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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Adv. Mater.

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.

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.

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

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]

D. G. Grier. �??A revolution in optical manipulation.�?? Nature 424, 810�??816 (2003).
[CrossRef] [PubMed]

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

Opt. Eng.

M. J. Escuti and G. P. Crawford. �??Holographic photonic crystals.�?? Opt. Eng. 43, 1973�??1987 (2004).
[CrossRef]

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

Phys. Rev. B

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]

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]

Phys. Rev. Lett.

A. R. Denton and H. Löwen. �??Stability of colloidal quasicrystals.�?? Phys. Rev. Lett. 81, 469�??472 (1998).
[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]

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]

Quasicrystals: an Introduction to Struct

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)

Rev. Sci. Instr.

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]

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]

Other

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

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

Supplementary Material (2)

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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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