Abstract

We have developed a method for designing the diffractive optics used in phase mask lithography. Genetic algorithms were used to inverse-design a grating’s relief profile and associated exposure conditions so that desired periodic structures are formed. An experimentally promising grating designed to produce helices is demonstrated.

© 2008 Optical Society of America

Full Article  |  PDF Article

Corrections

James W. Rinne, Sidhartha Gupta, and Pierre Wiltzius, "Inverse design for phase mask lithography: erratum," Opt. Express 16, 7804-7805 (2008)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-16-11-7804

References

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    [Crossref] [PubMed]
  2. S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [Crossref] [PubMed]
  3. S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
    [Crossref] [PubMed]
  4. S. Jeon, Y. S. Nam, D. J. L. Shir, and J. A. Rogers, “Three dimensional nanoporous density graded materials formed by optical exposures through conformable phase masks,” Appl. Phys. Lett. 89, 253101 (2006).
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  9. V. Berger, O. Gauthierlafaye, and E. Costard, “Photonic Band Gaps and Holography,” J. Appl. Phys. 82, 60–64 (1997).
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  11. 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).
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    [Crossref] [PubMed]
  13. 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).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  23. Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
    [Crossref]
  24. O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,” Science 292, 1133–1135 (2001).
    [Crossref] [PubMed]
  25. J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
    [Crossref] [PubMed]
  26. S. Huard, Polarization of Light (John Willey & Sons, New York, 1997).
  27. S. Jeon, V. Malyarchuk, J. A. Rogers, and G. P. Wiederrecht, “Fabricating three dimensional nanostructures using two photon lithography in a single exposure step,” Opt. Express 14, 2300–2308 (2006).
    [Crossref] [PubMed]
  28. W. M. Spears and K. A. De Jong, “On the Virtues of Parameterized Uniform Crossover,” in Proceedings of the Fourth International Conference on Genetic Algorithms, R. K. Belew and L. B. Booker, eds. (Kaufmann, M, 1991), pp. 230–236.
  29. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1991).

2007 (3)

2006 (5)

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids,  73 (2006).

S. Jeon, V. Malyarchuk, J. A. Rogers, and G. P. Wiederrecht, “Fabricating three dimensional nanostructures using two photon lithography in a single exposure step,” Opt. Express 14, 2300–2308 (2006).
[Crossref] [PubMed]

J. W. Rinne and P. Wiltzius, “Design of holographic structures using genetic algorithms,” Opt. Express 14, 9909–9916 (2006).
[Crossref] [PubMed]

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]

S. Jeon, Y. S. Nam, D. J. L. Shir, and J. A. Rogers, “Three dimensional nanoporous density graded materials formed by optical exposures through conformable phase masks,” Appl. Phys. Lett. 89, 253101 (2006).
[Crossref]

2005 (2)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86 (2005).
[Crossref]

2004 (1)

S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
[Crossref] [PubMed]

2001 (1)

O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,” Science 292, 1133–1135 (2001).
[Crossref] [PubMed]

2000 (3)

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[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]

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]

1999 (1)

P. V. Braun and P. Wiltzius, “Microporous materials - Electrochemically grown photonic crystals,” Nature 402, 603–604 (1999).
[Crossref]

1997 (2)

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]

V. Berger, O. Gauthierlafaye, and E. Costard, “Photonic Band Gaps and Holography,” J. Appl. Phys. 82, 60–64 (1997).
[Crossref]

1996 (1)

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]

1995 (2)

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1068–1076 (1995).
[Crossref]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings - enhanced transmittance matrix approach,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1077–1086 (1995).
[Crossref]

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]

Baroni, M. D.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Berger, V.

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

Bogart, G. R.

Boldrin, L.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Braun, P. V.

S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
[Crossref] [PubMed]

P. V. Braun and P. Wiltzius, “Microporous materials - Electrochemically grown photonic crystals,” Nature 402, 603–604 (1999).
[Crossref]

Cahill, D. G.

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]

Chan, T. Y. M.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids,  73 (2006).

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]

Christodoulou, C. G.

Cimetta, E.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Cirelli, R.

S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
[Crossref] [PubMed]

Costard, E.

V. Berger, O. Gauthierlafaye, and E. Costard, “Photonic Band Gaps and Holography,” J. Appl. Phys. 82, 60–64 (1997).
[Crossref]

Darmawikarta, K.

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86 (2005).
[Crossref]

De Coppi, P.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

De Jong, K. A.

W. M. Spears and K. A. De Jong, “On the Virtues of Parameterized Uniform Crossover,” in Proceedings of the Fourth International Conference on Genetic Algorithms, R. K. Belew and L. B. Booker, eds. (Kaufmann, M, 1991), pp. 230–236.

Denning, R. G.

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]

El-Kady, I. F.

Elvassore, N.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Flaibani, M.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1991).

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]

Gamba, P.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Gauthierlafaye, O.

V. Berger, O. Gauthierlafaye, and E. Costard, “Photonic Band Gaps and Holography,” J. Appl. Phys. 82, 60–64 (1997).
[Crossref]

Gaylord, T. K.

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1068–1076 (1995).
[Crossref]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings - enhanced transmittance matrix approach,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1077–1086 (1995).
[Crossref]

Gazzola, M. V.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[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]

Grann, E. B.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings - enhanced transmittance matrix approach,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1077–1086 (1995).
[Crossref]

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1068–1076 (1995).
[Crossref]

Hamza, 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]

Heitzman, C. E.

S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
[Crossref] [PubMed]

Herman, P. R.

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86 (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]

Highland, M.

Hodgkinson, I. J.

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[Crossref]

Holland, J. H.

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

Huard, S.

S. Huard, Polarization of Light (John Willey & Sons, New York, 1997).

Hwang, J.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[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]

Ishikawa, K.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

Jeon, S.

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]

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids,  73 (2006).

O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,” Science 292, 1133–1135 (2001).
[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]

Kenis, P. J. A.

S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
[Crossref] [PubMed]

Lakhtakia, A.

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[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]

Lin, Y.

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86 (2005).
[Crossref]

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]

Malerba, A.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Malyarchuk, V.

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]

Messina, C.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[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]

Mitchell, M.

M. Mitchell, An Introduction to Genetic Algorithms (The MIT Press, Cambridge, 1998).

Moharam, M. G.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings - enhanced transmittance matrix approach,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1077–1086 (1995).
[Crossref]

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1068–1076 (1995).
[Crossref]

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]

Nam, Y. S.

Nidetz, R.

Nishimura, S.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

Noda, S.

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]

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, B.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

Park, J. U.

S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
[Crossref] [PubMed]

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]

Piccoli, M.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Pommet, D. A.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings - enhanced transmittance matrix approach,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1077–1086 (1995).
[Crossref]

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1068–1076 (1995).
[Crossref]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1991).

Rinne, J. W.

Rogers, J. A.

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]

Sasaki, A.

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]

Sharp, D. N.

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]

Shir, D. J.

Shir, D. J. L.

Y. S. Nam, S. Jeon, D. J. L. Shir, A. Hamza, and J. A. Rogers, “Thick, three-dimensional nanoporous density-graded materials formed by optical exposures of photopolymers with controlled levels of absorption,” Appl. Opt. 46, 6350–6354 (2007).
[Crossref] [PubMed]

S. Jeon, Y. S. Nam, D. J. L. Shir, and J. A. Rogers, “Three dimensional nanoporous density graded materials formed by optical exposures through conformable phase masks,” Appl. Phys. Lett. 89, 253101 (2006).
[Crossref]

Song, M. H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

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]

Spears, W. M.

W. M. Spears and K. A. De Jong, “On the Virtues of Parameterized Uniform Crossover,” in Proceedings of the Fourth International Conference on Genetic Algorithms, R. K. Belew and L. B. Booker, eds. (Kaufmann, M, 1991), pp. 230–236.

Su, M. F.

Takanishi, Y.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

Takezoe, H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

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]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1991).

Toader, O.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids,  73 (2006).

O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,” Science 292, 1133–1135 (2001).
[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]

Toyooka, T.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

Turberfield, A. J.

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]

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]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1991).

Vitiello, L.

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[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]

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]

Wiederrecht, G. P.

Wiltzius, P.

J. W. Rinne and P. Wiltzius, “Design of holographic structures using genetic algorithms,” Opt. Express 14, 9909–9916 (2006).
[Crossref] [PubMed]

P. V. Braun and P. Wiltzius, “Microporous materials - Electrochemically grown photonic crystals,” Nature 402, 603–604 (1999).
[Crossref]

Wu, J. W.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

Wu, Q. H.

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[Crossref]

Yablonovitch, E.

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Yamamoto, N.

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]

Yang, S.

S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
[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]

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. Opt. (1)

Appl. Phys. Lett. (2)

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86 (2005).
[Crossref]

S. Jeon, Y. S. Nam, D. J. L. Shir, and J. A. Rogers, “Three dimensional nanoporous density graded materials formed by optical exposures through conformable phase masks,” Appl. Phys. Lett. 89, 253101 (2006).
[Crossref]

J. Appl. Phys. (1)

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. (2)

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1068–1076 (1995).
[Crossref]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings - enhanced transmittance matrix approach,” J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 12, 1077–1086 (1995).
[Crossref]

Jpn. J. Appl. Phys. (1)

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]

Nature (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]

P. V. Braun and P. Wiltzius, “Microporous materials - Electrochemically grown photonic crystals,” Nature 402, 603–604 (1999).
[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]

Nature Materials (1)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nature Materials 4, 383–387 (2005).
[Crossref] [PubMed]

Opt. Eng. (1)

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circular polarization filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[Crossref]

Opt. Express (3)

Phys. Rev. E: Stat. Phys. (1)

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids,  73 (2006).

Phys. Rev. Lett. (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]

Proc. Natl. Acad. Sci. U. S. A. (1)

S. Jeon, J. U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. U. S. A. 101, 12428–12433 (2004).
[Crossref] [PubMed]

Science (1)

O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,” Science 292, 1133–1135 (2001).
[Crossref] [PubMed]

Tissue Eng. (1)

L. Boldrin, N. Elvassore, A. Malerba, M. Flaibani, E. Cimetta, M. Piccoli, M. D. Baroni, M. V. Gazzola, C. Messina, P. Gamba, L. Vitiello, and P. De Coppi, “Satellite cells delivered by micro-patterned scaffolds: A new strategy for cell transplantation in muscle diseases,” Tissue Eng. 13, 253–262 (2007).
[Crossref] [PubMed]

Other (5)

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

M. Mitchell, An Introduction to Genetic Algorithms (The MIT Press, Cambridge, 1998).

S. Huard, Polarization of Light (John Willey & Sons, New York, 1997).

W. M. Spears and K. A. De Jong, “On the Virtues of Parameterized Uniform Crossover,” in Proceedings of the Fourth International Conference on Genetic Algorithms, R. K. Belew and L. B. Booker, eds. (Kaufmann, M, 1991), pp. 230–236.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1991).

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Figures (3)

Fig. 1.
Fig. 1.

The illustration in part (a) depicts the helix structure used as the target model. For clarity, we plot two turns of the helix and outline in bold a single primitive cell with dimensions a×a√3/2×c. Here, c/a describes the helices’ relative elongation and has a value of 2.2. Parts (b) and (c) depict the interference based structure that is produced by the optimized grating shown in (d). Comparison between the structure in (b) and the target in (a) results in a fitness of 93%. By plotting several repeat units in (c) the full 3D hexagonal periodicity becomes apparent.

Fig. 2.
Fig. 2.

Helices with various aspect ratios are obtained for phase masks optimized via GA. Parts (a)–(f) correspond c/a values of 1.2, 1.4, 1.6, 1.8, 2.0, and 2.2 respectively.

Fig. 3.
Fig. 3.

(a) Fitness of the best result from each generation plotted for a single GA run. (b) Grating relief profiles represented by a single unit cell of raised (light) and recessed (dark) elements with the polarization state depicted by the path a field vector traces at a point in space. (c) Corresponding interference structures produced during the generations are indicated by i–v in (a). Following GA optimization, the design produced at v was optimized further using a local search algorithm, producing the design and structure in vi. Because the diffraction is more accurately calculated during this step, the fitness at v was computed to be 92% (versus 94% as shown in (a)). After local optimization of the structure in v, a final fitness of 93% was achieved for the final design and structure in vi.

Equations (5)

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

γ pq = ( an _ λ 0 ) 2 ( p q ) 2 ( p + q ) 2 3 .
( an _ λ 0 ) 2 > ( p q ) 2 + ( p + q ) 2 3 .
I ( r ) = i = 1 N j = 1 N E ˜ i · E ˜ j * e i ( k i k j ) · r ,
Φ ( I ( r ) I th ) = { n _ , I ( r ) I th 1 ,   I ( r ) < I th .
c = a a n _ λ 0 ( a n _ λ 0 ) 2 4 3 .

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