Abstract

We have developed a general technique using genetic algorithms to design photonic crystals to be fabricated by holographic lithography. In contrast to current analytical approaches that rely almost exclusively on symmetry considerations, this technique allows for high-fidelity approximations to real-space structures without limiting the search space to a prescribed set of symmetries. We have used this new technique to design a structure having a complete photonic band gap of 28%, the largest yet reported for holographic lithography.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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2006 (2)

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures," Phys. Rev. Lett. 96,143904 (2006).
[CrossRef] [PubMed]

2005 (2)

A. Hakansson and J. Sanchez-Dehesa, "Inverse designed photonic crystal de-multiplex waveguide coupler," Opt. Express 13,5440-5449 (2005).
[CrossRef] [PubMed]

J. S. King, D. Heineman, E. Graugnard, and C. J. Summers, "Atomic layer deposition in porous structures: 3D photonic crystals," Appl. Surf. Sci. 244,511-516 (2005).
[CrossRef]

2004 (3)

O. Toader, T. Y. M. Chan, and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92,043905 (2004).
[CrossRef] [PubMed]

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3,593-600 (2004).
[CrossRef] [PubMed]

X. Y. Ao and S. L. He, "Two-stage design method for realization of photonic bandgap structures with desired symmetries by interference lithography," Opt. Express 12,978-983 (2004).
[CrossRef] [PubMed]

2003 (5)

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, "Effects of polarization on laser holography for microstructure fabrication," Phys. Rev. E 67,056619 (2003).
[CrossRef]

L. F. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68,035109 (2003).
[CrossRef]

C. K. Ullal, M. Maldovan, M. Wohlgemuth, and E. L. Thomas, "Triply periodic bicontinuous structures through interference lithography: a level-set approach," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 20,948-954 (2003).
[CrossRef] [PubMed]

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68,205102 (2003).
[CrossRef]

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

2002 (1)

2001 (1)

2000 (3)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53-56 (2000).
[CrossRef] [PubMed]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62,R7683-R7686 (2000).
[CrossRef]

1997 (2)

V. Berger, O. Gauthierlafaye and E. Costard, "Photonic Band Gaps and Holography," J. Appl. Phys. 82,60-64 (1997).
[CrossRef]

H. M. Yates, W. R. Flavell, M. E. Pemble, N. P. Johnson, S. G. Romanov, and C. M. Sotomayortorres, "Novel quantum confined structures via atmospheric pressure mocvd growth in asbestos and opals," J. Cryst. Growth 170,611-615 (1997).
[CrossRef]

1994 (3)

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. 89,413-416 (1994).
[CrossRef]

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials - low-loss bends and high q-cavities," J. Appl. Phys. 75,4753-4755 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho and C. M. Soukoulis, "A7 structure - a family of photonic crystals," Phys. Rev. B 50,1988-1991 (1994).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65,3152-3155 (1990).
[CrossRef] [PubMed]

1989 (1)

A. P. Philipse, "Solid Opaline Packings of Colloidal Silica Spheres," J. Mater. Sci. Lett. 8,1371-1373 (1989).
[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. Rev. Lett. 58,2486-2489 (1987).
[CrossRef] [PubMed]

1986 (1)

J. J. Grefenstette, "Optimization of Control Parameters for Genetic Algorithms," IEEE Trans. Syst. Man Cybern. 16,122-128 (1986).
[CrossRef]

Alerhand, O. L.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials - low-loss bends and high q-cavities," J. Appl. Phys. 75,4753-4755 (1994).
[CrossRef]

Ao, X. Y.

Berger, V.

V. Berger, O. Gauthierlafaye and E. Costard, "Photonic Band Gaps and Holography," J. Appl. Phys. 82,60-64 (1997).
[CrossRef]

Biswas, R.

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. 89,413-416 (1994).
[CrossRef]

Blanco, A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Blomquist, S.

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53-56 (2000).
[CrossRef] [PubMed]

Centeno, E.

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62,R7683-R7686 (2000).
[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. 89,413-416 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho and C. M. Soukoulis, "A7 structure - a family of photonic crystals," Phys. Rev. B 50,1988-1991 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65,3152-3155 (1990).
[CrossRef] [PubMed]

Chan, T. Y. M.

O. Toader, T. Y. M. Chan, and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92,043905 (2004).
[CrossRef] [PubMed]

Chen, L.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures," Phys. Rev. Lett. 96,143904 (2006).
[CrossRef] [PubMed]

Chomski, E.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Costard, E.

V. Berger, O. Gauthierlafaye and E. Costard, "Photonic Band Gaps and Holography," J. Appl. Phys. 82,60-64 (1997).
[CrossRef]

Datta, S.

C. T. Chan, S. Datta, K. M. Ho and C. M. Soukoulis, "A7 structure - a family of photonic crystals," Phys. Rev. B 50,1988-1991 (1994).
[CrossRef]

Denning, R. G.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68,205102 (2003).
[CrossRef]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53-56 (2000).
[CrossRef] [PubMed]

Deubel, M.

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

Devenyi, A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials - low-loss bends and high q-cavities," J. Appl. Phys. 75,4753-4755 (1994).
[CrossRef]

Felbacq, D.

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62,R7683-R7686 (2000).
[CrossRef]

Flavell, W. R.

H. M. Yates, W. R. Flavell, M. E. Pemble, N. P. Johnson, S. G. Romanov, and C. M. Sotomayortorres, "Novel quantum confined structures via atmospheric pressure mocvd growth in asbestos and opals," J. Cryst. Growth 170,611-615 (1997).
[CrossRef]

Forsythe, E.

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

Gauthierlafaye, O.

V. Berger, O. Gauthierlafaye and E. Costard, "Photonic Band Gaps and Holography," J. Appl. Phys. 82,60-64 (1997).
[CrossRef]

Gondarenko, A.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures," Phys. Rev. Lett. 96,143904 (2006).
[CrossRef] [PubMed]

Grabtchak, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Graugnard, E.

J. S. King, D. Heineman, E. Graugnard, and C. J. Summers, "Atomic layer deposition in porous structures: 3D photonic crystals," Appl. Surf. Sci. 244,511-516 (2005).
[CrossRef]

Grefenstette, J. J.

J. J. Grefenstette, "Optimization of Control Parameters for Genetic Algorithms," IEEE Trans. Syst. Man Cybern. 16,122-128 (1986).
[CrossRef]

Gu, M.

Hakansson, A.

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53-56 (2000).
[CrossRef] [PubMed]

He, S.

L. F. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68,035109 (2003).
[CrossRef]

He, S. L.

Heineman, D.

J. S. King, D. Heineman, E. Graugnard, and C. J. Summers, "Atomic layer deposition in porous structures: 3D photonic crystals," Appl. Surf. Sci. 244,511-516 (2005).
[CrossRef]

Hermatschweiler, M.

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

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. 89,413-416 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho and C. M. Soukoulis, "A7 structure - a family of photonic crystals," Phys. Rev. B 50,1988-1991 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65,3152-3155 (1990).
[CrossRef] [PubMed]

Ibisate, M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Joannopoulos, J. D.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials - low-loss bends and high q-cavities," J. Appl. Phys. 75,4753-4755 (1994).
[CrossRef]

John, S.

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

O. Toader, T. Y. M. Chan, and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92,043905 (2004).
[CrossRef] [PubMed]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

S. John, "Strong localization of Photons in certain disordered Dielectric Superlattices," Phys. Rev. Lett. 58,2486-2489 (1987).
[CrossRef] [PubMed]

Johnson, N. P.

H. M. Yates, W. R. Flavell, M. E. Pemble, N. P. Johnson, S. G. Romanov, and C. M. Sotomayortorres, "Novel quantum confined structures via atmospheric pressure mocvd growth in asbestos and opals," J. Cryst. Growth 170,611-615 (1997).
[CrossRef]

Kash, K.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials - low-loss bends and high q-cavities," J. Appl. Phys. 75,4753-4755 (1994).
[CrossRef]

King, J. S.

J. S. King, D. Heineman, E. Graugnard, and C. J. Summers, "Atomic layer deposition in porous structures: 3D photonic crystals," Appl. Surf. Sci. 244,511-516 (2005).
[CrossRef]

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

Leonard, S. W.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Lipson, H.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures," Phys. Rev. Lett. 96,143904 (2006).
[CrossRef] [PubMed]

Lipson, M.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures," Phys. Rev. Lett. 96,143904 (2006).
[CrossRef] [PubMed]

Lopez, C.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Maldovan, M.

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3,593-600 (2004).
[CrossRef] [PubMed]

C. K. Ullal, M. Maldovan, M. Wohlgemuth, and E. L. Thomas, "Triply periodic bicontinuous structures through interference lithography: a level-set approach," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 20,948-954 (2003).
[CrossRef] [PubMed]

Meade, R. D.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials - low-loss bends and high q-cavities," J. Appl. Phys. 75,4753-4755 (1994).
[CrossRef]

Meseguer, F.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Miguez, H.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Mondia, J. P.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Morton, D.

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

Neff, C. W.

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

Ozin, G. A.

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Park, W.

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

Pemble, M. E.

H. M. Yates, W. R. Flavell, M. E. Pemble, N. P. Johnson, S. G. Romanov, and C. M. Sotomayortorres, "Novel quantum confined structures via atmospheric pressure mocvd growth in asbestos and opals," J. Cryst. Growth 170,611-615 (1997).
[CrossRef]

Perez-Willard, F.

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

Philipse, A. P.

A. P. Philipse, "Solid Opaline Packings of Colloidal Silica Spheres," J. Mater. Sci. Lett. 8,1371-1373 (1989).
[CrossRef]

Preble, S.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures," Phys. Rev. Lett. 96,143904 (2006).
[CrossRef] [PubMed]

Robinson, J.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures," Phys. Rev. Lett. 96,143904 (2006).
[CrossRef] [PubMed]

Romanov, S. G.

H. M. Yates, W. R. Flavell, M. E. Pemble, N. P. Johnson, S. G. Romanov, and C. M. Sotomayortorres, "Novel quantum confined structures via atmospheric pressure mocvd growth in asbestos and opals," J. Cryst. Growth 170,611-615 (1997).
[CrossRef]

Sanchez-Dehesa, J.

Sharp, D. N.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68,205102 (2003).
[CrossRef]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53-56 (2000).
[CrossRef] [PubMed]

Shen, L. F.

L. F. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68,035109 (2003).
[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. 89,413-416 (1994).
[CrossRef]

Smith, D. A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials - low-loss bends and high q-cavities," J. Appl. Phys. 75,4753-4755 (1994).
[CrossRef]

Sotomayortorres, C. M.

H. M. Yates, W. R. Flavell, M. E. Pemble, N. P. Johnson, S. G. Romanov, and C. M. Sotomayortorres, "Novel quantum confined structures via atmospheric pressure mocvd growth in asbestos and opals," J. Cryst. Growth 170,611-615 (1997).
[CrossRef]

Soukoulis, C. M.

C. T. Chan, S. Datta, K. M. Ho and C. M. Soukoulis, "A7 structure - a family of photonic crystals," Phys. Rev. B 50,1988-1991 (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. 89,413-416 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65,3152-3155 (1990).
[CrossRef] [PubMed]

Straub, M.

Su, H. M.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, "Effects of polarization on laser holography for microstructure fabrication," Phys. Rev. E 67,056619 (2003).
[CrossRef]

Summers, C. J.

J. S. King, D. Heineman, E. Graugnard, and C. J. Summers, "Atomic layer deposition in porous structures: 3D photonic crystals," Appl. Surf. Sci. 244,511-516 (2005).
[CrossRef]

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

Tetreault, N.

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

Thomas, E. L.

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3,593-600 (2004).
[CrossRef] [PubMed]

C. K. Ullal, M. Maldovan, M. Wohlgemuth, and E. L. Thomas, "Triply periodic bicontinuous structures through interference lithography: a level-set approach," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 20,948-954 (2003).
[CrossRef] [PubMed]

Toader, O.

O. Toader, T. Y. M. Chan, and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92,043905 (2004).
[CrossRef] [PubMed]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

Turberfield, A. J.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68,205102 (2003).
[CrossRef]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53-56 (2000).
[CrossRef] [PubMed]

Ullal, C. K.

C. K. Ullal, M. Maldovan, M. Wohlgemuth, and E. L. Thomas, "Triply periodic bicontinuous structures through interference lithography: a level-set approach," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 20,948-954 (2003).
[CrossRef] [PubMed]

van Driel, H. M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

von Freymann, G.

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

Wang, H. Z.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, "Effects of polarization on laser holography for microstructure fabrication," Phys. Rev. E 67,056619 (2003).
[CrossRef]

Wang, X.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, "Effects of polarization on laser holography for microstructure fabrication," Phys. Rev. E 67,056619 (2003).
[CrossRef]

Wegener, M.

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

Wohlgemuth, M.

C. K. Ullal, M. Maldovan, M. Wohlgemuth, and E. L. Thomas, "Triply periodic bicontinuous structures through interference lithography: a level-set approach," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 20,948-954 (2003).
[CrossRef] [PubMed]

Xu, J. F.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, "Effects of polarization on laser holography for microstructure fabrication," Phys. Rev. E 67,056619 (2003).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58,2059-2062 (1987).
[CrossRef] [PubMed]

Yates, H. M.

H. M. Yates, W. R. Flavell, M. E. Pemble, N. P. Johnson, S. G. Romanov, and C. M. Sotomayortorres, "Novel quantum confined structures via atmospheric pressure mocvd growth in asbestos and opals," J. Cryst. Growth 170,611-615 (1997).
[CrossRef]

Ye, Z.

L. F. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68,035109 (2003).
[CrossRef]

Zheng, X. G.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, "Effects of polarization on laser holography for microstructure fabrication," Phys. Rev. E 67,056619 (2003).
[CrossRef]

Zhong, Y. C.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, "Effects of polarization on laser holography for microstructure fabrication," Phys. Rev. E 67,056619 (2003).
[CrossRef]

Adv. Mater. (1)

N. Tetreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates," Adv. Mater. 18,457-460 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

J. S. King, C. W. Neff, C. J. Summers, W. Park, S. Blomquist, E. Forsythe, and D. Morton, "High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition," Appl. Phys. Lett. 83,2566-2568 (2003).
[CrossRef]

Appl. Surf. Sci. (1)

J. S. King, D. Heineman, E. Graugnard, and C. J. Summers, "Atomic layer deposition in porous structures: 3D photonic crystals," Appl. Surf. Sci. 244,511-516 (2005).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

J. J. Grefenstette, "Optimization of Control Parameters for Genetic Algorithms," IEEE Trans. Syst. Man Cybern. 16,122-128 (1986).
[CrossRef]

J. Appl. Phys. (2)

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith and K. Kash, "Novel applications of photonic band gap materials - low-loss bends and high q-cavities," J. Appl. Phys. 75,4753-4755 (1994).
[CrossRef]

V. Berger, O. Gauthierlafaye and E. Costard, "Photonic Band Gaps and Holography," J. Appl. Phys. 82,60-64 (1997).
[CrossRef]

J. Cryst. Growth (1)

H. M. Yates, W. R. Flavell, M. E. Pemble, N. P. Johnson, S. G. Romanov, and C. M. Sotomayortorres, "Novel quantum confined structures via atmospheric pressure mocvd growth in asbestos and opals," J. Cryst. Growth 170,611-615 (1997).
[CrossRef]

J. Mater. Sci. Lett. (1)

A. P. Philipse, "Solid Opaline Packings of Colloidal Silica Spheres," J. Mater. Sci. Lett. 8,1371-1373 (1989).
[CrossRef]

J. Opt. Soc. Am. A-Opt. Image Sci. Vis. (1)

C. K. Ullal, M. Maldovan, M. Wohlgemuth, and E. L. Thomas, "Triply periodic bicontinuous structures through interference lithography: a level-set approach," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 20,948-954 (2003).
[CrossRef] [PubMed]

Nat. Mater. (1)

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3,593-600 (2004).
[CrossRef] [PubMed]

Nature (2)

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405,437-440 (2000).
[CrossRef] [PubMed]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53-56 (2000).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (4)

C. T. Chan, S. Datta, K. M. Ho and C. M. Soukoulis, "A7 structure - a family of photonic crystals," Phys. Rev. B 50,1988-1991 (1994).
[CrossRef]

L. F. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68,035109 (2003).
[CrossRef]

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62,R7683-R7686 (2000).
[CrossRef]

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68,205102 (2003).
[CrossRef]

Phys. Rev. E (1)

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, "Effects of polarization on laser holography for microstructure fabrication," Phys. Rev. E 67,056619 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures," Phys. Rev. Lett. 96,143904 (2006).
[CrossRef] [PubMed]

O. Toader, T. Y. M. Chan, and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92,043905 (2004).
[CrossRef] [PubMed]

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. Rev. Lett. 58,2486-2489 (1987).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in Periodic Dielectric Structures," Phys. Rev. Lett. 65,3152-3155 (1990).
[CrossRef] [PubMed]

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. 89,413-416 (1994).
[CrossRef]

Other (5)

S. Noda, N. Yamamoto and A. Sasaki, "New realization method for three-dimensional photonic crystal in optical wavelength region," Jpn. J. Appl. Phys. Part 2 35, L 909-L 912 (1996).
[CrossRef]

J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, Ann Arbor, 1975).

M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, Cambridge, Massachusetts, 1996).

S. Huard, Polarization of Light (John Wiley & Sons, Incorporated, Chichester, 1997).

J. W. Rinne and P. Wiltzius (to be published).

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Figures (4)

Fig. 1.
Fig. 1.

(a). Unit cell of the RCD structure having a PBG of 30%. (b). Best holographically definable structure approximating RCD. A PBG of 28% is obtained for a dielectric fill of 17%.

Fig. 2.
Fig. 2.

Bit layout for the binary parameters, y ij , within the chromosome. A specific case for which each parameter has a length of l=7 is used as an example. The subscripts i and j correspond to the beam and bit numbers respectively. For clarity, each bit having the same subscript j is labeled in the same shade of grey, where darker shades correspond to larger place values. The j th bit of each parameter is placed in the corresponding j th substring according to the arrangement shown at the bottom (for j=2). The substrings are then placed into the chromosome (right) using an alternating stacking method so that bits with a higher place value are clustered together.

Fig. 3.
Fig. 3.

The best fitness plotted as a function of generation (top). The unit cells (bottom) show the (111) view of the best structures at different generations during the run. Letters a - e match each unit cell to a different point on the graph. The unit cell of the RCD structure, which was used as the target, is shown at the bottom right for comparison.

Fig. 4.
Fig. 4.

(a) Gap width between the 2nd and 3rd bands plotted as a function of dielectric fill and dielectric contrast for the structure shown in Fig. 1(b). Negative gap widths correspond to the 3rd band dropping below the 2nd. At a dielectric fill of 17%, the optimized holographic structure shown in Fig. 1(b) achieves a 28% gap for silicon-air dielectric contrast (ε=12.96). (b) Density of states, g(ν), for the corresponding holographic structure shown in Fig. 1(b) having a dielectric fill of 17%.

Tables (1)

Tables Icon

Table 1. List of optimized parameters used to make structure shown in Fig. 1(b). All angles are given in radians.

Equations (3)

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

I ( r ) = i , j N E i E j ( e ̂ i * · e ̂ j ) exp i ( g ij · r + ij ) ,
e ̂ i = R ( θ i , φ i ) J ( γ i , χ i ) = [ cos φ i cos θ i sin φ i cos φ i sin θ i sin φ i cos θ i cos φ i sin φ i sin θ i sin θ i 0 cos θ i ] [ cos γ i e i χ i sin γ i 0 ] .
Θ ( I ( r ) I th ) = { 1 , I ( r ) I th 0 , I ( r ) < I th ,

Metrics