opal hydrogel pH sensors,” Adv. Mater. 15, 563–566 (2003).
[CrossRef]

Busch, K.

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

Calvo, M. E.

A. Mihi, M. E. Calvo, J. A. Anta, and H. Miguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112, 13–17 (2008).
[CrossRef]

Castillo-Martinez, E.

J. F. Galisteo-Lopez, E. Palacios-Lidon, E. Castillo-Martinez, and C. Lopez, “Optical study of the pseudogap in thickness and orientation controlled artificial opals,” Phys. Rev. B 68, 115109 (2003).
[CrossRef]

Centini, M.

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69, 057601 (2004).
[CrossRef]

Chen, J.

J. Chen, G. Von Freymann, S. Y. Choi, V. Kitaev, and G. A. Ozin, “Amplified photochemistry with slow photons,” Adv. Mater. 18, 1915–1919 (2006).
[CrossRef]

Chiang, Y. M.

C. H. Yip, Y. M. Chiang, and C. C. Wong, “Dielectric band edge enhancement of energy conversion efficiency in photonic crystal dye-sensitized solar cell,” J. Phys. Chem. C 112, 8735–8740 (2008).
[CrossRef]

Choi, S. Y.

J. Chen, G. Von Freymann, S. Y. Choi, V. Kitaev, and G. A. Ozin, “Amplified photochemistry with slow photons,” Adv. Mater. 18, 1915–1919 (2006).
[CrossRef]

Chutinan, A.

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78, 023825 (2008).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: A comprehensive analysis,” Phys. Rev. E 70, 016612 (2004).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69, 057601 (2004).
[CrossRef]

Dowling, J. P.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser—a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

Duan, X.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

Duché, D.

D. Duché, L. Escoubas, J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92, 193310 (2008).
[CrossRef]

El-Kady, I.

Escoubas, L.

D. Duché, L. Escoubas, J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92, 193310 (2008).
[CrossRef]

Feng, N.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

Fleming, J. G.

Flory, F.

D. Duché, L. Escoubas, J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92, 193310 (2008).
[CrossRef]

Frank, A. J.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

Galisteo-Lopez, J. F.

J. F. Galisteo-Lopez, E. Palacios-Lidon, E. Castillo-Martinez, and C. Lopez, “Optical study of the pseudogap in thickness and orientation controlled artificial opals,” Phys. Rev. B 68, 115109 (2003).
[CrossRef]

Galli, M.

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, “Photonic bands and group-velocity dispersion in Si/SiO2 photonic crystals from white-light interferometry,” Phys. Rev. B 69, 115107 (2004).
[CrossRef]

Ghebrebrhan, M.

Gratzel, M.

M. Gratzel, “Solar energy conversion by dye-sensitized photovoltaic cells,” Inorg. Chem. 44, 6841–6851 (2005).
[CrossRef] [PubMed]

B. O’Regan and M. Gratzel, “A low-cost, high efficiency solar-cell based on dye-sensitized colloidal TiO2 films,” Nature 353, 737–740 (1991).
[CrossRef]

Gu, B. Y.

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67, 155114 (2003).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

Halaoui, L. I.

S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
[CrossRef] [PubMed]

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

Heine, C.

Hirlimann, C.

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60, 1030–1035 (1999).
[CrossRef]

Ho, K. M.

Hoertz, P. G.

S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
[CrossRef] [PubMed]

Honerlage, B.

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60, 1030–1035 (1999).
[CrossRef]

Hong, C.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Irman, A.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

Joannopoulos, J. D.

John, S.

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78, 023825 (2008).
[CrossRef]

R. Wang and S. John, “Engineering the electromagnetic vacuum for controlling light with light in a photonic-band-gap microchip,” Phys. Rev. A 70, 043805 (2004).
[CrossRef]

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Lett. Rev. 58, 2486–2489 (1987).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

M. Ghebrebrhan, P. Bermel, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, “Global optimization of silicon photovoltaic cell front coatings,” Opt. Express 17, 7505–7518 (2009).
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

S. G. Johnson, Massachusetts Institute of Technology, Cambridge, Mass. (personal communication, 2008); online MEEP-DISCUSS forum at http://ab-initio.mit.edu/meep.

Kimerling, L. C.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

Kitaev, V.

J. Chen, G. Von Freymann, S. Y. Choi, V. Kitaev, and G. A. Ozin, “Amplified photochemistry with slow photons,” Adv. Mater. 18, 1915–1919 (2006).
[CrossRef]

Klein, G.

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60, 1030–1035 (1999).
[CrossRef]

Krauss, T. F.

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
[CrossRef]

Lee, S. H. A.

S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
[CrossRef] [PubMed]

Lee, Y. J.

Y. J. Lee and P. V. Braun, “Tunable inverse opal hydrogel pH sensors,” Adv. Mater. 15, 563–566 (2003).
[CrossRef]

Lewis, B. A.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

Li, Z. Y.

Lin, S. Y.

Liu, J.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

Lodahl, P.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

Lopez, C.

J. F. Galisteo-Lopez, E. Palacios-Lidon, E. Castillo-Martinez, and C. Lopez, “Optical study of the pseudogap in thickness and orientation controlled artificial opals,” Phys. Rev. B 68, 115109 (2003).
[CrossRef]

Mallouk, T. E.

S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
[CrossRef] [PubMed]

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

S. Nishimura, A. Shishido, N. Abrams, and T. E. Mallouk, “Fabrication technique for filling-factor tunable titanium dioxide colloidal crystal replicas,” Appl. Phys. Lett. 81, 4532–4534 (2002).
[CrossRef]

Marabelli, F.

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, “Photonic bands and group-velocity dispersion in Si/SiO2 photonic crystals from white-light interferometry,” Phys. Rev. B 69, 115107 (2004).
[CrossRef]

Mattiucci, N.

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: A comprehensive analysis,” Phys. Rev. E 70, 016612 (2004).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69, 057601 (2004).
[CrossRef]

Miguez, H.

A. Mihi, M. E. Calvo, J. A. Anta, and H. Miguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112, 13–17 (2008).
[CrossRef]

A. Mihi and H. Miguez, “Origin of light-harvesting enhancement in colloidal-photonic-crystal-based dye-sensitized solar cells,” J. Phys. Chem. B 109, 15968–15976 (2005).
[CrossRef]

Mihi, A.

A. Mihi, M. E. Calvo, J. A. Anta, and H. Miguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112, 13–17 (2008).
[CrossRef]

A. Mihi and H. Miguez, “Origin of light-harvesting enhancement in colloidal-photonic-crystal-based dye-sensitized solar cells,” J. Phys. Chem. B 109, 15968–15976 (2005).
[CrossRef]

Morf, R. H.

Nikolaev, I. S.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

Nishimura, S.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

S. Nishimura, A. Shishido, N. Abrams, and T. E. Mallouk, “Fabrication technique for filling-factor tunable titanium dioxide colloidal crystal replicas,” Appl. Phys. Lett. 81, 4532–4534 (2002).
[CrossRef]

O’Regan, B.

B. O’Regan and M. Gratzel, “A low-cost, high efficiency solar-cell based on dye-sensitized colloidal TiO2 films,” Nature 353, 737–740 (1991).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Overgaag, K.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

Ozin, G. A.

J. Chen, G. Von Freymann, S. Y. Choi, V. Kitaev, and G. A. Ozin, “Amplified photochemistry with slow photons,” Adv. Mater. 18, 1915–1919 (2006).
[CrossRef]

Palacios-Lidon, E.

J. F. Galisteo-Lopez, E. Palacios-Lidon, E. Castillo-Martinez, and C. Lopez, “Optical study of the pseudogap in thickness and orientation controlled artificial opals,” Phys. Rev. B 68, 115109 (2003).
[CrossRef]

Pavesi, L.

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, “Photonic bands and group-velocity dispersion in Si/SiO2 photonic crystals from white-light interferometry,” Phys. Rev. B 69, 115107 (2004).
[CrossRef]

Petit, S.

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60, 1030–1035 (1999).
[CrossRef]

Piirma, I.

I. Piirma, Emulsion Polymerization (Academic, 1982).

Pucker, G.

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, “Photonic bands and group-velocity dispersion in Si/SiO2 photonic crystals from white-light interferometry,” Phys. Rev. B 69, 115107 (2004).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Scalora, M.

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69, 057601 (2004).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: A comprehensive analysis,” Phys. Rev. E 70, 016612 (2004).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser—a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

Shishido, A.

S. Nishimura, A. Shishido, N. Abrams, and T. E. Mallouk, “Fabrication technique for filling-factor tunable titanium dioxide colloidal crystal replicas,” Appl. Phys. Lett. 81, 4532–4534 (2002).
[CrossRef]

Simon, J.

D. Duché, L. Escoubas, J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92, 193310 (2008).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

Torchio, P.

D. Duché, L. Escoubas, J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92, 193310 (2008).
[CrossRef]

van de Lagemaat, J.

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

van Driel, A. F.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

Vanmaekelbergh, D.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

Vervisch, W.

D. Duché, L. Escoubas, J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92, 193310 (2008).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60, 1030–1035 (1999).
[CrossRef]

Von Freymann, G.

J. Chen, G. Von Freymann, S. Y. Choi, V. Kitaev, and G. A. Ozin, “Amplified photochemistry with slow photons,” Adv. Mater. 18, 1915–1919 (2006).
[CrossRef]

Vos, W. L.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

Wang, R.

R. Wang and S. John, “Engineering the electromagnetic vacuum for controlling light with light in a photonic-band-gap microchip,” Phys. Rev. A 70, 043805 (2004).
[CrossRef]

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67, 155114 (2003).
[CrossRef]

Wang, X. H.

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67, 155114 (2003).
[CrossRef]

Wong, C. C.

C. H. Yip, Y. M. Chiang, and C. C. Wong, “Dielectric band edge enhancement of energy conversion efficiency in photonic crystal dye-sensitized solar cell,” J. Phys. Chem. C 112, 8735–8740 (2008).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72, 899–907 (1982).
[CrossRef]

Yang, G. Z.

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67, 155114 (2003).
[CrossRef]

Yi, Y.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

Yip, C. H.

C. H. Yip, Y. M. Chiang, and C. C. Wong, “Dielectric band edge enhancement of energy conversion efficiency in photonic crystal dye-sensitized solar cell,” J. Phys. Chem. C 112, 8735–8740 (2008).
[CrossRef]

Zeng, L.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

Zhao, X. S.

X. Zhou and X. S. Zhao, “Flow-controlled vertical deposition method for the fabrication of photonic crystals,” Langmuir 20, 1524–1526 (2004).
[CrossRef]

Zheltikov, A. M.

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: A comprehensive analysis,” Phys. Rev. E 70, 016612 (2004).
[CrossRef]

Zhou, X.

X. Zhou and X. S. Zhao, “Flow-controlled vertical deposition method for the fabrication of photonic crystals,” Langmuir 20, 1524–1526 (2004).
[CrossRef]

Adv. Mater. (2)

J. Chen, G. Von Freymann, S. Y. Choi, V. Kitaev, and G. A. Ozin, “Amplified photochemistry with slow photons,” Adv. Mater. 18, 1915–1919 (2006).
[CrossRef]

Y. J. Lee and P. V. Braun, “Tunable inverse opal hydrogel pH sensors,” Adv. Mater. 15, 563–566 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89, 111111 (2006).
[CrossRef]

D. Duché, L. Escoubas, J. Simon, P. Torchio, W. Vervisch, and F. Flory, “Slow Bloch modes for enhancing the absorption of light in thin films for photovoltaic cells,” Appl. Phys. Lett. 92, 193310 (2008).
[CrossRef]

S. Nishimura, A. Shishido, N. Abrams, and T. E. Mallouk, “Fabrication technique for filling-factor tunable titanium dioxide colloidal crystal replicas,” Appl. Phys. Lett. 81, 4532–4534 (2002).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Inorg. Chem. (1)

M. Gratzel, “Solar energy conversion by dye-sensitized photovoltaic cells,” Inorg. Chem. 44, 6841–6851 (2005).
[CrossRef] [PubMed]

J. Am. Chem. Soc. (1)

S. Nishimura, N. Abrams, B. A. Lewis, L. I. Halaoui, T. E. Mallouk, K. D. Benkstein, J. van de Lagemaat, and A. J. Frank, “Standing wave enhancement of red absorbance and photocurrent in dye-sensitized titanium dioxide photoelectrodes coupled to photonic crystals,” J. Am. Chem. Soc. 125, 6306–6310 (2003).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser—a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. Chem. B (2)

A. Mihi and H. Miguez, “Origin of light-harvesting enhancement in colloidal-photonic-crystal-based dye-sensitized solar cells,” J. Phys. Chem. B 109, 15968–15976 (2005).
[CrossRef]

S. H. A. Lee, N. M. Abrams, P. G. Hoertz, G. D. Barber, L. I. Halaoui, and T. E. Mallouk, “Coupling of titania inverse opals to nanocrystalline titania layers in dye-sensitized solar cells,” J. Phys. Chem. B 112, 14415–14421 (2008).
[CrossRef] [PubMed]

J. Phys. Chem. C (2)

C. H. Yip, Y. M. Chiang, and C. C. Wong, “Dielectric band edge enhancement of energy conversion efficiency in photonic crystal dye-sensitized solar cell,” J. Phys. Chem. C 112, 8735–8740 (2008).
[CrossRef]

A. Mihi, M. E. Calvo, J. A. Anta, and H. Miguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112, 13–17 (2008).
[CrossRef]

Langmuir (1)

X. Zhou and X. S. Zhao, “Flow-controlled vertical deposition method for the fabrication of photonic crystals,” Langmuir 20, 1524–1526 (2004).
[CrossRef]

Nat. Photonics (1)

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2, 448–450 (2008).
[CrossRef]

Nature (2)

B. O’Regan and M. Gratzel, “A low-cost, high efficiency solar-cell based on dye-sensitized colloidal TiO2 films,” Nature 353, 737–740 (1991).
[CrossRef]

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Lett. Rev. (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Lett. Rev. 58, 2486–2489 (1987).
[CrossRef]

Phys. Rev. A (2)

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78, 023825 (2008).
[CrossRef]

R. Wang and S. John, “Engineering the electromagnetic vacuum for controlling light with light in a photonic-band-gap microchip,” Phys. Rev. A 70, 043805 (2004).
[CrossRef]

Phys. Rev. B (3)

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, “Local density of states in three-dimensional photonic crystals: calculation and enhancement effects,” Phys. Rev. B 67, 155114 (2003).
[CrossRef]

J. F. Galisteo-Lopez, E. Palacios-Lidon, E. Castillo-Martinez, and C. Lopez, “Optical study of the pseudogap in thickness and orientation controlled artificial opals,” Phys. Rev. B 68, 115109 (2003).
[CrossRef]

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, “Photonic bands and group-velocity dispersion in Si/SiO2 photonic crystals from white-light interferometry,” Phys. Rev. B 69, 115107 (2004).
[CrossRef]

Phys. Rev. E (4)

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Density of modes and tunneling times in finite one-dimensional photonic crystals: A comprehensive analysis,” Phys. Rev. E 70, 016612 (2004).
[CrossRef]

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60, 1030–1035 (1999).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Centini, M. Scalora, and M. J. Bloemer, “Electromagnetic density of modes for a finite-size three-dimensional structure,” Phys. Rev. E 69, 057601 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Other (3)

S. G. Johnson, Massachusetts Institute of Technology, Cambridge, Mass. (personal communication, 2008); online MEEP-DISCUSS forum at http://ab-initio.mit.edu/meep.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

I. Piirma, Emulsion Polymerization (Academic, 1982).

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Figures (6)

Fig. 1
Fig. 1

Cross-sectional SEM images of (a) TiO 2 inverse opal (PC). The cross section view was obtained by fracturing through the sample. Inset reveals an ordered inverse opal structure. (b) Collapsed TiO 2 inverse opal (C-PC). Inset reveals a disordered structure. The scale bars represent 1 μ m in length.

Fig. 2
Fig. 2

(a) Reflectance measurement of TiO 2 inverse opal DSC with different opal films thicknesses: 2.92 (S), 5.53 (M), and 7.76 (L) μ m . λ 1 and λ 2 indicate the locations of air and dielectric band edges, respectively, on L specimen. (b) FDTD simulated peak reflectance position of TiO 2 inverse opals with varying number of layers (black line) and overlapping dots of measured reflectance peaks from (a).

Fig. 3
Fig. 3

Intensity field distribution of TiO 2 inverse opal with monochromatic irradiance: (a) air band, λ 1 ; (b) dielectric band, λ 2 . The distribution map is the top view of a FCC structure in [ 1 1 ¯ 0 ] direction, showing the repeating A B C plane sequence. Volume inside the spheres contains lower dielectric material (electrolyte) and the outside contains higher dielectric material ( TiO 2 ) .

Fig. 4
Fig. 4

The IPCE comparison graphs for three DSC devices with different electrode thicknesses (a) S, (b) M, and (c) L. The enhancement factor F IPCE is defined as ( IPCE PC IPCE C-PC ) / IPCE C-PC ( % ) and denoted as green triangular points. The IPCE graphs are PC (blue diamonds) and C-PC (pink squares) layer electrodes.

Fig. 5
Fig. 5

Numerical computation (solid line) of the enhancement in electric field intensity spectrum PC over C-PC layer, F E , for films (a) S ( N = 18 ) , (b) M ( N = 33 ) , and (c) L ( N = 48 ) . The enhancement factor F IPCE (black solid line) from the IPCE measurement as plotted in Figs. 4a, 4b, 4c. Δ denotes the peak offset between the numerical F E and the measured F IPCE .

Fig. 6
Fig. 6

The DOS, ρ ( ω ) , of a TiO 2 inverse opal for N = ( a ) 18, (b) 33, and (c) 48. The y-axes are normalized with the speed of light in vacuum, c. (d) Photonic band diagram (k-vector versus ω a / 2 π c ) of a TiO 2 inverse opal immersed in an electrolyte. A pseudo-gap exists at L direction between bands 2 and 3.

Equations (1)

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F E = 1 n | E PC ( ω , r ¯ ) | 2 | E C-PC ( ω , r ¯ ) | 2 | E C-PC ( ω , r ¯ ) | 2 ( % ) ,

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