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

  • View by:
  • |
  • |
  • |

  1. E. Yablonovitch, "Inhibited spontaneous emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [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).
    [CrossRef]
  5. 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]
  6. 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]
  7. A. P. Philipse, "Solid opaline packings of colloidal silica spheres," J. Mater. Sci. Lett. 8, 1371-1373 (1989).
    [CrossRef]
  8. 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]
  9. V. Berger, O. Gauthierlafaye and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
    [CrossRef]
  10. 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]
  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).
    [CrossRef]
  12. 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]
  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).
    [CrossRef]
  14. P. V. Braun and P. Wiltzius, "Microporous materials - Electrochemically grown photonic crystals," Nature 402, 603-604 (1999).
    [CrossRef]
  15. 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. 12, 1068-1076 (1995).
    [CrossRef]
  16. 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. 12, 1077-1086 (1995).
    [CrossRef]
  17. 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 071117 (2005).
    [CrossRef]
  18. S. Jeon, D. J. Shir, Y. S. Nam, R. Nidetz, M. Highland, D. G. Cahill, J. A. Rogers, M. F. Su, I. F. El-Kady, C. G. Christodoulou and G. R. Bogart, "Molded transparent photopolymers and phase shift optics for fabricating three dimensional nanostructures," Opt. Express 15, 6358-6366 (2007).
    [CrossRef] [PubMed]
  19. T. Y. M. Chan, O. Toader and S. John, "Photonic band-gap formation by optical-phase-mask lithography," Phys. Rev. E 73,046610 (2006).
  20. J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, Ann Arbor, 1975).
  21. M. Mitchell, An Introduction to Genetic Algorithms (The MIT Press, Cambridge, 1998).
  22. J. W. Rinne and P. Wiltzius, "Design of holographic structures using genetic algorithms," Opt. Express 14, 9909-9916 (2006).
    [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," Nat. Mater. 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)

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]

T. Y. M. Chan, O. Toader and S. John, "Photonic band-gap formation by optical-phase-mask lithography," Phys. Rev. E 73,046610 (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]

2005 (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 071117 (2005).
[CrossRef]

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," Nat. Mater. 4, 383-387 (2005).
[CrossRef] [PubMed]

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]

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]

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]

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. 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. 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 73,046610 (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 071117 (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]

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]

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, 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. 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. 12, 1068-1076 (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, 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. 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. 12, 1077-1086 (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 071117 (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]

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," Nat. Mater. 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," Nat. Mater. 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 73,046610 (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 071117 (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]

Moharam, M. G.

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. 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. 12, 1077-1086 (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," Nat. Mater. 4, 383-387 (2005).
[CrossRef] [PubMed]

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," Nat. Mater. 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. 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. 12, 1068-1076 (1995).
[CrossRef]

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]

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," Nat. Mater. 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]

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," Nat. Mater. 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," Nat. Mater. 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]

Toader, O.

T. Y. M. Chan, O. Toader and S. John, "Photonic band-gap formation by optical-phase-mask lithography," Phys. Rev. E 73,046610 (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," Nat. Mater. 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]

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," Nat. Mater. 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]

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 071117 (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. (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. 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. 12, 1077-1086 (1995).
[CrossRef]

Nat. Mater. (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," Nat. Mater. 4, 383-387 (2005).
[CrossRef] [PubMed]

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]

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 (1)

T. Y. M. Chan, O. Toader and S. John, "Photonic band-gap formation by optical-phase-mask lithography," Phys. Rev. E 73,046610 (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 (6)

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).

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. 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]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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 .

Metrics