Abstract

In this paper, we investigate three-dimensional (3D) band gap properties of quasiperiodic structure. We successfully demonstrate the fabrication of a 3D dielectric quasicrystalline heterostructures with five-fold planar symmetry using the holographic optical tweezers technique. Light transmitted through this quasicrystal is collected using the spatially resolved optical spectroscopy technique for both visible and infrared wavelength bandwidths in a far-field region. We investigate and analyze the transmission spectra for the same wavelength bandwidths in a near-field region by using computer simulations. The computational modeling indicates that for both TE and TM modes of propagating light in the XY plane there is a clear transmission band-gap of around 50 nm wide centered at 650 nm. This indicates that there is a rotational symmetry in the constructed quasicrystal along its XY plane. Future directions and applications are discussed.

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  1. S. E. Burkov, T. Timusk, and N. W. Ashcroft, “Optical conductivity of icosahedral quasi-crystals,” J. Phys. Condens. Matter4(47), 9447–9458 (1992).
    [CrossRef]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, 1995).
  3. M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
    [CrossRef]
  4. L. Jia, I. Bita, and E. L. Thomas, “Level Set Photonic Quasicrystals with Phase Parameters,” Adv. Funct. Mater.22(6), 1150–1157 (2012).
    [CrossRef]
  5. X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic crystals,” Phys. Rev. B63(8), 081105 (2001).
    [CrossRef]
  6. M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
    [CrossRef] [PubMed]
  7. J. Xu, R. Ma, X. Wang, and W. Y. Tam, “Icosahedral quasicrystals for visible wavelengths by optical interference holography,” Opt. Express15(7), 4287–4295 (2007).
    [CrossRef] [PubMed]
  8. A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
    [CrossRef] [PubMed]
  9. Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express13(14), 5434–5439 (2005).
    [CrossRef] [PubMed]
  10. E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optical elements,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
    [CrossRef]
  11. D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
    [CrossRef] [PubMed]
  12. E. D. Palik, Handbook of Optical Constant of Solids (Academic, 1985).
  13. W. Man, Photonic Quasicrystals and Random Ellipsoid Packings: Experimental Geometry in Condensed Matter Physics (Princeton University PhD Dissertation, 2005).
  14. P. M. Chaikin, “Photonic Quasicrystals,” http://www.physics.nyu.edu/~pc86/ .
  15. Version 4.3, “COMSOL Multiphysics Reference Guide,” http://www.comsol.com .
  16. W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
    [CrossRef] [PubMed]
  17. T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature383(6602), 699–702 (1996).
    [CrossRef]
  18. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
    [CrossRef]

2012 (1)

L. Jia, I. Bita, and E. L. Thomas, “Level Set Photonic Quasicrystals with Phase Parameters,” Adv. Funct. Mater.22(6), 1150–1157 (2012).
[CrossRef]

2009 (1)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

2008 (1)

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

2005 (2)

Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express13(14), 5434–5439 (2005).
[CrossRef] [PubMed]

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
[CrossRef] [PubMed]

2001 (1)

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic crystals,” Phys. Rev. B63(8), 081105 (2001).
[CrossRef]

1998 (1)

E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optical elements,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
[CrossRef]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

1996 (1)

T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature383(6602), 699–702 (1996).
[CrossRef]

1992 (1)

S. E. Burkov, T. Timusk, and N. W. Ashcroft, “Optical conductivity of icosahedral quasi-crystals,” J. Phys. Condens. Matter4(47), 9447–9458 (1992).
[CrossRef]

Ashcroft, N. W.

S. E. Burkov, T. Timusk, and N. W. Ashcroft, “Optical conductivity of icosahedral quasi-crystals,” J. Phys. Condens. Matter4(47), 9447–9458 (1992).
[CrossRef]

Bita, I.

L. Jia, I. Bita, and E. L. Thomas, “Level Set Photonic Quasicrystals with Phase Parameters,” Adv. Funct. Mater.22(6), 1150–1157 (2012).
[CrossRef]

Brand, S.

T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature383(6602), 699–702 (1996).
[CrossRef]

Burkov, S. E.

S. E. Burkov, T. Timusk, and N. W. Ashcroft, “Optical conductivity of icosahedral quasi-crystals,” J. Phys. Condens. Matter4(47), 9447–9458 (1992).
[CrossRef]

Cademartiri, L.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Chaikin, P. M.

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

Chan, C. T.

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic crystals,” Phys. Rev. B63(8), 081105 (2001).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optical elements,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
[CrossRef]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

Florescu, M.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

Grier, D. G.

Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express13(14), 5434–5439 (2005).
[CrossRef] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
[CrossRef] [PubMed]

E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optical elements,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
[CrossRef]

Hermatschweiler, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Jeong, H.-C.

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

Jia, L.

L. Jia, I. Bita, and E. L. Thomas, “Level Set Photonic Quasicrystals with Phase Parameters,” Adv. Funct. Mater.22(6), 1150–1157 (2012).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

Krauss, T. F.

T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature383(6602), 699–702 (1996).
[CrossRef]

Ledermann, A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Ma, R.

Man, W.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

Megens, M.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

Ozin, G. A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Rechtsman, M. C.

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

Roichman, Y.

Rue, R. M. D. L.

T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature383(6602), 699–702 (1996).
[CrossRef]

Steinhardt, P. J.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

Tam, W. Y.

Thomas, E. L.

L. Jia, I. Bita, and E. L. Thomas, “Level Set Photonic Quasicrystals with Phase Parameters,” Adv. Funct. Mater.22(6), 1150–1157 (2012).
[CrossRef]

Timusk, T.

S. E. Burkov, T. Timusk, and N. W. Ashcroft, “Optical conductivity of icosahedral quasi-crystals,” J. Phys. Condens. Matter4(47), 9447–9458 (1992).
[CrossRef]

Toninelli, C.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Torquato, S.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

von Freymann, G.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Wang, X.

Wegener, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Wiersma, D. S.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Xu, J.

Zhang, X.

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic crystals,” Phys. Rev. B63(8), 081105 (2001).
[CrossRef]

Zhang, Z. Q.

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic crystals,” Phys. Rev. B63(8), 081105 (2001).
[CrossRef]

Adv. Funct. Mater. (1)

L. Jia, I. Bita, and E. L. Thomas, “Level Set Photonic Quasicrystals with Phase Parameters,” Adv. Funct. Mater.22(6), 1150–1157 (2012).
[CrossRef]

J. Phys. Condens. Matter (1)

S. E. Burkov, T. Timusk, and N. W. Ashcroft, “Optical conductivity of icosahedral quasi-crystals,” J. Phys. Condens. Matter4(47), 9447–9458 (1992).
[CrossRef]

Nat. Mater. (1)

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5(12), 942–945 (2006).
[CrossRef] [PubMed]

Nature (4)

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature383(6602), 699–702 (1996).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature386(6621), 143–149 (1997).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. B (2)

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic crystals,” Phys. Rev. B63(8), 081105 (2001).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optical elements,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
[CrossRef]

Other (5)

E. D. Palik, Handbook of Optical Constant of Solids (Academic, 1985).

W. Man, Photonic Quasicrystals and Random Ellipsoid Packings: Experimental Geometry in Condensed Matter Physics (Princeton University PhD Dissertation, 2005).

P. M. Chaikin, “Photonic Quasicrystals,” http://www.physics.nyu.edu/~pc86/ .

Version 4.3, “COMSOL Multiphysics Reference Guide,” http://www.comsol.com .

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

Supplementary Material (1)

» Media 1: MP4 (4107 KB)     

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Figures (4)

Fig. 1
Fig. 1

Quasicrystal constructed from spherical silica particles. (a) Colloidal silica particles trapped in three dimensional configurations with holographic optical traps (Media 1). Brightness of a particle corresponds to different crystalline layer in Z-axis. From (b) to (e): schematic representations of different projections of the quasicrystal. Colors represent different heights of the crystalline planes in Z-axis. Orange, black, red, green and blue correspond to 3.7, 2.9, 0.4, −0.4 and −3.7 µm respectively.

Fig. 2
Fig. 2

The experimental setup consists of a Laser, SLM, Microscope, Charge Coupled Device (CCD) Camera, Optical Fiber and Spectrometer all connected to the Computer. Laser beam passes through a series of optical devices creating an array of a three dimensional traps in microscope’s conventional imaging plane. (a) Real-time spectrum of forward scattered light from quasicrystal is collected by the optical fiber mounted to the second eyepiece port and connected to the Spectrometer. (b) Real-time image of the constructed quasicrystal, obtained from the CCD camera mounted to the first eyepiece port of the microscope.

Fig. 3
Fig. 3

Visible and infrared transmission spectra of the quasicrystal sample obtained in far-field measurements along the Z-axis.

Fig. 4
Fig. 4

Transmission spectra calculated for both the TE and TM modes, for the light propagating along the (a) X-axis, (b) Y-axis, (c) Z-axis and (d) XY plane at 0, 45 and 90 degree angles corresponding to X, M and Y directions. The gap at 650 nm shows an evidence of the complete band gap for light propagating in XY plane. Arrows and dashed lines indicate the locations of band gaps.

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