Abstract

Quasicrystals have a higher degree of rotational and point-reflection symmetry than conventional crystals. As a result, quasicrystalline heterostructures fabricated from dielectric materials with micrometer-scale features exhibit interesting and useful optical properties including large photonic bandgaps in two-dimensional systems. We demonstrate the holographic assembly of two-dimensional and three-dimensional dielectric quasicrystalline heterostructures, including structures with specifically engineered defects. The highly uniform quasiperiodic arrays of optical traps used in this process also provide model aperiodic potential energy landscapes for fundamental studies of transport and phase transitions in soft condensed matter systems.

© 2005 Optical Society of America

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References

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  1. S. E. Burkov, T. Timusk, and N. W. Ashcroft. “Optical conductivity of icoahedral quasi-crystals.” J. Phys.: Condens. Matt. 4, 9447–9458 (1992).
    [Crossref]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn. Photonic Crystals (Princeton University Press, Princeton, 1995).
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    [Crossref]
  4. S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimentional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
    [Crossref]
  5. X. Zhang, Z. Q. Zhang, and C. T. Chan. “Absolute photonic band gaps in 12-fold symmetric photonic crystals.” Phys. Rev. B 63, 081105 (2001).
    [Crossref]
  6. T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka. “Photonic dispersion-relation in a one-dimensional quasi-crystal.” Phys. Rev. B 50, 4220–4223 (1994).
    [Crossref]
  7. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti. “Complete photonic bandgaps in 12-fold symmetric quasicrystals.” Nature 404, 740–743 (2000).
    [Crossref] [PubMed]
  8. E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
    [Crossref]
  9. D. G. Grier. “A revolution in optical manipulation.” Nature 424, 810–816 (2003).
    [Crossref] [PubMed]
  10. M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier. “Optimized holographic optical traps.” Opt. Express submitted for publication (2005).
    [Crossref] [PubMed]
  11. U. Grimm and M. Schrieber. “Aperiodic tilings on the computer.” In Quasicrystals: an Introduction to Structure, Physical Properties and Applications, edited by J. B. Suck, M. Shrieber, and P. Haussler (Springer, 2002).
  12. C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
    [Crossref]
  13. M. Bayindir, E. Cubukco, I. Bulu, and E. Ozbay. “Photonic band-gap effect, localization, and waveguiding in two-dimensional Penrose lattice.” Phys. Rev. B 63, 161104(R) (2001).
    [Crossref]
  14. M. J. Escuti and G. P. Crawford. “Holographic photonic crystals.” Opt. Eng. 43, 1973–1987 (2004).
    [Crossref]
  15. R. C. Gauthier and A. Ivanov. “Production of quasi-crystal template patterns using a dual beam multiple exposure technique.” Opt. Eng. 12, 990–1003 (2004).
  16. R. C. Gauthier and K. Mnaymneh. “Photonic band gap properties of 12 fold quasi-crystal determined through FDTD analysis.” Opt. Eng. 13, 1985–1998 (2005).
  17. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng. “Large-area two-dimensional mesoscopic quasi-crystals.” Adv. Mater. 15, 1526–1528 (2003).
    [Crossref]
  18. S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
    [Crossref]
  19. C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang. “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region.” Phys. Rev. B 61, 10762–10767 (2000).
    [Crossref]
  20. J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, J. Laczik, and Zsolt. “3D manipulation of particles into crystal structures using holographic optical tweezers.” Opt. Express 12, 220–226 (2004).
    [Crossref] [PubMed]
  21. G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik. “Assembly of 3-dimensional structures using programmable holographic optical tweezers.” Opt. Express 12, 5475–5480 (2004).
    [Crossref] [PubMed]
  22. P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
    [Crossref]
  23. W. Man, M. Megens, P. Steinhardt, and P. M. Chaikin. “Experiments on the phononic properties of icosahedral quasicrystals.” preprint (2005).
  24. S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada. “Finer features for functional microdevicecs.” Nature 412, 697–698 (2001).
    [Crossref] [PubMed]
  25. A. R. Denton and H. Löwen. “Stability of colloidal quasicrystals.” Phys. Rev. Lett. 81, 469–472 (1998).
    [Crossref]
  26. P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
    [Crossref] [PubMed]

2005 (1)

R. C. Gauthier and K. Mnaymneh. “Photonic band gap properties of 12 fold quasi-crystal determined through FDTD analysis.” Opt. Eng. 13, 1985–1998 (2005).

2004 (4)

2003 (2)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng. “Large-area two-dimensional mesoscopic quasi-crystals.” Adv. Mater. 15, 1526–1528 (2003).
[Crossref]

D. G. Grier. “A revolution in optical manipulation.” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

2002 (2)

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

2001 (3)

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada. “Finer features for functional microdevicecs.” Nature 412, 697–698 (2001).
[Crossref] [PubMed]

M. Bayindir, E. Cubukco, I. Bulu, and E. Ozbay. “Photonic band-gap effect, localization, and waveguiding in two-dimensional Penrose lattice.” Phys. Rev. B 63, 161104(R) (2001).
[Crossref]

X. Zhang, Z. Q. Zhang, and C. T. Chan. “Absolute photonic band gaps in 12-fold symmetric photonic crystals.” Phys. Rev. B 63, 081105 (2001).
[Crossref]

2000 (2)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti. “Complete photonic bandgaps in 12-fold symmetric quasicrystals.” Nature 404, 740–743 (2000).
[Crossref] [PubMed]

C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang. “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region.” Phys. Rev. B 61, 10762–10767 (2000).
[Crossref]

1999 (3)

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
[Crossref]

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimentional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

1998 (3)

A. R. Denton and H. Löwen. “Stability of colloidal quasicrystals.” Phys. Rev. Lett. 81, 469–472 (1998).
[Crossref]

E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
[Crossref]

Y. S. Chan, C. T. Chan, and Z. Y. Liu. “Photonic band gaps in two dimensional photonic quasicrystals.” Phys. Rev. Lett. 80, 956–959 (1998).
[Crossref]

1994 (1)

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka. “Photonic dispersion-relation in a one-dimensional quasi-crystal.” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

1992 (1)

S. E. Burkov, T. Timusk, and N. W. Ashcroft. “Optical conductivity of icoahedral quasi-crystals.” J. Phys.: Condens. Matt. 4, 9447–9458 (1992).
[Crossref]

Ashcroft, N. W.

S. E. Burkov, T. Timusk, and N. W. Ashcroft. “Optical conductivity of icoahedral quasi-crystals.” J. Phys.: Condens. Matt. 4, 9447–9458 (1992).
[Crossref]

Ban, S.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
[Crossref]

Baumberg, J. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti. “Complete photonic bandgaps in 12-fold symmetric quasicrystals.” Nature 404, 740–743 (2000).
[Crossref] [PubMed]

Bayindir, M.

M. Bayindir, E. Cubukco, I. Bulu, and E. Ozbay. “Photonic band-gap effect, localization, and waveguiding in two-dimensional Penrose lattice.” Phys. Rev. B 63, 161104(R) (2001).
[Crossref]

Bulu, I.

M. Bayindir, E. Cubukco, I. Bulu, and E. Ozbay. “Photonic band-gap effect, localization, and waveguiding in two-dimensional Penrose lattice.” Phys. Rev. B 63, 161104(R) (2001).
[Crossref]

Burkov, S. E.

S. E. Burkov, T. Timusk, and N. W. Ashcroft. “Optical conductivity of icoahedral quasi-crystals.” J. Phys.: Condens. Matt. 4, 9447–9458 (1992).
[Crossref]

Chaikin, P. M.

W. Man, M. Megens, P. Steinhardt, and P. M. Chaikin. “Experiments on the phononic properties of icosahedral quasicrystals.” preprint (2005).

Chan, C. T.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng. “Large-area two-dimensional mesoscopic quasi-crystals.” Adv. Mater. 15, 1526–1528 (2003).
[Crossref]

X. Zhang, Z. Q. Zhang, and C. T. Chan. “Absolute photonic band gaps in 12-fold symmetric photonic crystals.” Phys. Rev. B 63, 081105 (2001).
[Crossref]

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimentional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

Y. S. Chan, C. T. Chan, and Z. Y. Liu. “Photonic band gaps in two dimensional photonic quasicrystals.” Phys. Rev. Lett. 80, 956–959 (1998).
[Crossref]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu. “Photonic band gaps in two dimensional photonic quasicrystals.” Phys. Rev. Lett. 80, 956–959 (1998).
[Crossref]

Charlton, M. D. B.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti. “Complete photonic bandgaps in 12-fold symmetric quasicrystals.” Nature 404, 740–743 (2000).
[Crossref] [PubMed]

Cheng, B.

C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang. “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region.” Phys. Rev. B 61, 10762–10767 (2000).
[Crossref]

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
[Crossref]

Cheng, S. S. M.

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimentional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

Cooper, J.

Courtial, J.

Crawford, G. P.

M. J. Escuti and G. P. Crawford. “Holographic photonic crystals.” Opt. Eng. 43, 1973–1987 (2004).
[Crossref]

Cubukco, E.

M. Bayindir, E. Cubukco, I. Bulu, and E. Ozbay. “Photonic band-gap effect, localization, and waveguiding in two-dimensional Penrose lattice.” Phys. Rev. B 63, 161104(R) (2001).
[Crossref]

Denton, A. R.

A. R. Denton and H. Löwen. “Stability of colloidal quasicrystals.” Phys. Rev. Lett. 81, 469–472 (1998).
[Crossref]

Dufresne, E. R.

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
[Crossref]

Escuti, M. J.

M. J. Escuti and G. P. Crawford. “Holographic photonic crystals.” Opt. Eng. 43, 1973–1987 (2004).
[Crossref]

Gauthier, R. C.

R. C. Gauthier and K. Mnaymneh. “Photonic band gap properties of 12 fold quasi-crystal determined through FDTD analysis.” Opt. Eng. 13, 1985–1998 (2005).

R. C. Gauthier and A. Ivanov. “Production of quasi-crystal template patterns using a dual beam multiple exposure technique.” Opt. Eng. 12, 990–1003 (2004).

Grier, D. G.

D. G. Grier. “A revolution in optical manipulation.” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
[Crossref]

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier. “Optimized holographic optical traps.” Opt. Express submitted for publication (2005).
[Crossref] [PubMed]

Grimm, U.

U. Grimm and M. Schrieber. “Aperiodic tilings on the computer.” In Quasicrystals: an Introduction to Structure, Physical Properties and Applications, edited by J. B. Suck, M. Shrieber, and P. Haussler (Springer, 2002).

Hattori, T.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka. “Photonic dispersion-relation in a one-dimensional quasi-crystal.” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Ivanov, A.

R. C. Gauthier and A. Ivanov. “Production of quasi-crystal template patterns using a dual beam multiple exposure technique.” Opt. Eng. 12, 990–1003 (2004).

Jin, C.

C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang. “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region.” Phys. Rev. B 61, 10762–10767 (2000).
[Crossref]

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
[Crossref]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn. Photonic Crystals (Princeton University Press, Princeton, 1995).

Jordan, P.

Kawata, S.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada. “Finer features for functional microdevicecs.” Nature 412, 697–698 (2001).
[Crossref] [PubMed]

Kawato, S.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka. “Photonic dispersion-relation in a one-dimensional quasi-crystal.” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Korda, P. T.

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

Laczik, J.

Laczik, Z. J.

Ladavac, K.

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier. “Optimized holographic optical traps.” Opt. Express submitted for publication (2005).
[Crossref] [PubMed]

Leach, J.

Lee, S.-H.

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier. “Optimized holographic optical traps.” Opt. Express submitted for publication (2005).
[Crossref] [PubMed]

Li, L. M.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimentional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

Li, L.-M.

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

Li, Z.

C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang. “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region.” Phys. Rev. B 61, 10762–10767 (2000).
[Crossref]

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
[Crossref]

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu. “Photonic band gaps in two dimensional photonic quasicrystals.” Phys. Rev. Lett. 80, 956–959 (1998).
[Crossref]

Löwen, H.

A. R. Denton and H. Löwen. “Stability of colloidal quasicrystals.” Phys. Rev. Lett. 81, 469–472 (1998).
[Crossref]

Man, B.

C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang. “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region.” Phys. Rev. B 61, 10762–10767 (2000).
[Crossref]

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
[Crossref]

Man, W.

W. Man, M. Megens, P. Steinhardt, and P. M. Chaikin. “Experiments on the phononic properties of icosahedral quasicrystals.” preprint (2005).

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn. Photonic Crystals (Princeton University Press, Princeton, 1995).

Megens, M.

W. Man, M. Megens, P. Steinhardt, and P. M. Chaikin. “Experiments on the phononic properties of icosahedral quasicrystals.” preprint (2005).

Mnaymneh, K.

R. C. Gauthier and K. Mnaymneh. “Photonic band gap properties of 12 fold quasi-crystal determined through FDTD analysis.” Opt. Eng. 13, 1985–1998 (2005).

Nakatsuka, H.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka. “Photonic dispersion-relation in a one-dimensional quasi-crystal.” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Netti, M. C.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti. “Complete photonic bandgaps in 12-fold symmetric quasicrystals.” Nature 404, 740–743 (2000).
[Crossref] [PubMed]

Ng, C. Y.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng. “Large-area two-dimensional mesoscopic quasi-crystals.” Adv. Mater. 15, 1526–1528 (2003).
[Crossref]

Ozbay, E.

M. Bayindir, E. Cubukco, I. Bulu, and E. Ozbay. “Photonic band-gap effect, localization, and waveguiding in two-dimensional Penrose lattice.” Phys. Rev. B 63, 161104(R) (2001).
[Crossref]

Padgett, M.

Padgett, M. J.

Parker, G. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti. “Complete photonic bandgaps in 12-fold symmetric quasicrystals.” Nature 404, 740–743 (2000).
[Crossref] [PubMed]

Polin, M.

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier. “Optimized holographic optical traps.” Opt. Express submitted for publication (2005).
[Crossref] [PubMed]

Roichman, Y.

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier. “Optimized holographic optical traps.” Opt. Express submitted for publication (2005).
[Crossref] [PubMed]

Schrieber, M.

U. Grimm and M. Schrieber. “Aperiodic tilings on the computer.” In Quasicrystals: an Introduction to Structure, Physical Properties and Applications, edited by J. B. Suck, M. Shrieber, and P. Haussler (Springer, 2002).

Sheng, P.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng. “Large-area two-dimensional mesoscopic quasi-crystals.” Adv. Mater. 15, 1526–1528 (2003).
[Crossref]

Sinclair, G.

Spalding, G. C.

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

Steinhardt, P.

W. Man, M. Megens, P. Steinhardt, and P. M. Chaikin. “Experiments on the phononic properties of icosahedral quasicrystals.” preprint (2005).

Sun, B.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
[Crossref]

Sun, H.-B.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada. “Finer features for functional microdevicecs.” Nature 412, 697–698 (2001).
[Crossref] [PubMed]

Takada, K.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada. “Finer features for functional microdevicecs.” Nature 412, 697–698 (2001).
[Crossref] [PubMed]

Tam, W. Y.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng. “Large-area two-dimensional mesoscopic quasi-crystals.” Adv. Mater. 15, 1526–1528 (2003).
[Crossref]

Tanaka, T.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada. “Finer features for functional microdevicecs.” Nature 412, 697–698 (2001).
[Crossref] [PubMed]

Taylor, M. B.

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

Timusk, T.

S. E. Burkov, T. Timusk, and N. W. Ashcroft. “Optical conductivity of icoahedral quasi-crystals.” J. Phys.: Condens. Matt. 4, 9447–9458 (1992).
[Crossref]

Tsurumachi, N.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka. “Photonic dispersion-relation in a one-dimensional quasi-crystal.” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Wang, X.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng. “Large-area two-dimensional mesoscopic quasi-crystals.” Adv. Mater. 15, 1526–1528 (2003).
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Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn. Photonic Crystals (Princeton University Press, Princeton, 1995).

Zhang, D.

C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang. “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region.” Phys. Rev. B 61, 10762–10767 (2000).
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C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
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Zhang, X.

X. Zhang, Z. Q. Zhang, and C. T. Chan. “Absolute photonic band gaps in 12-fold symmetric photonic crystals.” Phys. Rev. B 63, 081105 (2001).
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Zhang, Z. Q.

X. Zhang, Z. Q. Zhang, and C. T. Chan. “Absolute photonic band gaps in 12-fold symmetric photonic crystals.” Phys. Rev. B 63, 081105 (2001).
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S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimentional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

Zoorob, M. E.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti. “Complete photonic bandgaps in 12-fold symmetric quasicrystals.” Nature 404, 740–743 (2000).
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Zsolt,

Adv. Mater. (1)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng. “Large-area two-dimensional mesoscopic quasi-crystals.” Adv. Mater. 15, 1526–1528 (2003).
[Crossref]

Appl. Phys. Lett. (1)

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun. “Band gap wave guiding effect in a quasiperiodic photonic crystal.” Appl. Phys. Lett. 75, 1848–1850 (1999).
[Crossref]

J. Phys.: Condens. Matt. (1)

S. E. Burkov, T. Timusk, and N. W. Ashcroft. “Optical conductivity of icoahedral quasi-crystals.” J. Phys.: Condens. Matt. 4, 9447–9458 (1992).
[Crossref]

Nature (3)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti. “Complete photonic bandgaps in 12-fold symmetric quasicrystals.” Nature 404, 740–743 (2000).
[Crossref] [PubMed]

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S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada. “Finer features for functional microdevicecs.” Nature 412, 697–698 (2001).
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M. J. Escuti and G. P. Crawford. “Holographic photonic crystals.” Opt. Eng. 43, 1973–1987 (2004).
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R. C. Gauthier and A. Ivanov. “Production of quasi-crystal template patterns using a dual beam multiple exposure technique.” Opt. Eng. 12, 990–1003 (2004).

R. C. Gauthier and K. Mnaymneh. “Photonic band gap properties of 12 fold quasi-crystal determined through FDTD analysis.” Opt. Eng. 13, 1985–1998 (2005).

Opt. Express (2)

Phys. Rev. B (6)

M. Bayindir, E. Cubukco, I. Bulu, and E. Ozbay. “Photonic band-gap effect, localization, and waveguiding in two-dimensional Penrose lattice.” Phys. Rev. B 63, 161104(R) (2001).
[Crossref]

S. S. M. Cheng, L.-M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang. “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region.” Phys. Rev. B 61, 10762–10767 (2000).
[Crossref]

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang. “Defect and transmission properties of two-dimentional quasiperiodic photonic band-gap systems.” Phys. Rev. B 59, 4091–4099 (1999).
[Crossref]

X. Zhang, Z. Q. Zhang, and C. T. Chan. “Absolute photonic band gaps in 12-fold symmetric photonic crystals.” Phys. Rev. B 63, 081105 (2001).
[Crossref]

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka. “Photonic dispersion-relation in a one-dimensional quasi-crystal.” Phys. Rev. B 50, 4220–4223 (1994).
[Crossref]

Phys. Rev. Lett. (3)

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P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
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Other (4)

W. Man, M. Megens, P. Steinhardt, and P. M. Chaikin. “Experiments on the phononic properties of icosahedral quasicrystals.” preprint (2005).

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier. “Optimized holographic optical traps.” Opt. Express submitted for publication (2005).
[Crossref] [PubMed]

U. Grimm and M. Schrieber. “Aperiodic tilings on the computer.” In Quasicrystals: an Introduction to Structure, Physical Properties and Applications, edited by J. B. Suck, M. Shrieber, and P. Haussler (Springer, 2002).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn. Photonic Crystals (Princeton University Press, Princeton, 1995).

Supplementary Material (2)

» Media 1: MPG (2120 KB)     
» Media 2: MPG (1220 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Two-dimensional colloidal quasicrystals organized with holographic optical traps. (a) 5-fold. (b) 7-fold. (c) 8-fold. (d) An octagonal quasicrystal with an embedded structured defect. The scale bar in (a) indicates 5 µm.

Fig. 2.
Fig. 2.

Four views of a rolling colloidal icosahedron. (a) 5-fold axis. (b) 2-fold axis. (c) 5-fold axis. (d) Midplane. Scale bar indicates 5 µm. The complete assembly and rolling process is shown in the associated movie. [Media 1]

Fig. 3.
Fig. 3.

Holographic assembly of a three-dimensional colloidal quasicrystal. (a) Colloidal particles trapped in a two-dimensional projection of a three-dimensional icosahedral quasicrystalline lattice. (b) Particles displaced into the fully three-dimensional configuration. The shaded region identifies one embedded icosahedron. (c) Reducing the lattice constant creates a compact three-dimensional quasicrystal. (d) Optical diffraction pattern showing ten-fold symmetric peaks. The three-dimensional assembly process is shown in the associated movie. [Media 2]

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